Exploring Digital Imaging and SEM Accretionary Lapilli

Universiteit Gent

Faculteit Ingenieurswetenschappen

Vakgroep Subatomaire en Stralingsfysica

Voorzitter: Prof. Dr. K. Heyde

Exploring the potential of digital image analysis ofSEM and Micro-CT images of accretionary lapilli

Wim Degruyter

Promotor : Prof. Dr. Luc Van Hoorebeke

Co-promotors: Dr. Bert Masschaele en Dr. Gerald Ernst

Scriptie ingediend tot het behalen van de graad van

burgerlijk natuurkundig ingenieur

Academiejaar 2005–2006

i

Preface

This thesis is a conjunction of engineering, physics, volcanology and mathematics. All these

fields are of great interest to me and so I’m very greatful I got the opportunity to do this.

Thanks to my promotor Luc Van Hoorebeke for all the help with Linux and the useful feedback.

Bert Masschaele, Manuel Dierick, Jelle Vlassenbroeck and Veerle Cnudde for the great work

atmosphere and fantastic support.

Special thanks to Gerald Ernst for getting me excited about volcanology and interpreting the

produced data. I would also like to thank Mary-Ann del Marmol, Matthieu Kervyn and all

students who came along to the Eifel and attended the volcanology seminars. Karen Fontijn

for bringing me back samples from Santorini. Mike James for sending me the article I had

trouble finding. Also many thanks to Brent Lindquist who helped me out compiling and better

understanding 3DMA-rock.

My parents, friends and fellow students for being there.

It was a great year!

Wim Degruyter 1 juni 2006

De auteur geeft de toelating deze scriptie voor consultatie beschikbaar te stellen en delen

van de scriptie te kopieren voor persoonlijk gebruik. Elk ander gebruik valt onder de

beperkingen van het auteursrecht, in het bijzonder met betrekking tot de verplichting de

bron uitdrukkelijk te vermelden bij het aanhalen van resultaten uit deze scriptie.

ii

Exploring the potential of digitized image analysis of SEM and Micro-CT images of

accretionary lapilli

Wim Degruyter

Scriptie ingediend tot het behalen van de graad van burgerlijk natuurkundig ingenieur.

Academiejaar 2005–2006

Promotor: Luc Van Hoorebeke

Co-promotors: Bert Masschaele en Gerald Ernst

Vakgroep Subatomaire en Stralingsfysica

Voorzitter: Prof. Dr. K. Heyde

Abstract

Accretionary lapilli (acc-laps) are commonly found in airfall tuffs from water-rich eruption

columns. Yet, the role of water and ice in the formation of acc-laps has not been systemat-

ically studied. This thesis examines the possibilty of extracting quantitative data from the ash

balls via digitized image analysis techniques. 2D images were collected with a Scanning Elec-

tron Microscope and analysed using Labview. 3D images were made at the UGCT facility with

the Micro-CT scanner. Analysis was done with the software packages µCTanalysis and 3DMA-

rock. Image analysis techniques can already provide valuable insights, but optimalisation and

standardisation will be necessary for fast and accurate use in the future.

CONTENTS iii

Contents

Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . i

Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ii

1 Introduction 1

2 Volcanoes 5

2.1 Products of eruptions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

2.2 Eruption model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

3 Accretionary lapilli 10

3.1 Aggregation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

3.2 Formation of accretionary lapilli . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

4 Digital images 15

4.1 Sampling frequency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

4.2 Spatial resolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

4.3 Brightness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

5 SEM image analysis 20

5.1 SEM principle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

5.2 Samples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

5.3 Grayscale histogram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

5.4 Segmentation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

5.5 Measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

5.5.1 Porosity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

5.5.2 Grainsize distribution and shape measurements . . . . . . . . . . . . . . . 26

5.5.3 Concentric layers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

CONTENTS iv

5.5.4 Vesicle size distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

5.6 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

6 Tomography 37

6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

6.2 CT principle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

6.2.1 Scanning configuration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

6.2.2 X-ray source . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

6.2.3 X-ray attenuation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

6.2.4 X-ray detectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

6.3 Acquisition of CT Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

6.3.1 Sample preparation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

6.3.2 Calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

6.3.3 Collection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

6.3.4 Reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

6.4 Resolution and size limitations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46

6.4.1 Spatial resolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46

6.4.2 Density/attenuation resolution . . . . . . . . . . . . . . . . . . . . . . . . 47

6.4.3 Size limitations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

6.5 Artifacts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

6.5.1 Beam hardening . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

6.5.2 Ring artifacts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

6.5.3 Other artifacts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

6.5.4 Partial-volume effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52

7 Micro-CT image analysis 53

7.1 Samples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53

7.2 Micro-CT images . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54

7.3 µCTanalysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

7.4 3DMA-rock . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56

7.4.1 Segmentation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56

7.4.2 Separation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56

7.5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60

CONTENTS v

8 Conclusions 63

A Nederlandstalige samenvatting 65

A.1 Inleiding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65

A.2 Accretionary lapilli . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66

A.2.1 Aggregatie . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66

A.2.2 De vorming van accretionary lapilli . . . . . . . . . . . . . . . . . . . . . . 67

A.3 SEM-beeldanalyse . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67

A.3.1 SEM principe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67

A.3.2 Grijswaarden histogram en segmentatie . . . . . . . . . . . . . . . . . . . 68

A.3.3 Metingen . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69

A.4 Micro-CT beeldanalyse . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70

A.4.1 Micro-CT principe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70

A.4.2 Micro-CT beelden . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70

A.4.3 Analysesoftware . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70

A.5 Besluit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72

Bibliography 73

1

Chapter 1

Introduction

Explosive eruptions can produce a volcanic plume, which is a dilute, turbulent cloud with ash

particles in suspension and volcanic gases. For air traffic, volcanic plumes are the most haz-

ardous eruption phenomenon, since they can cause failure of engines and navigation instruments.

Fallout from plumes of the largest eruptions may affect millions of square kilometers and em-

placement of volcanic pollutants into the atmosphere may significantly perturb the climate

(Sparks et al., [43]). Fundamentals on eruption poducts and volcanic plumes are described in

chapter 2.

Figure 1.1: Volcanic plume typical of explosive eruptions, as demonstrated here in the 1980 eruption of

Mt. St. Helens, [3].

2

Volcanic plumes can produce accretionary lapilli (acc-laps), small spherical balls of volcanic

ash that form from a wet nucleus falling through a volcanic ash cloud. Amongst other aggregation

products of a volcanic plume (chapter 2), these aggregates that form from wet fine ash can affect

the atmospheric dispersion of the plume, since they fall faster than single ash particles. Through

the way they form and are preserved acc-laps contain a record of processes in the volcanic plume.

So, they can provide constraints on eruption column dynamics. One immediate application is

for volcanic hazard assessment: acc-laps maximum sizes in a sequence of tuff layers can provide

information on eruption column height and its variation from one layer to the next (Durant and

Ernst, [8]).

Small spherules present in many of the images collected by Mars rovers have characteristics

very similar to acc-laps. The significance of acc-laps present on Mars is the following: on Earth,

they only form in a plume containing abundant water (Schumacher and Schmincke, [40]). So,

acc-laps on Mars, would suggest a volcanic magma body interacting directly with a body of

water producing a wet explosive volcanic eruption (Durant, [7]). Chapter 3 discusses acc-laps

in depth.

All the studied acc-laps samples come from fallout from an eruption column very rich in

water and ice due to the great heights they reached in the atmosphere which was at least up

to the local troposphere. At troposphere height the atmosphere temperature is tens of degrees

below zero (eg. -60 ℃ at 50 ◦N latitude and about -80 ℃ at the equator; see Rogers and Yau,

[35]; Houze, [13]). It is assumed that any steam from interaction between magma and external

water would first have to condense on ash and subsequently to freeze during ascent (about 5 km

of ascent at Santorini would have been enough to freeze condensed water on ash). Thus the

expectation is that water and ice are present in abundance together with ash (e.g. Rose et al,

[36]; Lacasse et al, [19] and refs therein) and that this leads to rather complex and fascinating

interactions leading to the formation of mixed-phase aggregates (Textor and Ernst, [44]; Textor

et al., [45] and [46]). Yet the role of water and ice in wet aggregation, in so-called phreato-

plinian style eruptions is not fully understood (Durant and Ernst, [8]). Thus came the idea for

the present project.

The formation of acc-laps can be constrained by collecting empirical data, carying out ex-

perimental laboratory simulations and developing theoretical modeling. Up to now, attempts to

produce acc-laps in the laboratory have failed (Durant and Ernst, [8]). In scientific research like

this there is a need for techniques, which generate quantitative data. Digital image analysis on

3

Figure 1.2: Fall deposit rich in acc-laps in Santorini, Greece. Photo courtesy of Durant and Ernst.

Scanning Electron Microscope (SEM) images is already a widely used imaging technique in the

earth and environmental sciences. chapter 4 gives an introduction to digital image acquisition.

However, SEM can only provide two dimensional information. Next to this, a relative new tech-

nique is gaining a lot of interest, Micro Computed Tomography (Micro-CT). Three dimensional

images can be rendered without the destruction of the investigated sample. An introduction of

tomography is given in chapter 6.

Once digital images have been generated, automated analysis is done with a combination

of specialized software. In this work LabVIEW, [29], IMAQ Vision, [28], ImageJ, [33] and

ImageTool, [6] were used for two dimensional image analysis, which is discussed in chapter

5. Three dimensional analysis was done with µCTanalysis, [4] and 3DMA-rock, [21]. This

is discussed in chapter 7. The main problem with image analysis, is the lack of a standard

procedure to follow. Most analysis is done in three major steps: segmentation, separation and

size/shape measurements. For all three steps there exist a lot of different algorithms.

The present study to explores how imaging analysis can help provide constraints on the role

of water and ice in the formation of acc-laps. The idea that large (above 6mm size) acc-laps such

as those of the US1 fallout unit of Santorini (see Druitt et al., [9] for details on US1 eruption;

Durant and Ernst, [8]) and those of the I4 phreatoplinian eruption of Atitlan caldera (Newhall,

[30]; Rose et al., [37]; G.G.J. Ernst and coworkers, work in progress) form in a way closely

analogous to that in which hailstones grow (i.e. by recycling in a vigorous convective updraft

and by riming) has been proposed by G.G.J. Ernst and presented at conferences. The present

project had two objectives:

4

1. exploring the advantages and limitations of the respective image analyses techniques ap-

plied here and

2. seeing to what extent the new observations and data enables to further evaluate a hailstone

growth style of formation for those large acc-laps.

5

Chapter 2

Volcanoes

This chapter is a summary derived from [3].

2.1 Products of eruptions

The eruptive products are highly variable and largely dependent on the composition, viscosity,

and gas content of the erupting magma. These products are essential to investigate and un-

derstand the nature of past eruptions. A general classification and a brief explanation of each

category is given.

Figure 2.1: Eruption products, [3].

2.1. PRODUCTS OF ERUPTIONS 6

Lava is molten rock that a volcano expels during an eruption. The word lava comes from

Italian, and is probably ultimately derived from the Latin word labes which means a fall, slide,

or sinking in. While still below the earth’s surface, molten rock is termed magma. Only ten

elements make up the bulk of most magmas: oxygen (O), silicon (Si), aluminum (Al), iron (Fe),

magnesium (Mg), titanium (Ti) calcium (Ca), sodium (Na), potassium (K), and phosphorous

(P). Because oxygen and silicon are by far the two most abundant elements in magma, it is

convenient to describe the different magma types in terms of their silica content (SiO2). The

magma types vary from mafic magmas, which have relatively low silica and high Fe and Mg

contents, to felsic magmas, which have relatively high silica and low Fe and Mg contents. Mafic

magma will cool and crystallize to produce the volcanic rock basalt, whereas felsic magma will

crystallize to produce dacite and rhyolite. Intermediate-composition magmas will crystallize to

produce the rock andesite. Because the mafic rocks are enriched in Fe and Mg, they tend to

be darker colored than the felsic rock types. Lava, when first exuded from a volcanic vent, is a

liquid at very high temperature: typically from 700 to 1200 ℃. Although the viscosity of lava is

100 000 times that of water, it can flow many miles before eventually cooling and solidifying.

Other than free oxygen, generated by photosynthesis, all atmospheric gases were derived

from inside the earth and released by volcanic eruptions. The gaseous portion of magma varies

from 1 to 5 % of the total weight. Water vapor constitutes 70 – 90%. The remaining gases

include CO2, SO2, and trace amounts of of N, H, CO, S, Ar, Cl, and F. These subordinate gases

can combine with hydrogen and water to produce numerous toxic compounds, such as HCl, HF,

H2SO4, H2S.

A variety of sulfur aerosols may be present and sulfur itself may condenseinto a crystalline

accumulation called sulfaterra (yellow ground). On some volcanoes, enough sulfur is present to

be mined as an economic resource. H2S is sometimes called sewer gas because it has a rotten

egg odor. It is an insidious poison that irritates the eyes, nose, and throat. SO2 on the other

hand, is the biting, chocking gas that you smell right after you’ve lit a kitchen match. When

these two gases occur together, they react quickly with each other (within minutes) to produce

sulfaterra and water vapor.

The rapid eruption of expanding gases results in the obliteration and fragmentation of magma

and rock. The greater the explosivity, the greater the amount of fragmentation. Individual

eruptive fragments are called pyroclasts (fire fragments). Tephra (Greek for ash) is a generic

term for any airborne pyroclastic accumulation. Whereas tephra is unconsolidated, a pyroclastic

2.2. ERUPTION MODEL 7

rock is produced from the consolidation of pyroclastic accumulations into a coherent rock type.

• Ashes are very fine-grained fragments (< 2 mm), generally dominated by broken glass

shards, but with variable amounts of broken crystal and lithic (rock) fragments.

• Lapilli are pea- to walnut-size pyroclasts (2 to 64 mm). They often look like cinders.

In water-rich eruptions, the accretion of wet ash may form rounded spheres known as

accretionary lapilli.

• Blocks and bombs are fragments > 64 mm. Bombs are ejected as incandescent lava frag-

ments which were semi-molten when airborne, thus inheriting streamlined, aerodynamic

shapes. Blocks are ejected as solid fragments with angular shapes.

Within this size classification, specific types of tephra can be further defined by physical at-

tributes.

A pyroclastic flow is a fluidized mixture of solid to semi-solid fragments and hot, expanding

gases that flows down the flank of a volcanic edifice. These awesome features are heavier-than-air

emulsions that move much like a snow avalanche, except that they are fiercely hot (100 – 800 ℃),

contain toxic gases, and move at phenomenal, hurricane-force speeds, often over 100 km/h. They

are the most deadly of all volcanic phenomena. Flows containing a high proportion of gas to

rock are known as pyroclastic surges. The lower density sometimes allows them to flow over

higher topographic features such as ridges and hills. They may also be cold, containing steam,

water and rock at less than 100 ℃. Cold surges can occur when the eruption is from a vent under

a lake or the sea.

Lahar is an Indonesian term for a volcanic mudflow. These lethal mixtures of water and

tephra have the consistency of wet concrete, yet they can flow down the slopes of volcanoes

or down river valleys at rapid speeds, similar to fast-moving streams of water. These mud

slurries carry debris ranging in size from ash to lapilli, to boulders more than 10 meters in

diameter. Lahars can vary from hot to cold, depending on their mode of genesis. The maximum

temperature of a lahar is 100 ℃, the boiling temperature of water.

2.2 Eruption model

The dynamics of an erupting volcano is demonstrated in the following cross-section, typical of a

so-called Plinian eruption. Eruptions are fed from a magma column that exists directly above

a magma chamber.


Figure 2.2: Cross-sectional model of a Plinian Eruption, [3].

The magma column contains two critical pressure surfaces that separate three magmatic

regimes which different physical properties:

1. a lower exsolution surface separates a non-vesiculated magma reservoir with dissolved

volatiles from an overlying zone of magma having exsolved gas bubbles, and

2. an upper fragmentation surface that separates the middle zone of magma with exsolved

gas from an upper zone of liquid to plastic pyroclasts and released gas.

The exsolution of gas from magma (or boiling) is called vesiculation. These gas bubbles

(vesicles) begin to form at the exsolution surface. Vesiculation is promoted by decompression of

magma as it rises upward (where the confining pressure is less than the dissolved gas pressure).

Fragmentation of the bubble walls then begins at the fragmentation surface; here, the gas bubbles

grow during ascent until they become unstable and explode. This occurs when the volume of

bubbles is about 75 % of the total volume of the magma column.

Gas release is confined to the diameter of the magma column, and the eruption velocity is

controlled mainly by the gas content. The low strength of surface rocks and the high initial exit

pressure commonly results in vent erosion, so that a flared vent shape develops which enhances

velocity. This marks an upward transition from subsonic to supersonic flow.

The region of hot gas and broken pyroclastic particals above the fragmentation surface

is called the eruption column. It transports pyroclastic materials from the ground into the

atmosphere. Common observed heights for plinian eruptive columns are between 2 and 45 km.

In general the eruptive column has three parts:


1. the gas thrust region in the lower column, driven by gas expansion,

2. the convective thrust region in the upper column, driven by the constant release of

thermal energy from internal ash, and

3. the umbrella region at the top of the eruption column. The umbrella region is also

known as the downwind plume.

The gas thrust region is a region of vertical movement of gas and plastic magma particles

that is internally powered by gas expansion (decompression) at the base of the eruptive column.

Its overall density depends on the particle-to-gas ratio. Initially, the gas thrust is denser than

air because of its incorporation of pyroclastic particles. However, as these particles fall out (as

ballistics), the density is reduced so that the hot gases in the column are now less than that of the

atmosphere. At this point, the gas thrust gives way to convective uprise and development of the

convective thrust region, which comprises about 90 % of the eruptive column. The convective

plume is driven by the constant release of thermal energy from internal ash. At some point,

the bulk density of the column will become equal to that of the atmosphere, so that its upward

mobility is only controlled by its momentum. The column thus spreads out in the umbrella

region. The bottom of umbrella region is where densities of the plume and the surrounding

air are equal. Continued upward mobility towards the top of the umbrella region is controlled

by momentum. The umbrella region is often asymmetric due to the effect of high atmospheric

winds in the stratosphere.

10

Chapter 3

Accretionary lapilli

3.1 Aggregation

Aggregation is a process occurring in volcanic plumes that clusters together and selectively binds

fine ash particles, which over time will form an aggregate consisting of 1 000 to 100 000 individual

particles. As the eruption cloud disperses, ash particles fall out according to their size. Within

days the eruption cloud typically thins out and disapears (Sparks et al., [43]). Geologists have

observed that many fine ash particles, typically less than 100 µm, fall from volcanic plumes as

aggregates. Aggregation of fine ash particles plays a critical role in controlling the dispersal of

particles, because they fall with higher terminal velocities than their components and can lead

to enhanced thickening of fall deposits. Formation of a particular type of aggregates depends

on the amount of liquid available during aggregation (Gilbert and Lane, [12]; Schumacher and

Schmincke, [40]; Sparks et al., [43]). There are three main categories (Sparks et al., [43]):

• Dry aggregates have relatively high porosities (40 – 90 %). They collapse on impact and

do not tend to be preserved in the geological record. The main binding mechanism of

these aggregates is assumed to be the electrostatic force.

• Accretionary lapilli are of intermediate liquid content during their formation with

porosities between 30 and 50%. They are tightly bound, approximately spherical col-

lections of particles. They are common in the geologic record particularly in facies of

phreatomagmatic eruptions which have been associated with magma-water interaction

and the generation of abundant fines. Some typical acc-laps can be seen in Figure 3.1 and

their characteristics are summed up in Table 3.1.

3.2. FORMATION OF ACCRETIONARY LAPILLI 11

• Mud rain is the most liquid rich type of aggregate and has zero porosity.

Aggregates within volcanic plumes grow via processes of contact, binding and breakup of solid

and liquid phases. Particle collisions within volcanic plumes are mainly caused by differences in

their terminal fall velocities, because the size range of the particles is between 1 and 1000µm.

Other possible contact mechanisms are electrostatic charge and liquid drop scavenging. Binding

mechanisms are surface tension (capillary) forces, electrostatic forces, secondary minerals and

ice crystals, Van der Waal force and mechanical interlocking (Gilbert and Lane, [12]).

Figure 3.1: SEM photographs of acc-laps from Kilauea, Hawaii (Durant, [7]).

diameter typically < 10 mm, maximum 60 mm

structure spherical; thin fine-grained rim; volumetrically dominant

coarser grained core; nucleus particle often present

porosity 30 – 50 %

density 1200 – 1600 kg/m3

Table 3.1: Typical characteristics of acc-laps (Sparks et al., [43]).

3.2 Formation of accretionary lapilli

Key recent articles that focus on the growth of acc-laps are Gilbert and Lane, [12], Schumacher

and Schmincke, [40] and Durant and Ernst, [8]. Gilbert and Lane, [12] tried to simulate acc-laps

formation in the lab, but failed. However, they were able to conclude the following. Binding

between initially cohesionless ash particles to form concentric acc-laps is provided primarily by

the capillary forces of liquid bridges from condensed moisture and by electrostatic attraction.

Capillary forces are strong bonds if the particles are in close contact, but they decrease rapidly

with increasing particle spacing. Electrostatic attraction between charged ash particles is much


weaker but effective over larger distances, increasing the frequency of collision between them.

The high fall velocity (UD) particle with diameter D collides with low velocity (Ud) particles

with diameter d within the swept volume (Figure 3.2). Deviations are caused by electrosta-

tic repulsive or attractive forces and small particles following streamlines around the growing

aggregate. Particles which collide with the aggregate may rebound and not contribute to ag-

gregate growth. The presence of liquids provides strong short-range bonding between particles.

Secondary minerals may precipitate from liquids and generate more permanent bonds.

Figure 3.2: Schematic representation of acc-lap growth processes (Gilbert and Lane, [12]).

Experimental results by Schumacher and Schmincke, [40] of liquid film binding of volcanic

ash showed that agglomeration was most successful between 15 and 25 wt.% of water inside

the eruption column, defining the agglomeration window for the formation of acc-laps. Below

5 – 10 wt.% and above about 25 – 30 wt.% of water, concentric agglomeration was inhibited.

Durant and Ernst, [8] did a detailed field and analytical study of the US1-A tuffs (fall deposits

rich in acc-laps) of Santorini, Greece and proposed the following conceptual model:

1. Successive collapses of a water-rich, pulsating column produce diluted turbulent ash-laden

density currents, which are called base surges, extending several kilometers from the vent

and elutriation clouds rich in fine ash.

2. Initially, before significant condensation of steam, single-grain clusters and fine-ash clusters

may instantaneously form due to electrostatic attraction.

3. Both in the column and base surge, temperature rapidly drops below 100 ℃ and ash par-

ticles (or small ash clusters) act as condensation nuclei for water vapour. Liquid films


condense around the ash particles. Only very few pure water drops can form. Conden-

sation releases latent heat so that the plume rise accelerates with height to velocities

exceeding tens of m/s.

4. During ascent, the core of ash aggregates starts to form by non-size-selective wet accretion

(in the presence of excess water) resulting from collisions induced by differential settling

and surface tension binding.

5. When the aggregates reach 5 – 6 km above sea level, ash-packed drops may have grown

up to 5 – 6 mm. Most large drops break up and result in a peak in the size distribution

at 2 – 3 mm. At that elevation, ambient air temperature falls below -13 ℃. Most wet ash

and wet aggregates will freeze by immersion nucleation and growth of aggregates by wet

accretion is eventually stopped. Freezing also releases latent heat, further accelerating the

vertical flow of the plume. As a result of this superbuoyancy, there is a possibility that

larger aggregates, which cannot be supported in the first few kms above the vent, may

be supported higher up and into the freezing zone by the accelerating upward flow. This

suggests that large acc-laps > 5 mm can only form in columns significantly higher than

about 5 km high.

6. Acc-laps and ash reach the umbrella-cloud well mixed. Turbulence is less vigorous there

and acc-laps can rapidly migrate to the cloud base, which leads to fall out, and which

upon impact sag into the wet ashbeds.

7. Below 4 km above sea level falling aggregates start to thaw from the outside in, forming

a thin film of liquid water at the rim. Size-selective wet accretion of fine rim ash takes

place as the acc-laps fall through elutriated base surge ash layers and through secondary

co-surge plume intrusions.

8. Acc-laps can be recycled, especially if the ash column is as intense as a severe thunderstorm

penetrating into the lower stratosphere, going through cycles of rim thawing, accretion of

fines and refreezing, and so on, forming multiple rims.

9. The fine ash loading of the umbrella cloud gradually increases as more material is fed into

the rising ash column and recycled. When the eruption stops, the fine ash and reentrained

mixed-phase acc-laps will rapidly migrate to the umbrella base. This is gravitationally un-

stable and will lead to a settling-driven instability where secondary intrusions develop and


remaining aggregates and frozen ash catastrophically fall out of suspension. This results

in rapid and massive deposition of much of the tuffs, and also in torrential rainshowers

of rare intensity feeding local flash floods responsible for deep gullies dissecting the whole

sequence of deposits already laid down. The formation of such gullies may be associated

with localised but severe hazards for eruption columns at 10 – 20 km elevation, especially

lahars and un-passable evacuation routes.

This conceptual model needs further investigation and quantitative data to back it up and

improve it. Methods for providing data on the grain and vesicle sizes within acc-laps, to place

constraints on how they form, with digital image analysis are discussed in the following chapters.

15

Chapter 4

Digital images

This chapter is a summary of [5]. When an image is read from a detector, an analog signal is

converted to a digital one. The target objective is to convert the image into an array of discrete

points that each contain specific information about brightness and can be described by a specific

digital data value in a precise location.

1. The sampling process measures the intensity at successive locations in the image and

forms a two-dimensional array containing small rectangular blocks of intensity information.

2. After sampling is completed, the resulting data is quantized to assign a specific digi-

tal brightness value to each sampled data point, ranging from black, through all of the

intermediate gray levels, to white.

The result is a numerical representation of the intensity, which is commonly referred to as a

picture element or pixel, for each sampled data point in the array.

The quality of a digital image, often referred to as image resolution, is determined by the

number of pixels and the range of brightness values available for each pixel utilized in the image.

Resolution of the image is regarded as the capability of the digital image to reproduce fine details

that were present in the original analog image. In general, the term spatial resolution is reserved

to describe the number of pixels utilized in constructing and rendering a digital image. This

quantity is dependent upon how finely the image is sampled during acquisition or digitization,

with higher spatial resolution images having a greater number of pixels within the same physical

dimensions. Thus, as the number of pixels acquired during sampling and quantization of a

digital image increases, the spatial resolution of the image also increases.

4.1. SAMPLING FREQUENCY 16

4.1 Sampling frequency

The sampling frequency, or number of pixels utilized to construct a digital image, is deter-

mined by matching the optical and electronic resolution of the imaging device and the computer

system utilized to visualize the image. A sufficient number of pixels should be generated by

sampling and quantization to faithfully represent the original scanned image. When analog

images are inadequately sampled, a significant amount of detail can be lost or obscured, as

illustrated by the diagrams in Figure 4.1. The original analog signal presented in Figure 4.1A

represents the image generated by a SEM. In this example, when 32 digital samples are acquired

(Figure 4.1B), the resulting image retains a majority of the characteristic intensities and spatial

frequencies present in the original analog image.

Figure 4.1: Illustration of aliasing, [5].

However, when the sampling frequency is reduced, some information present in the original

analog image is missed in the translation from analog to digital, and a phenomenon commonly

referred to as aliasing begins to develop. As is evident in Figure 4.1D, which represents the

digital image with the lowest number of samples, aliasing has produced a loss of high spatial

frequency data while simultaneously introducing spurious lower frequency data that does not

actually exist.

Because images are generally square or rectangular in dimension, each pixel that results

from image digitization is represented by a coordinate-pair with specific x and y values arranged

in a typical Cartesian coordinate system. The x coordinate specifies the horizontal position or

4.2. SPATIAL RESOLUTION 17

column location of the pixel, while the y coordinate indicates the row number or vertical position.

By convention, the pixel positioned at coordinates (0,0) is located in the upper left-hand corner

of the array.

4.2 Spatial resolution

The spatial resolution of a digital image is related to the spatial density of the image and

the optical resolution of the microscope utilized to capture the image. The number of pixels

contained in a digital image and the distance between each pixel, known as the sampling interval

are a function of the accuracy of the digitizing device. The optical resolution is a measure of

the microscope’s ability to resolve the details present in the original scene, and is related to the

quality of the optics, image sensor, and electronics. In conjunction with the spatial density

(the number of pixels in the digital image), the optical resolution determines the overall spatial

resolution of the image. In situations where the optical resolution of the optical imaging system

is superior to the spatial density, then the spatial resolution of the resulting digital image is

limited only by the spatial density.

All details contained in a digital image, ranging from very coarse to extremely fine, are

composed of brightness transitions that cycle between various levels of light and dark. The

cycle rate between brightness transitions is known as the spatial frequency of the image, with

higher rates corresponding to higher spatial frequencies. Varying levels of brightness in minute

specimens observed through the microscope are common, with the background usually consisting

of a uniform intensity and the specimen exhibiting a spectrum of brightness levels. In areas where

the intensity is relatively constant (such as the background), the spatial frequency varies only

slightly across the viewfield. Alternatively, many specimen details often exhibit extremes of light

and dark with a wide gamut of intensities in between.

The numerical value of each pixel in the digital image represents the intensity of the optical

image averaged over the sampling interval. Thus, background intensity will consist of a relatively

uniform mixture of pixels, while the specimen will often contain pixels with values ranging from

very dark to very light. The ability of a digital camera system to accurately capture all of

these details is dependent upon the sampling interval. Features seen in the microscope that are

smaller than the digital sampling interval (have a high spatial frequency) will not be represented

accurately in the digital image. The Nyquist criterion requires a sampling interval equal to

twice the highest specimen spatial frequency to accurately preserve the spatial resolution in the

4.3. BRIGHTNESS 18

resulting digital image. An equivalent measure is Shannon’s sampling theorem, which states

that the digitizing device must utilize a sampling interval that is no greater than one-half the

size of the smallest resolvable feature of the optical image. Therefore, to capture the best degree

of detail present in a specimen, sampling frequency must be sufficient so that two samples are

collected for each feature, guaranteeing that both light and dark portions of the spatial period

are gathered by the imaging device.

If too few pixels are utilized in sample acquisition, then all of the spatial details comprising

the specimen will not be present in the final image. Conversely, if too many pixels are gathered

by the imaging device (often as a result of excessive optical magnification), no additional spatial

information is afforded, and the image is said to have been oversampled. The extra pixels do

not theoretically contribute to the spatial resolution, but can often help improve the accuracy

of feature measurements taken from a digital image. To ensure adequate sampling for high-

resolution imaging, an interval of 2.5 to 3 samples for the smallest resolvable feature is suggested.

4.3 Brightness

The brightness of a digital image is a measure of relative intensity values across the pixel

array after the image has been digitized by an analog-to-digital converter. Pixel brightness is

an important factor in digital images, because it is the only variable that can be utilized by

processing techniques to quantitatively adjust a grayscale image.

After an object has been imaged and sampled, each resolvable unit is represented by a digital

integer. Regardless of the capture method, the image must be digitized to convert each intensity

represented within the specimen into a digital brightness value. The accuracy of the digital value

is directly proportional to the bit depth of the digitizing device.

The term bit depth refers to the binary range of possible grayscale values utilized by the

analog-to-digital converter to translate analog image information into discrete digital values

capable of being read and analyzed by a computer. For example, the most popular 8-bit digitizing

converters have a binary range of 28 or 256 possible values, while a 16-bit converter has 216,

or 65536 possible values. At most, the human eye can distinguish about 50 discrete shades of

gray within the intensity range of a video monitor, suggesting that the minimum bit depth of

an image should be 6 bits. However, for image analysis a minimum of 8 bits is prefered.

Ultimately, the decision on how many pixels and gray levels are necessary to adequately de-

scribe an image is dictated by the physical properties of the original specimen in the microscope.

4.3. BRIGHTNESS 19

Many low contrast, high-resolution images require a significant number of gray levels and pixels

to produce satisfactory results, while other high contrast and low resolution images (such as a

line drawing) can be adequately represented with a significantly lower pixel density and gray

level range. Finally, there is a trade-off in computer performance between contrast, resolution,

bit depth, and the speed of image processing algorithms. Images having a larger number of

variables will require more computer horsepower than those having fewer pixels and gray levels.

Improved digital cameras with CCD and CMOS image sensors capable of 12-bit resolution

characteristics permit the display of images with greater latitude than is possible for 8-bit images.

This occurs because the appropriate software can render the necessary shades of gray from a

larger palette (4096 grayscale levels) for display on computer monitors, which typically present

images in 256 shades of gray. As the magnification is increased during image processing, the

software can choose the most accurate grayscales to reproduce portions of the enlarged image

without changing the original data. This is especially important when examining shadowed

areas where the depth of a 12-bit digital image allows the software to render subtle details that

would not be present in an 8-bit image.

The accuracy required for digital conversion of analog video signals is dependent upon the

difference between a digital gray-level step and the root-mean-square noise in the camera output.

CCD cameras with an internal analog-to-digital converter produce a digital data stream that

does not require resampling and digitization in the computer. These cameras are capable of

producing digital data with up to 16-bit resolution (65,536 grayscale steps) in high-end models.

The major advantage of the large digital range exhibited by the more sophisticated CCD cameras

lies in the signal-to-noise improvements in the displayed 8-bit image and in the wide linear

dynamic range over which signals can be digitized.

20

Chapter 5

SEM image analysis

5.1 SEM principle

A Scanning Electron Microscope (SEM) creates magnified images using electrons. Because the

SEM illuminates them with electrons, samples have to be made to conduct electricity. SEM

samples are coated with a very thin layer of gold by a machine called a sputter coater. The

sample is placed inside the microscope’s vacuum column through an air-tight door. After the air

is pumped out of the column, an electron gun at the top emits a beam of high energy electrons.

This beam travels downward through a series of magnetic lenses designed to focus the electrons

to a very fine spot. Near the bottom, a set of scanning coils moves the focused beam back and

forth across the specimen, row by row. As the electron beam hits each spot on the sample,

secondary electrons are knocked loose from its surface. A detector counts these electrons and

sends the signals to an amplifier. The final image is built up from the number of electrons

emitted from each spot on the sample (Figure 5.1).

5.2 Samples

Lago de Atitlan is a large lake in the Guatemalan Highlands, which fill a caldera formed by

succesion of large explosive eruptions (Newhall, [30]; Rose et al., [37]; G.G.J. Ernst and cowork-

ers, work in progress). It is surrounded by other volcanoes. One of which is volcano Atitlan.

The region first saw volcanic activity about 11 million years ago, and since then has seen four

separate episodes of volcanic growth and caldera collapse (gravitational collapse of a volcano

vertically down into its shallow magma reservoir, leaving a large collapsed crater). The lake now

fills a large part of the caldera, reaching depths of up to 600m.

5.2. SAMPLES 21

Figure 5.1: Schematic diagram of a scanning electron microscope (Museum of Science, Boston, [27]).

The caldera-forming eruption is known as Los Chocoyos eruption, and ejected up to 300 km3

of tephra (Rose et al., [37]). The enormous eruption dispersed its ash over an area of some 6

million km2: its ash has been detected from Florida to Ecuador, and can be used as a strati-

graphic marker in both the Pacific and Atlantic oceans. (Note: A chocoyo is a type of bird

which is often found nesting in the relatively soft ash layer.)

Since the Los Chocoyos eruption, continuing volcanism has built three volcanoes in the

caldera. Volcan Atitlan lies on the northern rim of the caldera, while Volcan San Pedro and

Volcan Toliman lie within the caldera. San Pedro is the oldest of the three and seems to have

stopped erupting about 40 000 years ago. Toliman began growing after San Pedro stopped

erupting, and probably remains active, although it has not erupted in historic times. Atitlan

has grown almost entirely in the last 10 000 years, and remains active, with its most recent

eruption having occurred in 1853.

The acc-lap studied was produced in one of the more recent eruptions from the Atitlan caldera

(i.e. flooded vent) a few thousand years ago. The phreatomagmatic eruption is referred to as I4

and produced large volumes of white colored rhyolite tephra including major airfall tuffs full of

acc-laps. In magnitude, the I4 eruption is estimated to have been comparible to the Pinatubo

eruption of 1999 (eruption column height 30 km, 5 – 10 km3 material erupted). The acc-laps were

collected onshore very near the assumed vent (caldera lake) for the I4 eruption, 3 to 5 km away

from it, where the I4 deposits including the airfall tuffs are the thickest and maximum acc-laps

size the largest. 8-bit images were made at two different magnifications as seen on Figure 5.2.

Images with 25× magnification (pixel side 7,66 µm) were made by G.G.J. Ernst at Michigan

Tech for the whole acc-lap cross section, while images with 1000× magnification (pixel side

5.3. GRAYSCALE HISTOGRAM 22

0,192µm) were only made for traverses of the cross section. This was done for about 12 acc-laps

from the atitlan I4 phreatoplinian deposits andfor acc-laps from a similar geological context in

New Zealand (not discussed here). All together about 1200 SEM images wer collected by G.G.J.

Ernst who also produced mosaic images. Here only one set of images for one I4 acc-lap is studied

in detail.

Figure 5.2: SEM cross sections of acc-lap from Atitlan, Guatemala. (A) 25× magnification and (B)

1000× magnification. Images from G.G.J. Ernst.

5.3 Grayscale histogram

The intensity or brightness of the pixels comprising a digital image can be graphically depicted

in a grayscale histogram, which maps the number of pixels at each gray level present in the

image. A typical grayscale digital image and its corresponding histogram are presented in Figure

5.3. The grayscale values are plotted on the horizontal axis for the 8-bit image, and range from

0 to 255. In a similar manner, the number of pixels comprising each gray level is plotted on the

vertical axis. Each pixel in the image has a gray level corresponding to a value in the plot, so

the number of pixels in each gray level column of the histogram must add to produce the total

number of pixels in the image.

The histogram provides a convenient representation of a digital image by indicating the

relative population of pixels at each brightness level and the overall intensity distribution of the

image in general. Statistics derived from the histogram can be employed to compare contrast

and intensity between images, or the histogram can be altered by image processing algorithms

to produce corresponding changes in the image (e.g. segmentation).

5.4. SEGMENTATION 23

Figure 5.3: (A) 1000× magnification SEM grayscale image, 8-bit, 712× 484 pixels, image from G.G.J.

Ernst. (B) segmented image and (C) grayscale histogram. The single global threshold was chosen to be

gray value 87.

5.4 Segmentation

Segmentation is the image proces that converts a grayscale image to a binary (black-white)

image, dividing it up in a material phase and a void phase. The non-zero width of two peaks

in the grayscale histogram and their overlap makes general segmentation difficult. The simplest

approach is chosing a single global threshold. Every pixel with gray value larger is considered

as material, the other pixels as void. This can be done automatically, but my experience learns

that it’s best to chose the threshold with ones own judgement.

Another method is double thresholding. A weak and a strong threshold are chosen, which

determine the threshold window. All pixels with gray value below the weak threshold are

determined as void phase and all pixels with gray value above the strong threshold are considered

5.5. MEASUREMENTS 24

as material. The pixels with gray value in the threshold window, are evaluated according to

their neighbouring pixels. There are numerous ways to do this. Two methods are discussed in

chapter 7.

Since SEM images are very sharp, the use of a single global threshold is justified. The article

of Marcelino et al., [24] shows that the difference between single global thresholding and the

double thresholding method used in the software µCTanalysis on SEM images is small (less then

1 %). However, for micro-CT images double thresholding can’t be avoided, because images have

a greater level of noise. This will be discussed in chapter 7

5.5 Measurements

The first thing before measuring is calibration of the image, which means one designates a

real-world size to the pixels. Then, the area of a particle is the sum of calibrated pixels inside

it and the perimeter is the sum of the pixels making up the object boundary.

One can consider the 2D connection of pixels in two ways. Pixels are 4-connected if their

edges touch. This means that a pair of adjoining pixels are part of the same object only if they

are both on and are connected along the horizontal or vertical direction. Pixels are 8-connected

if their edges or corners touch. This means that if two adjoining pixels are on, they are part

of the same object, regardless of whether they are connected along the horizontal, vertical, or

diagonal direction. Throughout my analysis I used 8-connectivity.

To determine correct measurements of particles in an image, one needs to define a particle

diameter. There exists a large variety of diameter definitions. Table 5.1 gives the definition of

the two most commonly used diameters. See Figure 5.4 for illustrtions of these diameters.

equivalent diameter diameter of the disk having the same area

feret diameter length of the orthogonal projections of the particle on lines

at different angles

Table 5.1: Definition of particle diameters.

From the feret diameters, one can make an average, minimum and maximum feret diameter.

To determine a grainsize distribution the equivalent diameter seems to me the most suitable

diameter, because one needs to link the area of a particle to it’s diameter.

The importance of particle shape is discussed by Riley et al., [34]. The way an ash particle is

shaped can greatly affect its terminal fall velocity. The possibilities to determine particle shapes


Figure 5.4: Illustration of particle measurement concepts. (A) Equivalent diameter. (B) Feret diameters:

maximum feret Fmax, minimum feret Fmin, feret in x-direction Fx and feret in y-direction Fy. (C) Two

particles, shown in gray, and their respective convex hulls, the areas enclosed by black lines.

are almost endless (Kindratenko, [17]). I restricted myself to the ones used in the image analysis

programs IMAQ Vision, [28], ImageTool, [6] and the article of Riley et al., [34] listed in Table

5.2. The convex hull perimeter is the perimeter of the smallest convex polygon containing all

points in the particle (Figure 5.4).

aspect ratio maximum feret/ minimum feret

compactness (IMAQ Vision) area/(feret x-direction· feret y-direction)

compactness (ImageTool) equivalent diameter/maximum feret

compactness (Riley et al.) 4π· area/ (convex hull perimeter)2

elongation (IMAQ Vision) (maximum feret)2/area

elongation (ImageTool) maximum feret/longest segment perpindicular to the

maximum feret

form factor 4π· area/ (perimeter)2

roughness convex hull perimeter/perimeter

Table 5.2: Definition of particle shapes.

One also needs to take into account that there is going to be an error in the shape measure-

ment, because we work with digital images. To get an idea of the error size that is made, one

can consider the following problem. Place a circle inside a grid of 100× 100 pixels and let the

diameter of this circle vary between 1 and 100 pixels. Comparing the number of pixels (=area

of pixels), which have their center inside the circle to the area of that circle πd2/4, one sees in

Figure 5.5 that the size of the error is less than 5 % if the circle diameter is larger then 10 pixels.

However, the perimeter of a curved surface is usually off by a large amount no matter what

the resolution. The perimeter of a digital circle, obtained by counting pixel edges, is P = 4d,


not P = πd (Garboczi et al., [11]). Therefore, IMAQ Vision subsamples the boundary points to

approximate a smoother, more accurate perimeter.

Figure 5.5: Comparison of the area of a circle with a digital circle.

5.5.1 Porosity

Porosity differs greatly with the magnification of the images. To get meaningful results, the

image must sample a representative area of the porous material. Just as in the spatial resolution

section in chapter 4 one can use the Nyquist criterion and Shannon’s sampling theorem for a

minimum sampling criterion. A good rule of thumb is that the pixel size should be 5 times

smaller then the smallest pore size. The SEM cross sections with 1000× magnification can be

used to measure porosity. The measurement is very easy. After segmentation the number of

pixels in the void phase is divided by the total number of pixels. The result for the sample

studied was 49%.

5.5.2 Grainsize distribution and shape measurements

Since particle diameters typically span many orders of magnitude for natural sediments, one

must find a way to conveniently describe wide ranging data sets. The base two logarithmic φ

scale is one useful and commonly used way to represent grainsize information for a sediment

distribution. Logarithmic φ values (in base two) are calculated from particle diameter size


measures in millimeters as follows:

φ = − log2 d = −(

log10 d

log10 2

),

where φ is particle size in φ units, d is particle size in mm. The negative sign is affixed so that

commonly encountered sand sized sediments can be described using positive φ values. Normally

the y-axis in a grainsize distribution is weigth percent. Since it is not possible to determine the

weight of a particle in an image, I replaced this with area percent. I also plotted grainsize in

function of their relative number.

The images with pixelsize 1000× magnification were used, because individual particles can

be seen. The images are segmented and automated analysis was done with LabVIEW. Also, all

shapes described in Table 5.2 were calculated in the same program. The results can be seen

in Figure 5.6 and 5.7. The mean value of the grainsize distribution is 5, 65 φ = 19, 92 µm, the

mode is 5, 13 φ = 28, 57 µm and the standard deviation is 1, 28 φ. A distribution with Standard

deviation between 1 and 2 φ is called poorly sorted (Blott and Pye, [2]).

5.5.3 Concentric layers

If one tiles the images with 25× magnification, we get an image of the entire cross section of the

acc-lap. After masking and resizing to a region of interest we get Figure 5.8. One can clearly

see different layers, but trying to count the layers or see where they are interupted is difficult.

We worked out a program in LabVIEW trying to give more insight in the layer distribution.

The input file is the segmented image of Figure 5.8. The first step is to select a region of interest

(ROI) with rectangle shape that traverses the acc-lap. At every pixel position along the long

side of this ROI, pore density is measured by dividing the number of white pixels (pore pixels)

by the total number of pixels along the short side of the ROI. The pore density for one ROI

can be seen in Figure 5.9. Then we let this ROI rotate and do the same calculations at several

angles (angle step is 1 degree). The results are combined in a sinogram displayed in Figure 5.10.

5.5.4 Vesicle size distribution

The procedure for vesicle size distribution would be the same as for grainsize distribution, if

the vesicles seen in Figure 5.8 weren’t connected. The proces to disconnect these pores is called

separation. The easiest way to do this is via an erosion/dilation procedure.

The erosion operator takes two pieces of data as inputs. The first is the image which is

to be eroded. The second is a (usually small) set of coordinate points known as a structuring


Figure 5.6: Top: grainsize distribution of ash inside the acc-lap of Atitlan, Guatemala calculated in φ

scale. Bottom: relative number of ash particles in function of grainsize calculated in φ scale.


Figure 5.7: Shape measurements of ash inside the acc-lap of Atitlan, Guatemala. See Table 5.2 for shape

definitions.


Figure 5.8: SEM cross section of an acc-lap from Atitlan, Guatemala (based on collection of 35 25×

magnification SEM images, mosaic constructed by GGJ Ernst at Michigan Tech). The maximum feret

diameter is 25,5 mm and the minimum feret diameter is 18,7mm. Layers varying in vesicle distribution

can be seen (vesicles are black rounded or elliptical voids).

Figure 5.9: Pore density graph of one single ROI.


Figure 5.10: Pore density graphs of every angle combined in a sinogram.


Figure 5.11: A 3× 3 square structuring element.

Figure 5.12: Effect of erosion using a 3× 3 square structuring element.

element. It is this structuring element that determines the precise effect of the erosion on the

input image. Here, we used a 3× 3 square as structuring element, depicted in Figure 5.11.

To compute the erosion of a binary input image by this structuring element, we consider

each of the foreground (white) pixels in the input image in turn. For each foreground pixel

(which we will call the input pixel) we superimpose the structuring element on top of the input

image so that the origin of the structuring element coincides with the input pixel coordinates.

If for every pixel in the structuring element, the corresponding pixel in the image underneath is

a foreground pixel, then the input pixel is left as it is. If any of the corresponding pixels in the

image are background, however, the input pixel is also set to background value.

The effect of this operation (Figure 5.12) is to remove any foreground pixel that is not

completely surrounded by other white 8-connected pixels. Such pixels must lie at the edges of

white regions, and so the practical upshot is that foreground regions shrink. Dilation has the

opposite effect of an erosion because the dilation is equivalent to eroding the background. A

combination of erosion and dilation removes the smallest particles and the connections between

vesicles as can be seen in Figure 5.13.

Once this done the same procedure as for grainsize distribution can be followed. The result

can been seen in Figure 5.14. The mean value of the φ scale distribution is 2, 97 φ = 127, 6 µm,

the µm scale gives 58, 3 µm.

5.6. DISCUSSION 33

Figure 5.13: Removal of small pores and connections between vesicles through erosion/dilation.

5.6 Discussion

Altough the developed techniques in this chapter need to be optimized, three possible interpre-

tations of the produced data can be highlighted and are briefly discussed in turn:

1. The overall ash grainsize distribution was quantified. In phreatoplinian eruptions of the

intensity of the I4 Atitlan eruption, the fragmentation intensity is correspondingly extreme

so that the ash produced is expected to be much smaller than centimetric-scale ash balls

moving rapidly up and down the ash column and sampling all the ash particle sizes more or

less at random because of the high differential between the fall or ascend speeds of ash and

that of a large dense ashball (e.g. Sparks et al., [43]; Textor and Ernst, [44]; Textor el al,

[45] and [46]). Another reason why one expects the ashball to sample randomly is that like

for hailstones (e.g. Morgan and Summers, [26]; List, [23]) the acc-laps are oblate ellipsoids

(based on work in progress by Ernst and coworkers) and are expected to tumble during

fall, thereby maximising ash sampling and its distribution on the acc-lap during growth.

This is also why it is decided to discuss the largest acc-lap here, from I4, as much smaller

acc-lap are not expected to fall or tumble as vigorously as a pluricentimetric acc-lap. So

then, the expectation is that within an ashball of only a centimetre across or so, that there

could be a record of the typical size distribution produced in the phreatoplinian eruption.

This could be evaluated in future by detailed comparison between the size distribution

obtained via this approach with total grainsize reconstructions made based on field data

attempting to integrate grainsize information across the wide area of a plinian fall deposit.

The ash size data obtained here indeed suggests a regular curve for the total grainsize

5.6. DISCUSSION 34

Figure 5.14: Top: vesicle size distribution inside the acc-lap of Atitlan, Guatemala calculated in φ scale.

Middle: vesicle size distribution calculated in µm scale. Bottom: relative number of vesicles in function

of vesicle size in µm scale.

5.6. DISCUSSION 35

distribution erupted, with qualitatively a skewed lognormal distribution (i.e. not lognormal

sensu stricto in a rigorous mathematical sense). The distribution shows that all the ash

particles sampled by the ash ball were finer than about 100 µm with a striking mode at

30 µm (Figure 5.6).

The new grainsize distribution may prove very important if such grainsize data derived

from ash balls is really a good proxy for the total grainsize distribution erupted in the

corresponding eruption column. The approach of measuring it in a few ashballs by SEM

rather than through most tedious reconstructions based on hundreds of grainsizes at many

locations may also prove time and cost-effective. More work in the near-future will go

in the direction of putting the new proxy and method to the test - such a time-intensive

exercise was beyond the scope of the present effort.

2. The shape measurements of the ash inside the acc-lap studied showed that ash isn’t spher-

ical at all. Riley et al., [34] showed that deviations from the spherical shape have a great

affect on terminal velocities of ash particles. Thus ash particles shouldn’t be modelled as

small spheres in simulations of volcanic plumes (Textor et al., [45] and [46]).

3. If Ernst and coworkers are correct in interpreting the elliptical/round voids as air bubbles

from dissolved air expulsed during freezing events as occurs in hailstones during riming,

then the characteristic air bubble size ranges found in hailstones should also be observed

here. Quantification of the sizes of the elliptical/rounded voids was developed here and

carried out to evaluate this. The results show that the round vesicle sizes are in the range

50 to 400 µ or so with the smallest sizes being more volumetrically abundant (2D estimate).

Indeed, vesicles/voids in this size range closely match the range expected for air bubbles

forming in hailstones undergoing growth by riming (e.g. Morgan and Summers, [26]; List,

[23] and refs therein).

In detail riming dynamics is complex but suffice to say that black ice and white ice rime

layers in hailstones are characterised by contrasting concentrations of air bubbles also with

a contrasting modal size of air bubbles but always within the bubble size range being within

50 to 250 microns size range (coalescence is observed also as in the ashballs) consistent

with the present data for the I4 acc-lap. Smaller acc-laps examined are not considered here

as acc-laps below a 6mm size can indeed form by wet accretion in the absence of freezing

in the warmer lower parts of an eruption column (see Durant and Ernst, in review). Here,

5.6. DISCUSSION 36

in the I4 acclap, the grainsize distribution of air bubbles could not be determined for

each zone but was determined for a mix of zones. The vesicles measured appear to be

consistent with what one expects to get by adding up the grainsize distribution of air

vesicles in successive black and white ice layers.

In severe thunderstorms as in eruption columns, recycling of falling aggregates/hailstones

is a dominant process (e.g. Rogers and Yau, [35]; Houze, [13]; Lane et al., [20]; Ernst et al.,

[10]) and bring the wet or frozen ashballs or hailstones in contact with supercooled (ash-

filled) water drops in different humidity and temperature environments as the particles

cycle up and down the updraft (e.g. List, [23] and refs therein) so that a similar riming

process is expected in both cases. Ernst and coworkers observed evidence consistent with

growth by contact freezing as ash-filled drops are collected by ashballs on the surface of

acc-laps. This process leads to discontinuous concentric layering and indeed this is what

is thought to be observed here (sinogram, Figure 5.10).

37

Chapter 6

Tomography

This chapter is mainly based on the overview article of Ketcham and Carlson, [15] and the

websites of the UGCT and UTCT facilities, [47] and [48].

6.1 Introduction

Tomos is the Greek word for cut or section, and tomography is a technique for digitally cutting a

specimen open using X-rays to reveal its interior details. A Computer Tomography (CT) image

is typically called a slice, analogous to a slice from a loaf of bread. This analogy is apparent,

because just as a slice of bread has a thickness, a CT slice corresponds to a certain thickness

of the object being scanned. Therefore, whereas a typical digital image is composed of pixels

(picture elements), a CT slice image is composed of voxels (volume elements).

The gray levels in a CT slice correspond to X-ray attenuation, which reflects the relative part

of X-rays scattered or absorbed as they pass through each voxel. X-ray attenuation is primarily

a function of X-ray energy and the density and atomic number of the material being imaged.

A CT image is created by directing X-rays through the slice plane from multiple orientations

and measuring their resultant decrease in intensity. A specialized algorithm is then used to

reconstruct the distribution of X-ray attenuation in the slice plane. By acquiring a stacked,

contiguous series of CT images, data describing an entire volume can be obtained, in much the

same way as a loaf of bread can be reconstructed by stacking all of its slices.

First developed for widespread use in medicine for the imaging of soft tissue and bone, X-

ray CT was subsequently extended and adapted to a wide variety of industrial tasks. These

latter developments, which demanded imagery of denser objects across a range of size classes

6.2. CT PRINCIPLE 38

and resolution requirements, provided key advances that greatly enhanced the potential for

application of this technology to geological investigations.

Because industrial X-ray CT scanners are typically custom-built, no detailed description of

their principles and operation will apply in all cases. Instead, we provide here a description of

each component of the CT-scanning process, both in general terms and as specifically applied

at the University of Ghent CT Facility, UGCT.

6.2 CT principle

6.2.1 Scanning configuration

The elements of X-ray radiography are an X-ray source, an object to be imaged through which

the X-rays pass, and a detector that measures the extent to which the X-ray signal has been

attenuated by the object. A single set of X-ray intensity measurements on a detector for a given

object position and scanner geometry is termed a view. The fundamental principle behind

computed tomography is to acquire multiple views of an object over a range of angular orienta-

tions. By this means, additional dimensional data are obtained in comparison to conventional

X-radiography, in which there is only one view.

Rotate-only CT is sometimes referred to as third generation CT. It is the basic mode used

by most industrial CT systems. It requires the scanned object to fit within the field-of-view of

the detector and X-ray beam. The object is rotated one time per slice and is then repositioned

vertically by the distance of the slice width. Most slices can be acquired in seconds using this

scan mode. Of course the actual time depends upon the geometry of the particular scan the

material density of the object being scanned and the number of views acquired.

Offset rotate CT uses special algorithms to reconstruct an image of an object from less than

a full 360◦ rotation. The object is positioned slightly outside the field-of-view of the detector.

The object is then rotated 180◦ plus the fan angle of the X-ray beam during data collection.

The advantage of this technique is that the system can image a part that is between 1,5 and

1,9 times larger than the field-of-view of the detector depending on the magnification setting for

the scan. Offset rotate also allows the object to be spread across more detector channels which

improves resolution.


6.2.2 X-ray source

The important variables that determine how effective an X-ray source will be for a particular

task are the size of the focal spot, the spectrum of X-ray energies generated, and the X-ray

intensity. The focal-spot size partially defines the potential spatial resolution of a CT system

by determining the number of possible source-detector paths that can intersect a given point

in the object being scanned. The more such source-detector paths there are, the more blurring

of features there will be. The energy spectrum defines the penetrative ability of the X-rays, as

well as their expected relative attenuation as they pass through materials of different density.

Higher-energy X-rays penetrate more effectively than lower-energy ones, but are less sensitive to

changes in material density and composition. The X-ray intensity directly affects the signal-to-

noise ratio and thus image clarity. Higher intensities improve the underlying counting statistics,

but often require a larger focal spot.

The UGCT facility uses four types of X-ray sources. One is the microfocus tube, a medium

energy (up to 160 keV) open type Feinfocus tube. The maximum power of the directional tube

is 150 W, with spot sizes of 20 to 2 µm. The nanofocus tube is a state-of-the-art tomographic

X-ray tube also from Feinfocus. The maximum voltage is 160 kV. The tube has three different

modes: nano, micro and high power mode. The best focal spot size is 900 nm. This (theo-

retically) allows to detect details of 300 nm inside small samples. The resolution can never be

better than the size of the X-ray spot. The nano-CT and micro-CT tube use the same high

voltage generator and a tube base containing an X-ray filament. Two heads are attached to

the tube base and can therefore not be used at the same time. The medical CT system has

an X-ray spot sizes that range from 0,5 mm to 2mm. The linear particle accelerator, LINAC

has a variable maximum voltage of 2MV up to 15 MV. Most X-rays produced at the LINAC

have an energy below 1 MeV. The higher energies are not suitable for imaging due to their low

interaction probability in the detector.

The energy spectrum generated is usually described in terms of the peak X-ray energy (keV

or MeV), but actually consists of a continuum in which the level with maximum intensity is

typically less than half of the end point energy (Figure 6.1). The total effective spectrum is

determined by a number of factors in addition to the energy input of the X-ray source itself,

including

• autofiltering both by absorption of photons generated beneath the surface of a thick target

and by passage through the tube exit port,


• other beam filtration introduced to selectively remove low-energy X-rays,

• beam hardening in the object being scanned,

• the relative efficiency of the detectors to different energies.

As discussed below, changes in the X-ray spectrum caused by passage through an object can

lead to a variety of scanning artifacts unless efforts are made to compensate for them.

Figure 6.1: Theoretical energy spectra for a 420 kV X-ray source with a tungsten target, calculated

combining 5 keV intervals. The spectra consist of continuous Bremsstrahlung and characteristic K-series

peaks at 57 – 59 keV and 67 – 69 keV. The upper spectrum is modified only by inherent beam filtration by

3 mm of aluminum at the tube exit port. The mean X-ray energy is 114 keV. The lower curve represents a

spectrum that has also passed through 5 cm of quartz. The preferential attenuation of low-energy X-rays

causes the average energy to rise to 178 keV. Ketcham and Carlson, [15].

6.2.3 X-ray attenuation

As the X-rays pass through the object being scanned, the signal is attenuated by scattering and

absorption. The basic equation for attenuation of a monoenergetic beam through a homogeneous

material is Beer’s Law:

I = I0 exp(−µx)

where I0 is the initial X-ray intensity, µ is the linear attenuation coefficient for the material

being scanned (units: 1/length), and x is the length of the X-ray path through the material. If

the scan object is composed of a number of different materials, the equation becomes:

I = I0 exp

(−∑

i

µixi

)


where each increment i reflects a single material with attenuation coefficient µi over a linear

extent xi. To take into account the fact that the attenuation coefficient is a strong function of

X-ray energy, the complete solution would require solving the equation over the range of the

effective X-ray spectrum:

I =∫

I0(E) exp

(−∑

i

µi(E)xi

)dE

However, such a calculation is usually problematical for industrial CT, as the precise form of

the X-ray spectrum, and its variation at off-center angles in a fan or cone beam, is usually only

estimated theoretically rather than measured.

There are 4 types of X-ray interactions with matter that must be considered for the experi-

ments:

• Photoelectric absorption occurs when the total energy of an incoming X-ray photon is

transferred to an inner electron, causing the electron to be ejected. The atom that loses

the electron is excited and returns to its ground state via emission of characteristic X-rays.

• In Compton scattering, the incoming photon interacts with an outer electron, ejecting

the electron and losing only a part of its own energy, after which it is deflected in a different

direction.

• In pair production, the photon interacts with a nucleus and is transformed into a

positron-electron pair, with any excess photon energy transferred into kinetic energy in

the particles produced.

• Rayleigh scattering is scattering of a photon with a strongly bond electron, which

creates a vibrational disturbance. When the atom returns tot its groundstate it emits a

photon of the same wavelenght in a random direction. It is Rayleigh scattering off the

molecules of the air which gives rise to the blue sky.

In general for geological materials, the photoelectric effect is the dominant attenuation mech-

anism at low X-ray energies, up to approximately 50 – 100 keV. Compton scattering is dominant

at higher energies up to 5 – 10 MeV, after which pair production predominates. Thus, unless

higher-energy sources are used, only photoelectric absorption and Compton scattering need to

be considered. The practical importance of the distinction between mechanisms is that pho-

toelectric absorption is proportional to Z4−5, where Z is the atomic number of an atom in


the attenuating material, whereas Compton scattering is proportional only to Z. As a result,

low-energy X-rays are more sensitive to differences in composition than higher-energy ones.

The best way to gain insight into what one might expect when scanning a geological sample

is to plot the linear attenuation coefficients of the component materials over the range of the

available X-ray spectrum. These values can be calculated by combining experimental results for

atomic species. Mass attenuation coefficients must be multiplied by mass density to obtain linear

attenuation coefficients. To illustrate, we consider four minerals: quartz, orthoclase, calcite,

and almandine garnet. Quartz and orthoclase are very similar in mass density (2.65 g/cm3

vs. 2.59 g/cm3), but at low energy their attenuation coefficients are quite different because

of the presence of relatively high-Z potassium in the feldspar. With rising X-ray energy, their

attenuation coefficients converge, and at approximately 125 keV they cross; above 125 keV quartz

is slightly (but probably indistinguishably) more attenuating, owing to its higher density. Thus,

these two minerals can be differentiated in CT imagery if the mean X-ray energy used is low

enough, but at higher energies they are nearly indistinguishable (Figure 6.2). Calcite, though

only slightly denser (2.71 g/cm3) than quartz and orthoclase, is substantially more attenuating,

owing to the presence of calcium. Here the divergence with quartz persists to slightly higher

energies, indicating that it should be possible to distinguish the two even on higher-energy scans.

High-density, high-Z phases such as almandine are distinguishable at all energies from the other

rock-forming minerals examined here.

Figure 6.2: Linear attenuation coefficient as a function of X-ray energy for four rock-forming minerals.

Such curves, when combined with the X-ray spectrum utilized for scanning (Figure 6.1), allow prediction

of the ability to differentiate between minerals in CT images. Ketcham and Carlson, [15].

6.3. ACQUISITION OF CT DATA 43

6.2.4 X-ray detectors

Detectors for CT scanners make use of scintillating materials in which incoming X-rays produce

flashes of light that are counted (Knoll, [18]). Pixels influence image quality through their size

and quantity, and through their efficiency in detecting the energy spectrum generated by the

source. The size of an individual detector determines the amount of an object that is averaged

into a single intensity reading, while the number of pixels determines how much data can be

gathered simultaneously.

The efficiency of scintillation detectors varies with X-ray energy, precisely because higher-

energy X-rays are more penetrative than lower-energy ones, indicating that they are more capa-

ble of traveling through materials without interactions. This factor must be taken into account

when determining the level of expected signal after polychromatic X-rays pass through materials.

At the UGCT facility we used a Remote RadEye detector to scan the acc-laps. Typical

scan time is 10 min up to 2 hours for high-resolution tomography of specimens up to a few cm

in diameter. The system’s magnification, which increases with the specimen’s proximity to the

X-ray source, combined with the fixed pixel size of the X-ray detector determine the limits of

spatial resolution. The best spatial resolution is 2 µm. The detector has 1024× 1024 pixels

and a 12-bit digital output. The sample diameter divided by this number mostly defines the

CT resolution. In the mean time a new detector has arrived at the UGCT facility and is used

for scans with the nanofocus tube. It is a Photonic Science VHR detector, which has

4008× 2672 pixels and 12- or 16-bit digitisation.

6.3 Acquisition of CT Data

6.3.1 Sample preparation

Strictly speaking, the only preparation that is absolutely necessary for CT scanning is to ensure

that the object fits inside the field of view and that it does not move during the scan. Because

the full scan field for CT is a cylinder (i.e. a stack of circular fields of view), the most efficient

geometry to scan is also a cylinder. Thus, when possible it is often advantageous to have the

object take on a cylindrical geometry, either by using a coring drill or drill press to obtain

a cylindrical subset of the material being scanned, or by packing the object in a cylindrical

container with either an X-ray-transparent filler or with a material of similar density. For some

applications the sample can also be treated to enhance the contrasts that are visible.


6.3.2 Calibration

Calibrations are necessary to establish the characteristics of the X-ray signal as read by the

detectors under scanning conditions, and to reduce geometrical uncertainties. The latter cali-

brations vary widely among scanners.

The two principal signal calibrations are offset and gain, which determine the detector read-

ings with X-rays off, and with X-rays on at scanning conditions, respectively. An additional

signal calibration, called a wedge, used on some third-generation systems consists of acquiring

X-rays as they pass through a calibration material over a 360◦ rotation. The offset-corrected

average detector reading is then used as the baseline from which all data are subtracted. If the

calibration material is air, the wedge is equivalent to a gain calibration. A typical non-air wedge

is a cylinder of material with attenuation properties similar to those of the scanned object.

Such a wedge can provide automatic corrections for both beam hardening and ring artifacts,

and can allow utilization of high X-ray intensities that would saturate the detectors during a

typical gain calibration. Although widely employed in medical systems, which use phantoms of

water or water-equivalent plastic to approximate the attenuating properties of tissue, the wedge

calibration is relatively uncommon in industrial systems.

6.3.3 Collection

A good tomography measurement consists of projections, beam profile images (flat fields) and

dark images (offset images). Parallel beam geometry requires projection images with equi-

angular separation between 0◦ and 180◦. The last image at 180◦ is not used for the reconstruction

but it is used for the calculation of the rotation centre (COR). Fan and cone beam geometry

require projections over 360◦ or 180◦ plus opening angle of the fan or cone. This last range is

called short scan. In the case of large opening angles (large flat panel detectors) 360◦ scans are

advised.

Ideal projections are images free of noise. Of course in practice this is never the case. Noise

is always present due to the statistical nature of the measurement. Detectors need sufficient grey

levels (dynamic range). If the detector is 12 bit or less one should acquire a number of images

at every angle and use the sum or the average of these images. This approach improves the

reconstruction quality very much. The number of projections is theoretically defined as πN/2

or 1,5 times the number of detector row pixels. In practice 400 projections are enough for 1024

detector pixels per 180◦. More projections improve the statistics and therefore the quality of


the reconstruction.

Beam profile images are often called open beam images of flat field images. These images

are used to correct the beam profile and scintillator and/or taper imperfections. The sample

is out of the beam during the acquisition of the beam profile image. Every projection will be

divided by this open beam image. Every error in this beam profile image will be present in the

normalized images. This makes the beam profile image the most important image. In theory

one image is enough. In practice one should acquire many open beam images. At least 5 flat

fields are necessary but more is advised.

Offset images or dark images are needed to correct three detector features: dark current,

read-out noise and ADC offset. Only the first one depends on the acquisition or integration

time. Projections, flat fields and offset images are measured with the same integration time.

Also for the dark images it is advised to acquire a large number of images since these images

are subtracted from the projection images and the open beam images.

The raw data are displayed such that each line contains a single set of detector readings for

a view, and time progresses from top to bottom. This image is called a sinogram, as any single

point in the scanned object corresponds to a sinusoidal curve.

6.3.4 Reconstruction

Reconstruction is the mathematical process of converting sinograms into two-dimensional slice

images. The most widespread reconstruction technique is called filtered backprojection, in which

the data are first convolved with a filter and each view is successively superimposed over a square

grid at an angle corresponding to its acquisition angle.

During reconstruction, the raw intensity data in the sinogram are converted to CT numbers

or CT values that have a range determined by the computer system. Most medical and older

industrial systems use a 12-bit scale, in which 4096 values are possible, while most more recent

systems use a 16-bit scale, which allows values to range from 0 to 65535. On most industrial

scanners, these values correspond to the grayscale in the image files created or exported by the

systems. Although CT values should map linearly to the effective attenuation coefficient of the

material in each voxel, the absolute correspondence is arbitrary. The sofware package Octopus,

[50] was developed at the UGCT facility for reconstruction.

6.4. RESOLUTION AND SIZE LIMITATIONS 46

6.4 Resolution and size limitations

Industrial scanners can accomodate objects with a wide range of sizes, shapes, and materials.

Just as variable is the range of objectives for scanning, which can range from making precise

measurements to observing gross features. Successful scanning will rely on all of these factors.

6.4.1 Spatial resolution

The spatial resolution in a CT image is determined principally by the size and number of detector

elements, the size of the X-ray focal spot, and the source-object-detector distances. At the UGCT

facility, the source-to-detector distance and the sizes of the detector elements are variable. In

this situation, maximum resolution is achieved by minimizing the source-to-object distance to

give maximum magnification. By using offset geometries, in which the axis of rotation for the

specimen is not in the center of the X-ray beam, higher magnification is achieved, though at a

slight cost in image quality because fewer X-rays penetrate each volume element in the sample

than is the case in a centered geometry.

As a rule of thumb, a CT image should have about as many pixels in each dimension as there

are detector channels providing data for a view. For example, a 1024-channel linear detector

array justifies a 1024× 1024 pixels reconstructed image. If an offset scanning mode is used, up

to a 2048× 2048 pixels image may be justified.

Slice thickness, which governs the resolution in the third dimension, is determined by varying

the thickness of linear apertures in front of the detectors.

Because both X-ray generation and the scattering events that produce attenuation within

the object are stochastic processes, the X-ray signal is inherently noisy. The detector and its

amplification electronics contribute additional noise. Thus, variations in the X-ray signals aris-

ing from these effects can obscure the variations arising from the sample itself. This noise in

the intensity measurements limits the scanner’s ability to differentiate between nearby volume

elements with closely similar attenuation, thereby degrading the resolution of the image. In-

creasing the X-ray flux and/or the counting time for each intensity measurement will bolster

the signal-to-noise ratio and improve the resolution.

Because decreasing slice thickness correspondingly decreases the the X-ray flux on each

detector element, attempts to gain improved resolution by using thinner slices are eventually

thwarted by the need to maintain sufficient X-ray flux to generate satisfactory counting statis-

tics. Increasing the intensity of the incident beam can help, but this will tend to increase the

6.4. RESOLUTION AND SIZE LIMITATIONS 47

focal spot size, which results in additional blurring. Increasing the duration of each intensity

measurement can compensate without this compromise, but can prove prohibitively costly or

simply impractical if the required times are excessively long.

Conventional medical CT instruments provide resolutions on the order of 1 – 2 mm for meter-

scale to decimeter-scale objects. Ultra-high-resolution instruments, like the microfocus and

nanofocus system of the UGCT facility, provide resolutions on the order of a few µm for

centimeter-scale to millimeter-scale objects.

6.4.2 Density/attenuation resolution

The ability to differentiate materials depends on their respective linear attenuation coefficients.

In practical terms, successful imaging will depend on innate material properties of density and

atomic composition, and on the machine parameters of the X-ray spectrum utilized and the

signal-to-noise ratio. Materials with very divergent densities and/or atomic constituents are

easy to differentiate. In favorable circumstances, modern CT instruments are capable of dis-

criminating between values of that differ by as little as 0.1 %, but only if the regions being

tested are relatively large, spanning many voxels, and if there is sufficient X-ray flux to keep

image noise low. As a result, spatial and density/attenuation resolution are linked: if materi-

als are very different in their attenuation propoerties, very fine details or very small particles

can be imaged, but if they are similar only larger-scale details and/or particles can be reliably

distinguished.

6.4.3 Size limitations

Apart from the obvious constraint imposed by the size of the instrument’s sample holder, the

maximum size of objects that can be examined by CT is determined by the need to acquire

a sufficiently strong signal from the beam after it has been attenuated by passage though the

object. If the object is too thick, it will absorb too much energy, resulting in low X-ray flux and

poor image quality. A 160 kV X-ray tube generate beams capable of imaging geologic materi-

als (objects with average densities close to those of common silicate minerals) with maximum

dimensions up to perhaps tens of cm. Larger or denser objects can be imaged with special CT

instruments that use very high-energy sources such as the LINAC.

6.5. ARTIFACTS 48

6.5 Artifacts

Although the output of computed tomography is visual in nature and thus lends itself to straight-

forward interpretation, subtle complications can render the data more problematic for quanti-

tative use. Scanning artifacts can obscure details of interest, or cause the CT value of a single

material to change in different parts of an image. Partial-volume effects, if not properly ac-

counted for, can lead to erroneous determinations of feature dimensions and component volume

fractions. In this section we discuss commonly encountered problems, and some approaches for

solving them.

6.5.1 Beam hardening

The most commonly encountered artifact in CT scanning is beam hardening, which causes the

edges of an object to appear brighter than the center, even if the material is the same throughout

(Figure 6.3A). The artifact derives its name from its underlying cause: the increase in mean

X-ray energy, or hardening of the X-ray beam as it passes through the scanned object. Because

lower-energy X-rays are attenuated more readily than higher-energy X-rays, a polychromatic

beam passing through an object preferentially loses the lower-energy parts of its spectrum. The

end result is a beam that, though diminished in overall intensity, has a higher average energy

than the incident beam (Figure 6.1). This also means that, as the beam passes through an

object, the effective attenuation coefficient of any material diminishes, thus making short ray

paths proportionally more attenuating than long ray paths. In X-ray CT images of sufficiently

attenuating material, this process generally manifests itself as an artificial darkening at the

center of long ray paths, and a corresponding brightening near the edges. In objects with roughly

circular cross sections this process can cause the edge to appear brighter than the interior, but

in irregular objects it is commonly difficult to differentiate between beam hardening artifacts

and actual material variations.

Beam hardening can be a pernicious artifact because it changes the CT value of a material (or

void) depending upon its location in an image. Thus, the attempt to utilize a single CT number

range to identify and quantify the extent of a particular material can become problematic. One

measure that is sometimes taken is to remove the outer edges of the image and analyze only the

center. Although this technique removes the worst part of the problem, the artifact is continuous

and thus even subsets of the image are affected. Furthermore, if the cross-sectional area of the

object changes from slice to slice, the extent of the beam-hardening artifact also changes, making

6.5. ARTIFACTS 49

Figure 6.3: Scans through a 6-inch-diameter column of saprolite encased in PVC pipe, showing scanning

artifacts and the results of various strategies for remedying them. The scans all represent 1mm-thick

slices collected with the X-ray source at 420 kV and acquisition times of 3 minutes. Scan (A) shows both

ring and beam-hardening artifacts. The latter is visible most obviously as the bright ring around the

outer part of the PVC. Image (B) is the result of a software correction of the ring artifacts in (A). If

the grayscale fluctuations caused by the rings are smaller than for the features of interest, this approach

can be very successful. However, in this case some fractures close to the center have been obscured or

altered. Image (C) shows the result of pre-filtering the X-ray beam by passing it through 6,35mm of

brass. Beam-hardening and ring artifacts have been reduced markedly but not totally, and image noise

has increased considerably. The scan shown in (D) was done using a self-wedge calibration through

a relatively homogeneous portion of the column. The bright rim on the left was caused by imperfect

centering of the column; the image of the saprolite itself, however, has only very minor ring artifacts and

no beam hardening. Note that although the centers of images (B) and (D) are similar, the edges of the

saprolite are brighter in image (B). Thus it is evident that the beam hardening artifact in image (B) was

not confined strictly to the edge of the PVC casing, but was a continuous feature within the saprolite as

well. Also, the y-intersection of fractures just to the upper-left of center (indicated by arrows) appears

discontinuous in the software-corrected image (B). Ketcham and Carlson, [15].

6.5. ARTIFACTS 50

such a strategy prone to error.

There are a number of possible remedies for beam hardening, ranging from sample and scan-

ning preparation to data processing. The simplest approach is to use an X-ray beam that is

energetic enough to ensure that beam hardening is negligible, and can thus be ignored. Unfor-

tunately, most materials of geological interest are attenuating enough that beam hardening is

noticeable unless the sample is quite small. Furthermore, higher-energy beams are less sensitive

to attenuation contrasts in materials, and thus may not provide sufficient differentiation between

features of interest. Another possible strategy is to pre-harden (or post-harden) the X-ray beam

by passing it through an attenuating filter before or after it passes through the scanned object

(Figure 6.3C). Filters are commonly flat or shaped pieces of metal such as copper, brass or

aluminum. The drawback to beam filtration is that it typically degrades the X-ray signal at all

energies to some degree, thus leading to greater image noise unless longer acquisition times are

used. It is also characteristically only partially effective. Another method is to employ a wedge

calibration using a material of similar attenuation properties to the object (Figure 6.3D), as dis-

cussed above. To be effective, the wedge material should be cylindrical, and the scanned object

should either be cylindrical or packed in an attenuating material (ideally the wedge material)

to achieve an overall cylindrical form. If the latter is necessary, images may be noisier because

of the additional X-ray attenuation caused by the packing material. The wedge material in the

images also commonly interferes with 3-D analysis of the object of interest, in which case it must

be eliminated during image processing.

Beam hardening is characteristically more difficult to alleviate at the data-processing stage,

and such measures are usually available only in special circumstances. If the scanned object

is materially uniform, a correction can be applied to the raw scan data that converts each

reading to a non-beam-hardened equivalent before reconstruction takes place; unfortunately,

the requirement of uniformity is more often met in industrial applications than geological ones.

If the object is cylindrical and fairly uniform (i.e., a rock core), it may be possible to construct

an after-the-fact wedge correction by compiling a radial average of CT values for a stack of slices.

A Fourier filter that removes long-wavelength variations in CT value has also been effective in

some circumstances.

6.5. ARTIFACTS 51

6.5.2 Ring artifacts

Ring artifacts occur in third-generation scanning, appearing as full or partial circles centered

on the rotational axis (Figure 6.3A). They are caused by shifts in output from individual de-

tectors or sets of detectors, which cause the corresponding ray or rays in each view to have

anomalous values; the position of a ring corresponds to the area of greatest overlap of these rays

during reconstruction. A number of factors can cause such a shift, all of which have their basis

in detectors responding differently to changes in scanning conditions. Some factors, such as

change in temperature or beam strength, can be overcome by carefully controlling experimental

conditions or by frequent recalibrations. A more problematic source of detector divergence is

differential sensitivity to varying beam hardness. If the detector response calibration (gain or

wedge) is taken through air, the relative response of the detectors can change if the hardness of

the X-ray beam is sufficiently affected by passage through the scanned object. If the object is

uneven then different views can reflect different degrees of hardening, in which case only partial

rings may occur, possibly obscuring their nature as artifacts.

Because of their link to beam hardening, ring artifacts can be addressed at the scanning

stage with many of the same methods: by use of a filtered or sufficiently high-energy X-ray

beam, or employing a wedge calibration through a material of similar attenuating properties to

the scanned object.

Ring artifacts are somewhat more amenable to software remedies than beam hardening. A

series of anomalous readings from a single detector appears on a sinogram as a vertical line, and

thus it can potentially be detected and removed before reconstruction. Similarly, a reconstructed

image can be converted to polar coordinates, vertical lines detected and removed, and converted

back (Figure 6.3B). A drawback of these strategies, particularly the latter, is that any roughly

linear feature in the scanned object that is tangential to a circle centered on the rotational axis

may be erased, blurred, or otherwise altered, even if it does not coincide with a ring. This

can constitute a serious flaw in some applications, such as detecting sutures in fossils or tracing

fractures.

6.5.3 Other artifacts

A variety of other artifacts can arise in certain situations. If a highly attenuating object is

noncircular in cross-section, streaks that traverse the longest axes of the object can occur. For

example, a scanned cube of a dense material may have dark streaks connecting opposite corners.

6.5. ARTIFACTS 52

Figure 6.4: 100µm slice through fractured limestone. Scan field of view is 21.5mm, and individual pixels

are 42 µm on a side. After scanning the entire volume, the sample was cut and fractures were measured

in thin section. Fractures are visible despite being considerably thinner than the pixel width, because of

partial-volume effects. Ketcham and Carlson, [15].

These streaks can intensify ring artifacts where they overlap, making remediation more difficult.

If the scanned material includes features that are of much higher density than the surrounding

matrix, a starburst artifact can form in which bright streaks emanate from the object for

a short distance into nearby material, potentially obscuring features. It has been shown that

fossils that have been repaired with steel pins, result in severe artifacts (Ketcham and Carlson,

[15]). Similar artifacts have been caused by crystals of sulfide or oxide minerals.

6.5.4 Partial-volume effects

Because each pixel in a CT image represents the attenuation properties of a specific material

volume, if that volume is comprised of a number of different substances then the resulting CT

value represents some average of their properties. This is termed the partial-volume effect.

Furthermore, because of the inherent resolution limitations of X-ray CT, all material boundaries

are blurred to some extent, and thus the material in any one voxel can affect CT values of

surrounding voxels. Although these factors can make CT data more problematic to interpret

quantitatively, they also represent an opportunity to extract unexpectedly fine-scale data from

CT images. An example of the possible utility of partial-volume effects is shown in Figure 6.4.

53

Chapter 7

Micro-CT image analysis

7.1 Samples

Samples were collected from Santorini, Greece and the Eifel, Germany. Santorini is a small,

circular group of volcanic islands located in the Aegean Sea, about 200 km south-east from the

mainland of Greece. It had twelve documented large eruptions in the last 400 000 years and

over a 100 minor eruptions. One of the major eruptions occured about 57 000 years ago and is

referred to as the US1 eruption (Druitt et al., [9] for details on US1 eruption).

Of relevance for this thesis is the eruption started with a phreatomagmatic phase producing

base surges in air fall tuffs rich in acc-laps. The acc-lap samples come from the location on

Santorini, where the sequence is thickest and most complete (nearest to the vent, 5 km) and were

the acc-laps are the largest for this eruption. The typical eruption column height is thought to

be 10 km (Durant and Ernst, [8]).

The Eifel is bordered by the Moselle River in the south and the Rhine in the east. In the

north it is continued by the hills of the High Venn, in the west by the Ardennes. Ardennes and

Eifel are actually the same geological region. They are a single volcanic field, well known for

the occurence of a large number strombolian cones and maar craters.

In the Tertiary the Eifel was a site of extensive volcanic activity. Most of the hills are

volcanoes. The last eruptions took place around 10 000 years ago. Research has shown that the

Mantle plume is still active. The Eifel region is rising by 1 – 2 mm per year. Historically, the

Eifel volcanoes had inactive phases of 10 000 to 200 000 years between active phases, suggesting

there is a possibility of future eruptions.

Within the Eifel field there are also a few larger volcanoes including Laacher See, which is

7.2. MICRO-CT IMAGES 54

Figure 7.1: Acc-laps from Santorini, Greece.

located on a short distance south of Bonn and west of the Rhine. About 13 000 years ago the

most explosive eruption of Central Eruption for the past 100 000 years took place at Laacher See,

(Schumacher and Schmincke, [39]). In detail, the explosive eruption was complex with phases

more or less dominated by interactions with external water. Suffice to say that the eruption

was about in magnitude as that of Pinatubo in 1991 (eruption column height 30 km, 5 – 10km3

erupted material) and that the acc-lap studied is sampled from air fall tuffs some 5 km or so to

the soutwest of the Laacher See crater. The acc-laps are thought to have fallen out from very

water-rich ash columns also associated with base surges similar to that of the US1 eruption on

Santorini of that of the I4 Atitlan euption on Guatemala.

7.2 Micro-CT images

First we tried to scan a small sample (2 cm x 3 cm x 3 cm) of a fall deposit rich in acc-laps from

the Eifel. Unfortenately, due to a computer crash this data was lost before any form of analysis

could be done. Then we scanned two connected acc-laps from Santorini and one acc-lap from the

Eifel. Visualizations of the 3D volumes made in VGStudio, [49] can be seen in Figure 7.1 and

7.2. The voxels were cubes with side 9,6µm. This isn’t small enough for grainsize analysis or

porosity measurements, but is ideal for vesicle size distributions. The Santorini acc-laps seemed

to be hard to scan, since they are very dense and small (2 – 3mm). They also didn’t contain

enough vesicles for statistical analysis. On the other hand the Eifel acc-lap of about 7mm gave

contained numerous vesicles. We concentrated on the Eifel acc-lap for analysis.

Several software packages are developed to analyse micro-CT images (Ashbridge et al., [1];

7.3. µCTANALYSIS 55

Figure 7.2: Acc-lap from the Eifel, Germany. On the right we see the vesicles inside the acc-lap.

Cnudde, [4]; Ketcham, [16]; Lindquist, [21]). We tried to compare µCTanalysis, [4] and 3DMA-

rock, [21]. Both programs consist of three major steps. The first is segmentation for dividing the

images up in a material and void phase. The second part is separation for disconnecting pores

that are partly merged. This is necessary to measure correct vesicle sizes, otherwise connected

vesicles will be measured as one large vesicle. The final step is measuring the vesicle volumes.

Just like in 2D connection can be considered in different ways. Pixels are 6-connected if

their faces touch. Pixels are 18-connected if their faces or edges touch. Pixels are 26-connected

if their faces, edges, or corners touch. Another thing that is analogous to 2D analysis is the use

of an equivalent diameter. Now this is the diameter of the sphere with the same volume in stead

of the circle with the same area.

7.3 µCTanalysis

This software was written in MatLab for the Ph.D. thesis of Cnudde, [4]. It provides segmen-

tation, separation and 3D-measurement algorithms. The input files are a stack of reconstructed

2D bmp-files. The parameters that are needed are the voxelsize for calibration, a weak and

strong threshold for segmentation and the coordinates of a region of interest (if desired).

The conversion of voxels with gray values in the threshold window to binary values is done by

seed growing. The threshold filter selects all voxels with gray value above the strong threshold

(seeds), followed by all voxels with gray value lying in the threshold window range and are

connected to seeds via a 26-connected path of any length as void phase voxels.

The separation of connected pores is achieved with a 3D erosion and dilation proces just

7.4. 3DMA-ROCK 56

like in 2D (chapter 5). The pore-size distribution is the determined by using a (3D) structuring

element that approximates the shape of a sphere and fills every pore, progressing from the

smallest inscribed sphere to the largest. This proces provides data of largest inscribed sphere

and total volume of each pore.

7.4 3DMA-rock

The 3DMA code is a freeware package which runs on Linux, [21]. It is designed to take as input

a three dimensional digitized gray-scale image of several types (bmp, tiff, psd and others). It is

assumed that the image is bi-phase with the two phases arranged in a possibly complex, perhaps

random geometrical fashion. The goal of the code is to produce geometrical analyses of either

of the phases.

7.4.1 Segmentation

3DMA rock provides several methods for segmentation. The most recommended segmentation

method is indicator kriging. It is described in the article of Oh and Lindquist, [31]. Briefly, a

weak and strong threshold are chosen, just like in the seed growing method of µCTanalysis, but

the designation of the voxels in the threshold window is different. Indicator kriging provides a

maximum likelihood estimate for the voxel to be a material or void type. This requires a spatial

covariance function, which can be estimated with several algorithms (which one is decided by

the user). For any voxel, the kriging estimate of its type is determined using information from a

local, spherical neighborhood. All threshold identified voxels in this neighboorhood, as well as

the grey scale of all unidentified voxels in the neighborhood contribute to the kriging estimate.

We won’t elaborate on the kriging method itself, because it is very complex.

7.4.2 Separation

Separation is done in three steps:

1. distance labeling, where each pore voxel is assigned an integer describing its distance to

the closest grain voxel (lying on the void grain surface),

2. medial axis construction, which generates a one dimensional representation of the pore

phase,

3. throat construction, which determines the border of partly merged pores.

7.4. 3DMA-ROCK 57

The pore distance labeling proceeds by initializing every surface grain voxel with distance 0. Void

voxels that are 26-neighbors of any distance 0 voxel are labeled with distance 1. Continuing this

in an iterative manner designates a distance to each pore voxel, which is called a burn number.

Calculating the medial axis of a binary image is also called skeletonisation, because it

constructs a one dimensional representation of the void space, which is reminiscent of a tree-like

skeleton. Mathematically, the medial axis is the boundary of the cells of a Voronoi diagram.

A Voronoi diagram is the partitioning of a polygon (in our case the pores) with n points into

convex polygons such that each polygon contains exactly one generating point and every point

in a given polygon is closer to its generating point than to any other. The medial axis can also

be viewed (equivalently) as the points that can be the center of a circle that is entirely within

the polygon and touches the polygon in at least two places. The medial axis is constructed by

generating a sequence of erosions of the object until what is left is an unerodible spine.

For an oject in continuum space, the medial axis is the union of one dimensional curve

segments. Three or more curve segments join in a vertex. The number of curve segments

meeting at a vertex is referred to as the coordination number. The digital analog of a curve

segments is called a path. Since voxels have finite size, the digitized analog of a vertex may have

to consist of several medial axis voxels in order to join a required number of paths. Therefore

a cluster is defined as a contiguous set of medial axis voxels, each of which has at least three

medial axis neighbors. A cluster is thus the digitized analog of a vertex. If a cluster consists of

more then one voxel is called a surface remnant.

The medial axis is highly sensitive to noise. Therefore the 3DMA code consists of various

possibilities to clean up the medial axis. There are four major modifications available: trimming

of boundary voxels, path pruning, merging of clusters and reduction of surface remnants.

The loss of information at the boundary results in a correct medial axis segment accompanied

by a pile-up of incompletely resolved medial axis voxels along the boundary. The trimming

algorithm removes this pile-up.

Each path on the medial axis can be classified as one of three types: a branch-branch path

connects to a cluster at each end, a branch-lef path connects to a cluster at one end and a leaf-

leaf path is isolated, having no cluster connection at either end. In addition there is a special

branch-branch subtype, a needle-eye path, which connects to the same cluster at each of its

ends. A special case of leaf-leaf path is an isolated voxel. A path pruning algorithm provides

the oppurtunity to selectively remove all these types of paths. It’s up to the user to provide

7.4. 3DMA-ROCK 58

Figure 7.3: (A) A pore channel with its medial axis (colored voxels). (B) The medial axis for the same

channel when it is incompletely imaged. (C) The medial axis after boundary voxel trimming. The

rainbow coloring indicates the burn number of each voxel.

Figure 7.4: Illustration of the medial axis resulting from a coordination number 4 pore body.

correct criteria for this. We determined criteria by trial and error on simple images made in

Paint.

Conceptually paths in the medial axis correspond to channels in the void phase, and clusters

correspond to pore bodies where channels connect. Unfortunately, without further modification,

this 1-to-1 correspondence does not exist. While every channel has its corresponding path in the

skeleton, not every path corresponds to a channel. Similarily, while each pore body is represented

by some cluster on the medial axis, several clusters may occur in the same pore body. Thus the

lack of 1-to-1 correspondence occurs solely within pore bodies. The cluster merging algorithm

resolves this problem in the following manner. Consider a path of length L in Figure 7.4 which

joins the two clusters C1 and C2. Let Li denote the shortest distance from Ci to the pore grain

surface (i = 1, 2). If L < max(L1, L2) then the path and the two vertices it joins are considered

to be a single unit, namely a cluster C.

7.4. 3DMA-ROCK 59

Figure 7.5: A two dimensional surface remnant (red) (A) before and (B) after reduction.

Finally, a surface remnant reduction is done. The center of mass of the remnant is

located. From this center of mass voxel, the shortest route through the remnant to each path

attached to the remnant is traced (Figure 7.5). Any remnant voxel not lying on one of these

routes is deleted. The final medial axis structure of the Eifel acc-lap can be seen in Figure 7.6.

The next step is throat construction. A throat is the minimal cross-sectional area of each

channel in the void phase. The medial axis is used to determine the locations of throats in the

pore channels. Consider a path on the medial axis corresponding to a single pore channel. In a

manner analogous to the erosion procedure used to reduce the pore channel to its medial axis,

this medial axis segment is uniformely dilated in the radial direction perpendicular to its lenght

so that it becomes a cylinder. As the radius of the cilinder increases, the sides of the dilating

cylinder come into contact with the grain surface of the pore pathway. At points of contact the

cylinder dilation is halted. At some moment during the continued dilation, a 6-connected closed

loop of contacted grain points encircling the cylinder will form. As the dilation occurs along the

whole length of the cylinder at a uniform rate, this closed loop is the perimeter of the minimum

surface cross sectional area of the deformed cylinder. By definition, this is the perimeter of the

throat for this pore channel.

A minimal surface area is then constructed by connecting the center of the medial axis voxel

and the centers of the voxels in the perimeter loop via a tringulation algorithm. The throats

of the pores in the Eifel acc-lap are visualised in Figure 7.6. The proces of throat construction

requires numerous parameters which should be given in by the user. Since we weren’t familiar

with all criteria, we mostly used the default parameters.

A comparison of the results of µCTanalysis and 3DMA-rock can be seen in Figure 7.7 and

Table 7.1.

7.5. DISCUSSION 60

Figure 7.6: Left: the medial axis of the Eifel acc-lap. Right: The medial axis and the throat surfaces.

µCTanalysis 3DMA-rock

Mean 226,4µm 186,9µm

Standard deviation 106,8µm 77,3 µm

Mode 144 µm 201,9µm

Table 7.1: Vesicle size distribution statistics.

7.5 Discussion

A more in depth comparison between 3DMA-rock and µCTanalysis using artificial images and

CT images with known pore sizes, will be necessry to interprete thz differences shown in Figure

7.7 and Table 7.1.

From the CT study it was also possible to explore the potential of observing the texture of

volcanic objects like acc-laps. For example, the two-layer structure (core-rim) of the acc-laps

from Laacher See (e.g. Schumacher and Schmincke, [39]) is striking using 3D reconstructions

(Figure 7.2). Here as a non-destructive method CT is highly complementary to SEM in en-

abling to explore how features observed in 2D sections can be followed in the third dimension.

It was also possible to derive measurements of the type that are useful to constrain volcanolog-

ical processes but only for objects that are only a few millimetres across as resolution quickly

decreases for larger objects. The UGCT group is developing a subMicro-CT that should enable

to reach one micron resolution for study of volcanic objects with a size of a few millimetres.

This will enable the CT to combine both the high spatial resolution of the SEM and the 3D

7.5. DISCUSSION 61

capability. Features such as grainsize, vesicularity distributions will then be quantifiable with

confidence in 3D and enable to rigorously assess the 3D extrapolation-quantification derived

via studies of 2D sections using SEM for such parameters. The CT results were encouraging

and suggest that this will soon become achievable at the UGCT facility for volcanic objects of

significance to advance the understanding of volcanic processes.

7.5. DISCUSSION 62

Figure 7.7: 3DMA-rock vs. µCTanalysis. Vesicle size distribution of Eifel acc-lap, 428x470x345 voxels,

9.6µm voxel side.

63

Chapter 8

Conclusions

Digital image analysis on SEM images seems very useful for extracting quantitative data for

porosity and grain size distributions. However, a great part of the ash particles in the 1000×

magnification images are cut off by the image edge, so the measured size of these particles is

smaller then the actual size. It will also affect the shape measurements. I tried to solve this by

removing all border objects, but too much particles were lost in this proces. Tiling of the images

also didn’t solve this problem completely, because still a lot of the particles touched the borders.

Another possible solution could lie in a smaller magnification, e.g. 500× magnification.

Obtaining vesicle size distribution seems also possible with SEM images, but Micro-CT

images are recommended since more information can be extracted in a less amount of time.

With the SEM images we have to assume that the imaged cross section is a representative

part of the whole acc-lap, while with Micro-CT images no dimension will be lost. So, Micro-

CT images give more information, but bring along greater difficulties to overcome for analysis

as can be concluded from the discussion in chapter 7. Nonetheless, a good estimation of the

distribution of vesicle sizes is generated.

The following suggestions are made for any future software package trying to measure 3D

rock pore structures:

• The possibility to analyse various types of images (e.g. bmp, tiff, psd) with various bit

depths.

• Several methods for segmentation and seperation should be possible to choose from. This

way the user can decide between less computer time or more accuracy.

• An intelligent volume crop algorithm should replace the beam or cilinder type cropping,

64

which is now commonly used.

• Render statistics in an Excel output file.

• A graphical user interface can save a lot of time and give the program a widespread use.

On the volcanological front, the exploration of using SEM and CT has shown that important

constraints can be derived to constrain key volcanic processes. Here the study suggests that acc-

laps are consistent with a growth by riming as in hailstones as suggested by Durant and Ernst

and by Ernst and coworkers (work in progress). It also suggests that total grainsize estimation of

single acc-lap particles can be derived using SEM image analyses and probably have the potential

to constrain the total grainsize distribution erupted in phreatoplinian eruptions. This is one of

the most crucial input data needed in modelling ash dispersal and hazards from it and such

datasets are very scarce and extremely time-intensive to derive using other approaches. Besides

the ashball grainsize distribution is a major quantitative constrain that magma fragmentation

models will have to account for. Following the encouraging results with SEM and micro-CT,

it is expected that the combination of SEM and (Sub)micro-CT analyses should enable a leap

forward in quantification of volcanic product parameters and textures.

65

Appendix A

Nederlandstalige samenvatting

A.1 Inleiding

Explosieve vulkaanuitbarstingen produceren een vulkanische aswolk. Voor de luchtvaart is dit

het meest gevaarlijke vulkanisch fenomeen, omdat het de motoren en navigatie-instrumenten kan

beschadigen en doen uitvallen. De neerslag vanuit de aswolk kan bij de grootste uitbarstingen

miljoenen vierkante kilometer bedekken en vervuilende deeltjes, die in de atmosfeer worden

geınjecteerd kunnen het klimaat drastisch verstoren (Sparks et al., [43]). Een inleiding tot

vulkanologie wordt gegeven in hoofdstuk 2.

Vulkanische aswolken kunnen accretionary lapilli (acc-laps), letterlijk groeiende stenen, pro-

duceren. Het zijn kleine sferische bolletjes van vulkanische as. Samen met andere aggregaten

die zich vormen in de aswolk, beınvloeden deze bolletjes de atmosferische verspreiding van de as-

wolk, omdat ze sneller uitvallen dan enkelvoudige asdeeltjes. Door de manier waarop ze gevormd

en bewaard worden, bevatten acc-laps een registratie van gebeurtenissen binnenin de aswolk.

Ze bieden zo een mogelijkheid om het dynamisch gedrag van de aswolk te beschrijven. Een on-

middellijke toepassing is het inschatten van het gevaar van een vulkaan: de maximale groottes

van de acc-laps in een opeenvolging van afzetlagen kunnen informatie geven over de hoogte van

de aswolk en de variatie ervan van een laag t.o.v. een andere.

Kleine bolletjes, aanwezig in vele beelden gemaakt door Mars rovers, hebben veel overeen-

komsten met acc-laps. De aanwezigheid van acc-laps op mars is significant omdat op ze Aarde

enkel gevormd worden in een aswolk, die voldoende water bevat (Schumacher and Schmincke,

[40]). Dus de aanwezigheid van acc-laps op Mars zou suggereren dat een magma lichaam in

contact kwam met een omgeving van water om zo een natte explosieve eruptie te produceren

A.2. ACCRETIONARY LAPILLI 66

(Durant, [7]).

Om de vorming van acc-laps te modelleren, collecteert men empirische data, doet men ex-

perimentele simulaties in het laboratorium en stelt men uiteindelijk een theoretisch model op.

Voorlopig heeft men nog geen acc-laps kunnen vormen in het laboratorium. In wetenschap-

pelijk onderzoek zoals dit is er nood aan technieken, die kwantitatieve data kunnen genereren.

Digitale beeldanalyse met een Scanning Electron Microscoop (SEM) is reeds een veel gebruikte

techniek. Hoofdstuk 4 geeft een inleiding tot het maken van digitale beelden. Echter, SEM biedt

enkel tweedimensionele informatie. Een relatief nieuwe techniek begint hiervoor veel aangewend

te worden, Micro geComputeriseerde Tomografie (Micro-CT). Driedimensionele beelden kunnen

gemaakt worden zonder de vernietiging van het staal dat bestudeerd moet worden. Een inleiding

tot tomografie wordt gegeven in hoofdstuk 6.

Eenmaal de digitale beelden gegenereerd zijn, wordt geautomatiseerde analyse mogelijk met

een combinatie van gespecialiseerde software. Voor tweedimensionele analyse hebben we gebruik

gemaakt van LabVIEW, [29], IMAQ Vision, [28], ImageJ, [33] en ImageTool, [6]. Driedimen-

sionele analyse werd gedaan met µCTanalysis, [4] en 3DMA-rock, [21]. Het grootste probleem

bij beeldanalyse is het ontbreken van een standaardprocedure om te volgen. De meeste analyse

gebeurt in drie grote stappen: segmentatie, scheiding en grootte/vorm metingen. Voor alle

stappen zijn er veel verschillende algoritmes beschikbaar.

Samenvattend is het opzet van deze thesis tweezijdig:

1. de voordelen en beperkingen van beeldanalyse technieken nagaan voor toepassingen in de

vulkanologie en

2. onderzoeken in welke mate nieuwe observaties en data overeenkomen met het model van

Durant en Ernst, [8] dat zegt dat acc-laps groeien als hagelstenen.

A.2 Accretionary lapilli

A.2.1 Aggregatie

Aggregatie is een proces dat zich afspeelt in de vulkanische aswolk, waarbij fijne asdeeltjes worden

samengeklit tot een aggregaat dat bestaat uit 1 000 tot 100 000 individuele deeltjes. Wanneer

de aswolk zich uitspreidt, vallen de asdeeltjes er uit naargelang hun grootte. Na enkele dagen

dunt de wolk verder uit en verdwijnt. Geologen hebben vastgesteld dat vele fijne asdeeltjes,

typisch kleiner dan 100 µm, uit de aswolk vallen als aggregaten. Aggregatie speelt een kritische

A.3. SEM-BEELDANALYSE 67

rol in het controleren van de uitval van deeltjes, omdat ze met hogere snelheid uitvallen dan hun

samenstellende deeltjes. Dit kan leiden tot verhoogde verdikking van afzetlagen. De vorming

van een specifiek type van aggregaten is afhankelijk van de hoeveelheid vloeistof, die beschikbaar

is tijdens het vormingsproces (Gilbert en Lane, [12]; Schumacher en Schmincke, [40]; Sparks et

al., [43]).

Acc-laps hebben een middelmatige vloeistofinhoud met porositeiten tussen 30 en 50 %. Ze

hebben ongeveer een sferische vorm. Ze komen geregeld voor in geologische afzetlagen, vooral

in de afzettingen van phreatomagmatische uitbarstingen, die worden geassocieerd met magma-

water interactie en de generatie van overvloedig veel fijne asdeeltjes. Voorbeelden van typische

acc-laps kan je zien in Figuur 3.1 en hun karakteristieken vind je terug in tabel 3.1.

A.2.2 De vorming van accretionary lapilli

Gilbert and Lane, [12] hebben geprobeerd om acc-laps te vormen in een laboratorium, maar zijn

daarin niet geslaagd. Ze slaagden er echter wel in enkele conclusies te trekken. Binding tussen

initieel niet botsende asdeeltjes voor het vormen van een acc-lap wordt hoofdzakelijk verzorgd

door oppervlaktespanningskrachten veroorzaakt door condensatie van vocht op de asdeeltjes en

door de elektrostatische kracht.

Experimentele resultaten van Schumacher and Schmincke, [40] hebben aangetoond dat de

vulkanische aswolk tussen 15 en 25 gewicht% water moet bevatten om de groei van acc-lap

mogelijk te maken.

Durant en Ernst, [8] hebben een gedetailleerde veldstudie gedaan van afzetlagen rijk aan acc-

laps in Santorini, Griekenland en stelden als eerste een conceptueel model op voor de vorming

van acc-lap. Dit model moet nu verder onderzocht worden en heeft nood aan kwantitatieve

data om het te ondersteunen. De mogelijkheid om met digitale beeldanalyse data te genereren

over de grootte van de samenstellende asdeeltjes en de luchtbellen binnenin de acc-laps wordt

besproken in volgende secties.

A.3 SEM-beeldanalyse

A.3.1 SEM principe

Een Scanning Electron Microscope (SEM) creeert een vergroot beeld met behulp van elektronen.

Omdat de SEM de stalen belicht met elektronen, moeten ze ook geleidend worden gemaakt.


Daarom worden ze bedekt met een laagje goud met een sputter coater machine. Het staal wordt

dan in de vacuum kolom van de microscoop geplaatst, die wordt gesloten met een luchtdichte

deur. Nadat de lucht is weggepompt, straalt een elektronkanon een bundel hoog energetische

elektronen uit. Deze bundel passeert langs een aantal magnetische lenzen, die de elektronen

focusseren tot een heel smalle bundel. Daarna komt de bundel in een groep spoelen, die de

bundel rij per rij over het staal doet bewegen. Hierdoor worden secundaire elektronen vanop de

oppervlakte van het staal los geslagen. Een detector telt deze elektronen en zendt de signalen

naar een versterker. Het uiteindelijke beeld is dan opgebouwd met het aantal elektronen dat

wordt geemitteerd van elk punt op het staal (zie Figuur 5.1).

Er werden voor twee vergrotingen SEM beelden gemaakt van een acc-lap afkomstig van de

vulkaan Atitlan. Beelden met 25× vergroting (pixelgrootte 7,66 µm) werden gemaakt voor de

gehele acc-lap doorsnede en daarnaast zijn ook beelden met 1000× vergroting (pixelgrootte

0,192µm) gemaakt voor rechthoekige doorsneden doorheen de acc-lap.

A.3.2 Grijswaarden histogram en segmentatie

De intensiteit van de pixels van een digitaal beeld kunnen grafisch worden voorgesteld in een

grijswaarden histogram, dat het aantal pixels uitzet t.o.v. de grijswaarde in het beeld. Een

typisch voorbeeld van een digitaal grijswaarden beeld en zijn corresponderend histogram wordt

getoond in Figuur 5.3. De x-as stelt de grijswaarden voor van een 8-bit beeld (256 grijswaarden).

De y-as stelt dan het aantal pixels voor, dat voorkomt per grijswaarde.

Het histogram geeft een handige voorstelling weer van de intensiteitsdistributie van het

ganse beeld. De geleverde statistiek kan dan aangewend worden om beelden te vergelijken op

het gebied van contrast en intensiteit. Veel algoritmes die beelden bewerken maken gebruik van

het grijswaarden histogram, zoals segmentatie.

Segmentatie is het beeldproces dat een grijswaarden beeld omzet naar een binair (zwart-wit)

beeld, zodat een materiaal fase en leegte fase worden gecreeerd. De breedte van de pieken in

het grijswaarden histogram en hun overlap maken segmentatie over het algemeen moeilijk. De

eenvoudigste benadering is het kiezen van een globale threshold (drempelwaarde). De grijswaar-

den groter dan deze threshold worden beschouwd als materiaal, de ander pixels als leegte. De

keuze van de threshold kan automatisch gebeuren, maar onze ervaring leert ons dat het beter is

te vertrouwen op een eigen oordeel.

Een andere methode is het kiezen van een dubbele threshold. Een zwakke en sterke threshold


worden gekozen en deze bepalen een thresholdvenster. Alle pixels onder de zwakke threshold

worden bepaald als leegte en alle pixels boven de sterke threshold worden bepaald als mate-

riaal. De pixels met grijswaarden in het thresholdvenster, worden dan geevalueerd volgens de

waarde van hun naburige pixels. Er bestaan vele mogelijkheden om dit te verwezenlijken. Twee

methodes worden besproken in de sectie over micro-CT beeldanalyse.

Omdat SEM beelden zeer scherp zijn, is het gebruik van een enkele globale threshold gerecht-

vaardigd. Het artikel van Marcelino et al., [24] toont aan dat het verschil tussen een enkele

globale threshold en de dubbele threshold methode gebruikt in µCTanalysis (zie sectie micro-

CT beeldanalyse) toegepast op SEM beelden klein is (kleiner dan 1 %). Voor micro-CT beelden,

echter, kunnen dubbele thresholdmethodes niet meer vermeden worden, wegens de grotere ho-

eveelheid ruis.

A.3.3 Metingen

Alvorens over te gaan tot metingen moeten we de beelden calibreren, d.w.z. we kennen een

grootte toe aan de pixels in echte lengte eenheden (hier µm). De oppervlakte van een deeltje is

dan de som van de gecalibreerde pixels in het object en de omtrek is de som van de pixels die

de grens van het object uitmaken. Een diameter van een deeltje kan op verschillende manieren

worden gedefinieerd. We hebben gebruik gemaakt van de equivalente diameter, die de diameter

is van de cirkel met dezelfde oppervlakte als het beschouwde deelje.

De vorm van een asdeeltje is ook van belang voor de valsnelheid. Er zijn vele manieren om

een vorm van een deeltje bepalen. We hebben ons beperkt tot degene gebruikt in IMAQ Vision,

[28], ImageTool, [6] en het artikel van Riley et al., [34]. Ze staan gedefinieerd in tabel 5.2.

Met de 1000× vergroting beelden kunnen we de groottes en vormen van de asdeeltjes bepalen,

alsook de porositeit. De porositeit is heel eenvoudig te berekenen door het aantal zwarte pixels

te delen door het totaal aantal pixels. Zo werd een porositeit van 49% opgemeten. De resultaten

van groottes en vormen zijn te zien in Figuur 5.6 en 5.7.

Als we de 25× vergroting beelden samenleggen kunnen we de groottes van de luchtbellen

binnenin de ganse acc-lap doorsnede meten en de opbouw van de concentrische lagen beschouwen.

De uitwerking en de resultaten hiervan zijn te zien vanaf Figuur 5.9 tot Figuur 5.14.

A.4. MICRO-CT BEELDANALYSE 70

A.4 Micro-CT beeldanalyse

A.4.1 Micro-CT principe

Tomos is het Grieks woord voor snede, en tomografie is een techniek om een staal digitaal te

versnijden, gebruik makend van X-stralen, om de inwendige details te onthullen. Een CT beeld

wordt een slice (engels voor snede) genoemd, naar analogie met een broodsnede. Het is namelijk

zo dat net zoals een broodsnede een dikte heeft, een CT slice overeenkomt met een zekere dikte

van het object dat gescand wordt. In plaats van pixels, spreekt men dan ook van voxels.

De grijswaarden in een CT slice komen overeen met de X-straal attenuatie, die correspondeert

met de hoeveelheid X-stralen die worden verstrooid en geabsorbeerd als ze doorheen elke voxel

passeren. X-straal attenuatie is hoofdzakelijk een functie van X-straal energie en de dichtheid

en atoomnummer van het materiaal dat gescand wordt. Een CT beeld wordt gecreeerd door

X-stralen doorheen een snijvlak te richten voor verschillende orientaties en de hieruit volgende

daling in intensiteit te meten. Een gespecialiseerd algoritme wordt dan gebruikt om de distributie

van X-straal attenuatie in het snijvlak te reconstrueren. Door een stapel opeenvolgende CT

beelden te maken, kan data bekomen worden die een volledig volume beschrijft, net zoals een

brood kan gereconstrueerd worden, door zijn snedes te stapelen.

A.4.2 Micro-CT beelden

Samples om Micro-CT beelden te maken werden gecollecteerd in Santorini, Griekenland en de

Eifel, Duitsland. De eerste scan werd genoemen van een klein stukje afzetting rijk aan acc-

laps (2 cm x 3 cm x 3 cm). Jammergenoeg gingen de beelden van deze scan verloren, alvorens

analyse kon gedaan worden. Daarna werden twee aaneengehechte acc-laps van Santorini gescand

(grootte 2–3 mm) en een van de Eifel (grootte 7 mm). De voxels zijn kubussen met zijde 9,6µm.

Dit is niet klein genoeg voor het meten van de asdeeltjes of de porositeit, maar is ideaal om de

distributie van luchtbellen te meten. De Santorini acc-laps bleken weinig luchtbellen te bezitten

en dus niet zo geschikt voor analyse. De Eifel acc-lap had daarentegen wel veel luchtbellen in

zich zoals te zien is op Figuur 7.2.

A.4.3 Analysesoftware

Er is al heel wat software ontwikkeld om micro-CT beelden te analyseren (Ashbridge et al., [1],

Cnudde, [4], Ketcham, [16] and Lindquist, [21]). We hebben geprobeerd om µCTanalysis en

A.4. MICRO-CT BEELDANALYSE 71

3DMA-rock te vergelijken.

µCTanalysis

Deze software werd geschreven in MatLab tijdens de doctoraatsstudie van Cnudde, [4]. Ze is

voorzien van segementatie, scheiding en 3D-meting algoritmes. De input bestanden zijn een

reeks 2D-bmp-beelden. De parameters die moeten worden ingegeven zijn de voxelgrootte voor

calibratie, een zwakke en sterke threshold voor segmentatie en de coordinaten voor de selectie

van een subvolume (indien gewenst).

De omzetting van voxels met grijswaarden in het thresholdvenster naar binaire waarden

wordt gedaan met het groeien van een kiem. De thresholdfilter selecteert alle voxels met gri-

jswaarde boven de sterke threshold (kiemen), gevolgd door alle voxels met grijswaarde in het

thresholdvenster, die verbonden zijn met een kiem via een pad van een willekeurige lengte.

Scheiding van geconnecteerde porien gebeurd met een 3D-erosie en dilatie proces. De dis-

tributie van de groottes van de porien wordt dan bepaald door elke porie te vullen met een

digitale bol, die groeit van de klinst ingeschreven bol tot de maximale. Dit proces voorziet elke

porie van een volumewaarde en maximum ingeschreven bol diameter.

3DMA-rock

Deze software ontwikkeld voor Linux, [21] kan heel wat verschillende types beelden als input

verwerken. Verschillende mogelijkheden worden ter beschikking gesteld aan de gebruiker om te

segmeneteren. De methode, die het meest wordt aangeraden is een dubbele thresholdmethode,

indicator kriging, [31] genaamd. De voxels met grijswaarden in het thresholdvenster worden nu

omgezet met behulp van de statistiek van de grijswaarden van hun buren.

De scheiding wordt teweeg gebracht door het construeren van een medial axis. Hierbij wordt

het porie netwerk eendimensionaal gemaakt, zodat er enkel een skelet overblijft. De voxels

die deel uitmaken van deze medial axis hebben een nummer dat aangeeft hoe ver de dichtste

materiaalvoxel ligt. Dit skelet dient dan als een soort zoekpad voor het scheiden van porien.

Een voorbeeld van een medial axis kan gezien worden in Figuur 7.6. Uiteindelijk verkrijgen we

het volume van elke porie als output.

De resultaten van zowel µCTanalysis als 3DMA-rock zijn te zien in Figuur 7.7 en Tabel 7.1.

A.5. BESLUIT 72

A.5 Besluit

Digitale beeldanalyse is een handige techniek om kwantitatieve data te genereren voor porositeit

en metingen van korrelgroottes. Een groot deel van de asdeeltjes in de 1000× vergroting beelden

wordt echter afgesneden door de beeldrand, zodat de werkelijke diameter van de deeltjes groter

is dan degene die gemeten wordt. Het zal ook een invloed hebben op de vormmetingen. Indien

we alle deeltjes, die de rand raken weg laten gaat er te veel informatie verloren. Het tegelen

van de beelden bood niet echt een oplossing want nog steeds raakten vele deeltjes de rand. Een

mogelijke oplossing ligt in het gebruik maken van beelden met kleiner vergroting, bv. 500×

vergroting.

Als we er vanuit gaan dat de fout op de vormmetingen klein is kunnen we concluderen dat de

deeltjes helemaal niet sferisch zijn en dus zal een computer simulatie van een vulkanische aswolk

hiermee rekening moeten houden, omdat het de neerslag uit de aswolk sterk kan beınvloeden.

De bepaling van de distributie van de groottes van luchtbellen lijkt ook mogelijk met SEM,

maar Micro-CT beelden worden hiervoor aangeraden omdat ze veel meer informatie geven in

een kortere tijdsduur. Met de SEM beelden moet ook worden aangenomen dat de genomen

doorsneden representatief is voor de hele acc-lap, terwijl er bij Micro-CT geen dimensie verloren

gaat. Dus, Micro-CT beelden geven meer informatie, maar brengen ook groter moeilijkheden

met zich mee voor analyse. Niettemin kan een goede schatting gegeven worden van de groottes

van de luchtbellen binnenin een acc-lap.

Voor vulkanologie heeft het onderzoek naar het gebruik van SEM en CT aangetoond dat

belangrijke parameters kunnen afgeleid worden om vulkanische processen te modelleren. Deze

studie suggereert dat de groei van acc-laps gebeurt door de vorming van rijm zoals in hagelstenen

zoald voorgesteld door Durant en Ernst, [8] en Ernst en medewerkers (werk momenteel aan de

gang). Het suggereert ook dat de distributie van de asgrootte in een enkele acc-lap kan afgeleid

worden uit SEM analyse en dit heeft de mogelijkheid om de totale distributie van asgrootte in

een eruptie van een phreatopliniaanse uitbarsting. Dit is cruciale data voor het modelleren van

asuitval en de gevaren, die dit meebrengt en zulke datasets zijn uiterst zeldzaam en tijd-intensief

om te doen met andere methodes. Uit deze bemoedigende resultaten, wordt verwacht dat een

combinatie van SEM en (Sub)micro-CT analyse een stap voorwaarts zullen zijn om parameters

van eruptie producten te kwantificeren.

BIBLIOGRAPHY 73

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Exploring the potential of digitital image analysis ofSEM and Micro-CT images of accretionary lapilli

Wim Degruyter

Supervisor(s): Luc Van Hoorebeke, Bert Masschaele, Gerald Ernst

Abstract—Accretionary lapilli (acc-laps) are commonly found in airfalltuffs from water-rich eruption columns. Yet, the role of water and ice in theformation of acc-laps has not been systematically studied. This thesis ex-amines the possibilty of extracting quantitative data from the ash balls viadigitized image analysis techniques. 2D images were collected with a Scan-ning Electron Microscope and analysed using Labview. 3D images weremade at the UGCT facility with the Micro-CT scanner. Analysis was donewith the software packagesµCTanalysis and 3DMA-rock. Image analysistechniques can already provide valuable insights, but optimalisation andstandardisation will be necessary for fast and accurate use in the future.

Keywords—accretionary lapilli, image analysis, SEM, Micro-CT

I. I NTRODUCTION

EXPLOSIVE Eruptions Explosive eruptions produce a vol-canic plume, which is a dilute, turbulent cloud packed with

ash particles and volcanic gases. For air traffic, volcanic plumesare the most hazardous eruption phenomenon, since they cancause failure of engines and navigation instruments. Falloutfrom plumes of the largest eruptions may affect millions ofsquare kilometers and emplacement of volcanic pollutants intothe atmosphere may drastically perturb the climate (Sparks etal., [6]).

Volcanic plumes can produce accretionary lapilli (acc-laps),small spherical balls of volcanic ash that form from a wet nu-cleus falling through a volcanic ash cloud. Amongst other ag-gregation products of a volcanic plume, these rocks affect theatmospheric dispersion of the plume, since they fall faster thansingle ash particles. Through the way they form and are pre-served acc-laps contain a record of what happened in the vol-canic plume. So, they can povide constraints on eruption col-umn dynamics. One immediate application is for volcanic haz-ard assessment: acc-laps maximum sizes in a sequence of tufflayers can provide information on eruption column height andits variation from one layer to the next (Durant and Ernst, [2]).

The way to model the formation of acc-laps is collecting em-pirical data, doing experimental laboratory simulations and the-oretical modeling. Up to now, attempts to produce acc-laps inthe laboratory have failed. In scientific research like this thereis a need for techniques, which generate quantitative data. Digi-tal image analysis on Scanning Electron Microscope (SEM) im-ages is already a widely used technique. However, SEM canonly provide two dimensional information. Next to this, a rela-tive new technique is gaining a lot of interest, Micro ComputedTomography (Micro-CT). Three dimensional images can be ren-dered without the destruction of the investigated sample.

Once digital images have been generated, automated analysisis done with a combination of specialized software. In this work

W. Degruyter is with the Subatomic and Radiation Department, Ghent Uni-versity (UGent), Gent, Belgium. E-mail: [email protected].

LabVIEW, IMAQ Vision, ImageJ, and ImageTool were used fortwo dimensional image analysis. Three dimensional analysiswas done withµCTanalysis, [1] and 3DMA-rock, [4]. The mainproblem with image analysis, is the lack of a standard procedureto follow. Most analysis is done in three major steps: segmen-tation, separation and size/shape measurements. For all threesteps there exist a lot of different algorithms.

II. A CCRETIONARY LAPILLI

Gilbert and Lane, [3] tried to simulate acc-laps formation inthe lab, but failed. However, they were able to conclude the fol-lowing. Binding between initially cohesionless ash particles toform concentric acc-laps is provided primarily by the capillaryforces of liquid bridges from condensed moisture and by elec-trostatic attraction. Capillary forces are strong bonds if the parti-cles are in close contact, but they decrease rapidly with increas-ing particle spacing. Electrostatic attraction between chargedash particles is much weaker but effective over larger distances,increasing the frequency of collision between them.

Experimental results by Schumacher and Schmincke, [5] ofliquid film binding of volcanic ash showed that agglomerationwas most successful between 15 and 25 wt.% of water insidethe eruption column, defining the agglomeration window for theformation of acc-laps. Below 5 – 10 wt.% and above about 25 –30 wt.% of water, concentric agglomeration was inhibited.

Durant and Ernst, [2] were the first to derive a conceptualmodel of the formation of acc-laps. Methods for producingquantitative data to support this model are needed. Providingthis data of the grain and vesicle sizes within acc-laps with dig-ital image analysis are discussed in the following sections.

III. SEM IMAGE ANALYSIS

The acc-lap studied with SEM was produced by the volcanoAtitlan in Guatemala, collected 3 to 5 km from the vent. 8-bit images were made at two different magnifications. Imageswith 25×magnification (pixel side 7,66µm) were made for thewhole acc-lap cross section, while images with 1000×magnifi-cation (pixel side 0,192µm) were only made for traverses of thecross section.

With the 25× magnification images it was possible to mea-sure vesicle size and give better insight in the layer distributionof an acc-lap. With 1000× magnification it is possible to pro-duce porosity measurements, grain size (figure 1) and shape dis-tributions of the ash particles inside the acc-lap.

IV. M ICRO-CT IMAGE ANALYSIS

The acc-lap studied with Micro-CT came from the Eifel, Ger-many. The voxels were cubes with side9, 6 µm. With these im-

Fig. 1. SEM analysis. Grain size distribution of ash inside the acc-lap of Atitlan,Guatemala.

ages grain size distributions aren’t possible to produce, but theyare ideal for vesicle size distributions. Two Micro-CT imageanalysis sofware packages were used and compared. 3DMA-rock, [4] andµCTanalysis, [1].

Fig. 2. Micro-CT analysis. 3DMA-rock vs.µCTanalysis. Vesicle size distribu-tion of Eifel acc-lap.

V. CONCLUSIONS

Digital image analysis on SEM images seems very useful forextracting quantitative data for porosity and grain size distribu-tions. However, a great part of the ash particles in the 1000×magnification images are cut off by the image edge, so the mea-sured size of these particles is smaller then the actual size. Itwill also affect the shape measurements. I tried to solve this byremoving all border objects, but too much particles were lostin this proces. Tiling of the images also didn’t solve this prob-lem completely, because still a lot of the particles touched theborders. Another possible solution could lie in a smaller magni-fication, e.g. 500×magnification.

Assuming the error on the shape measurements isn’t toogreat, we can conclude that particles aren’t spherical at all andshouldn’t be modelled as such in computer simulations of vol-canic plumes, since this can greatly affect fall out from theplume.

Obtaining vesicle size distribution seems also possible withSEM images, but Micro-CT images are recommended sincemore information can be extracted in a less amount of time.With the SEM images we have to assume that the imaged cross

section is a representative part of the whole acc-lap, while withMicro-CT images no dimension will be lost. So, Micro-CT im-ages give more information, but bring along greater difficultiesto overcome for analysis. Nonetheless, a good estimation of thedistribution of vesicle sizes is generated.

The following suggestions are made for any future softwarepackage trying to measure 3D rock pore structures:• The possibility to analyse various types of images (e.g. bmp,tiff, psd) with various bit depths.• Several methods for segmentation and seperation should bepossible to choose from. This way the user can decide betweenless computer time or more accuracy.• An intelligent volume crop algorithm should replace the beamor cilinder type cropping, which is now commonly used.• Render statistics in an Excel output file.• A graphical user interface can save a lot of time and give theprogram a widespread use.

On the volcanological front, the exploration of using SEMand CT has shown that important constraints can be derived toconstrain key volcanic processes. Here the study suggests thataccretionary lapilli are consistent with a growth by riming asin hailstones as suggested by Durant and Ernst and by Ernstand coworkers (work in progress). It also suggests that totalgrainsize estimation of single accretionary lapilli particles canbe derived using SEM image analyses and probably have thepotential to constrain the total grainsize distribution erupted inphreatoplinian eruptions. This is one of the most crucial inputdata needed in modelling ash dispersal and hazards from it andsuch datasets are very scarce and extremely time-intensive to de-rive using other approaches. Besides the ashball grainsize distri-bution is a major quantitative constrain that magma fragmenta-tion models will have to account for. Following the encouragingresults with SEM and micro-CT, it is expected that the combina-tion of SEM and nano-CT analyses should enable a leap forwardin quantification of volcanic product parameters and textures.

ACKNOWLEDGMENTS

The author wishes to thank his supervisors Luc Van Hoore-beke, Bert Masschaele, Gerald Ernst and all the collaboratorsat the UGCT facility for the helpful discussions and supportthroughout the year.

REFERENCES

[1] Cnudde, V., Exploring the potential of X-ray tomography as a new non-destructive research tool in conservation studies of natural building stones,Ph.D. thesis, University of Ghent (2005)

[2] Durant, A.D., Ernst, G.G.J., Formation of accretionary lapilli as vol-canogenic hailstones, Bulletin of Volcanology, submitted for publication

[3] Gilbert, J.S., Lane, S.J.,The origin of accretionary lapilli, Bulletin ofVolcanology (1994) 56, 398-411

[4] Lindquist, W.B., 3DMA General Users Manual, SUNY-Stony Brook tech-nical report (1999)

[5] Schumacher, R., Schmincke, H.U.,Models for the origin of accretionarylapilli , Bulletin of Volcanology (1995) 56, 626-639

[6] Sparks, R.S.J., Bursik, M.I., Carey, S.N., Gibert, J.S., Glaze, L.S., Sigurds-son, H. and Woods, A.W.,Volcanic plumes, John Wiley and Sons (1997)

Exploring Digital Imaging and SEM Accretionary Lapilli

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