The Pennsylvania State University

The Graduate School

College of Earth and Mineral Sciences

THE FEBRUARY 1993 KILAUEA EAST RIFT ZONE DIKE INTRUSION

REVEALED THROUGH INSAR

A Thesis in

Geosciences

by

Sarah C. Moore

© 2017 Sarah C. Moore

Submitted in Partial Fulfillment

of the Requirements

for the Degree of

Master of Science

May 2017

ii

The thesis of Sarah C. Moore was reviewed and approved* by the following:

Christelle Wauthier

Assistant Professor of Geosciences

Thesis Advisor

Peter LaFemina

Associate Professor of Geosciences

Charles Ammon

Professor of Geosciences

Demian Saffer

Associate Professor of Geosciences and Head for Graduate Programs and Research

*Signatures are on file in the Graduate School

iii

ABSTRACT

Passive intrusions make forecasting and risk assessment difficult since they are not

preceded by inflation nor by large increases in seismicity. The February 1993 dike intrusion in the

East Rift Zone (ERZ) of Kīlauea Volcano, Hawaiʻi, was recognized from tilt and seismic data, but

the ground-based geodetic data were too sparse to constrain the characteristics of the intrusion.

Analysis of Interferometric Synthetic Aperture Radar (InSAR) from the Japan Aerospace

Exploration Agency (JAXA) JERS-1 satellite reveals ~30 cm of Line-of-Sight (LOS)

displacements occurring near Makaopuhi Crater in the middle ERZ of Kīlauea. We model this

deformation signal as a subvertical dike using a 3D-Mixed Boundary Element Method (3D-

MBEM) paired with a nonlinear inversion algorithm to find the best-fit model. The best-fit dike

model is located just to the west of Makaopuhi Crater and within 100 m of the surface. The best-

fit model dike is ~1.3 km in length by ~2.7 km in width, strikes N50°W, and has a total volume

increase of ~7.4 x 106 m3. Additionally, a post-intrusion interferogram from JERS-1 was analyzed.

The best-fit model for the 1993-1997 period consists of opening of the deep rift zones beneath the

Southwest Rift Zone (SWRZ), ERZ and the summit. The dike-like opening beneath the rift zones

ranges from depths of 3-12 km and has an average opening of about 0.5 meters. A sub-horizontal

detachment fault is connected to the seaward side of the vertical dike-like source to mimic the

décollement. We classify the 1993 dike intrusion as a passive intrusion similar to those that

occurred in 1997 and 1999. Passive intrusions lack of precursory inflation at Kīlauea’s summit and

the likely triggering mechanism is persistent deep rift opening combined with seaward motion of

the south flank along a basal décollement.

iv

Table of Contents LIST OF FIGURES v LIST OF TABLES vii ACKNOWLEDGEMENTS viii 1. INTRODUCTION 1 2. BACKGROUND 3 2.1 GEOLOGICAL SETTING 3 2.2 THE FEBRUARY 1993 INTRUSION & RECENT ERUPTIVE/INTRUSIVE HISTORY 5 3. METHODS 8 3.1 INSAR 8 3.2 FORWARD MODELING: 3D-MBEM [CAYOL & CORNET, 1997] 8 3.3 NONLINEAR INVERSION: NEIGHBOURHOOD ALGORITHM [SAMBRIDGE, 1999A,B] 10 4. RESULTS 12 4.1 INSAR DATA 12 4.1.1 THE FEBRUARY 1993 INTRUSION 12 4.1.2 POST-INTRUSION DEFORMATION (1993-1997) 12 4.2 MODELING RESULTS 12 4.2.1 THE FEBRUARY 1993 INTRUSION 12 4.2.2 POST-INTRUSION DEFORMATION (1993-1997) 13 5. DISCUSSION 18 5.1 DEFORMATION SOURCES 18 5.2 DIKE INTRUSION CLASSIFICATION AND COMPARISON 19 5.3 STATIC STRESS CHANGES IMPLICATIONS 19 5.4 MAGMA ORGIN 20 6. CONCLUSIONS 23 REFERENCES 24 APPENDIX A – ALTERNATE MODELS 26 APPENDIX B – TILTMETER DATA 27 APPENDIX C – WRAPPED INTERFEROGRAMS 28 APPENDIX D – NEIGHBOURHOOD ALGORITHM [SAMBRIDGE, 1999A,B] 29 APPENDIX E – INSAR UNCERTAINITES 36 APPENDIX F – RESIDUALS 38 APPENDIX G – SUPPLY RATE AND DECOLLEMENT SLIP 39

v

List of Figures Figure 1…………………………………………………………………………………………....6 A) Map of Kīlauea Volcano showing major features, including the Southwest Rift Zone (SWRZ) and East Rift Zone (ERZ), as well as locations and monitoring stations mentioned in the text. Black box shows area covered by Figure 2. UWE is the single-component tiltmeter located in the Uwekahuna Vault. MPR is the seismic station located at Makaopuhi Crater. Approximate locations of other seismic stations active during 1993 located on the map. Storage reservoirs are shown (H = Halema’uma’u, SC = South Caldera) Figure 2. …………………………………………………………………………………...............7 Map of Kīlauea’s summit and East Rift Zone showing locations of intrusive activity during 1993-2011. Seismicity (purple circles) are shown for February 1993 intrusion [Matoza et al., 2013]. Model geometries (colored lines) are given for dikes that were detected by deformation measurements (tilt, GPS and/or InSAR), including the 1997 Nāpau fissure eruption [Owen et al., 2002], 1999 noneruptive dike [Cervelli et al., 2002], 2007 Father’s Day intrusion/eruption [Montgomery-Brown et al., 2010] and 2011 Kamoamoa fissure eruption [Lundgren et al., 2013]. Figure 3. …………………………………………………………………………………...............7 Timeline of HVO Monthly Reports from February 1993. Geologic data shown in purple, Seismic data shown in green and deformation (tiltmeter) data shown in blue. Figure 4.………………………………………………………………………………………….15 2D map view (left) and 3D-view (right) of best-fit intrusion model for JERS-1 interferogram spanning 10 October 1992 to 1 March 1993. Coordinates are given in Universal Transverse Mercator (UTM). Figure 5.………………………………………………………………………………………….16 Best-fit post-intrusion deformation model from JERS-1 interferogram spanning 8 October 1993 to 3 July 1997. 2D map view (top) shows trace of rift zone with gray mesh shading of basal décollement at 12km depth. 3D view (bottom) shows blue mesh that represents the sub-horizontal basal décollement and red mesh is vertical deep rift connected below the summit caldera. Coordinates are given in Universal Transverse Mercator (UTM). Figure 6.……………………………………………………………………….…………………17 Data, model, and residuals (left, a-c) for the interferogram spanning 10 October 1992 – 01 March 1993. (right, d-f) Same for the interferogram spanning 08 October 1993 – 03 July 1997. The coordinates are given in Universal Transverse Mercator. Color corresponds to LOS displacements in meters (positive change is movement away from the satellite, or Line-of-Sight LOS subsidence). Red line is trace of 1993 dike intrusion in model (b) and residuals (c). Figure 7.…………………………………………………………………………….……………21 Post-Intrusion model (deep rift zone and decollement) shown in red unclamps (negative normal stress change) an area of 3.86x106 m2 of the 1993 dike. Elevation is relative to sea level.

vi

Figure 8.……………………………………………………………………………………….…21 1993 Intrusion model shown in red unclamps (negative normal stress change) an area of 1.35x107 m2 of the deep rift zones. Elevation is relative to sea level.

vii

List of Tables Table 1……………………………………………………………………………………….…...13 Best-fit source geometry and other information for February 1993 intrusion. Asterisks represent parameters that were inverted for. Parameters involving elevation have been corrected to be relative to sea level. More information on parameters and 95% confidence intervals (Figure S4 Table T2) can be found in supplementary materials. Table 2....………………………………………………………………………………….……..14 Best-fitting source geometries and other information for post-intrusion deformation interferogram spanning 8 October 1993 to 3 July 1997. Parameters involving elevation have been corrected to be relative to sea level. Asterisks (*) represent parameters that were inverted for. More information on parameters and 95% confidence intervals (Figure S6 Table T4) can be found in supplementary materials. Table 3.……………………………………………………………………………………....…..22 Table of best-fit geometries for intrusions that have been modeled and were detected by deformation measurements in Kilauea’s East Rift Zone between 1993-2011. 1Owen et al, 2000, 2Cervelli et al, 2002, 3Montgomery-Brown et al, 2010 and 4Lundgren et al., 2013.

viii

Acknowledgements

First, I would like to express my sincere gratitude to my advisor, Dr. Christelle Wauthier

for the continuous support of my Master’s study and related research, for her patience, motivation

and knowledge. Thank you to my committee members, Dr. Charles Ammon and Dr. Peter

LaFemina for their advice over the last two years. Thank you to the Department of Geosciences at

Penn State University for their coursework and teaching opportunities -- I appreciate all the

invaluable advice and opportunities along the way. I am also greatly appreciative of the support of

my friends and family, especially my partner Colin who has always been a great listener and

fantastic supporter.

This work was supported by the Geological Society of America. Thanks to USGS scientists

from the Hawaiian Volcano Observatory for their collaboration and data retrieval efforts,

especially Asta Miklius. I would like to thank Valerie Cayol for the useful discussion on the

modeling procedure. I also thank Kendall Wnuk and Kirsten Stephens for their helpful discussion

and the Japan Aerospace Exploration Agency and Yo Fukushima for the JERS-1 data. Last, but

not least, I would like to express my sincerest appreciation to Michael Poland for his continuous

support and guidance these last few years and for the helpful revisions and comments.

1

1. Introduction

Dike intrusions are a dominant means of magma transport at Kīlauea Volcano [Poland et

al., 2014]. Since the onset of Kīlauea’s 1983 to present East Rift Zone (ERZ) eruption, several

intrusions have interrupted the normal supply of magma to the PuʻuʻŌʻō and nearby eruptive vents,

causing pauses in lava effusion from the active vents and typically changes the vent location

[Heliker et al., 2003; Orr et al., 2015]. These dike intrusions are a result of both active and passive

processes that reflect stress conditions within the volcanic edifice. Active intrusions are driven by

high magma pressure in magma storage areas beneath the summit caldera, while passive intrusions

are motivated by extensional stresses within the ERZ [Poland et al, 2014].

Dike intrusions at Kīlauea Volcano have typically followed recognizable patterns since the

beginning of the PuʻuʻŌʻō eruption in 1983. Rapid summit deflation accompanies strong

seismicity that migrates along the ERZ, ERZ eruptive activity pauses for hours to days, and the

eruptive vent sometimes collapses. The end of the intrusion is marked by summit inflation, and

eruptive activity eventually resumes on the ERZ, often from a new vent. The 1993 Makaopuhi

dike intrusion does indeed follow this narrative but lacked sufficient geodetic data for an in-depth

characterization [Wright and Klein, 2014].

Prior to the start of regular Synthetic Aperture Radar (SAR) acquisitions in the 2000s and

the installation of continuous Global Positioning System (GPS) receivers in the late 1990’s

[Miklius et al, 2005], geodetic data at Kīlauea consisted of a few continuous tilt stations and

campaign tilt and trilateration data with poor spatial resolution along the ERZ. As a result, ERZ

intrusions from the early 1990s, while easy to detect, were difficult to characterize. One of the first

SAR satellites, Japanese Earth Resources Satellite 1 (JERS-1), acquired a few images of Kīlauea

in the 1990s. An interferogram from these data spanning 10 October 1992 to 01 March 1993

2

captured a large deformation signal on Kīlauea’s ERZ, with approximately 30 cm of line-of-sight

(LOS) deformation.

Here, we analyze InSAR data from JERS-1, investigating the 1993 intrusion as well as

subsequent post-intrusion deformation during the period of 1993-1997. We use a 3D Mixed

Boundary Element Method (3D-MBEM) [Cayol and Cornet, 1997], paired with a nonlinear

inversion procedure to constrain the geometry, location, and volume change of the intrusion that

contributed to the observed deformation. We then explore the mechanism and characteristics of

the intrusion in the context of other recent diking events at Kīlauea, as well as the overall

deformation of Kīlauea following dike emplacement episodes.

3

2. Background

2.1 Geological Setting & Recent Eruptive/Intrusive History

Kīlauea is a basaltic shield volcano on the Island of Hawaiʻi that has been continuously

erupting since 1983 [Heliker and Mattox, 2003]. Kīlauea’s magma plumbing system includes at

least two shallow (<5 km depth) reservoirs beneath the summit area: one just east of Halemaʻumaʻu

Crater at ~1.5 km depth [e.g., Bagnardi et al., 2014; Poland et al., 2014; Anderson et al., 2015]

and another located south of the caldera at 3-5 km depth [e.g. Dvorak et al., 1983; Cervelli and

Miklius, 2003; Baker and Amelung, 2012; Wauthier et al., 2016]. These reservoirs are connected

to two rift zones that radiate from the summit, the Southwest Rift Zone (SWRZ) and ERZ, along

which magma can be transported many tens of km from the summit (Figure 1).

Kīlauea’s activity is governed in large part by seaward motion of the volcano’s south flank.

This motion is accommodated along a décollement fault at the base of the volcanic pile, ~10 km

beneath the surface, and also involves opening of the deep rift zone below ~3 km depth [Delaney

et al., 1990; Owen et al., 2000a]. Motion along the décollement occurs as stable sliding [Owen et

al., 2000a], strong earthquakes (like the 1975 M7.7 event) [Owen and Bürgman, 2006], and quasi-

periodic slow slip events [Montgomery-Brown et al., 2013, 2015]. The forces driving deep rift

opening and south flank motion appear to be a combination of magma pressure and gravity [Poland

et al., 2014]. The deformation imparts an extensional stress on the shallow ERZ—rates of

extension were particularly high following the 1975 earthquake [Cayol et al., 2000; Dieterich et

al., 2003]. Rift zone extension is particularly strong in the vicinity of Makaopuhi Crater, where

numerous intrusions and eruptions have occurred since the 1960s, including the 1983-present

eruption [Wright and Klein, 2014] (Figure 1).

There have been numerous intrusions along the ERZ since the start of the PuʻuʻŌʻō

4

eruption in 1983 [Poland et al., 2014; Wright and Klein, 2014], including diking events in January

1997 [Owen et al., 2000b], noneruptive September 1999 [Cervelli et al. 2002], June 2007

[Montgomery-Brown et al., 2010], and March 2011 [Lundgren et al., 2013] that were well

characterized by geodetic data (Figure 2). Intrusions are thought to be caused by either increasing

the magma pressure in the summit reservoir (active intrusion) or by a decrease of the rift zone-

perpendicular normal stress (passive intrusion) [Poland et al, 2014; Montgomery-Brown et al.,

2010]. Summit inflation is a precursor to active dike intrusions at Kīlauea and is usually

accompanied by an increase in summit seismicity [Klein et al, 1987; Poland et al, 2014]. Passive

intrusions occurred in 1997 and 1999 [Poland et al, 2014]. The 1997 intrusion resulted in an

eruption near Nāpau crater that lasted 22-hours [Owen et al, 2000b; Thornber et al, 2003], while

the 1999 dike did not reach the surface [Cervelli et al, 2002]. These two passive intrusions are

thought to be a result of extensional stress due to deep rift zone opening. The passive nature of

these intrusions is supported by the fact that neither was preceded by summit inflation; instead, the

summit was deflating prior to both events and thus suggests that increasing magma pressure in the

summit reservoir did not trigger dike emplacement [Owen et al, 2000b; Cervelli et al., 2002]. The

June 2007 “Father’s Day” dike was an example of a ‘hybrid’ event that started as an active

intrusion driven by high summit magma overpressure. Intrusion of the dike encouraged slip on

the décollement that in turn facilitated continued dike emplacement and, ultimately, a small

eruption [Montgomery-Brown et al, 2010, 2015]. Lastly, the dike that fed the June 2011

Kamoamoa fissure eruption was a result of an active intrusion following months of summit

inflation.

5

2.2 The February 1993 Intrusion

An ERZ intrusion occurred on February 7-8, 1993 (Figure 4), in the vicinity of

Makaopuhi Crater (Figure 5). Seismic data show a large increase in earthquake activity along the

ERZ as well as in the summit area starting around 23:25 HST (UTC February 8 09:25)(Figure 3).

For two hours, volcanic tremor occurred at the Makaopuhi seismic station (MPR). Additionally,

the summit area deflated rapidly (ultimately by 8 microradians) measured at continuous

tiltmeters, while strong, shallow tremor was detected throughout the summit area and persisted

for about 18 hours [Okubo & Nakata, 2003](Figure 3). Seismicity started at the summit and

progressing down the ERZ towards Makaopuhi Crater. By February 9, over 5,000 earthquakes

had been counted [Okubo & Nakata, 2003]. Less than 24 hours after the volcanic tremor ceased,

ERZ eruptive activity had ceased and the floor of PuʻuʻŌʻō vent collapsed, presumably in

response to interruption in magma supply to the vent. The ERZ eruption resumed at PuʻuʻŌʻō 8

days later on February 16, 1993 [Heliker and Mattox, 2002].

6

Figure 1: Map of Kīlauea Volcano showing major features, including the Southwest Rift Zone (SWRZ) and East Rift Zone (ERZ), as well as locations and monitoring stations mentioned in the text. Black box shows area covered by Figure 2. UWE is the single-component tiltmeter located in the Uwekahuna Vault (UWE). MPR is the seismic station located at Makaopuhi Crater. Approximate locations of other seismic stations active during 1993 located on the map. Storage reservoirs are shown (H = Halema’uma’u, SC = South Caldera)

7

Figure 2. Map of Kīlauea’s summit and East Rift Zone showing locations of intrusive activity during 1993-2011. Seismicity (purple circles) are shown for the February 1993 intrusion [Matoza et al., 2013]. Model geometries (colored lines) are given for dikes that were detected by deformation measurements (tilt, GPS and/or InSAR), including the 1997 Nāpau fissure eruption [Owen et al., 2002], 1999 noneruptive dike [Cervelli et al., 2002], 2007 Father’s Day Intrusion/eruption [Montgomery-Brown et al., 2010] and 2011 Kamoamoa fissure eruption [Lundgren et al., 2013].

Figure 3: Timeline of HVO Monthly Reports from February 1993. Geologic data shown in purple, Seismic data shown in green and deformation (tiltmeter) data shown in blue.

Nāpau CraterMakaopuhi Crater

Pu`u `Ō`ō

Summit Caldera

Sept 1999June 2007

Jan 1997

March 2011

Feb 1993 (this study)

0 5Kilometers

M3M2M1

Feb 7-9, 1993 EQ

1993Feb7 8 9 10 11 12 13 14 15 16 17

EQSwarmBegins

PuʻuʻOʻocollapses

PitCraters

5,000EQCountedEruptionatPuʻuʻOʻo

beginsagain

ShallowVolcanicTremoratSummit

EruptionPausesat

PuʻuʻOʻo

SummitRapidlyDeflates

SummitSlowly

Inflates

Geologic Seismic Deformation- Tilt

| Background |Methods|Data | Results| Discussion| Conclusions|Questions|

HVOMonthlyReports:Seismic,Deformation(Tilt)andGeologicData

8

3. Methods

3.1 InSAR

Two JERS-1 interferograms were used for the February 1993 intrusion and post-intrusion

deformation. The first interferogram combines two descending SAR images from JERS-1 satellite

acquired on 10 October 1992 and 1 March 1993. The second interferogram spans 8 October 1993

to 3 July 1997. Both interferograms were processed using GAMMA software [Wegmuller and

Werner, 1997]. The topographic fringes in the interferograms were removed using the digital

elevation model created by the Shuttle Radar Topography Mission. The fringes due to the orbital

inaccuracies were removed by modifying the orbital data in such a way that large-wavelength

fringes disappear.

To make the inversion (see Equation 1) more manageable and computationally

manageable, the unwrapped interferograms were subsampled in order to reduce the number of data

points. For the 1993 intrusion interferogram, points in 200-meter spacing within a circle having a

radius of 4.5 km, centered at (271070 E, 2143185 N) in the given coordinate system, were used.

For the post-intrusion interferogram, points were subsampled in 100-meter spacing within a circle

having a maximum radius 36.2 km, centered at (262789 E, 2145489 N) [Fukushima et al., 2005].

3.2 Forward Modeling: 3D-MBEM [Cayol and Cornet, 1997]

We conducted a series of forward models to explore the displacements caused by various

shapes, depths, orientations, and overpressures of magmatic intrusions. The three-dimensional

Mixed Boundary Elements Method (3D-MBEM, [Cayol & Cornet, 1997]) was used to simulate

subsurface pressure sources, tensile cracks, and shear fractures beneath real surface topography.

The medium was assumed to be linearly elastic, homogenous and isotropic [Cayol & Cornet,

1997]. Precision of the 3D-MBEM has been carefully tested [Cayol, 1996; Cayol and Cornet,

9

1997], and this method has been applied to volcanic processes by several studies [e.g., Fukushima

et al., 2005,2010; Cayol et al., 2000; Dieterich et al., 2000; Wauthier 2012,2013a,2015]. An

average Poisson’s ratio of 0.25 was assumed [Wauthier et al., 2013b;2016]. From seismic

velocities [Okubo, et al., 1997] and estimation of mechanical properties of the crust [Dieterich et

al., 2003; Okubo et al., 1997, Cayol et al., 2000; Wauthier et al., 2012], a Young’s modulus of 5

GPa, corresponding to the upper two kilometers of the crust, was assumed in models of the 1993

dike. For the modeling deformation due to deep rift zone opening and décollement slip, a Young’s

modulus of 50 GPa was used [Dieterich et al., 2003; Okubo et al., 1997, Cayol et al., 2000].

The boundaries (sources and topography) were meshed with planar triangular elements.

The topographic surface mesh was constructed from a digital elevation model (30-meter SRTM).

The mesh size covered a circular area of 200 km in radius to ensure that edge effects would be

negligible [Fukushima et al., 2005; Cayol, 1996]. This area is about 5 times as large as the

presumed deformation source dimension. The mesh is denser close to the rift zones where

displacement gradients are large. Fukushima et al., 2005 found that model computation time is

proportional to the square of the number of calculation points when disk swap is not required. This

study found mesh densities that minimize computation time without significant loss of precision

using two error functions [Cayol 1996].

For the February 1993 intrusion, we used a quadrangular dislocation defined by seven

geometrical parameters, similar to the frequently used rectangular dislocation model of Okada

[1985] (See Appendix A). Due to the lack of eruptive fissures, the dike was not connected to the

topographic mesh. A constant magma overpressure (P0) was additionally used to make a total of

eight model parameters [Fukushima et al., 2005] (See Appendix E for additional parameter

information).

10

3.3 Nonlinear Inversion: Neighbourhood Algorithm [Sambridge, 1999a]

In order to find the best-fit parameters for the dike responsible for the observed InSAR

deformation signal, the 3D-MBEM models were used as forward input solutions [Fukushima et

al. 2005; 2010] with a Monte-Carlo type Neighborhood Algorithm that consisted of two stages:

search [Sambridge, 1999a] and appraisal [Sambridge, 1999b].

In the search stage, a best-fit model that minimizes a misfit function and quantifies the fit

between observed and the Line-of-Sight (LOS) displacement model was evaluated. The misfit

function is written as follow:

(1)

where uobs and umod are vectors of observed and modeled InSAR surface displacements, and CD is

the data covariance matrix. Correlated random noise is expressed by the autocorrelation function

or covariance function [Fukushima et al., 2005]. Once the noise variance and correlation

distance are estimated, the data covariance matrix CD is determined from these values. Correlation

distance and variance of the data noise for this study were kept at 500 m and 1x10-4 m2 [e.g.

Fukushima et al., 2005; 2010 & Wauthier et al. 2012; 2013a&b; 2015].

The search began with values chosen randomly within the defined initial parameter

boundaries until 30 acceptable low-misfit models were established. Now that the algorithm has

created a ‘neighborhood’ of acceptable values, defined by a Voronoi cell, 30 new lowest misfit

models were generated. This process was repeated until the mean standard deviation of misfits was

less than 0.5%. An RMS error was also calculated in order to provide a more intuitive data-model

fit indicator:

(2)

In the appraisal stage, the posterior probability density function (PPD) of all inverted model

χ 2 = (uobs −umod )T CD

−1(uobs −umod )

RMS(cm) =100* (uobs −umod )T (uobs −umod )N

11

parameters was computed. Using a Monte Carlo integration technique, the model misfit values

from the search stage were used to calculate the PPD [Sambridge, 1999b]. The appraisal stage

produced a 95% confidence interval for each inverted model parameter.

12

4. Results

4.1 InSAR

4.1.1 The February 1993 Intrusion

The JERS-1 interferogram, spanning 10 October 1992 and 1 March 1993, is shown in

Figure 6a. The main signal is composed mostly of motion towards the satellite of up to about 33

cm just east of Makaopuhi crater. There is a small signal showing motion away from the satellite

of up to about 11 cm to the west of the intruded area. Additionally, there is a small signal around

the lava flows at Pu’u’Ō’ō vent of less than 10 cm away from the satellite.

4.1.2 Post-Intrusion Deformation (1993-1997)

The interferogram spanning 8 October 1993 to 3 July 1997 reveals the deformation at

Kīlauea after the February 1993 ERZ intrusion (Figure 6d). There is a clear LOS subsidence signal

that covers all of the summit and most of the rift zone areas. The signal shows ~20 cm of motion

away from satellite in most of the summit and across both the rift zones. Incoherence was seen in

the Upper ERZ and northern slopes of the volcano, probably due to dense vegetation combined

with the long time interval, and the incoherent areas (masked in Figure 6d) were not used.

4.2 Geodetic Modeling

4.2.1 The February 1993 Intrusion

The best-fit model to the 10 October 1992 to 1 March 1993 interferogram consists of the

opening of a shallow dike located just to the northwest of Makaopuhi Crater (Figure 4). The model

has an average opening of about 1.2 m and extends between 0.1 and 2.7 km below the surface.

This result is consistent with seismicity data, which indicated an upward migration from the

inferred depth of the ERZ (~3 km) to about 100 meters below Makaopuhi Crater [Matoza et al.,

2013]. The modeled dike has a seaward dip of ~76 degrees with a strike of N50°E, and a modeled

13

overpressure of ~3.5 MPa (Table 1). The corresponding volume change is 7.4 x 106 m3. The RMS

value for this model is 1.8 cm (Figure 6c).

February 1993 Intrusion Parameters

Average Opening (m) 1.2

Dip (°)* 76

Overpressure (MPa)* 3.5

Elevation of lower side (km beneath surface)* 2.6

Distance to Surface (km)* 0.1

X1 Top Node* 269960

Y1 Top Node* 2142664

X2 Top Node* 271054

Y2 Top Node* 2143429

Top Length (km) 1.3

Average Width (km) 2.7

Volume (x 106 m3) 7.4

RMS error (cm) 1.8

Table 1: Best-fit source geometry and other information for February 1993 intrusion. Asterisks represent parameters that were inverted for. Parameters involving elevation have been corrected to be relative to sea level. More information on parameters and 95% confidence intervals (Figure S4 Table T2) can be found in supplementary materials.

4.2.2 Post-Intrusion Deformation (1993-1997)

The best-fit model for the 1993-1997 period consists of opening of the deep rift zones,

beneath both the SWRZ and ERZ and the summit (Figure 5). The dike-like opening beneath the

rift zones ranges from depths of 3-12 km and has an average opening of about 0.5 meters, and the

constant magma overpressure is ~1.1 MPa (Table 2). A sub-horizontal detachment fault is

14

connected to the seaward side of the vertical dike-like source to mimic the décollement. No stress

change is imposed on the décollement; however, both structures are mechanically interacting,

allowing deep rift zone opening to promote slip (~0.4 m) on the décollement. The amount of slip

is consistent to previous studies (Table T6 in Appendix G). The extent of this detachment is poorly

constrained by our inversions (Table T4 in Appendix D), however, it is consistent with previous

studies [Delaney at al. 1990 and Owen et al. 2000]. The RMS value for this model is 7 cm (Figure

6e).

Post-Intrusion Deformation Parameters

Average Opening (m) of Deep Rift Zones 0.55

Dip of Deep Rift Zones (°) 90

Overpressure (MPa)* 1.1

Distance to Top for the Deep Rift Zones (km) 3

Elevation of lower side of Deep Rift Zones and upper part

of decollement (km)* 12

Volume (x 106 m3) of Deep Rift Zone 378

Area (m2) of Decollement 6.44e+08

Dip of Decollement (°)* 20

Average Triggered Slip on Decollement (m) 0.4

RMS error (cm) 7

Table 2: Best-fitting source geometries and other information for post-intrusion deformation interferogram spanning 8 October 1993 to 3 July 1997. Parameters involving elevation have been corrected to be relative to sea level. Asterisk (*) represent parameters that were inverted for. More information on parameters and 95% confidence intervals (Figure S6 Table T4) can be found in supplementary materials.

15

Figure 4: 2D map view (left) and 3D-view (right) of best-fit intrusion model for JERS-1 interferogram spanning 10 October 1992 to 1 March 1993. Coordinates are given in Universal Transverse Mercator (UTM).

East (km)260 262 264 266 268 270 272 274 276 278 280

Nor

th (k

m)

2135

2140

2145

2150

Mak

Makaopuhi Crater

Summit

16

Figure 5. Best-fit post-intrusion deformation model from JERS-1 interferogram spanning 8 October 1993 to 3 July 1997. 2D map view (top) shows trace of rift zone with gray mesh shading of basal décollement at 12km depth. 3D view (bottom) shows blue mesh that represents the sub-horizontal basal décollement and red mesh is vertical deep rift connected below the summit caldera. Coordinates are given in Universal Transverse Mercator (UTM).

17

Figure 6: Data, model, and residuals (left, a-c) for the interferogram spanning 10 October 1992 – 01 March 1993. (right, d-f) Same for the interferogram spanning 08 October 1993 – 03 July 1997. The coordinates are given in Universal Transverse Mercator. Color corresponds to LOS displacements in meters (positive change is movement away from the satellite, or Line-of-Sight LOS subsidence). Red line is trace of 1993 dike intrusion in model (b) and residuals (c).

Residuals (f)

Model (e)

Data (d)Data (a)

Model (b)

Residuals (c)

0.05

0

-0.05

-0.1

-0.15

-0.2

-0.25

-0.3[m] [m]

0.2

0.15

0.1

0.05

0

-0.05

-0.1

Nor

th (k

m)

2148

2144

2140

2138

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2146

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th (k

m)

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2140

2138

2142

2146

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th (k

m)

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2144

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2146

262 264 266 268 270 272 274 276East (km)

250 260 270 280East (km)

2155

2145

2135

2130

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th (k

m)

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orth

(km

)

2155

2145

2135

2130

2140

2150

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2125

Nor

th (k

m)

Unwrapped Phase Unwrapped Phase

18

5. Discussion

Kīlauea Volcano is constantly deforming due to magma transport and storage beneath the

surface. However, only a few intrusional events have been modeled and characterized using

geodetic data. The February 1993 event had been lacking such data in order to compare and

contrast the event with other similar, modeled intrusions, as well as understand the roll of the deep

rift zone and decollement with passive intrusions.

5.1 Deformation Sources

The best-fit model for the deformation field in the ERZ between October 1992 and March

1993 is a subvertical shallow dike. Although the dike did not rupture the surface, the magnitude

of opening and location near Makaopuhi Crater is similar to other recent eruptive intrusions at

Kīlauea, like the 1997 Nāpau [Owens et al., 2000b] and 2011 Kamoamoa events [Lundgren et al.,

2013]. Our model dike also dips steeply to the south, which is a feature of all models of recent

ERZ dike intrusions, as well as dikes exposed by erosion in inactive Hawaiian volcanoes [see

Owen et al., 2000b]. The modeled volume for the 1993 dike, 7.4 x 106 m3, is small in comparison

to the 1997, 2007, and 2011 dikes, but larger than the 1999 intrusion (Table 3).

The best-fit model for the post-intrusion deformation period (1993-1997) is a 3-12 km deep

vertical dike with a sub-horizontal detachment fault, similar to that of Delaney at al. [1990] and

Owen et al. [2000a]. This model shows that deep-rift opening induces slip on the decollement,

which can explain the deformation pattern in both the SWRZ and ERZ and south of the caldera.

Interestingly, in contrast to Owen et al., 2000, no deflating summit reservoir is required to fit the

data during this post-intrusion deformation period. However, residuals can be seen around the

Nāpau Crater region and are inferred to be caused by the 1997 Nāpau Intrusion that occurred in

January 1997 [Owen et al, 2000]. The area of the intrusion is mostly incoherent and the

19

deformation indicated in Owen et al., [2002b] indicates that displacements were highly restricted

to the Nāpau Crater area, so this does not affect our overall model.

5.2 Dike Classification and Comparison

We classify the February 1993 dike intrusion as a “passive” intrusion, implying that it was

not driven by overpressure of the summit reservoir but instead by passive opening of the ERZ.

There was no summit inflation prior to the dike intrusion. This is evident by investigating time

series from the summit tiltmeter at Uwekahuna Vault (See Figure S2 in the supplementary

materials), which shows no significant precursory summit deformation in the weeks to months

prior to the intrusion and suggests that the pressure of the magma in the summit reservoir did not

change before the intrusion. This conclusion is consistent with that of the 1997 [Owen et al, 2000]

and 1999 [Cervelli et al., 2002] intrusions, neither of which was preceded by summit inflation

(Table 3). In contrast, the 2007 and 2011 dikes were preceded by summit inflation, suggesting that

they were driven by increases in pressure in the magmatic system. The persistent deep rifting in

the ERZ and seaward sliding of the south flank along the décollement creates a high tensile stress

region in the shallow part of the ERZ. This leads to failure in the crust above the deep rift zones,

allowing “opportunistic” dike intrusions in the region [Cervelli et al., 2002]. Passive intrusions

make forecasting difficult since they are not preceded by inflation or large increases in seismicity.

5.3 Static Stress Changes Implications

Static normal stress change modeling indicates that the deep rift zone and the décollement

model obtained from the 1993-1997 post-intrusion deformation unclamped (negative normal stress

change) a significant area (3.86x106 m2) of the 1993 dike surface, located above the deep rift zone

(Figure 7). These results further confirm our interpretation that the 1993 intrusion was driven by

passive opening of the deep rift zones beneath the ERZ. Conversely, an area of 1.35x107 m2 is

20

unclamped in the deep rift zone by the 1993 dike (Figure 8). Therefore, there could be a positive

feedback between ERZ dike intrusions and opening of the deep rift zones at Kīlauea Volcano. The

1993 dike also unclamps a potential Pu’u’Ō’ō’s shallow reservoir located at <1 km depth [e.g.

Poland et al., 2014, Heliker et al., 2003]. The 1993 dike indeed triggers a pressure decrease of

0.006 MPa in the host rocks at the level of Pu’u’Ō’ō reservoir. On the other hand, the 1993 dike

induces pressure increase in the host rocks at the levels of both the Halema’uma’u and south

caldera summit reservoirs. This result suggests that the conduit that connects Pu’u’Ō’ō to the ERZ

is available or ‘open’ for the eruption to resume.

5.4 Magma Origin

Kīlauea has erupted differentiated lavas with bulk compositions produced by multiphase

fractionation along its rift zones. This differs from the occurrence of olivine-rich lavas near

Kīlauea’s summit [Poland et al., 2014]. Active intrusions that occurred due to overpressure of the

summit magma reservoir could be inferred to have mostly summit, olivine-rich lavas. However,

the 2011 Kamoamoa fissure eruption was found to have a Pu’u’Ō’ō component to the lava. This

could also be the case for the 1993 intrusion. Although this intrusion was passive and did not erupt

at the surface, it is possible that the pressure decrease of the Pu’u’Ō’ō’ reservoir could have

contributed to the intruded magmas. Furthermore, passive intrusions versus active intrusions

cannot be distinguished based on lava compositions alone.

21

Figure 7: Post-Intrusion model (deep rift zone and decollement) shown in red unclamps (negative normal stress change) an area of 3.86x106 m2 of the 1993 dike. Elevation is relative to sea level.

Figure 8: 1993 Intrusion model shown in red unclamps (negative normal stress change) an area of 1.35x107 m2 of the deep rift zones. Elevation is relative to sea level.

22

Table 3: Table of best-fit geometries for intrusions that have been modeled and were detected by deformation measurements in Kilauea’s East Rift Zone between 1993-2011. 1Owen et al, 2000, 2Cervelli et al, 2002, 3Montgomery-Brown et al, 2010 and 4Lundgren et al., 2013.

Intrusion year Volume

(m3)

Strike

(°)

Average

Opening

(m)

Maximum

Depth

(km)

Dip

(°)

1993 (This study) 7.4e+06 N50°E 1.2 2.6 76

19971 23e+06 N67°E 1.6 2.4 76

19992 3.3e+06 N86°W 0.7 3.0 80

20073 16.6e+06 N80°W 1.8 3.9 80

20114 15.6e+06 ~N60°E 2.2 2.5 72

23

6. Conclusions

The 8 February 1993 earthquake swarm that occurred at Kīlauea Volcano was indeed

caused by a non-eruptive intrusion that was emplaced just west of Makaopuhi Crater. Our geodetic

modeling found a best-fit dike extending between 0.1 and 2.6 km below the surface, the deeper

part of which probably corresponds to the depth of the ERZ magmatic conduit, beneath which

deep rift opening is occurring due to seaward motion of the volcano’s south flank [Delaney et al.,

1990; Owen et al, 2000; Cayol et al., 2000]. This intrusion is comparable to other ERZ intrusions

at Kīlauea in terms of volume (3-17 MCM), opening (0.5-2 m), and dip (70-80 degrees). The best-

fit model for the 1993-1997 post-intrusion period consists of opening of the deep rift zones beneath

the SWRZ, ERZ and the summit. The dike-like opening beneath the rift zones ranges from depths

of 3-12 km and has an average opening of about 0.5 meters. The driving mechanism of the 1993

intrusion is likely passive opening of the shallow ERZ resulting from the extension of the deep rift

zones and slip on the décollement. Hence, we classify the 1993 dike as a passive intrusion, similar

to the subsequent 30 January 1997 and 12 September 1999 intrusions. The continued deep rifting

in the ERZ and seaward sliding of the south flank along the décollement creates a high tensile

stress region that allows dike intrusions to occur without overpressure in the summit reservoirs

[Cervelli et al., 2002]. These types of intrusions make forecasting and natural hazard assessment

difficult since they are not preceded by inflation nor by large increases in seismicity.

24

References

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Montgomery-Brown, E. K., D. K. Sinnet, M. Poland, P. Segall, T. Orr, H. Zebker, and A. Miklius (2010), Geodetic evidence for en echelon dike emplacement and concurrent slow slip during the June 2007 intrusion and eruption at Kilauea volcano, Hawaii, J. Geophys. Res., 115, B07405, doi:10.1029/2009JB006658. Montgomery-Brown, E. K., C. H. Thurber, C. J. Wolfe, and P. Okubo (2013), Slow slip and tremor search at Kilauea Volcano, Hawaii, Geochem. Geophys. Geosyst., 14, 367–384, doi:10.1002/ggge.20044. Okada, Y. (1985), Surface deformation due to a shear and tensile faults in a half-space, Bull. Seismol. Soc. Am., 75(4), 1135–1154. Okubo, P.G., Benz, H.M., and Chouet, B.A., (1997), Imaging the crustal magma sources beneath Mauna Loa and Kilauea volcanoes, Hawaii: Geology, v. 25, no. 10, p. 867–870. Okubo, P., and J. S. Nakata (2003), Tectonic pulses during Kilauea’s current long-term eruption, in The Pu‘u O‘o- Kupaianaha Eruption of Kılauea Volcano, Hawai‘i: The First 20 Years, U.S. Geol. Surv. Prof. Pap., 1676, edited by C. Heliker, D. A. Swanson, and T. J. Takahashi, chap. 11, pp. 173–186, U. S. Geological Survey, Reston, Va Orr T, Poland MP, Patrick MR, Thelen WA, Sutton AJ, Elias T, Thornber CR, Parcheta C, Wooten KM. 2015. Kīlauea’s 5-9 March 2011 Kamoamoa fissure eruption and its relation to 30+ years of activity from Pu‘u ‘Ō‘ō. In: Carey R, Poland M, Cayol V, Weis D, (eds) Hawaiian Volcanism: From Source to Surface: Hoboken, New Jersey, Wiley, American Geophysical Union Geophysical Monograph 208, p. 393-420. Owen, S., P. Segall, M. Lisowski, A. Miklius, M. Murray, M. Bevis, and J. Foster, (2000a) The January 30, 1997 eruptive event on Kilauea Volcano, Hawaii, as monitored by continuous GPS, Geophys. Res. Lett., 27, 2757 – 2760, Owen S, Segall P, Lisowski M, Miklius A, Murray M, Bevis M, Foster J (2000b) January 30, 1997 eruptive event on Kilauea Volcano, Hawaii, as monitored by continuous GPS. Geophys Res Lett 27(17):2757–2760 Owen, S., and R. Bürgmann (2006), An increment of volcano collapse: Kinematics of the 1975 Kalapana, Hawaii, earthquake, J. Volcanol. Geotherm. Res., 150, 163–185, doi:10.1016/j.jvolgeores.2005.07.012. Poland, M.P., Takahashi, T.J., and Landowski, C.M., eds., (2014), Characteristics of Hawaiian volcanoes: U.S. Geological Survey Professional Paper 1801, 428 p., http://dx.doi.org/10.3133/pp1801. Sambridge, M. (1999a), Geophysical inversion with a neighbourhood algorithm: I. Searching a parameter space, Geophys. J. Int., 138, 479– 494. Sambridge, M. (1999b), Geophysical inversion with a neighbourhood algorithm: II. Appraising the ensemble, Geophys. J. Int., 138, 727–746. Thornber, C. R. in The Pu‘u ‘Ō‘ō–Kūpaianaha Eruption of Kilauea Volcano, Hawai‘i: The First 20 Years (eds Heliker, C., Swanson, D. A. & Takahashi, T. J.) Ch. 7, 121–136 (US Geol. Surv. Prof. Pap. 1676, 2003). Wright, T.L., and Klein, F.W., (2014), Two hundred years of magma transport and storage at Kïlauea Volcano, Hawai‘i, 1790–2008: U.S. Geological Survey Professional Paper 1806, 240 p., 9 appendixes, http://dx.doi.org/10.3133/pp1806. Wauthier, C., V. Cayol, F. Kervyn, and N. d'Oreye (2012), Magma sources involved in the 2002 Nyiragongo eruption, as inferred from an InSAR analysis, J. Geophys. Res., 117, B05411, doi:10.1029/2011JB008257. Wauthier, C., Cayol, V., Poland, M., Kervyn, F., d'Oreye, N., Hooper, A., Samsonov, S., Tiampo, K., Smets, B. (2013). Nyamulagira's magma plumbing system inferred from 15 years of InSAR. Geol. Soc. Lond., Spec. Publ. 380 (1), 39–65. Wauthier, C., D. C. Roman, and M. P. Poland (2013), Moderate-magnitude earthquakes induced by magma reservoir inflation at Kīlauea Volcano, Hawai‘i, Geophys. Res. Lett., 40, 5366–5370, doi:10.1002/2013GL058082. Wauthier C., D. C. Roman and M. P. Poland (2016), Joint analysis of InSAR and earthquake fault-plane solution data to constrain magmatic sources: A case study from Kilauea Volcano, Earth and Planetary Science Letters, DOI:10.1016/j.epsl.2016.09.0 Wegmuller, U., and C. Werner (1997), Gamma SAR processor and interferometry software, The 3rd ERS Symposium on Space at the Service of our Environment, Florence, Italy. [Available at http://earth.esa.int/workshops/ers97/papers/wegmul

26

Appendix A – Alternate Models Okada [1985] provides analytical solutions for surface deformation due to shear and tensile faults in an elastic half-space. The Okada [1985] model differs from 3D-MBEM as it does not take into account realistic surface topographies, source interactions, has a more simplified shape (rectangle) and uniform opening. We compare the volume, geometry and average opening of the two models and find that they are similar.

Parameter: Okada [1985] 3D-MBEM [Cayol and Cornet, 1997]

Mean opening (m)** 1.6 1.2

Volume (x 106 m3) 6.0 7.4

Width (km)* 2.1 2.7

Length (km)* 1.8 1.34

Depth (km) 2.5 2.6

Dip (°)* 73 76

RMS (cm) 2.3 1.8 Table T1 - Comparison of 3D-MBEM and Okada best-fit models obtained for the 1993 intrusion. Asterix represent inverted parameters for Okada [1985] model only. Double asterix represents parameter inverted in the 3D-MBEM model was overpressure; opening for Okada model.

Figure S1: Data (left), Model (center), and Residuals (right) using Okada [1985] to model the 1993 intrusion. Red line represents intrusion trace on the surface.

260 265 270 275 280

East (km)

Nor

th (k

m)

2148

2144

2140

2138

2142

2146

260 265 270 275 280

East (km)260 265 270 275 280

East (km)

Data Model Residuals

[cm]

Wrapped Phase

0

11.8

27

Appendix B – Tiltmeter Data The only available tiltmeter data from 1993 was from a single-component (E-W) electronic tiltmeter at the Uwekahuna Vault (UWE) which is still active today. Kilauea is consistently going through inflation and deflation cycles (DI Event) which vary between 2-3 microradians. The inflation signal seen before the intrusion is that of a DI event. The rapid (<1 day) deflation of 8 microradians is seen on this tiltmeter on February 8, 1993.

Figure S2: Tiltmeter data from the Uwekahuna Vault spanning a 3-month time period of January 1993 to the end of March 1993. For this tiltmeter, east direction is negative so that a downward trend on the plot would be indicative of deflation. The large deflation signal occurred prior and during the intrusion. X-axis is HST time and the y-axis is tilt in microradians.

Dec 28, 92 Jan 11, 93 Jan 25, 93 Feb 08, 93 Feb 22, 93 Mar 08, 93 Mar 22, 93

Tilt

(mic

rora

dian

s)

22

23

24

25

26

27

28

29

30

31

32Single-Component Electronic Tiltmeter (E-W)

8 Feb 1993 Intrusion

Event

Infla

tion

Deflation

DI Event

28

Appendix C – Wrapped Interferograms Wrapped interferograms show fringes of displacement instead of absolute displacement in unwrapped interferograms. Figure S3(a-b): (a) February 1993 Intrusion wrapped interferogram spanning between 10 October 1992 and 1 March 1993. (b) Post-Intrusion wrapped interferogram spanning between 8 October 1993 and 3 July 1997.

29

Appendix D – Neighbourhood Algorithm [Sambridge, 1999a,b] Using Sambridge (1999a,b) Neighbourhood algorithm, we simultaneously invert for the dike geometry, location and constant overpressure. The algorithm consists of two stages: search (Sambridge, 1999a) and appraisal (Sambridge 1999b). In the search stage, random values are chosen within the defined initial parameter boundaries until 30 acceptable low-misfit models were established. Now that the algorithm has created a ‘neighborhood’ of acceptable values, defined by a Voronoi cell, 30 new lowest misfit models were generated. Fukushima et al., 2005 showed that values of 10-70 n lead to robust results. Since InSAR data are computational extensive, n was taken to be 30 (Table T5). This process was repeated until the mean standard deviation of misfits was less than 0.5%. During the search stage, a best-fit model that minimizes a misfit function and quantifies the fit between observed and the Line-of-Sight (LOS) displacement model was evaluated (Equation 1). Correlated random noise is expressed by the autocorrelation function or covariance function [Fukushima et al., 2005]. Once the noise variance and correlation distance are estimated, the data covariance matrix CD is determined from these values. For this study, correlation distance and variance of the data noise were kept at 500 m and 1x10-4 m2 [e.g. Fukushima et al., 2005; 2010 & Wauthier et al. 2012; 2013a&b; 2015]. In the appraisal stage of Sambridge 1999b, posterior probability density functions are calculated using misfit values computed during the search stage. Model statistical characteristics such as the mean model and marginal posterior probability density functions (PPDs) are estimated. Confidence intervals (95%) for the model parameters can be obtained from the one-dimensional marginal PPDs (shown here), while two-dimensional marginal PPDs show trade-offs between pairs of model parameters. The applicability of the method has been confirmed by synthetic test by Fukushima et al., 2005. An unconstrained parameter is one without a Gaussian (normal) distribution that is not well constrained. These are indicated by UC+ on Tables T2-4. Trade-offs can be seen between the overpressure (P0), bottom elevation (botelev) and the distance to the top (D_top) making some of the 95% confidence intervals of these parameters unconstrained. These large confidence intervals are likely a result of data noise from unidentified atmospheric effects, the presence of other minor deformation sources or more complex source geometry, analytical model oversimplification (for the Okada [1985] model), and trade-offs between inverted parameters. A total of seven parameters were inverted for the 1993 intrusion. Six geometrical parameters were used to define the quadrangle shape of the dike. The top of the dike was assumed to be a straight line fixed at 1, determined by D_top, the average depth to the top of the dike. Two parameters, the dip angle (θ) and the elevation of the bottom middle point (Botelv) determined the location of the bottom midpoint (X0 Y0 Z0). The other four geometrical parameters determined the position of the dike. We inverted for the top nodes (X, Y) of the dike which are shown above in UTM coordinates (Zone 5).

30

Figure S4: February 1993 1-D Marginal Probability Density Functions shown for each inverted parameter considering a 3D-MBEM dike model. The 1-D PPDs show 3 unconstrained parameters: overpressure, bottom elevation (Botelev) and the distance to the top (D_top) hence the non-Gaussian distributions. All three parameter trends converge near parameter bounds. The rest of the parameters show Gaussian distributions with the best-fit model occurring near the average value. Dashed red dotted line indicates best-fit model parameter. Green bar represents 95% confidence interval. All parameters related to elevation are not relative to sea level but to topographic mesh. The average height of the Makaopuhi Crater region is ~900 m.

31

Figure S5: February 1993 1-D Marginal Probability Density Functions shown for each inverted parameter considering an Okada dike model. All parameters show normal distribution with best-fit models occurring near the average value. Solid red dotted line indicates best-fit model parameter. Green bar represents 95% confidence interval. A total of 8 parameters were inverted for in the Okada [1985] model. The average opening of the dike was inverted for which differs from the 3D-MBEM models where overpressure is inverted for. The top of the dike was assumed to be a quadrangle shape determined by Width, the average depth to the top of the dike, Strike, the dip angle (θ) and Length. The location of the bottom midpoint (X0 Y0 Z0) was also inverted for which are shown above in UTM coordinates.

Opening (m)1 1.5 2 2.5

0

0.5

1

1.5

2

Width (m) 2000 2500 3000 3500

10-3

0

0.5

1

1.5

2

2.5

3

3.5

Length (m)1000 1500 2000 2500 3000

10-3

0

0.5

1

1.5

Strike (degrees)45 50 55 60 65

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

X0 (m) 1052.69 2.695 2.7 2.705 2.71

10-3

0

0.5

1

1.5

Y0 (m) 1062.1412 2.1416 2.142 2.1424

10-3

0

0.5

1

1.5

2

2.5

3

Z0 (m)2000 2500 3000 3500

10-3

0

0.5

1

1.5

2

2.5

3

Dip (degrees)65 70 75

0

0.1

0.2

0.3

0.4

0.5

x x x

xx

xx

32

Figure S6: Post-Intrusion 1-D Marginal Probability Density Functions shown for each inverted parameter. The 1-D PPDs show multiple unconstrained parameters: overpressure, bottom elevation (Botelev), quadtop (x1 & y1), end of the decollement, and dip of the decollement hence the non-Gaussian distributions. The decollement geometry and expanse is poorly constrained by our data. Unlike the 1993 intrusion unconstrained parameters, not all post-intrusion unconstrained parameter trends converge near parameter bounds. Only decollement width and start node show normal (Gaussian) distributions with the best-fit model occurring near the average value. Dashed red dotted line indicates best-fit model parameter. Green bar represents 95% confidence Interval. All parameters related to elevation are not relative to sea level but to topographic mesh. Six geometrical parameters were used: the dip angle (θ) of the decollement and the elevation of the bottom middle point (Botelv) determined the location of the bottom midpoint (X0 Y0 Z0) of the deep rift zone and the upper part of the decollement. The other four geometrical

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parameters determined the position of the deep rift zone and decollement. We inverted for the top nodes (X, Y) of the deep rift which are shown above in UTM coordinates (Zone 5) and (X,Y) nodes of the decollement. Additionally, the decollement width was inverted for as well making a total of eight inverted parameters.

Table T2: 95% confidence intervals for 1993 Intrusion parameters considering a 3D-MBEM dike model.+ Unconstrained.

Parameter Best-Fit Minimum 95% Maximum 95%

Minimum initial boundary

Maximum initial boundary

Overpressure (MPa)+

3.6 0.6 UC+ 0 4

Dip (degrees) 76 61 87 60 90

Elevation of lower side (km beneath

surface)

-2.6 UC+ UC+ -1 -4

Distance to Surface (km)

0.1 UC+ 1.36 0.1 3

X1 Top Node 269960 269102 270778 268960 270960 Y1 Top Node 2142664 2141907 2143522 2141664 2143664 X2 Top Node 271054 270156 271851 270054 272054 Y2 Top Node 2143429 2142914 2144327 2112429 2114429

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Parameter Best-Fit Minimum 95%

Maximum 95%

Minimum initial boundary

Maximum initial boundary

Mean Opening (m) 1.3 1 1.7 1 10

Width (m) 2267 2027 2811 500 5000

Length (m) 1826 1150 2330 1000 10000

Strike (degrees) 52 50 57 20 70

Bottom Left X0 Node 269833 269406 270566 269000 274000 Bottom Left Y0 Node 2141728 2141499 21441972 2140000 2145000

Bottom Left Z0 Node 2683 2235 3270 1000 5000

Dip (Degrees) 73 69 74 60 90

Table T3: 95% confidence intervals for 1993 Intrusion parameters considering an Okada dike model. A total of 8 parameters were inverted.

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Parameter Best-Fit Minimum 95%

Maximum 95%

Minimum initial boundary

Maximum initial boundary

Overpressure (MPa) 0.9 UC+ 2.15 0.5 10

Elevation of lower side of Deep Rift Zones and upper part of decollement (km) -12 UC+ -3.7 -3 -13

Deep Rift X1 Top Node 13 UC+ UC+ 1 19

Deep Rift Y1 Top Node 54 UC+ UC+ 20 66

Decollement X2 Top Node 5 1 10 1 10 Decollement Y2 Top Node 31 15 UC+ 11 32

Dip of Decollement (degrees) 20 4 UC+ 3 20

Decollement Width (m) 12400 2500 UC+ 1000 20000 Table T4: 95% confidence intervals for Post-Intrusion parameters. A total of eight parameter were inverted.+ Unconstrained.

Inversion Parameters 1993 Intrusion Post-Intrusion NS0 30 10 NS1 30 10 NS2 30 10 NR 30 10

Std Dev Threshold 0.05 0.05 Total Acceptable Models 12930 2640

Table T5: Inversion parameters used for 1993 intrusion and post-intrusion period. NS0 = initial number of acceptable model for iteration zero NS1 = sample size for first iteration, NS2 = sample size for other iterations, NR = number of cells to resample.

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Appendix E – InSAR Uncertainties Interferometric Synthetic Aperture Radar, or InSAR, is a widely used method to study deformation associated with a broad range of volcanic and seismic events. This geodetic method uses two (or more) SAR images to generate interferograms (or deformation maps) using the differences in the phase of the return waves. The method provides high spatial resolution of ground displacements over large distances. However, InSAR has some uncertainties that should be mentioned. The phase contribution must remain constant between the two phase images. Decorrelation or incoherence, is the phenomenon that destroys the organized fringe pattern in an interferogram. Each pixel undergoes a random phase change, and an area of randomly colored speckles appears in the interferogram [Massonet and Feigl 1998]. Extreme cases include areas that are covered by water, which has no stability. This also applies to tidal areas near coastlines. The maximum detectable deformation is gradient is on fringe per pixel (or the ratio of the pixel size to the wavelength). This value is dependent on the satellite. For JERS-1 the value is 13x10-3. If this threshold is exceeded, incoherence is created [Massonet and Feigl 1998]. Conventional InSAR techniques suffer from several limitations. First, temporal decorrelation can be caused by vegetation or scattering properties. Dense vegetation covers parts of the East Rift Zone (ERZ) at Kilauea, which causes strong decorrelation of the InSAR signal. This problem can be limited by using longer wavelength data, e.g. L-Band like JERS-1. The post-intrusion interferogram is more affected by this. A second limitation is perpendicular baseline decorrelation. During InSAR processing, interferogram flattening is used as an operation to subtract the perpendicular baseline (known from precise orbital data) from the interferometric phase. As a result, this operation generates a phase map proportional to the relative terrain altitude. The altitude of ambiguity is defined as the altitude difference that generates an interferometric phase change of 2π after interferogram flattening. The altitude of ambiguity is inversely proportional to the perpendicular baseline. There is an optimum perpendicular baseline that maximizes the signal to noise ration. Typically, an optimum baseline is about 300-400 meters which is a function of the radar wavelength [Ferretti et al., 2007](Figure S7).

Figure S7: Perpendicular Baselines for both descending interferograms spanning between October 1992 and March 1993, and July 1993 and October 1997.

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A third limitation is atmospheric delays. InSAR measurements are often significantly affected by the atmosphere as the radar signals propagate through the atmosphere whose state varies both in space and in time [Hanssen, 2001]. In recent years, efforts have been made to better understand the properties of the atmospheric effects and to develop methods for mitigating the effects. For the 1993 intrusion and post-intrusion interferograms, atmospheric delays were not corrected for. Lastly, Digital Elevation Model (DEM) errors are a limitation of InSAR. DEM’s are used to remove fringes caused by the topography [Hanssen, 2001]. When processing the data, if the ground surface geometries measured by SAR observation and the DEM are different, the difference is shown as a phase difference in the image. This would appear as a false deformation signal.

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Appendix F – Residuals Both analytic and numerical models produce some residual deformation. The 3D-MBEM models for both 1993 dike intrusion and 1993-1997 post-intrusion period produced acceptable RMS errors and leave little residual deformation. The residual fringes present in the modeled 1993 dike intrusion interferogram are located near the trace of the dike intrusion and could be attributed to the meshing. The post-intrusion period has a large RMS error value (7 cm) and has more residual deformation around the edges of the coherent data. Some of these residuals could be attributed to 1997 Nāpau dike intrusion that occurred just before the second SAR acquisition in January 1997. This intrusion occurred in the areas that are incoherent, however some residuals can be seen around the edges. Because the post-intrusion period was over four years, some residuals are likely a result of data noise from temporal decorrelation.

Figure S8: JERS-1 Post-Intrusion (1993-1997) interferogram showing location of the 1997 Nāpau Crater Intrusion in East Rift Zone. Incoherence south of Nāpau Crater and Pu’u’Ō’o are likely a result of high displacement gradient exceeding the phase change threshold due to the 1997 Nāpau Intrusion (See Appendix E).

155˚W

0.2

0

-0.2

-0.1

0.1

LOS Displacement (m)

155.3° W

19.4° N

19.2° N

N

January 1997Nāpau Intrusion

Nāpau CraterPu`u `Ō`ō

155° W

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Appendix G – Supply Rate and Decollement Slip Seaward movement of the south flank is an essential component of magma supply at Kilauea. Continuous seaward spreading has been documented by numerous studies using triangulation, EDM, GPS (Table T6). At the start of the Pu’u’Ō’o eruption in 1983, average slip rates were larger and began to slow down with time. Since the 1990’s, the south flank motion has been more or less constant at 5-6 cm/year with the except of small offsets accompanying intrusions [Wright and Klein, 2014].

Time Period Average Slip (cm/yr) Method Reference

1983-1991 25 EDM Delaney et al., 1993

1990-1993 20 GPS Owen et al., 1995

1990-1996 20-28 GPS Owen et al., 2000

1991-1994 8 EDM Wright and Klein, 2014

1994-1998 5 GPS Wright and Klein, 2014

2000-2003 8 GPS Wright and Klein, 2014

1993-1997 10 InSAR This study

Table T6: Table of decollement slip estimates from various studies. Average slip rates range between 5-28 cm/year from previous studies using various methods [EDM, GPS, InSAR]. More information on slip rates and magma supply can be found in Appendix G. The relationship between spreading rate and magma supply rate helps us to understand the mechanism behind deep rift zone spreading [Wright and Klein, 2014]. During the Pu’u’Ō’o–Kupaianaha eruption, motion of the south flank was mostly smooth and slightly declining, with only small offsets from large earthquakes and eruptions. Throughout the eruption, magma supply continued to increase with a surge of magma occurring between 2005-2006. Spreading of the deep rift system is thought to be associated with dilation of the rift zones, thus creating additional space for magma to occupy. Furthermore, overpressure in the deep rift zones induces creep on the decollement.

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Time Period Supply (km3/yr) Method Reference

1983-1991 0.025 EDM modeling Delaney et al., 1993

1990-1993 0.06 GPS modeling Owen et al., 1995

1990-1996 0.045 GPS modeling Owen et al., 2000

1991-1997 0.14 Rift Dilation Rate Wright and Klein, 2014

1983-2002 0.12 Pu’u’Ō’o eruption volumes Heliker and Mattox, 2003

1983-2002 0.12 S02 emissions from ERZ Sutton et al., 2003

1991 0.08 Deformation and effusion rates Delinger, 1997

2005-2006 0.18-0.19 S02 emissions from ERZ Poland et al., 2012

1993-1997 0.1 InSAR modeling This study

Table T7: Table of supply rate estimates from various studies. Average supply rates range between 0.025-0.19 km3/year from previous studies using various methods.