Seismology

Seismology and Earth’s interior

Joachim Vogt

Jacobs University Bremen

Course 210392Earth and Planetary Physics

Spring 2009

Joachim Vogt (Jacobs University Bremen) Seismology and Earth’s interior Course 210392, Spring 2009 1 / 43

Motivation

Earthquakes cause seismic waves that propagate through and thus probethe Earth’s interior.

What are the key mechanisms ?

How are seismic data used to identify earthquake parameters ?

The internal structure of our planet is modeled mainly on the basis ofseismic recordings.

How do seismic waves propagate in the Earth’s interior ?

How can we reconstruct material parameters from seismic data ?

Travel-time seismology cannot fully resolve the internal structure of theEarth.

What other information can be used to constrain Earth models ?

Which physical assumptions are appropriate ?


Overview

Part I: Earthquakes and seismic recordings

Terminology, earthquake distribution, fault types

Seismic measurements and focal mechanism reconstruction

Part II: Seismic waves in the Earth’s interior

Reflection and refraction, seismic phases

Travel-time curves and seismic velocity profiles

Part III: Modeling Earth’s internal structure

Spectrum of free oscillations

Mass, moment of inertia, Adams-Williamson equation

Density, gravity, and pressure from reference Earth models


Seismology and Earth’s interior– Part I

Earthquakes andseismic recordings


Earthquake location terminology

Δ

Hypocenter

Observatory

h

Epicenter

θ

Key terms:

Hypocenter = focus: location in theground (subsurface).

Focal depth h: depth of hypocenter.

Epicenter : associated surface point(projection).

Epicentral distance ∆ or θ: distanceof epicenter to seismologicalobservatory (in km or degrees):

∆ = RE θ .


Elastic rebound mechanism

[(1) USGS]

[(1) USGS]


Fault types (1)

fault line strike

northdip gravity

Terminology:

Fault line: intersection of faultplane and surface.

Strike: angle between north andfault line.

Dip: angle between surface andfault plane.

The two blocks of rock can move

vertically → dip slip faults (= normal or thrust/reverse faults)

horizontally → strike slip faults(= transform or conservative or lateral faults),

both, vertically and horizontally → oblique slip faults.


Fault types (2)

Normal fault

Reverse fault

Transform fault

Oblique slip fault

[(2) IRIS]


Geographical distribution of earthquake foci (1)

[(3) Great Globe Gallery]


Geographical distribution of earthquake foci (2)

Most earthquakes occur at mid-ocean ridges, ocean-continent boundaries,continental rift zones: earthquake activity is associated with platetectonics.

Distribution of earthquakes with depth

0–70 km: 85% of total seismic energy released in earthquakes.

70–300 km: 12%.

300–720 km: 3%.

Earthquakes below 720 km have not been recorded.


Measures of earthquake strength

Mercalli scale = earthquake intensity. Measure of surface effects(damages to structures). Range I (felt by only a few) to XII (totaldestruction). Depends on epicentral distance, building materials,design of buildings, ground material. Not suited for seismologicalstudies.

Richter magnitude = “local” magnitude ML. Based on the logarithmof the amplitude A of seismic waves as read from seismograms of thesame type at different locations. Initially (1935) used only forearthquakes in California.

Moment magnitude MW. Function of displacement, area of the break,rock rigidity. Gives better estimate of energy, no saturation effects.

Estimate of earthquake energy:

E[Joule] = 104.8+1.5M .


Richter magnitude scale

Invented by Richter and Gutenberg in 1935. Based on the logarithm of theamplitude A measured by a certain type of seismometers:

ML = log10A − log10A0(∆) .

Problem: limitations of that particular instrument for ML > 6.8(saturation effects). Variants: MB (uses body waves only) and MS

(surface wave only).

log (100 km) 10 10log Δ

log A10

Δ( )log10A0

different earthquakes

instrument sensitivity


Seismic moment and moment magnitude scale

The moment magnitude MW (subscript W refers to work) is a measure ofthe total energy released by an earthquake. Like for ML, the scale islogarithmic. With M0 in units if 10−7 N m (ergs):

MW =23

log10(M0) − 10.7 .

The seismic moment M0 is defined as the product of the area A of thefault rupture, the average displacement U and the rock rigidity µ.

[(4) USGS]

Formula: M0 = µAU .

Typical values for µ:

crust ∼ 32 GPa,

mantle ∼ 75 GPa.

Figure: U = D, A = L ·W .


Seismographs (seismometers)

Ground motions caused by seismic waves are recorded by seismographs.

[(5) Earth Science Australia]

Measured is the relativedisplacement of the movingground and a (heavy) mass(large inertia – only looselycoupled to the ground).

Displacement is a vector: three such instruments are needed.


Seismograms

Recordings of seismometers are called seismograms.

[(6) USGS]

Onsets of differenttypes of waves areclearly distinguishableand yield travel timeinformation (e.g.,TS − TP ).

The onsets are also called first breaks, and the first motion data (initialexcursion up or down) allow to study the focal mechanism.


Reconstruction of the focal mechanism

[(7) Wikipedia Commons, (8) USGS]


Part I : Earthquakes and seismic recordings – Summary

Important terminology

Earthquake location: hypocenter (focus), focal depth, epicenter,epicentral distance.

Source mechanisms and parameters: elastic rebound mechanism, faulttype, fault geometry and motion.

Earthquake strength: Richter magnitude and moment magnitudescale, definition of seismic moment.

Measurement of ground motion caused by seismic waves:seismographs (seismometers), seismograms, first breaks.

Focal mechanism can be reconstructed from first motion data.


Seismology and Earth’s interior– Part II

Seismic waves in theEarth’s interior


Wave propagation in inhomogeneous media

Seismic body waves (P-waves and S-waves) are solutions of the elasticwave equations in homogeneous media. Solutions in generalinhomogeneous media can be obtained numerically.

Geometrical optics (ray optics) approach to seismic wave propagation

If the wavelengths λ are small compared with the inhomogeneitylength scales of the medium L∇V = V/|∇V |, we can think of theseismic wave field as a collection of rays.

Rays may be curved, and the direction of the ray is given by the(local) wave vector k = k(r).

The rays are perpendicular to the wavefronts.

Boundaries: abrupt changes in wave velocity lead to refraction andreflection, and can be addressed through Snell’s law.


Refraction and reflection, Snell’s law (1)

[(9) Brown & Musset]

Relationships between the directions of the incident and the refracted/reflected

beam (Snell’s law) can be derived from Huygens’ principle, Fermat’s principle, or

continuity requirements for plane wave parameters at the interface.


Refraction and reflection, Snell’s law (2)

α 2

α 11v

2v

incident beam

refracted beam

Snell’s law of refraction:

sinα1

V1=

sinα2

V2.

Reflection: The same relationshipholds if the beam is reflected and amode conversion takes place (e.g.,from S-wave to P-wave):

sinαi

Vi=

sinαr

Vr.

vi

α iα r

vrincident beam reflected beam


Shadow zones and the core-mantle boundary

[(10) C. Ammon/PennState]

Fundamental seismological findings:shadow zones.

P-waves cannot be observed at epicentraldistances between ∼100◦ and ∼140◦

because of refraction at the core-mantleboundary. VP in the core must be smallerthan in the mantle.

S-waves cannot be observed at epicentraldistances & 100◦ because they cannotpropagate in the liquid outer core.


Ray paths and wave travel times (1)


Layered medium: wave velocity Vchanges with depth z.

Ray parameter:

q =sinα(z)V (z)

= const .

Construct ray paths that endat epicentral distances ∆.

Travel time:

T =∫

ray

dsV

.

Travel time curve:

T = T (∆) .


Ray paths and wave travel times (2)

[(11) Stein/Wysession]

Travel time T is a unique function ofdistance ∆ only if V is increasingwith depth (dV/dz > 0).

Low velocity zones where dV/dz < 0create ambiguities in the ray pathgeometry: travel time T is no longera unique function of distance ∆.

Inversion of travel-time curves refers to the problem of reconstructing thevelocity profile V = V (z) from the observed T = T (∆).

In the language of inverse theory, the construction of T (∆) from V (z) isthe associated forward problem.


Observed travel time curves

[(12) USGS]

Travel time curves and seismogramrecordings at three different locationscan be used to locate an earthquake.

Identify the onsets of S-wavesand P-waves in the seismogramsand find the time difference.

Use the travel time curves todetermine the distance.

Draw circles around your seismicstations and get the earthquakesource location (epicenter) astheir intersection point.


Seismic phases


Nomenclature

P,S: direct waves.

PP, PS, SS: reflectionat the Earth’s surface.

PKP, PKS: mantle →(outer) core → mantle.

PcP, PcS: reflection atthe core-mantleboundary (CMB).

PKIKP, PKJKP:mantle → outer core→ inner core → outercore → mantle.


Inversion of travel-time curves (1)

The Wiechert-Herglotz-Bateman procedure is one method to reconstruct thevelocity profile V (r) from the travel time curve T (∆). Here we work in sphericalgeometry, and r is the radial distance from the Earth’s center.

The ray parameter for spherically stratified media is given by

p =r sinα(r)V (r)

= const =r0

V0

where r0 and V0 are the distance and the velocity at the apex of the path.

Differentiate the travel time curve to get the ray parameter:

p =dTd∆

.

This means that the ratio r0/V0 can be directly determined from the data.

The radial distance r0 can be found through an integral transform:

r0(∆) = RE exp

[− 1π

∫ ∆

0

arcosh

(p(∆′)p(∆)

)d∆′

].


Inversion of travel-time curves (2)

v(r)

r

(v( ),r ( ))∆ ∆0 0

Now that r0(∆) and p(∆) areknown, compute the velocity at theapex V0 = V (r0) = r0(∆)/p(∆).

Draw pairs of values (r0, V0) into adiagram to obtain the velocity profilewith radial distance.

Other inversion methods exist, see e.g. the textbook of Bullen and Bolt.

Seismic tomography of the Earth’s interior: fully three-dimensionalinversion of seismological observations.


[(10) C. Ammon/PennState]

Velocity profiles according to PREM(Preliminary Reference Earth Model)

Sharp changes at the surface, thecore-mantle boundary, and betweenthe inner and outer core: differentchemical compositions and phasechanges.

Gradual changes throughout the innercore, the outer core, and the lowermantle: compression of material dueto pressure increase.

Upper mantle and transition zone:changes in mineralogy – magnesiumsilicates (Mg Si O3) in different phases(olivine, spinel, perovskite, . . . ).

How is the density profile %(r) obtained ?


Seismic tomography (1)

[(12) Su et al., JGR 1994]


Seismic tomography (2)

[(12) Su et al., JGR 1994]


Part II : Seismic waves in the Earth’s interior – Summary

The ray approximation allows to study seismic wave propagation in theinhomogeneous interior of the Earth.

Rays are smoothly curved where the wavelengths are small comparedto the inhomogeneity length scale.

Directional changes at sharp boundaries are described by Snell’s law.

Travel-time curves give the propagation time T as a function ofepicentral distance ∆.

Inversion of travel-time curves is the procedure that reconstructs thewave velocity profiles VP (r) and VS(r) from the observed T (∆).

The wave velocity profiles reveal the shell structure of the Earth’sinterior: inner core, outer core, lower mantle, upper mantle, andcrust. Upper mantle variations are due to changes in mineralogy.

Seismic tomography shows lateral variations in the Earth’s interior.


Seismology and Earth’s interior– Part III

ModelingEarth’s internal structure


Free oscillations of the solid Earth


Large earthquakes excite freeoscillations (eigen-oscillations)of the whole Earth.

Two types:

spheroidal oscillations

nSm` , and

torsional oscillations nTm` .

Spectrum of observed freeoscillation frequencies allowsto constrain Earth models.


Observed Earth’s free oscillation spectrum



Integral density constraints

Total mass M and moment of inertia I of a spherically symmetric planet:

M = 4π∫ R

0%(r) r2dr ,

I =8π3

∫ R

0%(r) r4dr .

Moment of inertia ratio: I/MR2.

Mass M is derived from gravity measurements.

Moment of inertia can be determined from observations of the Earth’snon-ideal rotation (precession).

Model density profiles % = %(r) must be consistent with the observedvalues M = 5.97 · 1024 kg and I/MR2 = 0.331.


Adams-Williamson procedure

The Adams-Williamson procedure models the radial distribution of themass density %(r) on the basis of the observed wave velocity profiles VP (r)and VS(r). Assumptions:

hydrostatic equilibrium,

state variables (p and %) change adiabatically with depth,

density variations only through compression (no changes in chemicalcomposition or phase).

Numerical integration of the system of equations:

d%dr

= −GMr2

%

V 2P − (4/3)V 2

S

,

dMdr

= 4π%r2 .


Derivation of the Adams-Williamson equation

Adiabatic variations of pressure, mass density, and volume are related through

dp = −K dVV

= Kd%%

=(V 2

P −43V 2

S

)d%

where K is the bulk modulus, and VP , VS are the seismic velocities.

Combine with the hydrostatic equilibrium condition dp = −g % dr to yield

d% =dp

V 2P − (4/3)V 2

S

= − g %

V 2P − (4/3)V 2

S

dr .

For a spherically symmetric mass distribution, the gravity can be written as

g = g(r) =GM(r)r2

=4πGr2

∫ r

0

%(r′) r′2 dr′

where G denotes the gravitational constant.

We finally obtain the Adams-Williamson equation

d%dr

= −4πGr2

%(r)V 2

P − (4/3)V 2S

∫ r

0

%(r′)r′2dr′ .


Profiles of density, pressure, and gravity


Density:

4–5 g/cm3 in the mantle,

10–13 g/cm3 in the core.

Gravity:

∼10 m/s2 throughout themantle,

linear decrease in the core.

Pressure:

smooth profile at the CMB,

∼4 Mbar in the center.


Part III : Modeling Earth’s internal structure – Summary

Travel-time seismology yields the radial velocity profiles of the two types ofseismic body waves. Since VP and VS depend on three materialparameters (bulk modulus, shear modulus, and density), furtherinformation is necessary to model the Earth’s interior.

Free oscillations of the whole Earth.

Integral density constraints: total mass and moment of inertia.

Adams-Williamson equation for chemically homogeneous regions.

Results are summarized in reference models, e.g., the PREM.

Gravity g ∼ 10 m/s2 throughout the mantle.

Values in the central core: % ∼ 13 g/cm3, P ∼ 4 Mbar.


Figure references

(1) The sketch and the photograph were taken from the web sitehttp://earthquake.usgs.gov/regional/nca/1906/18april/reid.php maintained bythe US Geological Survey (USGS). The photograph is from the Steinbrugge Collection ofthe UC Berkeley Earthquake Engineering Research Center (26 July 2007).

(2) Fault motion animation web page maintained by IRIS (Incorporated Research Institutionsin Seismology) http://www.iris.edu/gifs/animations/faults.htm (26 July 2007).

(3) Image credit: http://www.staff.amu.edu.pl/~zbzw/glob/glob34f.htm, The GreatGlobe Gallery (26 July 2007).

(4) Image file seismogenic.gif from the USGS Visual Glossary (3 March 2009), seehttp://earthquake.usgs.gov/learning/glossary/images/seismogenic.gif .

(5) Image seismograph.gif from Earth Science Australia (3 March 2009) athttp://earthsci.org/education/teacher/basicgeol/earthq/seismograph.gif .

(6) Sample seismogram taken from the public outreach web page ’Teleseisms’ of the USGeological Survey USGS (26 July 2007), seehttp://quake.usgs.gov/recent/helicorders/Examples/teleseism.html

(7) Image files Focal mechanism 01.jpg, Focal mechanism 02.jpg, andFocal mechanism 03.jpg from Wikipedia Commons: http://en.wikipedia.org/

(3 March 2009).

(8) Image file beachball.gif the web site of the US Geological Survey (USGS) athttp://quake.usgs.gov/recenteqs/beachball.html (3 March 2009).


Figure references (continued)

(9) Figures from the textbook The Inaccessible Earth by G.C. Brown and A.E. Musset (Allen& Unwin, 1981).

(10) Figure files p rays.gif and prem.gif from the web site of the course SLU EAS-A 193 AnIntroduction to Earthquakes & Earthquake Hazards by Charles Ammon, PennsylvaniaState University (6 March 2009). Seehttp://eqseis.geosc.psu.edu/~cammon/HTML/Classes/IntroQuakes/Notes/ .

(11) Figures from the textbook An Introduction to Seismology, Earthquakes, and EarthStructure (Blackwell Publishing) by Seth Stein and Michael Wysession. The figures areavailable in electronic format from the web pagehttp://epscx.wustl.edu/seismology/book/ (6 March 2009).

(12) Image file ttgraph.gif from the web site of the US Geological Survey (USGS) athttp://neic.usgs.gov/neis/travel times/ttgraph.html (6 March 2009).

(13) The maps show variations in seismic shear-wave speed with respect to the value of thePREM at 100 km depth and at 2,880 km depth, just above the core mantle boundaryModel S12 WM13, from W.-J. Su, R. L. Woodward and A. M. Dziewonski, Degree-12Model of Shear Velocity Heterogeneity in the Mantle, Journal of Geophysical Research,vol. 99(4) 4945-4980, 1994. The figures hrv0100km.gif and hrv2880km.gif weredownloaded from the web site of the course SLU EAS-A 193 An Introduction toEarthquakes & Earthquake Hazards by Charles Ammon, Pennsylvania State University.See http://eqseis.geosc.psu.edu/ cammon/HTML/Classes/IntroQuakes/Notes/

(6 March 2009).


Further reading

Stein, Seth, and Michael Wysession, An Introduction to Seismology,Earthquakes, and Earth Structure, Blackwell Publishing, 2003.

Bullen, K. E. und B. A. Bolt, An introduction to the theory of seismology,Cambridge University Press, 1985.

Telford, W. M., L. P. Geldart und R. E. Sheriff, Applied Geophysics,Cambridge University Press, 1990.

Brown, G. C., und A. E. Musset, The inaccessible Earth, Allen & Unwin,1981.

Fowler, C. M. R., The solid Earth, Cambridge University Press, 1990.


Seismology

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