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Modeling and Imaging Elastic Waves in Heterogeneous Media

Kuang He

Department of Physics

University of Connecticut Storrs, CT 06269

June 1, 2010

Ph.D. Defense

Acknowledgements

•Committee members: Vernon Cormier, LanboLiu, Winthrop Smith, Richard Jones, Ronald Mallett

Outline •Seismic waveform tomography

•Simulation of the effects of receiver-side heterogeneities on the wavefrontsat different angles

•Strong ground motion simulation using a hypothetical M8 earthquake in Beijing

•Texture of the uppermost inner core from seismic coda waves

Outline •Seismic waveform tomography

•Simulation of the effects of receiver-side heterogeneities on the wavefrontsat different angles

•Strong ground motion simulation using a hypothetical M8 earthquake in Beijing

•Texture of the uppermost inner core from seismic coda waves

Seismic Waveform Tomography5

Seismic tomography is an inverse problem.

Seismic travel-time tomography

Seismic tomography uses seismic waves with different ray paths to map three-dimensional velocity structure in the earth.

where

mis model parameter (velocity) |

G is forward modeling operator dis data (seismic data)

Seismic Waveform Tomography6

Why waveform tomography?

–Uses ray-tracing based forward modeling technique

(Ray-theory based wave equation solution is an approximation that becomes exact at infinite frequency)

–Tries to fit the whole waveform instead of just the travel times –Higher accuracy; better resolution

Seismic Waveform Tomography7

Acoustic waveform tomography

: pressure field : source

: frequency px z p xz px z s xz xz x xz x z xz z p s

(i.e., the difference between the o |

: vector of residuals bserved data and synthetic data)

: weighting operator

Cm d W d d W

(Operto, 2006)

Seismic Waveform Tomography8

•Model updating using the steepest-descent method: •Stop the iterations when:

Acoustic waveform tomography (cont’d) *

: gradient of the object function

:step length controlling the amplitude of the perturbations : Jacobian matrix

:data residuals

(A depends on the frequency and t md m m mC J W d

J d

A JA p properties of the medium)

Seismic Waveform Tomography9

Multi-scale waveform tomography

Each frequency has a limited, finite-band contribution to the wavenumber spectrum of the gradient image.

(Sirgue and Pratt, 2004)

Seismic Waveform Tomography10

The Foothill model

(The velocities in this model range from 3600 m/sto 5700 m/s.)

True ModelInitial Model

Model size: 25 km x 6 km (832 x 200 grids)

Gray and Marfurt(1995)

Seismic Waveform Tomography11

Waveform tomography results

Waveform inversion results from after accumulating contributions from progressively higher frequencies.

Seismic Waveform Tomography12

Conclusions

•Waveform tomography is an imaging technique that tries to minimize the difference between the observed data and the synthetic data by fitting the whole waveform.

•Higher accuracy and resolution; more computationally intensive.

•Result very sensitive to the initial model; therefore challenging to apply this technique to field data.

Outline •Seismic waveform tomography

•Simulation of the effects of receiver-side heterogeneities on the wavefrontsat different angles

•Strong ground motion simulation using a hypothetical M8 earthquake in Beijing

•Texture of the uppermost inner core from seismic coda waves

Wave-Equation Redatuming 14

The Berryhill example

Horizont al Grid Number

(a) Berryhill Model

(b) Original Recor d

Tr ace Num be r

(c) w/ Dow nw ard Cont inu.

Trace Nu mber

(d) w/ Down/ upw ard Cont inu.

Trace Nu mber (Berryhill, 1979)

Wave-Equation Redatuming 15

The XiangyinTunnel GPR study co ncr etetunnel floor

(b ) (c)

Wave-Equation Redatuming 16

Conclusions

•GPR is a non-destructive testing technique widely used at public transportation infrastructure construction and maintenance sites in urban environments for quality control purposes.

•Application of wave-equation redatumingthrough downward and upward continuation to a public transportation engineering project has been demonstrated.

•This approach is an effective and economical way to suppress and eliminate the strong reflections and diffractions from rebarsin the surface concrete.

Outline •Seismic waveform tomography

•Simulation of the effects of receiver-side heterogeneities on the wavefrontsat different angles

•Strong ground motion simulation using a hypothetical M8 earthquake in Beijing

•Texture of the uppermost inner core from seismic coda waves

Receiver-Side Heterogeneities 18

PKiKP and PcP ray paths and seismograms

20great circle distance PKiKP/PcP amplitude ratio density jump at the ICB

(Tkalcicet al., 2010)

Receiver-Side Heterogeneities 19 Anti-correlation of PKiKP and PcP observations

Receiver-Side Heterogeneities 20

M=5.9 explosion located at the Lop Nor test site and dated 10/07/1994.

(Tkalcicet al., 2010)

Receiver-Side Heterogeneities 21

(a)Heterogeneity with isotropic 2 km scale length

(b)Horizontally stretched heterogeneity (c)Vertically stretched heterogeneity

Different receiver-side heterogeneity models

Receiver-Side Heterogeneities 2 Receiver-Side Heterogeneities 2

Receiver-Side Heterogeneities 23 Receiver-Side Heterogeneities 23

Receiver-Side Heterogeneities 24 Receiver-Side Heterogeneities 24

Receiver-Side Heterogeneities 25

Conclusions

•Strong negative correlation is observed in the detection of PcP and PKiKP waves from both an earthquake event and an explosion event.

•2-D pseudospectral modeling indicates that volumetric heterogeneity in the crust and upper mantle on the receiver (or source) side can have big effects on the wave amplitudes.

Outline •Seismic waveform tomography

•Simulation of the effects of receiver-side heterogeneities on the wavefrontsat different angles

•Strong ground motion simulation using a hypothetical M8 earthquake in Beijing

•Texture of the uppermost inner core from seismic coda waves

Strong Ground Motion Simulation27

Modeled area Beijing, China

Strong Ground Motion Simulation28

Pseudospectral modeling Modeling parameters:

•Model size: 512 x 256 x 64 •dx= dy= dz= 0.18 km

Strong Ground Motion Simulation29

Rupture model

Source intensity in terms of particle velocity (m/s) of the point sources on the fault plane.

Rupture starts here!

PGV and PGA plots

Upper: Surface Peak Ground Velocity (PGV) Lower: Surface Peak Ground Acceleration (PGA)

(m/s)

Strong Ground Motion Simulation31

Horizontal versus vertical (H/V) PGV calculation

(Left)Horizontal PGV VH=sqrt(VN-S^2+V W- E ^2)

(Middle) Vertical PGV (Right)Horizontal PGV divided by vertical PGV (the H/V ratio)

Strong Ground Motion Simulation32

Conclusions

•Numerical modeling is effective in seismic hazard assessment and provides valuable information for mitigating losses for possible earthquakes in the future.

•First 3-D strong ground motion simulation for the Beijing area.

•PGV and PGA plots and H/V calculations are very useful for earthquake engineering purposes.

•Sediment layers are known to trap seismic energy, causing more damages.

Outline •Seismic waveform tomography

•Simulation of the effects of receiver-side heterogeneities on the wavefrontsat different angles

•Strong ground motion simulation using a hypothetical M8 earthquake in Beijing

•Texture of the uppermost inner core from seismic coda waves

Texture of Uppermost Inner Core34

Texture of the uppermost inner core from seismic coda waves

(Cormier, 2007)

Texture of Uppermost Inner Core35

Seismograph stations and data coverage yellow triangles: seismograph arrays from the International Monitoring System black stars: earthquake events grey lines: PKiKP ray paths red dots: the bounce points at the inner core boundary

Texture of Uppermost Inner Core36

Array data processing example

Mb =6.4 earthquake in Fiji Islands dated 12/18/2000, epicenter depth = 600 km, PKiKP turning point at (2.12N, 169.30W).

(Filtered around 2Hz)

Texture of Uppermost Inner Core37

Array data processing (cont’d)

Illustration of the Multiple Signal Classification (MUSIC) Estimator in the APT software package.

Texture of Uppermost Inner Core38 Coda map at 1Hz

Texture of Uppermost Inner Core39 Coda map at 2Hz

Texture of Uppermost Inner Core40 Coda map at 3Hz

Texture of Uppermost Inner Core41 Coda map at 4Hz

Texture of Uppermost Inner Core42 Coda map at 5Hz

Texture of Uppermost Inner Core43

Radiative transfer theory (RTT)

•Was introduced in astrophysics to describe energy transport of light through the atmosphere. (Chandrasekhar, 1960)

•Wu (1985), Gusev& Abubakirov(1987) and Hoshiba (1991) introduced the RTT into seismology to explain the generation of seismic coda waves.

•RTT describes energy transportthrough a random heterogeneous mediumneglecting phase information and has been frequently used to simulate observed envelopes of high-frequency waves.

Texture of Uppermost Inner Core44

Radiative transfer equations in 3-D

P p p

SP P sp ps sS s s

PS ps sp

Ix kt kg radI xkt gk k I xk t dk g I xkt g k I xk t dk g I xkt Q xkt

Ix kt kg radI xkt gk k I xkt dk g I xkt gk k I xkt dk g I xk

(Przybillaand Korn, 2008)

Texture of Uppermost Inner Core45

Schematic illustration of the Monte Carlo simulation

Texture of Uppermost Inner Core46

Random medium

(Fehler, 2000)

Texture of Uppermost Inner Core47

Monte-Carlo simulation results: with and without inner core scattering

Texture of Uppermost Inner Core48

Monte-Carlo simulation results: scattering layers of different thickness

PKiKP coda waves synthesized using with volumetric heterogeneity in the uppermost 100 km (red)vs. 300 km (black)of the inner core.

Texture of Uppermost Inner Core49

Monte-Carlo simulation results: different scale lengths

(red)1 km isotropic scale length (black)5 km isotropic scale length (green)10 km isotropic scale length

Strongest back scattering:

Texture of Uppermost Inner Core50

Monte-Carlo simulation results: different intrinsic Q values

(black)intrinsic Qic= 360 (red)intrinsic Qic= 100