High-F Project Plan

High Frequency Deterministic Ground Motion Simulation (High-F)

Project Planning Document

Contributors to Project Plan:* Jacobo Bielak, Yifeng Cui, Steven Day, Robert Graves, Thomas Jordan, Philip Maechling, Kim

Olsen, Ricardo Taborda

Document Revision Date: September 5, 2012

* In alphabetical order.

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1 Executive Summary:

The SCEC High Frequency (or “High-F”) project will integrate various scientific modeling and

simulation efforts within the Southern California Earthquake Center (SCEC) with the objective

of reproducing earthquake physics and effects at high frequencies (up to 10 Hz) using

deterministic modeling approaches. The High-F project will use current forward wave-

propagation simulation capabilities as a point of departure for improving current simulation

methods and developing new modeling approaches in order to better reproduce the ground

response at higher frequencies. The High-F project will incorporate high-frequency

characteristics in the source representation and the structural heterogeneity of the seismic

velocity models by considering aspects such as geometrical complexity of the faults, the random

distributions of slip, rupture velocity, and rise time, and the stochastic characteristics of the

material properties of near-surface layers. One, or more, historic earthquakes in Southern

California will be selected as target events, and the results of high-frequency ground motion

simulations will be compared with observed data from these earthquakes. The High-F project

will help to define a reference framework for the evaluation of alternative simulation methods,

such as the stochastic simulation methods developed within the SCEC Broadband Platform, and

will seek to identify the threshold frequency at which deterministic and stochastic methods

provide a viable tradeoff for hybrid approaches.

2 Background and Motivation:

Previous ground motion modeling efforts within SCEC, including the TeraShake (Olsen et al.,

2006), the ShakeOut (Graves et al., 2008; Olsen et al., 2009; Bielak et al., 2010), and the M8

(Cui et al., 2011) scenario-earthquake simulations have made us confident about the progress

trend and potential of SCEC’s computational tools to produce physics-based ground motion

synthetics of realistic value to seismologists and engineers.

These SCEC simulations, however, were predominantly limited to low maximum frequencies

(less than or equal to 1 Hz), and relatively high values of minimum shear wave velocity (greater

than or equal to 500 m/s). Recent efforts by SCEC scientists have shown that it is now feasible

to produce forward wave propagation simulations at a scale of refinement not thought possible

before. Mayhew and Olsen (2010), for instance, produced a series of simulations of the Mw 5.4

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2008 Chino Hills, California, earthquake up to 1.6 Hz, which were later continued by Withers et

al. (2010) and used for evaluating the accuracy of the velocity models CVM-S and CVM-H at

frequencies up to 2 Hz. This work was extended by Taborda and Bielak (2012), who produced a

simulation of the same event over a simulation domain of 180 km x 135 km x 62 km (Figure 1)

for a maximum frequency, f_max = 4 Hz and a minimum shear wave velocity, Vs_min = 200

m/s. Using a finite element (FE) application, they reproduced 100 s of the ground motion, and

achieved reasonable levels of agreement when comparing the synthetics with data in over 300

strong-motion stations (Figures 2 and 3).

The quality of these validation ground motion simulations, however realistic, tends to deviate

from observations as the frequency increases, especially above 1 and 2 Hz (Figure 4). A detailed

analysis of the possible causes for these discrepancies at higher frequencies indicate that they are

related to our limited description of the source and material models, which lack the level of

resolution carried by the simulation. Taborda and Bielak observed that there remain of a small

number of locations where the match between synthetics and data is still satisfactory, even at

frequencies between 2 and 4 Hz. These observations suggest that, if provided with better models,

current simulation tools will be able to reproduce earthquake effects at even higher frequencies.

2.1 Scientific Challenges

Accomplishing realistic 10-Hz simulations, as well as satisfactory goodness-of-fit values at a

larger number of stations for 4-5 Hz simulations, will require addressing several scientific

challenges, some of which are currently being addressed by different research groups within

SCEC. In order for the High-F project to make significant advances, SCEC researchers will

need to improve modeling capabilities in the following areas.

2.1.1 Source Models

High-frequency simulations will require new source models capable of reproducing high-

resolution realistic rupture processes on the fault. This entails addressing aspects such as the

roughness in the fault due to geometrical point-by-point variations in strike, dip and rake angles,

and the spatial heterogeneity in the distributions of slip, rupture velocity, and rise time. There

are several ongoing efforts within SCEC to tackle this problem. For example, the hybrid method

used by Graves and Pitarka (2010) combines a low-wavenumber deterministic kinematic

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description of the source with a high-wavenumber stochastic component to account for the

randomness in the rupture characteristics (Figure 5). While this method has not been studied

extensively for source signals above >~1Hz, we will examine whether realistic source

characteristics may be generated at higher frequencies as well. Another method to be evaluated

for creating high frequency source descriptions is based on fully deterministic methods such as

those being pursued by Eric Dunham’s research group at Stanford University, Steve Day’s group

at SDSU, and Ralph Archuleta’s group at UCSB. These groups are using dynamic rupture

simulations to investigate the idea that high-frequency waves are generated by irregular rupture

propagation due to the geometrical complexity of the faults. According to this, slip on non-planar

faults generates huge stress perturbations that can either accelerate or decelerate the rupture as it

propagates. This process releases bursts of seismic waves with wavelengths comparable to the

size of the non-planar features—which will, in turn, generate high-frequency waves (Figure 6).

2.1.2 Velocity and Attenuation Models

Although we have local measures of fine-scale velocity structure (down to meter scales) at

boreholes, there is no sufficient density of such samples to facilitate the development of a

deterministic regional model at the resolution levels required for high-frequency simulations

(Figure 7), which are usually based on standard velocity models such as CVM-S or CVM-H. In

order to better resolve near-surface small-scale amplification effects—typical of soft-soil

deposits in sedimentary basins, we need to incorporate this spatial heterogeneity into such

velocity modelsIn recent studies, researchers have introduced random spatially-correlated

perturbations into velocity models artificially and analyzed their effects in regional-scale

simulations (Hartzell et al., 2010; Olsen and Jacobsen, 2011). These studies have shown that

material fine-scale heterogeneities may have a significant effect on the ground motion, even at

low frequencies < 1–2 Hz (Figure 8). SCEC researchers are currently pursuing other alternatives

to incorporate fine-scale variations into material models based on statistical characteristics

observed in the raw data extracted from well logs in combination with stochastic realizations of

velocity perturbations (Figure 9). The High-F project will provide an opportunity to test the

effects of these perturbations at the realistic fine-scale for which they are intended.

In addition, there are indications that ground motion simulations at the high frequencies

contemplated here will depend much more strongly on the attenuation structure of the medium

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than previous, low-frequency, simulations. Researchers are using the ambient seismic field--

seismic waves present in the Earth at all times--to estimate the anelastic structure at regional

scales (Prieto et al 2009). In past simulations, SCEC researchers have used different

(viscoelastic) models to represent the internal friction of the material (e.g., Day, 1998; Graves

and Day, 2003; Bielak et al., 2011). These models are typically expressed in terms of the inverse

quality factor, Q-1, defined at a certain reference frequency, fo. Q-1 is understood to be constant

up to a certain upper threshold frequency, fmax (e.g., Aki and Richards, 1980), above which Q-1

may decrease with frequency (Aki 1980). In turn, the value of Q-1 at fo has been usually

expressed in terms of Vs and Vp values using empirical rules (e.g., Olsen et al., 2003; Brocher,

2008). The attenuation structure of the upper crust, however, is highly heterogeneous and poorly

known. The High-F project will investigate these issues and improve existing or propose new

attenuation models, independently or in association with the seismic velocity models (CVMs).

The project will also serve as a test-bed for other ongoing efforts such as comparative

evaluations of the CVM-S and CVM-H models, the Unified Community Velocity Model

(UCVM), and the results of full 3D tomography studies in the region (Chen, 2012).

2.1.3 Wave Propagation

Producing realistic seismograms at high frequencies will require improvements in our anelastic

wave-propagation simulation engines. Beyond the computational challenges in terms of cycles

efficiency and memory management—which have, for the most part, been resolved—some

algorithms will need to be revised to account for new developments and frequency dependent

parameters. In particular, more realistic source models may not come in the form of a collection

of in-plane double-couple forces (as typically extracted from standard rupture formats), but as a

collection of general moment tensors. This will require modifications to interpret kinematic

representations of the source models correctly. As just discussed above, new and improved

intrinsic attenuation models will be required to account for the frequency dependency of Q-1—

especially at the higher frequencies. Therefore, new solution schemes will need to be developed

and tested.

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2.2 Objectives

The High-F project objectives express scientific and technical goals and milestone selected to

help define the scope of the High-F project. Each objective should define distinct scientific or

computational progress.

1. Produce realistic high-frequency simulations (up to 10 Hz) that are comparable, through

qualitative and quantitative validation tests, to observations from historical earthquakes in

Southern California, using the physics-based, deterministic modeling and simulation tools.

2. Incorporate the spatial variability and heterogeneity of the fault geometry and the rupture

dynamics into kinematic or pseudo-dynamic source models that can be used in regional

earthquake simulations.

3. Incorporate the fine-scale material heterogeneities that are characteristic of soft-soil

structures in sedimentary basins and near-surface deposits into the regional velocity models

used for large-scale earthquake simulations.

4. Use appropriate goodness-of-fit metrics to investigate the consistency of deterministic and

stochastic simulations in the band 1-10 Hz and their ability to reproduce observed

seismograms for well-characterized historical earthquakes.

5. Improve SCEC’s framework for a physics-based approach to seismic hazard analysis by

advancing theoretical methods and computational applications intended to reproduce

earthquake effects at the high fidelity required for engineering applications.

6. Engage SCEC in a multi-scale interdisciplinary effort to analyze and compare simulation

results and data

7. Improve and develop the analytical methods and computational modeling tools used in

earthquake system science.

2.3 Computational Tools and Resources

Recent simulations (Taborda and Bielak, 2012; Isbiliroglu et al., 2012; Cui et al., 2010) have

shown that, codes such as Hercules and AWP-ODC have the capability to simulate earthquakes

at maximum frequencies equal to 4 and 5 Hz, using only a fraction of the resources available in

supercomputing facilities today (Table 1). Estimates based on these results indicate that higher

frequency simulations (up to 10 Hz) are possible in the near future (see Table 2 for performance

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estimates for Hercules; equi-spaced grid approaches such as AWP-ODC require additional

resources dependent on the scenario parameters). AWP-ODC and AWP-Graves are already

being used by a number of researchers in the SCEC community. CMU’s Quake Group has

started the process of producing and releasing a version of Hercules as a SCEC community code.

Several alternative high-frequency wave propagation codes are needed for the verification and

validation efforts necessary to support the proposed activities—especially for evaluating the new

source, velocity, and attenuation models at high frequencies but smaller physical scales. We also

intend to be able to support code improvement in order to reach the performance objectives of

the High-F project.

Table 3 shows a preliminary estimate of the computational resources needed over the lifetime of

the project based on the performance of Hercules.

The efforts directed to improve velocity models will be oriented to build upon and contribute to

the development of the UCVM platform (Small et al., 2011). And the efforts directed to the

development of source models that are high-frequency compatible will be oriented to operate

along the standards set by the SCEC-USGS Dynamic Rupture Code Verification Group (Harris

et al., 2011).

2.4 Project Plan

We envision the High-F project being developed over a period of 3-to-4 years and divided into

the following phases.

2.4.1 Phase I: High-F Spark (year 1)

• Target southern California historical events will be selected. Desired characteristics of the

selected events include: (i) magnitude larger than 6, and (ii) availability of a good number

(>100) of records within a 50 km range of the epicenter, in both rock and soil sites. Smaller

events may be considered for specific tasks, such as the CVM improvement efforts (see

2.4.2).

• A simulation domain will be defined that is appropriate for the selected target event. High-

resolution discrete representations (in formats used by the SCEC rupture and wave

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propagation codes) of the available velocity models valid for simulations up to 5 Hz and

down to 200 m/s will be constructed.

• 5-Hz deterministic simulations of the target event will be run using selected source and

seismic velocity models. These initial simulations are intended to show that forward

simulation capabilities at 5Hz and low minimum Vs are already possible.

2.4.2 Phase II: High-F Improvement Challenges (year 1 and 2)

• High-F Source Improvement Challenge. High-F researchers will run simulations of the

target event using currently available source representations at frequencies up to 5 Hz. Then,

researchers working on earthquake simulators and rupture dynamics will be asked to

develop improved source descriptions that will improve the fit to data. Researchers will then

run simulations of the target event(s) at 5Hz using the updated source descriptions to show

the impact of the source improvements on ground motion results.

• High-F Velocity Models Improvement Challenge. High-F researchers will run simulations

of the target event(s) using currently available velocity models at frequencies up to 5 Hz.

Then, researchers will be asked to develop improved current community velocity models at

the structural level (by direct upgrades or through tomography updates) and/or to include

(stochastic) representations of the near-surface layers that will yield better results in

simulations up to 5 Hz. Better attenuation models will also be solicited. Once improved

velocity model representations have been developed, High-F researchers will upgrade the

simulations of the target event(s) at 5Hz using the refined velocity models to show the

impact the velocity model modifications had on the ground motion results.

• High-F Wave Propagation Improvement Challenge. High-F researchers will run simulations

of the target event using currently available deterministic wave propagation codes at

frequencies up to 5 Hz. Then, researchers will be asked to develop improved anelastic wave

propagation alternatives that will yield better results in simulations up to 5 Hz. Alternatives

to include off-fault plasticity effects will be solicited. Measurements such as time to

solution, SU usage, and peak performance will be collected. Then, the simulation groups

will advance numerical models and computational methods for improving the physics of

simulations and the computational scalability, performance, and efficiency of codes. Once

improved wave propagation software implementations have been developed, High-F

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researchers will then run simulations of the target event(s) at 5Hz to show the capabilities of

the improved wave propagation software.

2.4.3 Phase III: High-F Validation (years 2 and 3)

• High-F research groups will implement the new developments in the simulation engine(s)

and further test our improved simulation capabilities at 5 and 10 Hz.

• High-F researchers will construct updated high-resolution discrete representation of the

available velocity models valid for simulations up to 10 Hz and down to 200 m/s.

• High-F researchers will compile simulations sets using the different alternatives developed

during Phase II. Each viable variation of the rupture process, velocity models, or wave

propagation methods will be validated with data using quantitative measures (GOF). At this

phase, simulations and validations will be performed for a maximum frequency equal to 5

Hz.

2.4.4 Phase IV: High-F Integration (year 4)

• High-F simulation groups capable of 10-Hz simulations will integrate appropriate improved

source representations, anelastic models, and wave propagation methods to run 10-Hz

deterministic simulations for selected validation events.

• High-F researchers will run simulations of the target event(s) using selected models and

alternatives at a maximum frequency of 10 Hz.

• High-F researchers will compare and analyze simulation results using observational data and

stochastic methods.

2.4.5 Phase V: High-F Beyond (if possible)

• High-F researchers will use the newly developed simulation knowledge and tools to produce

a suite of scenario-earthquake simulations at a maximum frequency equal to 10 Hz.

2.5 Contribution to SCEC4 Goals

The High-F project will directly address several of SCEC4 science plan objectives in the

fundamental problems of earthquake physics and the interdisciplinary research initiatives. In

particular, the High-F project will be driven by the objectives laid out for the problem of seismic

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wave generation and scattering: prediction of strong ground motions (section 3.B.1.f. in SCEC4

proposal), its priorities and requirements. It will also address one of the system science

challenges described in the SCEC4 proposal, that is, to predict ground motions and their effects

by simulating earthquakes with realistic source characteristics and three-dimensional

representations of geologic structures, and will combine the efforts of disciplinary groups

(computational science), interdisciplinary focus groups (fault and rupture mechanics), special

projects (CME), and technical activity groups (rupture dynamics, ground motion simulation and

validation).

2.6 Project Support and Funding

We plan to support the initial activities of the High-F project—especially those oriented to the

continued development of existing computational tools—through NSF award SI2-SSI: A

Sustainable Community Software Framework for Petascale Earthquake Modeling (2012–2015;

PI: T.H. Jordan, Co-PIs: J. Bielak, Y. Cui, K.B. Olsen), and with the general support of the

SCEC research program, which is funded by NSF Cooperative Agreement EAR-0106924 and

USGS Cooperative Agreement 02HQAG0008. Access to supercomputing centers and resources

will be supported through SCEC/CME allocations at XSEDE and INCITE.

We expect researchers participating in the High-F project to coordinate task groups around the

different scientific challenges to request additional support from funding agencies over the

following phases of the project.

2.7 References

Aki, K. (1980). Attenuation of shear-waves in the lithosphere for frequencies from 0.05 to 25 Hz, Phys. Earth Planet. Int., 21, 50-60.

Aki, K. and Richards, P. G. (1980). Quantitative Seismology: Theory and Methods. W.H. Freeman & Company, New York, NY.

Anderson, J. G. (2004). Quantitative measure of the goodness-of-fit of synthetic seismograms. In Canadian Association for Earthquake Engineering, editor, Proceedings of the 13th World Conference on Earthquake Engineering, Vancouver, British Columbia, Canada. International Association for Earthquake Engineering. Paper 243.

Bielak, J., Graves, R. W., Olsen, K. B., Taborda, R., Ramirez-Guzman, L., Day, S. M., Ely, G. P., Roten, D., Jordan, T. H., Maechling, P. J., Urbanic, J., Cui, Y., and Juve, G. (2010). The

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ShakeOut earthquake scenario: Verification of three simulation sets. Geophys. J. Int., 180(1):375–404.

Bielak, J., Karaoglu, H. and Taborda, R. (2011). Memory-efficient displacement-based internal friction for wave propagation simulation. Geophysics, 76(6):T131.

Brocher, T. M. (2008). Compressional and shear-wave velocity versus depth relations for common rock types in northern California. Bull. Seism. Soc. Am., 98(2):950–968.

Chen, P. (2011). Full-3D waveform tomography for Northern and Southern California. SCEC CVM Meeting, April 3, Los Angeles, California.

Cui, Y., Olsen, K., Jordan, T., Lee, K., Zhou, J., Small, P., Roten, D., Ely, G., Panda, D., Chourasia, A., Levesque, J., Day, S., and Maechling, P. (2010). Scalable earthquake simulation on petascale supercomputers. In SC’10: Proceedings of the 2010 ACM/IEEE International Conference for High Performance Computing, Networking, Storage and Analysis, pages 1–20.

Day, S. M. (1998). Efficient simulation of constant Q using coarse-grained memory variables. Bull. Seism. Soc. Am., 88(4):1051–1062.

Graves, R., B. Aagaard, K. Hudnut, L. Star, J. Stewart and T. H. Jordan (2008). Broadband simulations for Mw 7.8 southern San Andreas earthquakes: Ground motion sensitivity to rupture speed, Geophys. Res. Lett., 35, L22302, doi: 10.1029/2008GL035750.

Graves, R. and Day, S. M. (2003). Stability and accuracy analysis of coarse-grain viscoelastic simulations. Bull. Seism. Soc. Am., 93(1):283–300.

Graves, R. W. and Pitarka, A. (2010). Broadband ground-motion simulation using a hybrid approach. Bulletin of the Seismological Society of America, 100(5A):2095–2123.

Harris, R.A., Barall, M., Archuleta, R., Aagaard, B., Ampuero, J.P., Andrews, D.J., Cruz-Atienza, V., Dalguer, L., Day, S., DeDontney, N., Duan, B., Dunham, E., Gabriel, A.A., Galvez, P., Kaneko, Y., Kase, Y., Kozdon, J., Lapusta, N., Ma, S., Mai, P.M., Noda, H., Oglesby, D., Olsen, K., and Somala, S. (2011). The SCEC-USGS Dynamic Earthquake Rupture Code Verification Exercise. SCEC Annual Meeting, Palm Springs, California, September 2011.

Hartzell, S., Harmsen, S. and Frankel A. (2010). Effects of 3D random correlated velocity perturbations on predicted ground motions. Bulletin of the Seismological Society of America, 100(4):1415–1426.

Isbiliroglu Y., Taborda R. and Bielak J. (2012). Dynamic response and ground-motion effects of building clusters during large magnitude earthquakes. Proceedings of the 2012 SSA Annual Meeting, San Diego, CA, USA, April 17–19.

Jordan, T.H., Shaw, J.H. and Plesch, J. (2012). Stochastic descriptions of basin velocity structure from analyses of sonic logs and the SCEC Community Velocity Model (CVM-H). 2012 SCEC Proposal (funded).

Mayhew, J. and Olsen, K.B. (2010). Goodness-of-fit criteria for broadband synthetic seismograms, with application to the 2008 Mw 5.4 Chino Hills, California, earthquake. Seismological Research Letters, 81(5):715–723, doi:10.1785/gssrl.81.5.715.

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Olsen (2012). Development and validation of stochastic representation of small-scale velocity and attenuation structure in SCEC CVMs. 2012 SCEC Proposal (funded).

Olsen, K. B., Day, S. M., and Bradley, C. R. (2003). Estimation of Q for long-period (> 2 sec) waves in the Los Angeles basins. Bull. Seism. Soc. Am., 93(2):627–638.

Olsen, K.B., S.M. Day, L.A. Dalguer, J. Mayhew, Y. Cui, J. Zhu, V.M. Cruz-Atienza, D. Roten, P. Maechling, T.H. Jordan, D. Okaya & and A. Chourasia (2009), ShakeOut-D: Ground motion estimates using an ensemble of large earthquakes on the southern San Andreas fault with spontaneous rupture propagation, Geophys. Res. Lett., 36, L04303, doi:10.1029/2008GL036832.

Olsen, K. B. and Jacobsen, B. H. (2011). Spatial variability of ground motion amplification from low-velocity sediments including fractal inhomogeneities with special reference to the Southern California basins, SCEC Annual Meeting, Palm Springs, CA.

Prieto, G. A., J. F. Lawrence, and G. C. Beroza, Anelastic Earth structure from the coherency of the Ambient seismic field, J. Geophys. Res., 114, B07202, doi:10.1029/2008JB006067

Small, P., Maechling, P., Jordan, T., Ely, G. and Taborda, R. (2011). SCEC UCVM — Unified California velocity model. SCEC Annual Meeting, Palm Springs, California, September 2011.

Taborda and Bielak (2012). Ground-motion simulation and validation of the 2008 Chino Hills, California, earthquake. Bulletin of the Seismological Society of America, In review.

Withers, K., Olsen, K.B., Small, P. and Maechling, P. (2010). On the accuracy of CVM4 and CVMH-6.2. SCEC Annual Meeting, Palm Springs, California, September, 2010.

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3 Tables

Table 1. Summary of the computational performance of Hercules measured during two simulations at maximum frequencies equal to 4 and 5 Hz for the 2008 Chino Hills and the 1994 Northridge earthquakes (after Taborda and Bielak, 2012; and Isbiliroglu et al., 2012).

Chino Hills Northridge Max Freq. 4 Hz 5 Hz Min Vs 200 m/s 200 m/s Sim. Time 100 s 60 s Delta t 0.00075 s 0.0008 s Min Size Elem. 5.5 m 5 m Domain Size 180 x 135 x 62 km3 82 x 82 x 41 km3 Number of Elem. 4.9 billion 2.6 billion Number of Cores 24,000 18,000 Total Running Time 31 hr 7 min 15 hr 10 min Time For Meshing 760 s 334 s

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Table 2. Estimates of computational cost for 5 and 10 Hz simulations using Hercules in a generic simulation domain of about 100 km x 100 km x 50 km.

Max. Frequency 5 Hz 10 Hz Min. Vs 200 m/s 200 m/s Simulation Time 100 s 100 s Delta t 0.0008 s 0.0004 s Min. Size Elem. 5 m 2.5 m Number of Elem. 2.5 billion 20 billion CPU Hours 750,000 12,000,000 Typical Num. of Cores 25,000 200,000 Wall clock Time 30 hrs 60 hrs

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Table 3. Preliminary estimates of the computational resources needed over the lifetime of the High-F project based on the computational costs and parameters shown in Table 2.

Year Description 1 2 3 4 5 Phase Num Runs SUs/run Total SUs 5 Hz Simulations • I, II 5 800,000 4,000,000 • II, III 10 750,000 7,500,000 • II, III 20 700,000 14,000,000 10 Hz Simulations • II 2 12,000,000 24,000,000 • III 4 11,000,000 44,000,000 • IV 6 10,000,000 60,000,000 • V 8 9,000,000 72,000,000 Source Simulations • I, II • II, III • II, III • IV • V CVM Improvements • I, II • II, III • II, III • IV • V 5 Hz Etrees • I 2 16,000 32,000 • II 4 14,000 56,000 • III 8 12,000 96,000 10 Hz Etree • II 2 140,000 280,000 • II,III 4 120,000 480,000 • IV 6 100,000 600,000 • V 8 80,000 640,000 Sub-Totals • 4,032,000 • 31,836,000 • 58,576,000 • 60,600,000 • 72,640,000

Total 227,684,00

0

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4 Figures

Figure 1. Horizontal projection of the simulation domain used by Taborda and Bielak (2012) in

the 4-Hz simulation and validation of the Mw 5.4, 2008 Chino Hills earthquake.

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Figure 2. Selected comparisons between data and synthetics for the simulation of the 2008

Chino Hills earthquake (after Taborda and Bielak, 2012). Each comparison shows the EW

velocity time series on top of the amplitude of the Hilbert transform, accompanied by the Energy

time integral. The left margins indicate the station code, the distance to the epicenter, and the

goodness-of-fit score obtained using the criterion proposed by Anderson (2004).

Data Synthetics

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Figure 3. Comparisons of response spectra between data and synthetics for the simulation of the

2008 Chino Hills earthquake (after Taborda and Bielak, 2012). The left margins indicate the

station code, the distance to the epicenter, and the goodness-of-fit score obtained using the

criterion proposed by Anderson (2004).

Data Synthetics

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Figure 4. Spatial distribution of the quantitative validation of the results obtained by Taborda

and Bielak (2012) for the simulation of the 2008 Chino Hills earthquake at different frequency

bands. The color scale indicates the quality of the match between synthetics and data using the

goodness-of-fit criterion defined by Anderson (2004), where a value of 10 represents a perfect

match.

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Figure 5. Examples of slip distributions generated using the wavenumber filtering approach with

random phasing (after Graves and Pitarka, 2010). For hypothetical scenario earthquakes, one

starts with uniform slip having (a) tapered edges and then apply wavenumber filtering and

scaling such that (b) the standard deviation of the resulting slip distribution slip is 85% of the

mean. For previous earthquakes, one starts with (c) a low-pass filtered representation of the slip

distribution, and then apply the same processing as with the scenario case to obtain (d) the final

result. Mean and maximum slip values are indicated at top right of each panel. The color version

of this figure is available only in the electronic edition.

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(a)

(b)

Figure 6. (a) Ground motion from a rough fault model. The fault profile is a band-limited self-

similar fractal curve. Click on the figure to watch a movie showing how high-frequency seismic

waves are generated as the rupture accelerates and decelerates. (b) Velocity seismograms from

the station shown above.

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Figure 7. Plot of Vp for the location of the La Tijera-1 well from the CVM-H 11.9 (black). The

raw sonic log measurements (grey) and the smoothed log measurements (red) that were used to

interpolate the CFM-H model.

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Figure 8. Comparison of simulations of the 2010 El Mayor Cucapah earthquake (0–1.5 Hz) with

and without fractal perturbations (after Olsen and Jacobsen, 2011).

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Figure 9. Vertical sections through realizations of the 3D Goff-Jordan stochastic model. Left

panel shows the isotropic case (η = 1) and two levels of anisotropy (η = 5, 10) for σ = 2% and ν

= 0.8. Right panel shows three values of the self-affine scaling (ν = 0.8, 0.5, 0.2) corresponding

to fractal dimensions of 3.2, 3.5, and 3.8.