broadband waveform modeling of moderate earthquakes in the san francisco bay area and preliminary...

8/2/2019 Broadband Waveform Modeling of Moderate Earthquakes in the San Francisco Bay Area and Preliminary Assessmen

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Broadband Waveform Modeling of Moderate Earthquakes in the

San Francisco Bay Area and Preliminary Assessment

of the USGS 3D Seismic Velocity Model

by Arthur Rodgers, N. Anders Petersson, Stefan Nilsson,Bjrn Sjgreen, and Kathleen McCandless

Abstract Recently, the United States Geologic Survey Earthquake Hazards Pro-gram developed a3D seismic velocity model of Northern California based on geology,

including a detailed model of the urbanized San Francisco Bay Area. In this study, we

report comparisons of observed three-component broadband (0.030.25-Hz) wave-

forms with synthetic seismograms computed with the new 3D model using an elastic

finite difference method. We selected a set of 12 moderate earthquakes (Mw 4:05:1)

that occurred within the greater San Francisco Bay Area, having well-constrained

source parameters and broadband recordings with high signal-to-noise ratios. The ob-

jective of this study was to investigate how well the 3D velocity model predicts ob-served waveforms and to identify features of the model that may require revision to

improve the waveform fits and predictions of ground motions for future events. We

show for the 3 September 2000 Yountville earthquake that reported source parameters

accurately predict waveforms at two close strong-motion stations (approximately

10 km from the epicenter). By comparing synthetics for the average 1D model

GIL7 (Stidhamet al., 1999) and the 3D structures we show that the effects of seismic

wave propagation in the 3D model become important for frequencies at and above

0.1 Hz (periods less than 10 sec). Comparison of observed and synthetic seismograms

for the 3D model consistently shows that the model predicts energy arriving earlier

than is observed, particularly for the surface waves, indicating that the shear velocities

in the upper crust must be reduced. We cross correlated the observed and synthetic

waveforms and recorded the delay time and linear correlation for best alignment of thedata and delayed synthetic. The results indicate that generally the 3D model predicts

the observed waveforms well (mean linear correlations 0.41) and includes features

that arise from the interaction of the wave field with 3D structure, especially the major

sedimentary basins in San Pablo Bay, San Francisco Bay, Santa Clara Valley, and

Livermore Valley. Simple conversion of the observed delay times for optimal align-

ment suggests shear velocities should be reduced by 4%5% on average. Based on

these findings, we conclude that the model is an excellent first step, suggesting that the

overall structure of the model is accurate (i.e., the basin and discontinuity geometry).

However, the velocities must be reduced to improve the observed timing of surface-

wave arrivals.

Introduction

Strong ground motions are the result of the combined

effects of the earthquake source and interaction of the seis-

mic wave field with complex 3D geologic structure. An

accurate 3D seismic velocity model is required to predict

ground motion for scenario earthquakes and to account for

propagation and site effects when imaging earthquake rup-

tures from strong motion waveforms. Advances in numerical

methods and computational power are facilitating simula-

tions of large (Mw >6:0) scenario earthquakes for the pur-

poses of strong ground-motion prediction. Pioneering studies

(e.g., Vidale and Helmberger, 1988; Kawase and Aki, 1989;

Dreger and Helmberger, 1990; Scrivner and Helmberger,

1994) demonstrated that2D elastic finite difference modeling

can be used to predict ground motions in the presence of

969

Bulletin of the Seismological Society of America, Vol. 98, No. 2, pp. 969988, April 2008, doi: 10.1785/0120060407


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strong heterogeneity, including basin edge effects. Several

more recent studies reveal the power of simulations to predict

ground motions in the complex 3D structure of southern Cal-

ifornia (Olsen et al., 1995; Olsen et al., 1997; Wald and

Graves, 1998; Olsen, 2000; Komatitsch et al., 2004; Olsen

et al., 2006) and the San Francisco Bay Area (Graves, 1993;

Stidhamet al., 1999). While advances in methods and com-

putational power facilitate the simulation of ground motions,the accuracy of the resulting predictions are limited by the

accuracy of the 3D earth model and ignorance of detailed

earthquake rupture kinematics.

This study focuses on ground-motion prediction in the

San Francisco Bay Area using a new 3D earth model devel-

oped by the United States Geological Survey (USGS) Earth-

quake Hazards Program. The model (USGS, 2005; Brocher

et al., 2006; Jachens et al., 2006, hereafter referred to as the

USGS 3D model) has been used for an investigation of the

1906 San Francisco earthquake at its centenary (Aagaard,

2006; Graves, 2006; Larsen et al., 2006; Petersson et al.,

2006; Rodgers, Petersson, Nilsson, Sjgreen, and McCand-

less, 2006; Rodgers, Petersson, Nilsson, Sjgreen, McCand-less, and Tkalcic, 2006; Aagaard, Brocher, Dolenc, Dreger,

Graves, Harmsen, Hartzell, Larsen, McCandless, et al.,

2008) as well as the 1989 Loma Prieta earthquake (Aagaard,

Brocher, Dolenc, Dreger, Graves, Harmsen, Hartzell, Larsen,

Zoback, 2008). It is based on detailed geologic and geophys-

ical mapping of the region and rules for converting lithologic

properties to density, seismic compressional and shear wave

speeds and attenuation (Brocher, 2005a,b,c) and represents

an improvement in detail over a previous model reported

by Stidhamet al. (1999). We compared ground motions ob-

served from moderate earthquakes (Mw 4:05:1) to those

computed with an elastic finite difference computer code

using the 3D model. These events have well-determined lo-

cations, depths, and focal mechanisms and should be well

represented as simple point sources for the periods consid-

ered. These factors help to eliminate the variability in ground

motion due to earthquake source complexity and isolate the

effects of3D structure. We focus on modeling the frequency

band 0.030.25 Hz in order to determine if the 3D model

reproduces the main features of seismograms. While these

frequencies are lower than is typically calculated in scenario

earthquake simulations, the goal is to assess the model in

this frequency band before increasing the bandwidth and

to resolve more subtle differences possibly due to smaller

scale structure. For the highest frequencies considered (0.2

0.25 Hz), the wavelengths of surface waves within the San

Francisco Bay Area (shear velocities 13 km=sec) are about

415 km, allowing for sampling of features on the same scale

length. Results indicate that the USGS 3D model predicts

many important features of the observed broadband seismo-

grams. However, the model can be improved by reducing the

shear velocities in order to predict the observed surface-wave

arrival times. In the following sections, we describe the data,

3D model, and simulation algorithm used in the analysis, the

results are presented and summarized, and we conclude with

a discussion of the implications of this analysis for improved

modeling of ground motions in the region.

Earthquake and Waveform Data

Earthquakes in the San Francisco Bay Area are routinely

detected and located by the USGS Advanced National Seis-

mic System (ANSS). Locations are made based on traveltimes to the dense short-period ANSS network. Travel times

are modeled with regional crustal velocity models and station

corrections (see, e.g., Oppenheimeret al., 1993, although lo-

cation procedures, available data, and corrections are con-

tinually evolving). These events are also typically recorded

by additional stations operating in the region, including the

broadband instruments operated by the University of Califor-

nia Berkeley Digital Seismic Network (BDSN) and strong-

motion instruments operated by the USGS and the California

Geologic Survey California Strong Motion Instrumentation

Program (CGS-CSMIP). Moment-tensor solutions are esti-

mated by time-domain waveform and surface-wave spectral

modeling by the University of California Berkeley Seismo-logical Laboratory for events over magnitude 3.5 (Romano-

wicz, et al., 1993; Pasyanos et al., 1996).

We chose events with moderate moment magnitudes,

Mw 4:05:1, with the most reliable focal parameters esti-

mated from time-domain waveform modeling. These events

typically have good signal-to-noise ratios (SNR) on broad-

band recordings in the frequency band 0.030.25 Hz at local

to near-regional distances (0200 km). Smaller magnitude

events (including some we consider here) show poor SNR at

lower frequencies (100 km).

Figure 1 shows the region studied and includes the extent of

the computational domain and the earthquakes, stations, and

paths considered. We selected the largest events, but also

tried to achieve the most balanced geographic sampling of

the region by choosing the best-recorded events from clusters

(e.g., San Juan Bautista, Geysers). The event parameters are

listed in Table 1. Also shown in Figure 1a is the extent of the

USGS detailed Bay Area model.

We chose to model a slightly larger domain than the de-

tailed Bay Area model (see next section) in order to include

paths from events in the Geysers and paths to the broadband

station HOPS (Hopland, California). These paths sample the

northern regions of the Bay Area including the Santa Rosa,

Sonoma, and Napa Valleys. Santa Rosa experienced ex-

tremely large ground motions (modified Mercalli intensitiesof IXX) during the 1906 San Francisco earthquake (Boat-

wright and Bundock, 2005). Because details of the 1906 rup-

ture are limited by the available data, it is important to be able

to separate if this strong ground motion was due to propaga-

tion, site response, and rupture effects.

Broadband waveforms were collected from the Northern

California Earthquake Data Center (NCEDC) operated by the

University of California Berkeley Seismological Laboratory

(http://www.ncedc.org/, last accessed February 2008). Wave-

form data were converted to absolute ground displacement,

970 A. Rodgers, N. A. Petersson, S. Nilsson, B. Sjgreen, and K. McCandless


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and horizontal components were rotated to radial and trans-

verse components. The observed waveforms were modeled

using the locations and origin times reported by the USGS

and UCB. However, the source parameters (depth, seismic

moment, strike, dip, and rake) were set to the values esti-

mated by the focal mechanism procedure using time-domain

waveform modeling rather than surface-wave spectral analy-

sis (Dreger, 2003). Depths from waveform modeling were

often close (within 12 km) of the depths reported by the

USGS locations based on travel times. Waveforms were mod-

eled with the estimated double-couple focal mechanisms.

Three-Dimensional Model of theSan Francisco Bay Area

The USGS-Menlo Park recently developed and released

a3D seismic velocity model of northern California, including

a detailed model of the greater San Francisco Bay Area. Themodel will be useful for a number of future projects such as

predicting ground motion for possible scenario earthquakes

and locating earthquakes more accurately. It is based on

detailed geologic and geophysical mapping of the region

(Jachens et al., 2006) and rules for converting lithologic

Figure 1. Map of our study area showing events, stations and paths considered. (a) Events (circles), stations (triangles), and paths withdouble-couple focal mechanisms (Table 1). The extents of the USGS San Francisco Bay Area detailed model (dashed yellow line) and ourCartesian finite-difference model domain (dashed black line) are indicated. (b) Events (circles) and stations (triangles) with codes indicated.Red lines are major faults (see Fig. 2a for fault names).

Table 1Source Parameters for Events Analyzed in This Study

Event Date Time (UTC) Latitude (N) Longitude (W) Depth (km) Mw M0 (N m) Focal Mechanism (Strike/Dip/Rake)

San Jose 21 May 1996 20:50:20 37.365 121.739 14 4.8 1:69E16 320/87/154

San Juan Bautista 12 August 1998 14:10:25 36.755 121.464 8 5.1 5:32E16 136/64/177

Bolinas 18 August 1999 01:06:18 37.907 122.686 8 4.6 7:87E15 320/47/104Geysers 10 January 2000 21:41:27 38.757 122.913 5 4.3 3:80E15 3/65/155

Yountville 3 September 2000 08:36:30 38.377 122.414 11 5.0 3:74E16 60/75/18

Gilroy 14 May 2002 05:00:29 36.967 121.600 8 4.9 2:86E16 212/87/6

Dublin 2 February 2003 18:22:58 37.740 121.937 16.5 4.1 1:36E15 67/88/19

Santa Rosa 25 May 2003 07:09:33 38.460 122.700 7 4.2 1:96E15 245/86/4

Healdsburg 30 July 2003 04:50:06 38.679 122.910 5 4.0 1:08E15 311/86/176

Geysers 18 February 2004 20:37:46 38.834 122.765 5 4.5 5:46E15 14/50/100

Glen Ellen 4 August 2006 03:08:12 38.363 122.589 9 4.7 5:64E15 256/86/16

Geysers 20 October 2006 17:00:08 38.867 122.787 4 4.6 9:88E15 254/68/39

Parameters are from http://seismo.berkeley.edu/~dreger/mtindex.html (last accessed February 2008). Focal mechanisms are specified as strike/dip/

rake in degrees.

Broadband Waveform Modeling of Moderate Earthquakes in the San Francisco Bay Area 971


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properties to density, seismic compressional, and shear wave

speeds and attenuation (Brocher, 2005a,b,c). Details about

the model can be found on a web site maintained by the

USGS (2005).

The model is stored as an octant tree (etree), and a soft-

ware package is included for easily querying the model pa-

rameters at a specified point (Akceliket al., 2003, Tu et al.,

2003). The etree technology allows the model parameters(density, shear and compressional velocities, and quality fac-

tors) to be stored in a compact binary format. The values for a

given location in the model can be quickly accessed through

an efficient storage and search scheme. The detailed Bay

Area model is represented with a horizontal resolution of

100 m and vertical resolution of 25 m from the surface to

a depth of 400 m below sea level. The resolution decreases

with depth as resolution of structure decreases. Software in-

cluded with the package allows the model to be rendered on

a user-specified grid spacing in such a way as to maintain

the correct volume-averaged properties when rendering the

model at coarser scales.

Figure 2 shows the shear velocity at the surface in map

view along with cross sections through the model across the

generally northwestsoutheast trending faults and features.

The model reveals the complex geology and physical proper-

ties of the region. Low shear velocities are reported in the

San Francisco and San Pablo Bays and the basins (Cotatiand Windsor Basins in the Santa Rosa Valley, Sacramento

San Joaquin Delta, Central Valley, Evergreen and Cupertino

Basins in Santa Clara Valley, Livermore Basin, Monterey

Bay coast, and Salinas Valley). High shear velocities are

reported in the Franciscan complex, granitic, and volcanic

rocks of the hills and mountain ranges (e.g., Diablo Range,

Santa Cruz mountains). The cross sections (Fig. 2b) transect

the northwestsoutheast trending faults (San Andreas, Hay-

ward, Greenville, and Green Valley) and reveal the basins in

the shallow low-velocity crust. Often the basins are bounded

Figure 2. USGS San Francisco Bay Area seismic velocity model. (a) Map of shear velocity at the surface. (b) Cross sections AA0 and BB0

from (a) across the model from the Pacific Ocean to the Central Valley.



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by these faults. The broad thickening of the crust from

the Pacific Ocean to the Great Valley can also be seen. At

the scale of the crust, shear velocities are generally low

(


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can be important for long periods at local to regional dis-

tances (Ichinose et al., 2000). An important observation for

our analysis is that there is no apparent bias in the arrival

times of energy between the WPP and reflectivity synthetics.

We ran WPP simulations of the 12 events and paths

shown in Figure 1 (source parameters from Table 1) using

the USGS northern California3D velocity model. Simulations

were performed on the multiprogrammatic computing re-source (MCR) and thunder LINUX clusters operated by

Livermore Computing. Computational limitations preclude

us from modeling the band 0.030.25 Hz using the lowest

seismic velocities at the finest resolution of the model.

The velocity model was rendered on a Cartesian grid with

a grid spacing of 200 m, and the minimum shear velocity

was set to 500 m=sec. Water regions (e.g., bay, ocean) were

modeled as acoustic media with the shear modulus identi-

cally zero. Using a grid spacing of 200 m largely ignores

the near-surface geotechnical structure and averages material

properties over several shallow zones of the model. The cal-

culations set the minimum shear velocities to 500 m=sec.

The observatory-quality broadband stations we consideredare all installed in hard rock sites where the shear velocity

is higher than 500 m=sec. The shear velocities in sedimen-

tary basins in the near-surface layers are often lower than

500 m=sec (Fig. 2). The synthetic seismograms were valid in

the frequency range 00.25 Hz. Lower near-surface veloci-

ties within the sedimentary basins can be expected to amplify

ground motions, but we did not try to model motions at sed-

imentary sites. The response was computed for 200 sec to

include the direct and scattered surface waves for the farthest

stations. Details of the simulations are compiled in Table 2.

Note that our computational domain reached beyond the de-

tailed geologic model (yellow dashed lines in Fig. 1) and in-

cluded the less-detailed extended model. The detailed model

tapers smoothly into the extended model; however, differ-

ences in the surface shear velocities in the Central Valley

can be seen in Figure 2.

Source Parameter Validation

It must be established that the events studied have ac-

curate locations, depths, origin times, focal mechanisms, and

moments in order to interpret the fits of computed waveforms

to observed waveforms for earth structure. Some of the larger

events were well recorded by strong motion stations operated

by the USGS at fairly close distances (


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In Figure 5b, we show the waveforms filtered 0.03

0.25 Hz. We observed that the waveform timing and ampli-

tudes are very similar when we scale the smaller Yountville

event by 1.42, based on the ratio of the seismic moments

(Table 1). We further changed the polarity of the Rayleigh

waves for the Yountville to SAO path to account for radiation

pattern differences. The onset times of the direct Pnl, Ray-

leigh, and Love waves agree very well and the later-arriving

scattered surface waves show good agreement of the phase

and amplitudes. Cross correlating the pairs of waveforms in-

dicates that shifts of 0.7 sec or less are required to optimally

align the waveforms (these estimated delays are shown in

Fig. 5b, but the waveforms are displayed with the time

relative to the reported origin times). Path length difference

would result in travel time differences of at most 0.2 and

0.5 sec for the Pnl and Rayleigh waveforms, respectively.

In fact, the delay times from cross correlations show that the

shorter path (San Juan Bautista to CVS) must be advanced(positive delay) relative to the longer path (Yountville to

SAO), indicating that the relative timing of arrivals after the

events is consistent with their relative locations. Location er-

rors of magnitude greater than twice the path length differ-

ence are unlikely given the small delays needed to align the

waveforms. The poorer waveform similarity seen for the Pnl

waveforms may result from different event depths or dip of

the focal mechanisms (Table 1). The excellent similarity be-

tween these waveforms for reciprocal paths, especially the

timing, suggests that location and origin-time errors are small

for the frequencies considered. In the following, we assume

the reported source parameters are correct. In future analy-

sis of these events, it may be desirable to include detailed

confirmation and possible modification of the source param-

eters as well as estimation of the source-time function (espe-

cially if higher frequencies were considered). However, for

the modeling considered in this study, we accepted the re-

ported source parameters and interpreted misfit between ob-

served and synthetic waveforms in terms of seismic velocity

structure.

Comparing Observed and Simulated Waveforms

Synthetic seismograms for the 12 events and reported

source parameters (Table 1) were computed with our WPP

code. In order to understand the impact of 3D structure on

the seismic response in the region, we compared the syn-

thetics for the average 1D GIL7 model (Stidham et al.,1999; Baise et al., 2003) and the 3D USGS model, both

computed with WPP. Figure 6 shows the comparisons be-

tween 1D and 3D synthetics for four stations that recorded

the 18 August 1999 Bolinas earthquake (see Fig. 1 for event

and station locations) in three frequency bands (0.030.05,

0.030.1, and 0.030.25 Hz). We did not consider frequen-

cies below 0.03 Hz (periods of 33 sec) because signal-to-

noise levels decrease for long periods, and the wavelengths

of such long periods become comparable to or larger than the

event-station distance. Note in Figure 6 that the waveforms at

Figure 4. Modeling of the Yountville earthquake with local USGS strong motion data. (a) A map of the event and the two nearest stations:1761 (Sonoma Fire Station #1) and 1765 (Napa Fire Station #3). Comparison of observed records (solid) with synthetics computed with WPPfor the USGS 3D model (dashed). Three-component velocity records filtered 0.21.25 Hz at stations (b) 1761 and (c) 1765. For each station,the data and synthetics are shown with the same amplitude and time scales for all three components.



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the lowest frequencies (0.030.05 Hz, 3320 sec) are quite

similar for each path, with only slight differences in surface-

wave phase. In the intermediate band (0.030.1 Hz, 33

10 sec), the waveform shapes and dispersion character are

quite similar for some paths and components (e.g., POTR,

WENL); however, phase delays are more obvious, especially

for the surface waves on longer paths (e.g., HOPS, SAO).

Body waves are generally very consistent between data

and synthetic in the intermediate band. For this band, the

3D synthetics could probably be reproduced by synthetics

computed for a path-averaged 1D model derived from the

3D model. In this case, an average 1D model such as GIL7

could reproduce the response with appropriate frequency-

dependent delays for specific portions of the seismograms,

as demonstrated by Zhao and Helmberger (1994), Zhu

and Helmberger (1996), and Tan and Helmberger (2007).

In the highest frequency band (0.030.25 Hz, 334 sec),

the 1D and 3D synthetics are very different, especially the

surface waves. These comparisons suggest that 3D structure

affects ground motions in the Bay Area for frequencies at and

above 0.1 Hz (10 sec) corresponding to surface-wave wave-

lengths of 2030 km. At the highest frequencies (0.25 Hz),

the computed 3D responses at all stations show a long-

duration surface-wave coda probably due to multipathing

through the intervening faults and basin structures in Santa

Rosa Valley (HOPS), San Leandro and Livermore Basins

(WENL), San Pablo Bay (POTR), and Santa Clara Valley

(SAO); however, note that attenuation is not included in

our simulations. We will see next that such long-duration

surface wave is often observed in the broadband response.

We now compare the observed and synthetic seismo-

grams for the 3D model. To begin, we simply compared

the waveforms in absolute time and amplitude. Figure 7

shows selected three-component observed (solid) and syn-

thetic (dashed) waveforms in record section format for the

18 August 1999 Bolinas and 3 September 2000 Yountville

earthquakes. These records are filtered 0.030.15 Hz (33

7 sec) in order to emphasis the gross differences between

data and synthetic, which ought to be more robust than dif-

ferences at higher frequencies possibly caused by smaller-

scale, more poorly resolved features. The amplitudes and

waveform shapes are predicted very well at this frequency

band; however, we find that the synthetics for the 3D model

are systematically early relative to the data. The phase dif-

Figure 5. Reciprocal waveform example to evaluate the source parameters. (a) Map of the 12 August 1998 San Juan Bautista and 3 Sep-tember 2000 Yountville earthquakes, focal mechanisms, and the stations CVS and SAO. The paths linking events to stations are shown.(b) Three-component displacement waveforms for the two paths scaled by the ratio of the seismic moments (1.42) and filtered 0.030.25 Hz.The time axis is relative to the reported origin times. Time delays, t, estimated by cross correlating the waveform pairs, are shown (but notapplied). The vertical and radial componentPnlwaveforms are amplified by a factor of 5 to emphasize the details. The Rayleigh waveformsfor the Yountville event at SAO are reversed to match the polarity of the San Juan Bautista event.



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ferences are most apparent for the surface-wave arrivals.

These phase delays tend to increase with distance, suggesting

they arise from systematically fast velocities rather than

event origin time or location errors. Origin time errors would

appear as static delays, and mislocation errors would appear

as prediction of later arrivals for paths toward the true loca-

tion and prediction of earlier arrivals for paths away from the

true location. Both of these types of errors should to first or-

der be independent of distance. For the misfit of surface-wave arrivals for the Bolinas event (Fig. 7ac), the paths

to the north (CVS and HOPS) and to the south (BRK, JRSC,

WENL, and MHC) show delays increasing with distance,

suggesting systematic fast velocities in the middle to upper

crust of the 3D model where Rayleigh- and Love-wave sen-

sitivity for these frequencies is peaked. The 3 September

2000 Yountville event shows similar delays increasing with

distance (Fig. 7df). We further emphasize evidence for

systematically fast velocities by showing comparisons for

two other events: Geysers 20 October 2006 (Fig. 8ac)

and 14 May 2002 Gilroy (Fig. 8df). These events are at

the northern and southern extremes of the 3D model extent,

and the available waveforms sample longer, more structur-

ally complex paths. The waveform comparisons show simple

response at the closest stations with only a slight phase delay

and increasing waveform complexity and surface-wave delay

with distance. The delays appear to be larger for the surface

waves, but the body waves are often predicted to be early

also, suggesting both the compressional and shear velocitiesmust be reduced. The response is more complex with dis-

tance as the wave field interacts with 3D structure along

the paths.

In order to quantify the performance of the USGS 3D

model, we computed quantitative measures of misfit between

the observed and synthetic waveforms. Specifically, we

extracted portions of the filtered observed and synthetic dis-

placement seismograms and then cross correlated the wave-

forms to obtain the delay time for optimal alignment. The

data and synthetics were interpolated to a common sample

3D (USGS)

1D (GIL7)

HOPS POTR

WENL SAO

(a) (b)

(c) (d)

Figure 6. Comparison of three-component1D GIL7 (dashed lines) and 3D USGS (solid lines) synthetics for the 18 August 1999 Bolinasearthquake at stations (a) HOPS, (b) POTR, (c) WENL, and (d) SAO, computed with WPP. Displacement waveforms at each station arefiltered in three frequency bands (0.030.05 Hz, 0.030.1 Hz, and 0.030.25 Hz). Note that in this figure, waveforms for each station-frequency band combination are shown with correct relative amplitudes between the three components.



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0

20

40

60

80

100

120

140

Distance,

km

20 0 20 40 60

Reduced Time, t / 6.0, seconds

BRK

CVS

HOPS

JRSC

MHC

POTR

WENL

data

3Devent: BOLINAS_1999

channel: Z filter: 0.03 - 0.15 Hz

0

20

40

60

80

100

120

140

Distance,

km

20 0 20 40 60


BRK

CVS

HOPS

JRSC

MHC

POTR

WENL

data


channel: R filter: 0.03 - 0.15 Hz

0

20

40

60

80

100

120

140

Distance,

km

20 0 20 40 60


BRK

CVS

HOPS

JRSC

MHC

POTR

WENL

data


channel: T filter: 0.03 - 0.15 Hz

0

20

40

60

80

100

120

140

Distance,

km

20 0 20 40 60


BDM

BRK

HOPS

JRSC

MHC

POTR

data

3D

event: YOUNTVILLE_2000


0

20

40

60

80

100

120

140

Distance,

km

20 0 20 40 60


BDM

BRK

HOPS

JRSC

MHC

POTR

data

3D



0

20

40

60

80

100

120

140

Distance,

km

20 0 20 40 60


BDM

BRK

HOPS

JRSC

MHC

POTR

data

3D



(a) (b) (c)

(d) (e) (f)

Figure 7. Observed (solid) and 3D synthetic (dashed) three-component displacement seismograms for the (a)(c) 18 August 1999 Bo-linas and (d)(f) 3 September 2000 Yountville earthquakes. Data and synthetic are filtered 0.030.07 Hz and displayed as a record sectionwith velocity reduction of6:0 km=sec. Note that in this figure, waveforms for each data-synthetic combination are shown with correct relativeamplitudes, but the amplitudes for different stations are not to scale.



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0

20

40

60

80

100

120

140

160

180

200

Distance,

km

20 0 20 40 60 80


SAO

BRK

CVS

JRSC

MHC

POTR

data

3D

event: GILROY_2002


0

20

40

60

80

100

120

140

160

180

200

Distance,

km

20 0 20 40 60 80


SAO

BRK

CVS

JRSC

MHC

POTR

data

3D

event: GILROY_2002


0

20

40

60

80

100

120

140

160

180

200

Distance,

km

20 0 20 40 60 80


SAO

BRK

CVS

JRSC

MHC

POTR

data

3D

event: GILROY_2002


0

20

40

60

80

100

120

140

160

180

200

220

Distance,

km

20 0 20 40 60 80


HOPS

CVS

MCCM

BRK

BDM

JRSC

MHC

WENL

data3D

event: GEYSERSchannel: Z filter: 0.03 - 0.15 Hz

0

20

40

60

80

100

120

140

160

180

200

220

Distance,

km

20 0 20 40 60 80


HOPS

CVS

MCCM

BRK

BDM

JRSC

MHC

WENL

data3D

event: GEYSERSchannel: R filter: 0.03 - 0.15 Hz

0

20

40

60

80

100

120

140

160

180

200

220

Distance,

km

20 0 20 40 60 80


HOPS

CVS

MCCM

BRK

BDM

JRSC

MHC

WENL

data3D

event: GEYSERSchannel: T filter: 0.03 - 0.15 Hz

(a) (b) (c)

(d) (e) (f)

Figure 8. Similar to Figure 7 but for the (a)(c) Geysers 20 October 2006 and (d)(f) 14 May 2002 Gilroy events. Note that the time anddistance range is larger than Figure 7.



12/20

rate of20 samples=sec. The alignment is best determined by

considering just the leading portion of the records, including

the body waves and fundamental mode surface wave, rather

than a longer duration that often includes scattered surface

waves. We illustrate this method in Figure 9. First we use

a group velocity window to isolate the leading portion of

the filtered observed and synthetic seismograms, taking

the window from the origin time to 2:5 km=sec (Fig. 9a).These records are cross correlated to determine the delay

time, t, for optimal alignment. We only allow the synthetic

to shift in time by plus or minus the minimum period

(4 sec for a frequency of 0.25 Hz) to avoid possible cycle

skipping. The synthetic is shifted by the delay time, and the

linear correlation, r, is computed for a longer window, typi-

cally out to a group velocity of 0:5 km=sec or 200 sec,

whichever is shortest (Fig. 9b). In all cases, the linear corre-

lation is reported after the time delay has been applied to the

synthetic. Even with the limitation for shifting the synthetic,

the automatic algorithm sometimes accepts alignments that

clearly miss the first motion, especially when the station is

nodal for surface wave or when the response is complex. We

computed the delay time and linear correlation for each sta-

tion component separately, finding different time shifts for

each station component. This is unsatisfactory because the

3D model should reproduce the best fits without time shifts,

or the shifts should at least be consistent for a given path. Our

method attempts to determine the delay times for the large

amplitude surface waves; however, each component has

different excitation by the source and sensitivity to structure

(e.g., Pnl, Rayleigh, and Love) and different signal-to-noise

properties. It is possible that crustal anisotropy could lead to

different delays ofSV- and SH-polarized waves. We did find

that the vertical and radial components often have similar

time shifts, suggesting that the Pnl and Rayleigh waves re-

quire the model to be perturbed in a similar fashion. A moresophisticated algorithm for isolating specific phases based on

cross correlation with synthetics could be used (e.g., Maggi

et al., 2006); however, this is challenging for local distances

because the phases are not well separated.

The waveform fits for 18 August 1999 Bolinas earth-

quake are summarized and example fits are shown in Fig-

ure 10. Figure 10a shows the linear correlation values

plotted at the station locations in map form for each com-

ponent (vertical, radial, and transverse). The records for this

(Mw 4.6) event have good signal-to-noise, and fits are quite

good, as seen by the color-coded linear correlation values.

The delay times are plotted versus distance, and for this

event, we see a clear decrease in the time delay as a functionof distance as we showed in the record sections of lower fre-

quency waveforms for this event (Fig. 7ac). The delay times

are regressed against distance, and the best-fitting linear

trend is shown. The outlier in this plot is for a poor fit

for the transverse component at station MHC (110 km).

In Figure 10b, we show example waveform fits for 6 of

11 BDSN stations that recorded the event within the greater

Bay Area. For each station, we show the three-component

observed (blue) and synthetic (red) seismograms after the

time shifted was applied. The time shift, t, and linear cor-

relation, r, are reported for each component. Note that paths

crossing the San Pablo Bay and San Francisco Bay show

quite complex response (e.g., BDM, POTR, and WENL) and

that these records are often well fit by the synthetics. Also

note that these paths have nearly equal delay times for the

vertical and radial components, but slightly different delays

for the transverse component. This may indicate different

depth sensitivity of the Rayleigh and Love waves to improve

the fits. In order to interpret these results, it is worth consid-

ering the linear correlation values in terms of the visual fit to

the data. Values of 0.7 or higher often show excellent fits of

the direct body and surface waves and possibly the later-

arriving scattered surface waves (e.g., stations BDM, BRK,

WENL.Z). Linear correlation values above 0.3 and below 0.7

can be quite good (e.g., HOPS.R, POTR.T,WENL.R, WENL.T).

Further quantitative assessment of the waveform fits is

shown for the 30 July 2003 Dublin (Fig. 11) and 3 August

2006 Glen Ellen events (Fig. 12). The Dublin event is the

smallest and deepest event we were able to model in the fre-

quency band (0.030.25 Hz) for appreciable distances. This

event provides good sampling of the San RamonLivermore

Valley (BDM, BRIB, WENL) and Santa Clara Valley

(JRSC). The fits are quite good with most linear correlations

above 0.4 and many above 0.6 (Fig. 11a). The distance trend

20 0 20 40 60 80 100 120


BRK.T

t = 0.0

BRK.T

t = -2.2

r = 0.22

event: HEALDSBURG filter: 0.03 - 0.25 Hz

data3D synthetic

(a)

(b)

absolute time

synthetic shiftedin time

Figure 9. Illustration of our method for computing the wave-form fit for the transverse component displacement recording at sta-tion BRK (Berkeley) of the 30 July 2003 Healdsburg earthquake.(a) Data and synthetics in absolute time, each windowed from theorigin time to a group velocity of2:5 km=sec. These traces are crosscorrelated to determine the time delay for optimal waveform align-ment of these segments. (b) The synthetic is shifted by the valuedetermined from cross correlation (t 2:2 sec), and the linearcorrelation (r 0:22) is computed for the longer window shown. Inboth cases, the data and synthetics are filtered 0.030.25 Hz and areshown as solid and dashed lines, respectively.



13/20

of the time delays is consistent with the Bolinas event

(Fig. 10a). The waveform fits (Fig. 11b) show the complex

response of the Livermore Valley for the path to station

WENL that is well fit by the model with time delays. The

path to station POTR samples the western portion of the

SacramentoSan Joaquin Delta, and the transverse compo-

nent response is quite complex. The 3D model predicts late

arriving, scattered surface waves for this path; however, the

timing of this energy can be improved. Stations CVS and

SAO are about 95 and 115 km, respectively, from this event,

Figure 10. Comparison of waveforms for the 18 August 1999 Bolinas earthquake. (a) Maps of linear correlation, r, between data andsynthetic for the vertical (Z), radial (R), and transverse (T) components in the band 0.030.25 Hz. Also shown are the delay times, t, as afunction of distance along with a linear trend estimated by regression. (b) Waveform plots showing the data (blue) and synthetic (red). Theseare plotted with the delay time and linear correlation, r, for each station component.



14/20

and notice that the noise levels seen at preevent times are

starting to make it difficult to distinguish late-arriving scat-

tered surface-wave energy from noise. This illustrates the

need for strong excitation of broadband energy and quiet

sites to perform this analysis.

The 3 August 2006 Glen Ellen event (Fig. 12) shows

moderately good fits and the same decrease in the delay time

with distance as observed previously. This event shows a

fairly simple response for the short path to station MCCM.

The response at station HOPS is more complex and requires

time delays approaching 4 sec, suggesting the velocities in

Santa Rosa Valley and further north must be reduced. We

show three paths crossing the San Pablo Bay that display

very complex, large-amplitude, late-arriving energy (stations

BDM, BRIB, and BKS). The records for station BDM are

well fit for the vertical and radial components for the direct

Figure 11. Comparison of waveforms for the 2 February 2003 Dublin earthquake, similar to Figure 10.



15/20

energy at early times. The transverse component response

shows large amplitude Love-wave energy that is not well

fit. The horizontal components show large amplitude energy

well after the direct fundamental mode surface waves have

passed. While the details of this energy are not well fit, the

character of the surface-wave coda predicted by the model is

consistent with the data. The paths to stations BKS and BRIB

show large-amplitude late energy similar to station BDM.

The later-arriving energy at station BKS is remarkably well

fit by the 3D model. However, the fit is better for the trans-

verse then the radial component. Finally, the path to station

JRSC crosses the San Pablo and San Francisco Bays. The

direct fundamental model energy is well fit by the 3D model

as well as lower-amplitude, later-arriving energy.

Figure 12. Comparison of waveforms for the 3 August 2006 Glen Ellen earthquake, similar to Figure 10.



16/20

Further sampling of the Bay Area is provided by two

more events shown in Figure 13 (21 May 1996 San Jose

and 14 May 2002 Gilroy). Here we show waveform fits

for three paths for each event. The San Jose event was re-

corded at stations BKS and BRIB, along nearly adjacent

paths. The path to BKS is along the Hayward fault, while

the path to BRIB samples the East Bay Hills. The 3D model

predicts large-amplitude energy after the direct Love wave onthe transverse component that is not observed; this may re-

sult from multipathing along the San Ramon Valley. The path

to station JRSC across the Santa Clara Valley is well fit by

the 3D model. The Gilroy event has several well-fit paths,

including the path to FARB with mixed continental and oce-

anic structures, the path to BRIB crossing the Hayward fault,

and the path to POTR crossing the East Bay Hills, Livermore

Valley, and Delta. The waveforms for these three paths are

complex; however, the 3D model is able to reproduce the

complexity in the observed waveforms. Finally, we return

to the reciprocal paths considered in Figure 5. The predic-

tions from the 3D model are shown in Figure 14. The strongLove-wave energy is well fit for both paths, but the vertical

and radial components are not particularly well fit, except for

the early arriving direct waves and general character of the

later portions.

For the six events shown in Figures 1014, we see that

delay times are generally negative and decrease with distance

to as much as 2 to4 sec over distances of 200 km. This is

further indicated in Figure 15, where we plotted the delay

time and linear correlation values for all individual wave-form comparisons as function of distance and in histogram

form. The delay times have a mean value of1:69 sec and

show a general decrease with distance. The fundamental-

mode surface waves considered have a group velocity of

2:53:0 km=sec, implying that the velocities must be de-

creased by 4%5% on average to reduce this trend. Some

particular paths with more negative time delays imply that

some parts of the model may require greater reductions of

the velocities. Conversely, some paths produce very small

time delays, suggesting the model velocities need little mod-

ification. It is currently not known if the minimum velocity

we used (500

m=sec) strongly biases this estimate. When thetime shifts are allowed, the waveform fits are often quite

20 0 20 40 60 80 100 120

Reduced Time, t D / 6.0, seconds

FARB.Z

t = 2.7r = 0.19

FARB.R

t = 3.6

r = 0.36

FARB.T

t = 4.0r = 0.76

event: GILROY_2002 filter: 0.03 - 0.25 Hz

20 0 20 40 60 80 100 120


BRIB.Z

t = 1.8r = 0.18

BRIB.R

t = 1.5

r = 0.42

BRIB.T

t = 2.3r = 0.52


20 0 20 40 60 80 100 120


POTR.Z

t = 4.4r = 0.21

POTR.R

t = 2.7

r = 0.47

POTR.T

t = 3.8r = 0.27


20 0 20 40 60 80


BKS.Z

t = 1.3r = 0.60

BKS.R

t = 1.8r = 0.51

BKS.T

t = 1.9

r = 0.66

event: SANJOSE_1996 filter: 0.03 - 0.25 Hz

20 0 20 40 60 80


BRIB.Z

t = 1.3r = 0.23

BRIB.R

t = 1.1r = 0.18

BRIB.T

t = 1.7

r = 0.48


20 0 20 40 60 80


JRSC.Z

t = 1.8r = 0.51

JRSC.R

t = 1.2r = 0.54

JRSC.T

t = 3.6

r = 0.12


(a)

(b)

Figure 13. Comparison of waveforms for the (a) 21 May 1996 San Jose and (b) 14 May 2002 Gilroy earthquakes. In both cases, the dataand synthetics are filtered 0.030.25 Hz and are shown in blue and red, respectively.



17/20

good, suggesting that the main features of the model, such as

the main structures and the shapes of the basins, are accurate.The mean linear correlation in Figure 15 is 0.41. Inspection

of the waveform plots (Figs. 1014) shows that a linear cor-

relation of 0.4 or higher indicates a good fit, that is, the main

phases have the correct relative timing and amplitude. So,

on average, the 3D model predicts waveform shapes well.

Note that the amplitudes of the direct waves are often well

modeled and the amplitudes of the late-arriving waves are

often consistent between the observed and synthetic wave-

forms, suggesting that attenuation does not greatly impact

the analysis at the frequencies considered.

Conclusions

We have shown that the USGS 3D seismic velocity

model of the greater San Francisco Bay Area can predict

many important features of observed broadband seismo-

grams. This study provides a preliminary assessment of

the model and indicates that the model performs well.

The complexity that arises from interaction of the seismic

wave field with complex 3D structure is reproduced by syn-

thetic seismograms computed with the model, even for fre-

quencies as low as 0.15 Hz (periods of 7 sec). While the

observed waveform shapes are often well modeled, we report

a systematic bias in the model of faster velocities. Based on

detailed analysis of a few events, we can rule out large loca-

tion, depth, and origin-time errors and attribute the travel-

time delays to model error. Analysis of the time delays

obtained from waveform cross correlation indicates that

the bias in seismic velocities is on average about 4%5%

too fast. Reduction of seismic velocities will reduce the shifts

required to align the synthetics and possibly improve the

waveform fits. Reduction of the velocities will increaseamplitudes and possibly change the timing of interfering

arrivals, resulting in different ground-motion amplitudes

and geographic patterns. Thus, improved travel time and

ground-motion amplitude predictions can be expected if fits

to the broadband data are improved by modifications of the

3D model.

The geographic coverage of the Bay Area seismic veloc-

ity model is limited by the available moderate (Mw 45)

events and broadband stations. The available earthquakes

tend to occur along the main faults in the northern, eastern,

and southern regions of the detailed model domain. These

paths mostly sample the Franciscan complex lithologies. Ad-

ditional stations along and near the coastal area and eventsalong the San Andreas fault would improve sampling of the

region and help constrain the structure in populated areas of

Santa Cruz, Santa Clara, San Mateo, San Francisco, and

Marin Counties. Recent advances in obtaining surface-wave

dispersion measurements from ambient noise cross correla-

tions (Moschetti et al., 2007) may provide new data to con-

strain shallow shear velocity structure in the Bay Area for

ground-motion calculations (Rodgers et al., 2007).

Ideally, the 3D model must predict the relatively low

frequencies considered here before deterministic ground-

motion predictions above 0.25 Hz can be used for scenario

earthquake simulations. For example, the basin geometryand seismic velocities and velocity contrasts must be accu-

rate so that basin-generated surface waves are modeled cor-

rectly. The analysis in this study clearly shows that the basins

have a strong effect on the observed ground motions. In par-

ticular, the San Pablo Bay, Santa Clara Valley, and the San

RamonLivermore Valley and Delta amplify motions. We

found the velocities in the Santa Rosa Valley must be re-

duced, suggesting that simulations of the 1906 San Francisco

earthquake may underpredict basin response (Aagaard, Bro-

cher, Dolenc, Dreger, Graves, Harmsen, Hartzell, Larsen,

20 0 20 40 60 80 100 120 140


SAO.Z

t = 2.6

r = 0.03

SAO.R

t = 3.8r = 0.04

SAO.T

t = 2.3r = 0.41

event: YOUNTVILLE filter: 0.03 - 0.25 Hz

20 0 20 40 60 80 100 120 140


CVS.Z

t = 0.4

r = 0.03

CVS.R

t = 0.4

r = 0.14

CVS.T

t = 3.6

r = 0.67

event: SAN_JUAN_BAUTISTA filter: 0.03 - 0.25 Hz

(a)

(b)

Figure 14. Reciprocal waveforms showing predictions of theUSGS 3D model. (a) 3 September 2000 Yountville and (b) 12 August1998 San Juan Bautista earthquakes at stations SAO and CVS, re-spectively. Synthetics are shifted by the estimated delay time, t,and reported with the linear correlation, r.



18/20

Zoback, 2008; Aagaard, Brocher, Dolenc, Dreger, Graves,

Harmsen, Hartzell, Larsen, McCandless, et al., 2008). These

features will be important for determining ground motions

from possible future major earthquakes. In particular, the

San Pablo Bay, San Francisco Bay, Santa Rosa Valley, Santa

Clara Valley, and Livermore Valley will likely experience

strong shaking for a major earthquake on the Hayward

Rodgers Creek fault system. Future modeling should in-

clude realistic geotechnical velocities if possible (e.g., Holzer

et al., 2005).

The creation of a3D seismic velocity model based on a

wealth of geologic and geophysical data is a major achieve-

ment and is a great step toward the laudable goal of providing

improved earthquake ground-motion prediction. Clearly, 3D

modeling of earthquakes must strive to increase numerical

resolution by reducing the grid spacing at the surface and in-

cluding the known low-geotechnical velocities. The calcula-

tion of ground motions for scenario earthquakes and imaging

of complex finite earthquake ruptures from local strong-

motion data will require an accurate 3D model to compute

the response. The USGS 3D model of the San Francisco

Bay Area is a step toward that goal, but clearly improvements

can be made. Among the possibilities for improving the

model is waveform inversion using adjoint methods (e.g.,

Tromp et al., 2005; Liu and Tromp, 2006).

Acknowledgments

We are grateful to Brad Aagaard and Tom Brocher for providing the

USGS model and software and to Mary Lou Zoback for inviting us to partic-

ipate in the San Francisco 1906 Centenary simulation effort. Waveform data

for this study were obtained from the Berkeley Digital Seismic Network

operated by Berkeley Seismological Laboratory, University of California

Berkeley. We appreciate support from the Lawrence Livermore National La-boratory (LLNL) Laboratory Science and Technology Office under Labora-

tory Directed Research and Development Project Number 05-ERD-079. We

are grateful to the staff of Livermore Computing (LC) for operation of the

MCR and Thunder LINUX clusters, where we performed parallel calcula-

tions. We thank Brian Carnes, Greg Tomaschke, and David Dannenberg for

assistance with LC allocations and dedicated allocation time, without which

we could not have completed this study. Comments by Thomas Brocher and

Michael Pasyanos and reviews by Greg Beroza (guest editor), Don Helm-

berger, and an anonymous reviewer improved the original manuscript. This

work was performed under the auspices of the U.S. Department of Energy

by University of California, LLNL, under Contract Number W-7405-Eng-48.

This is LLNL Contribution Number UCRL-JRNL-228251.

-1.0

-0.5

0.0

0.5

1.0

Correlation,r

0 50 100 150 200

Distance, km

0

10

20

Frequency,

(%)

-1.0 -0.5 0.0 0.5 1.0

Correlation, r

Mean r = 0.41

-5

-4

-3

-2

-1

01

2

3

4

5

DelayTim

et,s

0 50 100 150 200

Distance, km

0

10

20

Frequency,

(%)

-5 -4 -3 -2 -1 0 1 2 3 4 5

Delay Time t, s

Mean t = -1.69

Figure 15. Delay times (upper panels) and linear correlations (lower panels) as a function of distance and in histogram form. The solidline in the distance plots shows the regression of the data against distance and reveals a negative slope. Included in the histogram plots are themean values.



19/20

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Atmospheric, Earth and Energy DivisionChemistry, Materials, Earth and Life Sciences Directorate

Lawrence Livermore National Laboratory7000 East Avenue, L-205Livermore, California [email protected]

(A.R.)

Center for Applied Scientific ComputingComputations Directorate

Lawrence Livermore National Laboratory7000 East Avenue, L-550Livermore, California 94551

(N.A.P., S.N., B.S.)

Computer Applications and Research DepartmentComputations Directorate

Lawrence Livermore National Laboratory7000 East Avenue, L-463Livermore, California 94551

(K.M.)

Manuscript received 5 March 2007


broadband waveform modeling of moderate earthquakes in the san francisco bay area and preliminary...

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