A 𝑉𝑆30-derived Near-surfaceSeismic Velocity Model

Geoffrey Ely (gely@usc.edu),Patrick Small, Thomas H. Jordan, Philip J. Maechling, Feng Wang.Southern California Earthquake Center,University of Southern California, Los Angeles, CA 90089.

IntroductionShallow material properties, S-wave velocity in particular, strongly in-fluence ground motions, so must be accurately characterized for ground-motion simulations. Available near-surface velocity information generallyexceeds that which is accommodated by crustal velocity models, such ascurrent versions of the SCEC Community Velocity Model (CVM-S v4.0)or the Harvard model (CVM-H v6.3). The elevation-referenced CVM-Hvoxel model introduces rasterization artifacts in the near-surface due tocourse sample spacing, and sample depth dependence on local topographicelevation. To address these issues, we propose a method to supplementcrustal velocity models, in the upper few hundred meters, with a modelderived from available maps of 𝑉𝑆30 (the average S-wave velocity down to30 meters). The method is universally applicable to regions without directmeasures of 𝑉𝑆30 by using 𝑉𝑆30 estimates from topographic slope (Wald,et al. 2007). In our current implementation for Southern California, thegeology-based 𝑉𝑆30 map of Wills and Clahan (2006) is used within Califor-nia, and topography-estimated 𝑉𝑆30 is used outside of California.

Depth dependenceVarious formulations for S-wave velocity depth dependence, such as linearspline and polynomial interpolation, were evaluated against the followingpriorities: (a) capability to represent a wide range of soil and rock veloc-ity profile types; (b) smooth transition to the crustal velocity model; (c)ability to reasonably handle poor spatial correlation of 𝑉𝑆30 and crustalvelocity data; (d) simplicity and minimal parameterization; and (e) com-putational efficiency. The favored model includes cubic and square-rootdepth dependence, with the model extending to a transition depth 𝑧𝑇 . Atransition depth of 𝑧𝑇 = 350 m is used to ensure adequate sampling ofCVM-H (shallower depths may be unsampled by the CVM-H near topo-graphic features). S-wave velocity at the surface is derived from 𝑉𝑆30 bya uniform scaling. 𝑉𝑃 , and in turn density, are inferred from surface 𝑉𝑆

via the scaling laws of Brocher (2005). 𝑉𝑆 and 𝑉𝑃 are independently in-terpolated between the surface values and those extracted from the crustalvelocity model at the transition depth. Density is derived from interpo-lated 𝑉𝑃 via the Nafe-Drake law of Brocher. Depth dependence for theinterpolation is parameterized with

𝑧 = 𝑧′/𝑧𝑇𝑓(𝑧) = 𝑧 + 𝑏(𝑧 − 𝑧2)

𝑔(𝑧) = 𝑎− 𝑎𝑧 + 𝑐(𝑧2 + 2√𝑧 − 3𝑧)

𝑉𝑆(𝑧) = 𝑓(𝑧)𝑉𝑆𝑇 + 𝑔(𝑧)𝑉𝑆30

𝑉𝑃 (𝑧) = 𝑓(𝑧)𝑉𝑃𝑇 + 𝑔(𝑧)𝑃 (𝑉𝑆30)

𝜌(𝑧) = 𝑅(𝑉𝑃 )

where 𝑧′ is depth, 𝑉𝑆𝑇 and 𝑉𝑃𝑇 are S- and P-wave velocities extracted fromthe crustal velocity model at depth 𝑧𝑇 , 𝑃 () is the Brocher P-wave velocityscaling law, and 𝑅() is the Nafe-Drake law. The coefficient 𝑎 controls theratio of surface velocity to original 30 meter average, 𝑏 controls overallcurvature, and 𝑐 controls near-surface curvature.The coefficients 𝑎 = 1/2, 𝑏 = 2/3, and 𝑐 = 3/2 were chosen by trial-and-error fitting Boore and Joyner’s (1997) generic rock profile and CVM-Sgeneric soil profiles, as well as to produce smooth and well-behaved profileswhen applied to the CVM-H at the selected CyberShake sites.

0 aVS30 VS30 VST

S-wave velocity

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(m

)

f(z)VST +

g(z)VS30

g(z)V S

30 f(z)VST

Figure 1: Generic S-wave velocity profile for all soil types is a summationof shallow component 𝑔(𝑧) scaled by 𝑉𝑆30 (red), and deep component 𝑓(𝑧)scaled by 𝑉𝑆𝑇 (blue).

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Boore-Joyner generic rock Magistrale NEHRP BC

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Magistrale NEHRP C Magistrale NEHRP CD

0.0 0.5 1.0 1.5 2.0 2.5S-wave velocity (km/s)

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Magistrale NEHRP D

0.0 0.5 1.0 1.5 2.0 2.5S-wave velocity (km/s)

Magistrale NEHRP DE

Figure 2: Generic 𝑉𝑆 profiles (dashed lines) of Boore and Joyner (1997)and Magistrale (2000) with proposed model (solid lines).

ImplementationThe new near-surface model (know at the geotechnical layer, or GTL) hasbeen implemented as a Python library using CVM-H v6.3 voxet data, andis available as part of the Computational Seismology Tools. In testing,extraction of a 18.5 billion node, 208 Gb mesh, using three processors (oneeach for 𝜌, 𝑉𝑃 and 𝑉𝑆) on the NICS Kraken machine, takes 4 hours. Thenew GTL is also integrated into the SCEC CVM Toolkit by Patrick Small,to be released in early 2011.

ReferencesBoore, D. M., and W. B. Joyner (1997), Site amplifications for generic rock

sites, Bulletin of the Seismological Society of America, 87 (2), 327–341.

Brocher, T. M. (2005), Empirical relations between elastic wavespeeds anddensity in the Earth’s crust, Bulletin of the Seismological Society ofAmerica, 95 (6), 2081–2092, doi:10.1785/0120050077.

Ely, G. P., S. M. Day, and J.-B. H. Minster (2008), A support-operatormethod for visco-elastic wave modeling in 3D heterogeneous media, Geo-phys. J. Int., 172 (1), 331–344, doi:10.1111/j.1365-246X.2007.03633.x.

Kohler, M. D., H. Magistrale, and R. W. Clayton (2003), Mantle het-erogeneities and the SCEC reference three-dimensional seismic velocitymodel version 3, Bulletin of the Seismological Society of America, 93 (2),757–774, doi:10.1785/0120020017.

Magistrale, H., K. McLaughlin, and S. Day (1996), A geology-based 3Dvelocity model of the Los Angeles basin sediments, Bulletin of the Seis-mological Society of America, 86 (4), 1161–1166.

Magistrale, H., S. M. Day, R. W. Clayton, and R. W. Graves (2000), TheSCEC southern California reference three-dimensional seismic velocitymodel version 2, Bulletin of the Seismological Society of America, 90 (6B),S65–76, doi:10.1785/0120000510.

Wald, D. J., and T. I. Allen (2007), Topographic slope as a proxy for seismicsite conditions and amplification, Bulletin of the Seismological Society ofAmerica, 97 (5), 1379–1395, doi:10.1785/0120060267.

Wills, C. J., and K. B. Clahan (2006), Developing a map of geologically de-fined site-condition categories for California, Bulletin of the SeismologicalSociety of America, 96 (4A), 1483–1501, doi:10.1785/0120050179.

CVM-S v4.0

Figure 3: CVM-S v4.0 surface S-wave velocity with marked cross-sectionand vertical profile locations. Color scale is clipped at 400 m/s.

Figure 4: CVM-S v4.0 S-wave velocity cross-section through the Los An-geles basin and San Gabriel Mountains.

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0S-wave velocity (km/s)

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Depth

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Figure 5: CVM-S v4.0 S- and P-wave velocity profiles.

CVM-H v6.3

Figure 6: CVM-H v6.3 surface S-wave velocity with marked cross-sectionand vertical profile locations. White areas indicate locations where thevoxet model does not reach the ground surface.

Figure 7: CVM-H v6.3 S-wave velocity cross-section through the Los An-geles basin and San Gabriel Mountains.

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0S-wave velocity (km/s)

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Figure 8: CVM-H v6.3 S- and P-wave velocity profiles.

CVM-H v6.3 + GTL

Figure 9: GTL surface S-wave velocity derived from Wills and Clahan(2006) geology based 𝑉𝑆30 map, supplemented outside of California withWald et al. (2007) map.

Figure 10: CVM-H v6.3 + GTL S-wave velocity cross-section through theLos Angeles basin and San Gabriel Mountains.

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0S-wave velocity (km/s)

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Figure 11: CVM-H v6.3 + GTL S- and P-wave velocity profiles.

Ground motion simulationsGround motions from the 2008 𝑀𝑤 5.4 Chino Hills, CA earthquake arecompared to simulations using the CVM-S 4.0 and CVM-H 6.3 + GTL.The source is a point double couple and CLVD moment tensor obtainedfrom the Southern California Seismic Network, with a time function 𝑚(𝑡) =𝑡/𝑇 2𝑒−𝑡/𝑇 where 𝑇 = 0.25 sec. The minimum S-wave velocity is truncatedat 500 m/s, obscuring some details of the GTL model. The velocity modelsare sampled at 50 meter resolution, requiring 5.5 billion mesh points for thesimulation domain (Fig. 12). Simulations were computed with the SupportOperator Rupture Dynamics code (SORD, Ely, et al., 2008), using 15,360processes on the NICS Kraken super-computer, requiring eight hours runtime per simulation. These preliminary results show general agreement inamplitude and character among the observed and synthetic data (Figs. 13-15). Additional analysis and simulations are needed to adequately quantifyeffects of the new GTL model.

BFS

BRE

CHF

CHN

DEC

DLA

FON

FUL

GSA

HLLKIK

LAF

LFP

LLS

LTP

MLS

OGC

OLI

PDU

PLS

PSRRIO

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RVR

SAN

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WTT

20 kmEW

S

N

Figure 12: Simulation region and station map with CVM-S 4.0 (red) andCVM-H 6.3 (blue) basins delineated by dashed contour of 𝑉𝑠 = 2.5 km/s,at 1 km depth.

East-West North-South Vertical

CHN3.2

2.6

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PSR2.6

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PDU1.4

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PLS0.6

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RIO1.7

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BFS0.7

0.9

1.2

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FON0.7

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0.8

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RVR0.2

0.7

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KIK1.0

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CHF0.3

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50.0 s

Figure 13: Recorded 0.1 - 1.0 Hz ground velocity (black) at stations northand east of the epicenter, compared to CVM-S 4.0 (red) and CVM-H 6.3 +GTL (blue) simulations. Peak values in cm/s are indicated on each trace.

East-West North-South Vertical

OLI1.5

0.8

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RUS1.6

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GSA1.7

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LTP2.6

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LAF1.0

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HLL0.6

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DEC0.6

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LFP0.9

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50.0 s

Figure 14: Recorded 0.1 - 1.0 Hz ground velocity (black) at stations north-west of the epicenter, compared to CVM-S 4.0 (red) and CVM-H 6.3 +GTL (blue) simulations. Peak values in cm/s are indicated on each trace.

East-West North-South Vertical

SRN0.9

0.3

1.7

3.2

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3.1

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0.7

1.0

FUL4.8

2.2

2.5

2.8

1.2

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1.1

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OGC2.2

1.7

2.6

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BRE7.0

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SAN3.3

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STG0.6

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DLA4.9

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LLS4.6

1.8

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STS2.3

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SDD1.3

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50.0 s

Figure 15: Recorded 0.1 - 1.0 Hz ground velocity (black) at stations south-west of the epicenter, compared to CVM-S 4.0 (red) and CVM-H 6.3 +GTL (blue) simulations. Peak values in cm/s are indicated on each trace.