by Geoffrey Ely, Patrick Small, Thomas Jordan, Philip Maechling, and Feng Wang
Shallow material properties, S-wave velocity in particular, strongly influence ground motions, so must be accurately characterized for ground-motion simulations. Available near-surface velocity information generally exceeds that which is accommodated by crustal velocity models, such as current versions of the SCEC Community Velocity Model (CVM-S v4.0 by Magistrale, McLaughlin, and Day 1996; Magistrale et al. 2000; Kohler, Magistrale, and Clayton 2003) or the Harvard model (CVM-H v6.3 by Shaw et al. 2015). The elevation-referenced CVM-H voxel model introduces rasterization artifacts in the near-surface due to course sample spacing, and sample depth dependence on local topographic elevation. To address these issues, we propose a method to supplement crustal velocity models, in the upper few hundred meters, with a model derived from available maps of VS30 (the average S-wave velocity down to 30 meters). The method is universally applicable to regions without direct measures of VS30 by using VS30 estimates from topographic slope (Wald and Allen 2007). In our current implementation for Southern California, the geology-based VS30 map of Wills and Clahan (2006) is used within California, and topography-estimated VS30 is used outside of California.
Various formulations for S-wave velocity depth dependence, such as linear spline and polynomial interpolation, were evaluated against the following priorities: (a) capability to represent a wide range of soil and rock velocity profile types; (b) smooth transition to the crustal velocity model; (c) ability to reasonably handle poor spatial correlation of VS30 and crustal velocity data; (d) simplicity and minimal parameterization; and (e) computational efficiency. The favored model includes cubic and square-root depth dependence, with the model extending to a transition depth zT. A transition depth of zT = 350 m is used to ensure adequate sampling of CVM-H (shallower depths may be unsampled by the CVM-H near topographic features). S-wave velocity at the surface is derived from VS30 by a uniform scaling. VP, and in turn density, are inferred from surface VS via the scaling laws of Brocher (2005). VS and VP are independently interpolated between the surface values and those extracted from the crustal velocity model at the transition depth. Density is derived from interpolated VP via the Nafe-Drake law of Brocher. Depth dependence for the interpolation is parameterized with
|z||= zʹ / zT|
|f(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)|
where zʹ is depth, VST and VPT are S- and P-wave velocities extracted from the crustal velocity model at depth zT, P() is the Brocher P-wave velocity scaling law, and R() is the Nafe-Drake law. The coefficient a controls the ratio of surface velocity to original 30 meter average, b controls overall curvature, 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-S generic soil profiles, as well as to produce smooth and well-behaved profiles when applied to the CVM-H at the selected CyberShake sites.
Figure 1. Generic S-wave velocity profile for all soil types is a summation of shallow component g(z) scaled by V30, and deep component f(z) scaled by VT.
Figure 2. Map of VS30 from CVM-S v4.0 with Boore, Gibbs, and Rodriguez (2003) sites.
Figure 3. Map of VS30 from CVM-H v6.3 with Boore, Gibbs, and Rodriguez (2003) sites.
Figure 4. Map of VS30 with Wills’ (2006) geologic proxy within California and Wald’s (2007) topographic proxy elsewhere.
Figure 5. Comparison of various VS30 models with Boore, Gibbs, and Rodriguez (2003) measurements.
Figure 6. Comparison of various VP30 models with Boore, Gibbs, and Rodriguez (2003) measurements.
Figure 7. S-wave velocity pofiles (upper 60 meters) for CVM-H (red), GTL model (blue) and Boore, Gibbs, and Rodriguez (2003) measurements (dashed).
Figure 8. P-wave velocity pofiles (upper 60 meters) for CVM-H (red), GTL model (blue) and Boore, Gibbs, and Rodriguez (2003) measurements (dashed).
Figure 9. Correlation of P- to S-wave velocity compiled from Boore, Gibbs, and Rodriguez (2003) sites with Brocher (2005) scaling law indicated by the dashed line. Brocher does a reasonable job of modeling VP greater than 1500 m/s at depths below the water table. Shallow depths (and hence VP30) are not well modeled by Brocher.