A compilation of compressional-wave (Vp) and shear-wave (Vs) velocities and densities for a wide variety of common lithologies is used to define new nonlinear, multivalued, and quantitative relations between these properties for the Earth's crust. Wireline borehole logs, vertical seismic profiles, laboratory measurements, and seismic tomography models provide a diverse dataset for deriving empirical relations between crustal Vp and Vs. The proposed Vs as a function of Vp relations fit Vs and Vp borehole logs in Quaternary alluvium and Salinian granites as well as laboratory measurements over a 7-km/sec-wide range in Vp. The relations derived here are very close to those used to develop a regional 3D velocity model for southern California, based on pre-1970 data, and thus provide support for that model. These data, and these relations, show a rapid increase in Vs as Vp increases to 3.5 km/sec leading to higher shear-wave velocities in young sedimentary deposits than commonly assumed. These relations, appropriate for active continental margins where earthquakes are prone to occur, suggests that amplification of strong ground motions by shallow geologic deposits may not be as large as predicted by some earlier models.

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