Compressional and Shear-Wave Velocity versus Depth Relations for Common Rock Types in Northern California by Thomas M. Brocher Abstract This article presents new empirical compressional and shear-wave veloc- ity (Vp and Vs) versus depth relationships for the most common rock types in north- ern California. Vp versus depth relations were developed from borehole, laboratory, seismic refraction and tomography, and density measurements, and were converted to Vs versus depth relations using new empirical relations between Vp and Vs. The relations proposed here account for increasing overburden pressure but not for varia- tions in other factors that can influence velocity over short distance scales, such as lithology, consolidation, induration, porosity, and stratigraphic age. Standard devia- tions of the misfits predicted by these relations thus provide a measure of the impor- tance of the variability in Vp and Vs caused by these other factors. Because gabbros, greenstones, basalts, and other mafic rocks have a different Vp and Vs relationship than sedimentary and granitic rocks, the differences in Vs between these rock types at depths below 6 or 7 km are generally small. The new relations were used to derive the 2005 U.S. Geological Survey seismic velocity model for northern California em- ployed in the broadband strong motion simulations of the 1989 Loma Prieta and 1906 San Francisco earthquakes; initial tests of the model indicate that the Vp model generally compares favorably to regional seismic tomography models but that the Vp and Vs values proposed for the Franciscan Complex may be about 5% too high. Introduction This article presents empirical compressional and shear- wave velocity versus depth relationships for the most com- mon rock types in northern California. These relations were used to construct a new 3D seismic velocity model for north- ern California (U.S. Geological Survey [USGS] Bay Area Seismic Velocity Model 05.1.0 [www.sf06simulation.org/, last accessed January 2008]). That model was first con- structed as a 3D structural and geologic model and was then converted into a compressional and shear-wave velocity, den- sity, and intrinsic attenuation model (http://quake.wr.usgs .gov/research/3Dgeologic/index.html, last accessed January 2008). The 3D velocity model has been used to calculate strong ground motions for scenario earthquakes in the San Francisco Bay Area, including the 1989 Loma Prieta and the 1906 San Francisco earthquakes (e.g., Aagaard, 2006; Graves, 2006; Larsen et al., 2006; Rodgers et al., 2006). Results of these calculations are presented in Aagaard, Brocher, Dolenc, Dreger, Graves, Harmsen, Hartzell, Larsen, and Zoback (2008) and Aagaard, Brocher, Dolenc, Dreger, Graves, Harmsen, Hartzell, Larsen, McCandless, et al. (2008). For this study, I have fit existing compressional-wave velocity data solely as a function of depth, to account for increasing overburden pressure, but ignoring other important causes of spatial variation such as stratigraphic age, consoli- dation, induration, and lithology. Regional relations were de- veloped because they provide a benchmark to which local measurements can be compared. Another motivation for this approach was that available sonic log data in northern Cali- fornia are more limited than in other parts of California such as in the Los Angeles basin (Magistrale et al., 1996; Brocher et al., 1998; Suess and Shaw, 2003), and stratigraphic and lithologic variations are simply not well sampled in much of northern California. As noted in Figure 1, there are a num- ber of Cenozoic sedimentary basins in northern California, but they tend to be smaller and have a thinner sedimentary cover than basins elsewhere in California, particularly in the Los Angeles area (Suess and Shaw, 2003; Brocher, 2005c). Regression curves were fit to the available observations for each rock type. The order of polynomial used for each rock type was varied to maximize the coefficient of determi- nation, R 2 . R 2 ranges between 0 and 1 and indicates how closely the data match the regression curve: values close to 1 indicate that the data are well predicted by the regression curve. In some cases, sparse data were simply fit by eye using linear gradients. Generally, the lowest order polyno- mial that best fit the data is provided in this report. 950 Bulletin of the Seismological Society of America, Vol. 98, No. 2, pp. 950–968, April 2008, doi: 10.1785/0120060403