Using modified Mercalli intensities to estimate acceleration response spectra for the 1906 San Francisco earthquake

We derive and test relations between the Modified Mercalli Intensity (MMI) and the pseudo-acceleration response spectra at 1.0 and 0.3 s-SA(1.0 s) and SA(0.3 s)-in order to map response spectral ordinates for the 1906 San Francisco earthquake. Recent analyses of intensity have shown that MMI >= 6 correlates both with peak ground velocity and with response spectra for periods from 0.5 to 3.0 s. We use these recent results to derive a linear relation between MMI and log SA(1.0 s), and we refine this relation by comparing the SA(1.0 s) estimated from Boatwright and Bundock's (2005) MMI map for the 1906 earthquake to the SA(1.0 s) calculated from recordings of the 1989 Loma Prieta earthquake. South of San Jose, the intensity distributions for the 1906 and 1989 earthquakes are remarkably similar, despite the difference in magnitude and rupture extent between the two events. We use recent strong motion regressions to derive a relation between SA(1.0 s) and SA(0.3 s) for a M7.8 strike-slip earthquake that depends on soil type, acceleration level, and source distance. We test this relation by comparing SA(0.3 s) estimated for the 1906 earthquake to SA(0.3 s) calculated from recordings of both the 1989 Loma Prieta and 1994 Northridge earthquakes, as functions of distance from the fault.