Empirical relationships between Modified Mercalli Intensity and response spectra

We develop empirical relationships between response spectra (5% damped horizontal-component pseudo-acceleration, PSA) and Modified Mercalli Intensity (MMI) based on observations from 29 California earthquakes in the moment magnitude range from 4.9 to 7.4, recorded over the distance range from 1 to 300 km. Corresponding relationships for peak ground-motion parameters are also developed. The relationship between PSA at low frequencies (or peak ground displacement) and MMI depends strongly on magnitude, while the relationship between PSA at high frequencies (or peak ground acceleration) and MMI depends strongly on distance. If the magnitude and location of the earthquake are known, then PSA and peak ground motions may be estimated from MMI to within a factor of two in most cases.