The Relation Between Ground Motion, Earthquake Source Parameters, and Attenuation: Implications for Source Parameter Inversion and Ground Motion Prediction Equations

Abstract

AbstractTheoretical equations relating the root‐mean‐square (rms) of the far‐field ground motions with earthquake source parameters and attenuation are derived for Brune's omega‐squared model that is subject to attenuation. This set of model‐based predictions paves the way for a completely new approach for earthquake source parameter inversion and forms the basis for new physics‐based ground motion prediction equations (GMPEs). The equations for ground displacement, velocity, and acceleration constitute a set of three independent equations with three unknowns: the seismic moment, the stress drop, and the attenuation parameter. These are used for source parameter inversion that circumvents the time‐to‐frequency transformation. Initially, the two source parameters and the attenuation constant are solved simultaneously for each seismogram. Sometimes, however, this one‐step inversion results in ambiguous solutions. Under such circumstances, the procedure proceeds to a two‐step approach, in which a station‐specific attenuation parameter is first determined by averaging the set of attenuation parameters obtained from seismograms whose one‐step inversion yields well‐constrained solutions. Subsequently, the two source parameters are solved using the averaged attenuation parameter. It is concluded that the new scheme is more stable than a frequency domain method, resulting in considerably less within‐event source parameter variability. The above results together with rms‐to‐peak ground motion relations are combined to give first‐order GMPEs for acceleration, velocity, and displacement. In contrast to empirically based GMPEs, the ones introduced here are extremely simple and readily implementable, even in low‐seismicity regions, where the earthquake catalog lacks strong ground motion records.