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

Theoretical 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.