Earthquake source scaling and self‐similarity estimation from stacking P and S spectra

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Abstract
We study the scaling relationships of source parameters and the self‐similarity of earthquake spectra by analyzing a cluster of over 400 small earthquakes (ML = 0.5 to 3.4) recorded by the Anza seismic network in southern California. We compute P, S, and preevent noise spectra from each seismogram using a multitaper technique and approximate source and receiver terms by iteratively stacking the spectra. To estimate scaling relationships, we average the spectra in size bins based on their relative moment. We correct for attenuation by using the smallest moment bin as an empirical Green's function (EGF) for the stacked spectra in the larger moment bins. The shapes of the log spectra agree within their estimated uncertainties after shifting along the ω−3 line expected for self‐similarity of the source spectra. We also estimate corner frequencies and radiated energy from the relative source spectra using a simple source model. The ratio between radiated seismic energy and seismic moment (proportional to apparent stress) is nearly constant with increasing moment over the magnitude range of our EGF‐corrected data (ML = 1.8 to 3.4). Corner frequencies vary inversely as the cube root of moment, as expected from the observed self‐similarity in the spectra. The ratio between P and S corner frequencies is observed to be 1.6 ± 0.2. We obtain values for absolute moment and energy by calibrating our results to local magnitudes for these earthquakes. This yields a S to P energy ratio of 9 ± 1.5 and a value of apparent stress of about 1 MPa.

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