Application of an improved spectral decomposition method to examine earthquake source scaling in Southern California

Earthquake source spectra contain fundamental information about the dynamics of earthquake rupture. However, the inherent tradeoffs in separating source and path effects, when combined with limitations in recorded signal bandwidth, make it challenging to obtain reliable source spectral estimates for large earthquake data sets. We present here a stable and statistically robust spectral decomposition method that iteratively partitions the observed waveform spectra into source, receiver, and path terms. Unlike previous methods of its kind, our new approach provides formal uncertainty estimates and does not assume self-similar scaling in earthquake source properties. Its computational efficiency allows us to examine large data sets (tens of thousands of earthquakes) that would be impractical to analyze using standard empirical Green's function-based approaches. We apply the spectral decomposition technique to P wave spectra from five areas of active contemporary seismicity in Southern California: the Yuha Desert, the San Jacinto Fault, and the Big Bear, Landers, and Hector Mine regions of the Mojave Desert. We show that the source spectra are generally consistent with an increase in median Brune-type stress drop with seismic moment but that this observed deviation from self-similar scaling is both model dependent and varies in strength from region to region. We also present evidence for significant variations in median stress drop and stress drop variability on regional and local length scales. These results both contribute to our current understanding of earthquake source physics and have practical implications for the next generation of ground motion prediction assessments. Plain Language Summary Just as a line of music can be characterized in terms of its amplitude and pitch, earthquakes can be characterized in terms of their magnitude and frequency content. The frequency content of an earthquake depends on its size, with smaller earthquakes having systematically higher pitches than larger ones. Previous studies in earthquake seismology have assumed that the frequency content of earthquakes exhibits a particularly simple form of scaling with earthquake size known as self-similarity. Under this paradigm, large earthquakes are perfectly scaled-up versions of small ones, with the physical properties of the earthquake scaling in much the same way as font size does on a computer. In this article, the authors develop a new method to examine the frequency content of tens of thousands of earthquakes occurring in different regions of Southern California over the past 15 years. The authors find that the frequency content of these earthquakes deviated significantly from the self-similar model, with larger earthquakes being enriched in more high-frequency energy than expected. This result has important implications for earthquake hazard, as the most damaging ground motions are generated by the high-frequency seismic waves of the largest earthquakes.