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

Abstract

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.

The hidden simplicity of subduction megathrust earthquakes

“…By itself, the corner frequency estimate data is not sufficient to test the scaling break either, because it contains very few events above the presumed scaling break at M w ~7.0. Notably, the study that extends the approach of the two corner frequency studies to large subduction zone earthquakes (35) finds the same scaling break that we report from M 0 1/3 to M 0 1/2 at M w ~7.0. However, owing to limitations of the employed methods they had to change methods at just the critical M w ~7.0.…”

Source Spectral Properties of Small to Moderate Earthquakes in Southern Kansas

“…For steps (1) and (2), we consider P wave spectra of earthquakes with local magnitude M L 1.5 and greater, recorded on vertical‐component, high‐broadband, and short‐period channels (HHZ, HNZ, and EHZ), at stations within 150 km distance. For the spectral estimates, we use a magnitude‐dependent window length ranging from a minimum length of 1.5 s to a maximum length of 4.5 s, where longer windows correspond to larger events in order to permit adequate corner frequency resolution (Abercrombie et al, ; Ross & Ben‐Zion, ; Trugman & Shearer, ). We define the signal window to begin 0.05 s before the catalog‐listed P phase arrival time, truncate each window before the catalog‐listed S phase arrival when necessary, and define a noise window that immediately precedes the signal window and is of equal length.…”

“…To estimate the EGF correction term (step 3), we use the technique described by Trugman and Shearer () that fits stacked relative source spectra, averaged in bins of spectral moment Ω 0 to a Brune‐type theoretical spectrum of the form where f c and Ω 0 are the corner frequency and spectral moment of each stacked spectra, and the high‐frequency falloff rate n is fixed to 2 per the widely used ω −2 model (Aki, ; Brune, ). In contrast to previous implementations of the spectral decomposition method (e.g., Shearer et al, ), our technique does not require an assumption of self‐similar or constant stress drop scaling and instead infers the optimal scaling directly from the shape of the stacked spectra.…”

“…In contrast to previous implementations of the spectral decomposition method (e.g., Shearer et al, ), our technique does not require an assumption of self‐similar or constant stress drop scaling and instead infers the optimal scaling directly from the shape of the stacked spectra. Here we find that the optimal fit requires an EGF with non‐self‐similar scaling such that stress drop increases with spectral moment (Figure ), a result in agreement with a recent analysis of earthquakes in California (Trugman & Shearer, ). Inference of the EGF is an essential part of the spectral decomposition technique because the source terms e i produced by the solution to equation are relative (median amplitude 0) and thus must be corrected for propagation effects that are common to all sources.…”

“…Note that this result is based only on observations within the 2.5 to 25 Hz band where we have good signal‐to‐noise ratio and does not require resolving corner frequencies outside of this band. However, as discussed in Trugman and Shearer (), the case for an increase in average stress drop with moment does depend upon the assumption of the Brune spectral model and its f −2 high‐frequency falloff rate, as reasonable fits to the stacked spectra are possible for self‐similar models with high‐frequency falloff rates less than 2.…”