How <i>S</i> / <i>P</i> Amplitude Ratio Data Can Bias Earthquake Focal Mechanism Estimates

Abstract Earthquake focal mechanisms provide crucial information about subsurface fault geometry and stress orientations. Focal mechanisms are typically inferred through analysis of seismic radiation patterns, for example, using P-wave first-motion polarities, potentially in combination with S/P amplitude ratios, to identify nodal planes. The motivation for this procedure is well-founded, as P- and S-wave radiation patterns depend fundamentally on the fault orientation. However, in practice, S/P amplitude ratio measurements can be strongly influenced by factors that are unrelated to the source mechanism. In this study, I characterize several underappreciated issues with S/P amplitude ratio data that are relevant to focal mechanism inversion. The analysis combines synthetic tests with new waveform measurements from ∼64,000 ML≥1.0 earthquakes in Nevada and California. Key findings include that (1) the statistical distribution of S/P amplitude ratio data differs markedly in shape and width from the theoretical expectation, (2) S/P amplitude ratios decay systematically with source-station distance beyond ∼60 km or so, (3) this distance effect is more severe for smaller earthquakes than for larger ones, and (4) modifying the frequency band in which amplitudes are measured can shift the observed amplitude ratio distribution but does not significantly mitigate issues (1)–(3). Taken together, these findings indicate that S/P amplitude ratio measurements are influenced by differential path attenuation and signal-to-noise effects that are not accounted for with existing workflows. Using independent moment tensor solutions, I systematically test various strategies to incorporate S/P amplitude ratios into focal mechanism solutions. The best-performing strategies transform S/P amplitude data to better match the theoretical expectation. Overall, S/P amplitude ratio data appear helpful in improving a typical mechanism solution, but even with the best-performing strategies considered here, the inclusion of S/P amplitude ratio data is expected to hinder rather than improve the solution for a subset of events.