Estimating Earthquake Source Parameters from P-wave Spectra: Lessons from Theory and Observations

Abstract:

Observations make clear that some earthquakes radiate relatively more high frequency energy that others of the same moment. But translating these differences into traditional source parameter measures, such as stress drop and radiated energy, can be problematic. Some of the issues include: (1) Because of directivity and other rupture propagation details, theoretical results show that recorded spectra will vary in shape among stations. Observational studies often neglect this effect or assume it will average out when multiple stations are used, but this averaging is rarely perfect, particularly considering the narrow range of takeoff angles used in teleseismic studies. (2) Depth phases for shallow events create interference in the spectra that can severely bias spectral estimates, unless depth phases are taken into account. (3) Corner frequency is not a well-defined parameter and different methods for its computation will yield different results. In addition, stress drop estimates inferred from corner frequencies rely on specific theoretical rupture models, and different assumed crack geometries and rupture velocities will yield different stress drop values. (4) Attenuation corrections may be inaccurate or not fully reflect local 3D near-source attenuation structure. The use of empirical Green's function (EGF) events can help, but these often have signal-to-noise issues or are not very close to the target earthquake. (5) Energy estimates typically rely on some degree of extrapolation of spectra beyond their observational band, introducing model assumptions into what is intended to be a direct measure of an earthquake property. (6) P-wave spectra are analyzed much more than S-wave spectra because of their greater frequency content, but they only carry a small fraction of the total radiated seismic energy and thus total energy estimates may rely on poorly known Es/Ep scaling relations. We will discuss strategies to address these problems and to compute improved source parameter estimates with more realistic error bounds.