What we can and cannot learn about earthquake sources from the spectra of seismic waves

Earthquake sources are commonly viewed as shear dislocations. This imposes distinct limitations on what source parameters can be realistically determined from radiated shear-wave spectra. First, the slip velocity on the fault is the real parameter that controls the strength of the high-frequency radiation; it can be directly determined from acceleration spectra by fitting their high-frequency level. Second, the relationship between corner frequency of the spectrum and the radius of the source is fundamentally unclear. As a result, the source dimensions cannot be accurately determined from the spectra; such an estimate would be as accurate as any other informed guess. Third, the stress drop only serves as a proxy for the source radius in the relationship between the radius and the corner frequency; it thus cannot be reliably determined from the spectra. The quantity usually obtained from the spectra and referred to as the stress drop is a poorly defined parameter that may bear little relevance to the actual stresses acting on faults. This parameter has little meaning unless converted to the maximum slip velocity, which is the only quantity that can be accurately determined from the spectra. The typical value of stress drop of 100 bars, established from the spectra of California events, may imply that the typical slip velocities have been on the order of 0.5 m/sec, although it is more accurate to determine slip velocities directly from the spectra.