We combine earthquake spectra from multiple studies to investigate whether the increase in stress drop with depth often observed in the crust is real, or an artifact of decreasing attenuation (increasing Q) with depth. In many studies, empirical path and attenuation corrections are assumed to be independent of the earthquake source depth. We test this assumption by investigating whether a realistic increase in Q with depth (as is widely observed) could remove some of the observed apparent increase in stress drop with depth. We combine event spectra, previously obtained using spectral decomposition methods, for over 50,000 earthquakes (M0 to M5) from 12 studies in California, Nevada, Kansas and Oklahoma. We find that the relative high-frequency content of the spectra systematically increases with increasing earthquake depth, at all magnitudes. By analyzing spectral ratios between large and small events as a function of source depth, we explore the relative importance of source and attenuation contributions to this observed depth dependence. Without any correction for depth-dependent attenuation, we find a systematic increase in stress drop, rupture velocity, or both, with depth, as previously observed. When we add an empirical, depth-dependent attenuation correction, the depth dependence of stress drop systematically decreases, often becoming negligible. The largest corrections are observed in regions with the largest seismic velocity increase with depth. We conclude that source parameter analyses, whether in the frequency or time domains, should not assume path terms are independent of source depth, and should more explicitly consider the effects of depth-dependent attenuation.

The spectra of earthquake waveforms can provide important insight into rupture processes, but the analysis and interpretation of these spectra is rarely straightforward. Here we develop a Bayesian framework that embraces the inherent data and modeling uncertainties of spectral analysis to infer key source properties. The method uses a spectral ratio approach to correct the observed waveform spectra of nearby earthquakes for path and site attenuation. The objective then is to solve for a joint posterior probability distribution of three source parameters -- seismic moment, corner frequency, and high-frequency falloff rate -- for each earthquake in the sequence, as well as a measure of rupture directivity for target events with good azimuthal station coverage. While computationally intensive, this technique provides a quantitative understanding of parameter tradeoffs and uncertainties and allows one to impose physical constraints through prior distributions on all source parameters, which guide the inversion when data is limited. We demonstrate the method by analyzing in detail the source properties of 14 different target events of magnitude M5 in southern California that span a wide range of tectonic regimes and fault systems. These prominent earthquakes, while comparable in size, exhibit marked diversity in their source properties and directivity, with clear spatial patterns, depth-dependent trends, and a preference for unilateral directivity. These coherent spatial variations source properties suggest that regional differences in tectonic setting, hypocentral depth or fault zone characteristics may drive variability in rupture processes, with important implications for our understanding of earthquake physics and its relation to hazard.

The spatial patterns of earthquake ground motion amplitudes are commonly represented using a double couple model that corresponds to shear slip on a planar fault. While this framework has proven successful in explaining low-frequency seismic recordings, at higher frequencies the wavefield becomes more azimuthally isotropic for reasons that are not yet well understood. Here we use a dense array of nodal seismometers in Oklahoma to study the radiation patterns of earthquakes in the near-source region where wavefield scattering effects are limited. At these close distances, the radiation pattern is predominantly double couple at low frequencies (<15Hz). At higher frequencies, the recorded wavefield contains significant isotropic and residual components that cannot be explained as path or site effects, implying complexity in the rupture process or local fault zone structure. These findings demonstrate that earthquake source complexity can drive variability in the ground motions that control seismic hazard.