Does Earthquake Stress Drop Increase With Depth?

We combine earthquake spectra from multiple studies to investigate whether the increase in stress drop with depth, that is often observed in the crust, is real or an artefact of variation in attenuation (Q) with depth. Shearer et al. [2006] developed spectral decomposition, in which spectra from large numbers of earthquakes and stations are stacked and inverted to separate the source radiation (event spectra) from the effects of path and site. This approach stabilizes the results and decreases the uncertainties by stacking a large number of recordings. The empirical path and attenuation corrections are usually assumed to be the same for all earthquakes in the study region, regardless of 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 from over 50,000 earthquakes (M0-5) from 11 studies in northern California [Hardebeck & Aron, 2009; Trugman & Shearer, 2018; Zhang et al., 2019], southern California [Chen & Shearer, 2011; Trugman & Shearer, 2017; Shearer et al., 2019, Trugman, 2020], Kansas [Trugman et al., 2017], Oklahoma [Chen & Abercrombie, 2020; Pennington, 2020] and Nevada.

For different magnitude bins, we compare the ratio of the high- to low-frequency amplitudes and find that the relative high-frequency content (and corner frequency) always increases with increasing earthquake depth. 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 the observed depth dependence in high-frequency radiation and corner frequency.

Without any correction for depth-dependent attenuation, we find a systematic increase in stress drop with depth (or increase in rupture velocity), as has previously been observed. When we add an empirical attenuation correction, the depth dependence of stress drop systematically decreases, often becoming negligible. The largest corrections are observed in regions with the largest velocity increase with depth. We conclude that spectral decomposition analyses should not assume path terms are independent of source depth, and should more explicitly consider depth-dependent attenuation models.