5.3 Implications for stress drop scaling with depth and
magnitude
We find that including reasonable corrections for depth dependent
attenuation and rupture velocity can remove all need for any systematic
dependence of stress drop on source depth in the upper 15 km at
Parkfield. This is consistent with the previous results of AS2007. It is
also in agreement with a recent meta-analysis (Abercrombie et al., 2020)
that showed that previously reported increases in stress drop with depth
could potentially be artefacts of inadequate correction for depth
dependent path effects.
Less intuitively, improving corrections for depth variation in
attenuation and velocity also decreased the resulting magnitude
dependence of the stress drop results. The magnitude dependence is weak
to the point of negligible above M1.75, but at lower magnitudes, some
increase in stress drop with magnitude remains, regardless of correction
strategy (see Figures 3, S6 and Table 1). We also observe increased
variability at smaller magnitudes (Figure 8), probably largely
reflecting increasing uncertainties. Based on previous analysis of the
effects of frequency bandwidth limitations (e.g., Abercrombie, 2021) and
our own analysis discussed above, we interpret this is a resolution
effect, rather than a real physical effect.