Investigating uncertainties in empirical Green's function analysis of earthquake source parameters

I use a well-recorded earthquake sequence to investigate the uncertainties of earthquake stress drops calculated using an empirical Green's function (EGF) approach. The earthquakes in the largest (M similar to 2.1) repeating sequence targeted by the San Andreas Observatory at Depth (SAFOD), Parkfield, California, are recorded by multiple borehole stations and have simple sources, well-constrained stress drops, and abundant smaller earthquakes to use as EGFs. I perform three tests to estimate quantitatively the likely uncertainties to arise in less optimal settings. I use EGF earthquakes with a range of cross-correlation values and separation distances from the main earthquakes. The stress drop measurements decrease by a factor of 3 as the quality of the EGF assumption decreases; a good EGF must be located within approximately one source dimension of the large earthquake, with high cross correlation. I subsample the large number of measurements for the main earthquakes to investigate the expected stress drop uncertainties in studies where fewer stations or EGFs are available. If only one measurement is available, the uncertainties are likely to be at least 50%. The uncertainties decrease to <20% with five or more measurements; using multiple EGFs is a good alternative to multiple stations. To investigate the effects of limited frequency bandwidth, I recalculate the corner frequencies after progressively decimating the sample rate. Decreasing the high-frequency limit of the bandwidth decreases the estimate of the corner frequency (and stress drop). The corner frequency may be underestimated if it is within a factor of 3 of the maximum frequency of the signal.