Confidence intervals for earthquake source parameters

We develop a method to obtain confidence intervals of earthquake source parameters, such as stress drop, seismic moment and corner frequency, from single station measurements. We use the idea of jackknife variance combined with a multitaper spectrum estimation to obtain the confidence regions. The approximately independent spectral estimates provide an ideal case to perform jackknife analysis. Given the particular properties of the problem to solve for source parameters, including high dynamic range, non-negativity, non-linearity, etc., a log transformation is necessary before performing the jackknife analysis. We use a Student's t distribution after transformation to obtain accurate confidence intervals. Even without the distribution assumption, we can generate typical standard deviation confidence regions. We apply this approach to four earthquakes recorded at 1.5 and 2.9 km depth at Cajon Pass, California. It is necessary to propagate the errors from all unknowns to obtain reliable confidence regions. From the example, it is shown that a 50 per cent error in stress drop is not unrealistic, and even higher errors are expected if velocity structure and location errors are present. An extension to multiple station measurement is discussed.