Estimation of seismic source parameters in 3D elastic media using the reciprocity theorem

Abstract

We have developed a novel method based upon reciprocity principles to simultaneously estimate the location of a seismic event and its source mechanism in 3D heterogeneous media. The method finds double-couple (DC) and non-DC mechanisms of microearthquakes arising from localized induced and natural seismicity. Because the method uses an exhaustive search of the 3D elastic media, it is globally convergent. It does not suffer from local minima realization observed with local optimization methods, including Newton, Gauss-Newton, or gradient-descent algorithms. The computational efficiency of our scheme is derived from the reciprocity principle, in which the number of 3D model realizations corresponds to the number of measurement receivers. The 3D forward modeling is carried out in the damped Fourier domain with a 3D finite-difference frequency-domain fourth- and second-order code developed to simulate elastic waves generated by seismic sources defined by forces and second-order moment density tensors. We evaluate the results of testing this new methodology on synthetic data for the Raft River geothermal field, Idaho, as well as determine its applicability in designing optimal borehole monitoring arrays in a fracking experiment at the Homestake Mine, South Dakota. We also find that the method proposed here can retrieve the moment tensors of the space distributed source with data arising from spatially restricted arrays with limited aperture. The effects of uncertainties on the source parameter estimation are also examined with respect to data noise and model uncertainty.