Constraining the source separation with coda wave interferometry: Theory and application to earthquake doublets in the Hayward fault, California

The relative location of seismic sources is of importance for the location of aftershocks on a fault, for the positioning of sources in repeat seismic surveys, and for monitoring induced seismicity. In this paper we show how the seismic coda can be used to infer a measure of the source separation of two identical seismic sources from the correlation of the waveforms recorded at a single receiver. The theory is applicable to an explosive source in an acoustic or elastic medium and for a point force or double couple in an elastic medium. For an explosive source the source separation is constrained to be located on a sphere, while for a point force and a double couple the source separation can be constrained to be located on an ellipsoid whose symmetry axis is determined by the point force or double couple. We validate the theory with synthetic seismograms and apply the theory to earthquake doublets on the Hayward fault, California. The distance between events obtained from the coda waves agrees with the distance obtained from the double-difference method.