A Double-Difference Earthquake Location Algorithm: Method and Application to the Northern Hayward Fault, California

TLDR: In this paper, a least square solver is found by iteratively adjusting the vector difference between hypocentral pairs to minimize residuals between observed and theoretical travel-time differences.

Abstract: We have developed an efficient method to determine high-resolution hypocenter locations over large distances. The location method incorporates ordinary absolute travel-time measurements and/or cross-correlation P-and S-wave differential travel-time measurements. Residuals between observed and theoretical travel-time differences (or double-differences) are minimized for pairs of earthquakes at each station while linking together all observed event-station pairs. A least-squares solu- tion is found by iteratively adjusting the vector difference between hypocentral pairs. The double-difference algorithm minimizes errors due to unmodeled velocity struc- ture without the use of station corrections. Because catalog and cross-correlation data are combined into one system of equations, interevent distances within multiplets are determined to the accuracy of the cross-correlation data, while the relative lo- cations between multiplets and uncorrelated events are simultaneously determined to the accuracy of the absolute travel-time data. Statistical resampling methods are used to estimate data accuracy and location errors. Uncertainties in double-difference locations are improved by more than an order of magnitude compared to catalog locations. The algorithm is tested, and its performance is demonstrated on two clus- ters of earthquakes located on the northern Hayward fault, California. There it col- lapses the diffuse catalog locations into sharp images of seismicity and reveals hor- izontal lineations of hypocenters that define the narrow regions on the fault where stress is released by brittle failure.