An Accurate Earthquake Localization Algorithm Using the TDOA Measurements between P and S Waves

Abstract

This paper investigates the problem of earthquake localization based on the time-difference-of-arrival (TDOA) measurements between P and S waves. The measuring method not only offers the advantage of easy implementability but also effectively lowers the error caused by insufficient understanding of crustal structure. Combining semidefinite programming (SDP) technique and Picard iteration method, an effective algorithm is proposed to accurately locate earthquake focus. Firstly, we derive a nonconvex estimator from the maximum likelihood estimator (MLE), then apply the SDP technique to the derived nonconvex estimator and develop a convex estimator. To further improve the location performance of the focal depth, we append a Picard iteration method to the convex estimator with the result by the convex estimator as the initial value. The proposed algorithm is then extended to the more general case when propagation speed is unknown. The corresponding Cramér-Rao lower bounds (CRLBs) are derived as performance benchmarks. Finally, simulation results show that the proposed algorithm outperforms the existing approaches and attains the CRLB.