Simultaneous Inversion of Hypocenters and Velocity Structure using the Quasi-Newton Method and Trust-Region Method

Abstract

We propose a hybrid algorithm, which combines the quasi-Newton method and the trust-region method in a least square form, to simultaneously determine hypocenters and velocity structure. Our numerical tests indicate that the Hessian matrix constructed by the quasi-Newton method, with the positive definiteness and the satisfaction of the quasi-Newton condition, is more efficient and stable than the analytical one though only the first-order derivatives of the objective function are used in the quasi-Newton method. Furthermore, combining with the trust-region method, our algorithm of simultaneous determination of hypocenters and velocity structure has been proven to be a more accurate and efficient and has better convergent property than the classic method. With our method, we relocate the hypocenter of the Chi-Chi earthquake of Taiwan and obtain the result: latitude 23.86°N, longitude 120.80°E, focal depth 10km, and origin time 17:47:16.0. This result is consistent with the previous credible result, and is robust with different initial values and different data sets. Finally, we apply our method to simultaneously determine the hypocenters and 1-D velocity structure of the North China area by using the selected 971 high quality direct and refracted P arrivals of 64 earthquakes from 40 stations of the North China Seismic Network from 1998 to 2001. We find that the upper crust in this area has low velocity with a sharp increase at depth of 4km, the middle crust has high velocity (~6km/s), and the lower crust has a positive velocity gradient.