Total Least Squares Method Inversion for Coseismic Slip Distribution

doi:10.11947/j.AGCS.2017.20160212

Abstract

Abstract: The coefficient matrix (Green matrix) is composed of surface point offset caused by unit slip of sub-fault patches. The elements of the coefficient matrix are related to the location, geometry of rupture surface, assumption of model and other factors. In this paper, we attempted to consider the Green'function matrix (coefficient matrix) errors in order to compensate for the effects of above-mentioned factors to some extent. The total least squares (TLS) method, which both errors of coefficient matrix and observation vector are considered, is proposed for fault slip inversion. So we dealt with the errors in both of coefficient matrix and observation at same time. And by analysis of the relations between observation vector and coefficient matrix elements, we obtained the covariance matrix of coefficient matrix elements and observation vector. Considering the coefficient matrix was ill-posed, we used the second-order Laplace smoothing to constrain the slip parameters each other, then we used the regularized total least squares method to estimate slip distribution. the total least squares (TLS)slip inversion method was applied to simulate oblique fault event and Mw6.3 earthquake occurred in L'Aquila (central Italy) on April 6, 2009, respectively. To L'Aquila earthquake, the results by total least squares method indicate that the inverted geodetic moment is 3.63×10¹⁸ N·m (Mw6.34). With a maximum slip of 0.95 m, and a average rake of -96.4°, the main slip occurred at depth of 4 km-15 km. The difference of slip distribution solutions between total least squares and least squares method is less than 10^-4 order.

Key words: coseismic slip distribution, total least squares inversion, regularization, L'Aquila earthquake

CLC Number:

P227

WANG Leyang, LI Haiyan, WEN Yangmao, XU Caijun. Total Least Squares Method Inversion for Coseismic Slip Distribution[J]. Acta Geodaetica et Cartographica Sinica, 2017, 46(3): 307-315.

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