Adaptive regularization of earthquake slip distribution inversion

• Adaptive regularization can achieve a significantly smaller mean square error than uniform one.
• An adaptive regularization method based on weighted total least squares is proposed.
• The proposed method can derive a smaller mean square error than uniform regularization.

Regularization is a routine approach used in earthquake slip distribution inversion to avoid numerically abnormal solutions. To date, most slip inversion studies have imposed uniform regularization on all the fault patches. However, adaptive regularization, where each retrieved parameter is regularized differently, has exhibited better performances in other research fields such as image restoration. In this paper, we implement an investigation into adaptive regularization for earthquake slip distribution inversion. It is found that adaptive regularization can achieve a significantly smaller mean square error (MSE) than uniform regularization, if it is set properly. We propose an adaptive regularization method based on weighted total least squares (WTLS). This approach assumes that errors exist in both the regularization matrix and observation, and an iterative algorithm is used to solve the solution. A weight coefficient is used to balance the regularization matrix residual and the observation residual. An experiment using four slip patterns was carried out to validate the proposed method. The results show that the proposed regularization method can derive a smaller MSE than uniform regularization and resolution-based adaptive regularization, and the improvement in MSE is more significant for slip patterns with low-resolution slip patches. In this paper, we apply the proposed regularization method to study the slip distribution of the 2011 Mw 9.0 Tohoku earthquake. The retrieved slip distribution is less smooth and more detailed than the one retrieved with the uniform regularization method, and is closer to the existing slip model from joint inversion of the geodetic and seismic data.