Coseismic slip distribution inversion with unequal weighted Laplacian smoothness constraints

Abstract

In coseismic slip distribution inversion, the Laplacian smoothness constraint is used to avoid the rank deficiency of the coefficient Green matrix and ensure the smoothness among the patches of the fault plane. However, by introducing the classic Laplacian smoothness constraint, the inversion of the maximum slip is commonly underestimated. To better solve this problem, here we propose a new method of weighting to the Laplacian second-order smoothness matrices by the slip. The Laplacian smoothness constraint with unequal weights and the classic Laplacian constraint are used to carry out the simulation experiments. The simulation experiments show that the accuracy of the estimated maximum slip from our method is outperforming the classical Laplacian method by 12–19 per cent. Moreover, the estimations of the average slip and moment magnitude have been enhanced, which improved ranging from 4 to 12.5 per cent and 0.4 to 9 per cent over the inversion results of classic Laplacian smoothness constraint, respectively. In order to further validate the general applicability of the proposed method, we conduct the experiments in terms of the inversion of L'Aquila and Taiwan Meinong earthquakes. The maximum slip inversion results show that the inversion of Laplacian smoothness constraint with unequal weights are larger than that of the classic Laplacian smoothness constraint, which is consistent with the conclusion of simulation experiments. In addition, the parameters inversion results of the actual earthquake from the proposed method are in agreement with other studies which also indicate the feasibility and effectiveness of our method.