Providing regularization on finite-fault inversion solution to increase the solution stability and certainty in the case of the 2004 Mw 6.1 Parkfield earthquake
摘要
The matrix inversion of seismic data for finite-fault source parameters is based on the formulation of the representation theorem as a linear inverse problem. The way the problem is parameterized involves substantial, and often subjective, decision-making. The inversion solution involves several levels of uncertainties and instabilities. In inversion solutions, the connection between model and data null spaces, solution uniqueness, and the ability to fit data is important. Therefore, these aspects are discussed in this research. We aim to reduce model space errors to arrive at more reliable and stable solutions. The Tikhonov method and the truncated singular value decomposition are used to explain the properties of rank-deficient and ill-conditioned linear inverse problems. The background of the essential trade-off between solution stability and data fitting. The 2004 Mw 6.1 Parkfield earthquake, a well-documented event, is chosen as our case study. The results show that the Tikhonov model with 0.15 m maximum slip and 5.8 moment magnitude produces the most stable model. By imposing a moment magnitude constraint on the Tikhonov solution, a maximum slip of 0.22 m is achieved.