Abstract
In geodetic data inversion, insufficient observational data and smoothness constraints for model parameters make it difficult to clearly resolve small-scale heterogeneous structures with discontinuous boundaries. We therefore developed a novel regularization scheme for the inversion problem that uses discontinuity, sparsity, and smoothness constraints. In order to assess its usefulness and applicability, the proposed method was applied to synthetic displacements calculated by a ring-shaped and sharply varying afterslip distribution on a plate interface. The afterslip was obtained from reasonable numerical simulation of earthquake generation cycle with a rate- and state- dependent friction law and realistic three-dimensional plate geometry. The obtained afterslip distribution was heterogeneous, and the discontinuous boundary was sharper than that obtained by using smoothness constraint only. The same inversion test was conducted with a smoothly varying circular slip distribution with large slips inside the ring-shaped distribution. The method accurately reproduces the smooth distribution of the slip area as well as the ring-shaped distribution. Therefore, the method could be applied to any slip distribution, with both discontinuous and continuous boundaries. Adopting this method for measured data will make it possible to obtain detailed heterogeneous distributions of physical structures on fault planes. The proposed method is therefore applicable to various geophysical inversion problems that exhibit discontinuous heterogeneity.
Highlights
Earthquake generation is related to the heterogeneous distribution of fault slips and locking conditions on the fault planes; for example, a heterogeneous distribution is observed in coseismic slip distribution (e.g., Ide 2007), source areas of large interplate earthquakes with magnitudes greater than seven (Yamanaka and Kikuchi 2004), and small repeating earthquakes (Uchida and Matsuzawa 2011)
For the ring-shaped slip distribution test using the smoothness regularization, the estimated spatial distribution showed a wider slip area with a smoother boundary compared to the true slip distribution (Fig. 4a and b)
Conclusions and future work We demonstrated that the spatial distribution of both ring-shaped and smoothly varying circular slip distributions can be reproduced by the same method
Summary
Earthquake generation is related to the heterogeneous distribution of fault slips and locking conditions on the fault planes (or plate interfaces); for example, a heterogeneous distribution is observed in coseismic slip distribution (e.g., Ide 2007), source areas of large interplate earthquakes with magnitudes greater than seven (Yamanaka and Kikuchi 2004), and small repeating earthquakes (Uchida and Matsuzawa 2011). Optimization using smoothness, discontinuity, and sparsity constraints A numerical inversion test was conducted to assess how efficiently the proposed method can reproduce the original distribution of slip from noise-overlapped synthetic displacement data. The model parameter (s), which minimizes the evaluation function in Eq 4, is expected to be the best solution in terms of satisfying the reproducibility of the observation, the continuity of the slip with a discontinuous boundary, and the sparsity of a slip area.
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