Geodetic inversion for spatial distribution of slow earthquakes under sparsity constraints

Abstract

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 applied sparse modelling to geodetic data inversion. In this paper, we reported two examples; one is 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 the plate interface beneath the Hyuga-nada region in southwest Japan. The discontinuous boundary was sharper than that obtained by using smoothness constraint only. The other is used the fused regularization, a type of sparse modelling suitable for detecting discontinuous changes in the model parameters. We estimated spatial distribution of the long-term slow slip events beneath the Bungo channel in southwest Japan. We found that the largest slip abruptly becomes zero at the down-dip limit of the seismogenic zone, and is immediately reduced to half at the up-dip limit of the deep low-frequency tremors, and becomes zero near its down-dip limit. Such correspondences imply that some thresholds exist in the generation processes for both tremors and SSEs. These results suggest that geodetic data inversion with sparse modelling can detect such abrupt changes and discontinuous boundaries in the slip distribution of slow earthquakes.