Simultaneous estimation of slip distribution and correlation length using Bayesian optimization and the impact of inhomogeneous observation network distribution

SUMMARY This study develops a Bayesian optimization method of coseismic slip distributions and the correlation lengths of the von Kármán autocorrelation function, which can realize more reliable regularization grounded in geophysical analysis (VKR). To validate VKR and its dependence on the observation, synthetic tests using data from inhomogeneously distributed Global Navigation Satellite System (GNSS) stations and Synthetic Aperture Radar (SAR) were conducted. When observation stations surround the source fault, the assumed slip distribution and the correlation length were well recovered with some artificially extended slip due to the inhomogeneity of the observation network. Moreover, when observation stations exist only on one side of the fault, the method recovered the slip and other parameters with accuracy comparable to that of the surrounding-case scenario, albeit with slightly increased uncertainty of the parameters. This highlights the importance of uncertainty evaluation for slip and correlation length parameters, especially under biased observation networks. Applying existing Laplacian smoothing methods to the same experiments produced models globally consistent with VKR, demonstrating that the proposed method, despite additional nonlinear parameters, achieves comparable estimation accuracy. Existing method showed isotropic correlations of slip variables, whereas VKR exhibited correlations elongated along the strike direction, reflecting its ability to independently regularize along strike and dip via correlation length parameters. These correlation patterns were most pronounced in deeper fault regions, where regularization dominated over observational constraints. Cluster analysis of the Markov samples revealed that VKR captured a more diverse set of slip distribution models, with cluster differences most evident in deeper fault regions. These analyses underscore the importance of regularization choice and its impact when evaluating and interpreting slip distributions. We also applied VKR to the actual data of the 2024 Noto Peninsula earthquake in Japan, observed by dense GNSS networks and SAR. The estimated slip distribution featured multiple slip areas in the eastern and western peninsula, consistent with previous studies and Laplacian smoothing-based results. The correspondence between estimated slip distribution and correlation length was confirmed, although it did not match previous empirical findings. To further examine the effect of observation network configuration, we performed additional inversions using a reduced set of actual data. The resulting slip distribution was smoother, and the estimated correlation lengths were larger and more uncertain. Our results reconfirm that simultaneous estimation of slip distribution and correlation length produces mutually consistent values, both of which depend on the spatial distribution of observation points. The results also demonstrate the strong dependence of estimated slip distribution and correlation lengths on the observation network. Therefore, future studies of coseismic slip self-similarity, using observed data, should incorporate parameter analyses that account for network resolution effects.