SUMMARY
Inappropriate mathematical treatment of prediction errors associated with inaccurate forward modelling in an inversion scheme may result in significant unnatural short-wavelength components in the estimated slip distribution, which is a typical consequence of overfitting data. When geodetic data in observation stations following a non-uniform spatial distribution are used in a geodetic slip inversion, the spatial non-uniformity of the observation can possibly influence the distribution pattern of the short-wavelength components significantly, which may be confused with slip patterns that are geophysically meaningful. Such situations often occur when land and seafloor geodetic data are used in combination in slip inversions. To avoid overfitting, this study proposes a method that incorporates covariance components in the covariance matrix of the misfit vector, which originate from prediction errors. Because the proposed method retains the linearity of the inversion problem, widely known approaches that introduce prior constraints to a linear inversion problem are easily combined with the proposed method. This study demonstrates a combination of the newly introduced covariance components with a prior constraint on the smoothness of slip distribution, constructing a Bayesian model with unknown hyperparameters, which are objectively determined by minimizing Akaike’s Bayesian information criterion. In the synthetic tests, the proposed method estimated slip deficit rate (SDR) distributions that are closer to the true one, avoiding overfitting the geodetic data with spatial non-uniformity. By contrast, a conventional approach, which does not introduce covariance components, estimates unnaturally rough SDR distributions using the same synthetic data. The proposed method was applied to the estimation of SDR in the Nankai Trough subduction zone, using geodetic data of displacement rates provided by land GNSS stations and seafloor GNSS-Acoustic stations. This method estimates a reasonably smooth distribution of SDR, avoiding overfitting. The spatial distribution of residuals of the displacement rates suggests that the proposed method avoids overfitting some portions of the observed displacement rates that the forward model set for the analyses could not fundamentally explain.
Energy‐based scenarios for great thrust‐type earthquakes in the Nankai trough subduction zone, southwest Japan, using an interseismic slip‐deficit model
