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In addition, a spatiotemporal smoothing constraint on the slip (Sekiguchi et al. 2000) is imposed.
We performed inversions using several combinations of V ftw and weight of smoothing constraint.
In addition, we impose a spatiotemporal smoothing constraint on slips (Sekiguchi et al. 2000); the weight of the smoothing constraint is determined based on Akaike's Bayesian Information Criterion (Akaike 1980).
This is in contrast with the static core field that is not significantly affected by the smoothing constraint.
To suppress instability or excessive complexity, a smoothing constraint was applied to differences in the moment release.
Therefore, characteristics of our afterslip distribution are attributed to both weighting of datasets and a priori smoothing constraint.
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Among a number of possible stabilizing functionals, smoothing constraints are most commonly used, which produce spatially smooth inversion results.
Smoothing constraints, the difference between adjacent model parameters as an approximation of a derivative to control solution roughness, were also used (e.g., Menke, 1984).
This spline order is set to higher value than for GRIMM, such that it is consistent with time smoothing constraints that are presented below.
To obtain more stable results, we applied smoothing constraints to the slip distribution with respect to time and space, adopting an optimized ABIC (Akaike, 1980; Fukahata et al., 2003, 2004) to determine the smoothness parameter.
To obtain a stable inversion solution, we used the data covariance matrix from the observation and modeling errors, incorporated smoothing constraints and determined their optimal values by using the Akaike Bayesian Information Criterion ABICC).
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