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A variety of smoothing constraints can also be applied and in this study a spatial first derivative minimization constraint is employed.
Among a number of possible stabilizing functionals, smoothing constraints are most commonly used, which produce spatially smooth inversion results.
This spline order is set to higher value than for GRIMM, such that it is consistent with time smoothing constraints that are presented below.
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).
Note here that smoothing constraints were imposed not to the integration of square differentials of the values in time but to the sums of the square differences of the sequential values of consecutive earthquakes.
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.
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A Tikhonov-type smoothing constraint was applied to stabilise the retrieval.
One is the new conduction function for adaptive smoothing, and the other is the smoothing constraint for more accurate description of real environments.
We performed inversions using several combinations of V ftw and weight of smoothing constraint.
In addition, a spatiotemporal smoothing constraint on the slip (Sekiguchi et al. 2000) is imposed.
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).
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