Variance component adaptive estimation algorithm for coseismic slip distribution inversion using interferometric synthetic aperture radar data

When conducting coseismic slip distribution inversion with interferometric synthetic aperture radar (InSAR) data, there is no universal method to objectively determine the appropriate size of InSAR data. Currently, little is also known about the computing efficiency of variance component estimation implemented in the inversion. Therefore, we develop a variance component adaptive estimation algorithm to determine the optimal sampling number of InSAR data for the slip distribution inversion. We derived more concise variation formulae than conventional simplified formulae for the variance component estimation. Based on multiple sampling data sets with different sampling numbers, the proposed algorithm determines the optimal sampling number by the changing behaviors of variance component estimates themselves. In three simulation cases, four evaluation indicators at low levels corresponding to the obtained optimal sampling number validate the feasibility and effectiveness of the proposed algorithm. Compared with the conventional slip distribution inversion strategy with the standard downsampling algorithm, the simulation cases and practical applications of five earthquakes suggest that the developed algorithm is more flexible and robust to yield appropriate size of InSAR data, thus provide a reasonable estimate of slip distribution. Computation time analyses indicate that the computational advantage of variation formulae is dependent of the ratio of the number of data to the number of fault patches and can be effectively suitable for cases with the ratio smaller than five, facilitating the rapid estimation of coseismic slip distribution inversion.