Factors influencing the effectiveness of SM-VCE method in solving 3D surface deformation

Abstract

The recovery of coseismic 3-dimensional (3D) surface deformation field plays a crucial role in studying seismic source characteristics and earthquake hazards. As of now, there are two main types of methods for recovering coseismic 3D surface deformations: the first type is to solve the problem directly by using the least squares method based on observations from three or more viewpoints, and the second type solves the problem by combining ascending and descending InSAR line-of-sight (LOS) observations with constraint models. The former type is mainly applicable to surface rupture earthquakes, because when an earthquake ruptures to the surface, we can usually obtain surface deformation observations from three or more views. The latter type applies to earthquakes that do not cause surface ruptures and have extensive blind faults. Currently, most research focuses on improving the above types of methods. However, some key factors in the coseismic 3D surface deformation inversion are rarely mentioned, such as the influence of window size on the inversion results in the strain model and variance component estimation method (SM-VCE), and whether the outliers in the observational data are considered. So, we developed a new chain of integrating InSAR observation and SM-VCE model to systematically assess the impacts of window size and outliers on coseismic 3D surface deformation inversions. Through simulation experiments, we observed that the selection of window size significantly impacts the accuracy of the results. Specifically, larger window sizes lead to wider residuals ranges in the fault region, resulting in the loss of extreme solution values when using a window of 15 × 15 pixels (i.e., 7.5 km × 7.5 km). Hence, we recommend utilizing windows with 7 × 7 pixels or 9 × 9 pixels for optimal accuracy, as larger window sizes diminish the significance of the outcomes. The elimination of points displaying different deformation directions helps reduce residuals and preserves near-field deformation results. Furthermore, the residuals along the 3D direction can be reduced by 10%–30% when a small set of points is selected using a method based on Euclidean distances. However, when 441 points were selected, the vertical residuals increased by 22% compared to 81 points. Integration of the SM-VCE algorithm with robust estimation techniques effectively minimizes far-field deformation errors in data, thereby marginally enhancing the near-field deformation solution.