Estimating three-dimensional coseismic deformations with the SM-VCE method based on heterogeneous SAR observations: Selection of homogeneous points and analysis of observation combinations

The previously proposed Strain Model and Variance Component Estimation (SM-VCE) method estimates three-dimensional (3-D) deformations based on heterogeneous synthetic aperture radar (SAR) observations from three or more distinct observing geometries. This method establishes an observation function by exploiting the spatial correlation of adjacent point deformations based on a geo-kinematic model (i.e., SM), and it determines an accurate weight of heterogeneous observations using the VCE algorithm; this method has been demonstrated to be superior to the traditional pixel-by-pixel-based weighted least square (WLS) method. However, since the SM-VCE method employs the adjacent points' observations to estimate 3-D deformations at a target point, it is inevitable that it results in a bias in the solution near the deformation jump area (e.g., the fault zone in an earthquake). In this paper, a Strain Model-based Adaptive Neighborhood Determining (SMAD) method is proposed to identify homogeneous deformation observations in such a way that the accuracy of the 3-D deformations estimated by the SM-VCE method can be increased, especially near the surface rupture area. This method is used for mapping 3-D coseismic deformations associated with the 2016 Mw7.8 KaikOura earthquake in New Zealand. Furthermore, with increasing SAR data available for a single event, the effect of the number/type of independent observations on the accuracy of the 3-D deformations remains poorly understood and requires further discussion. To accomplish this goal, we define a term, the deformation dilution of precision (DDOP), to represent the quality of the 3-D deformation vector; this term is similar to the position dilution of precision (PDOP) in global navigation satellite system (GNSS), and we investigate different combinations with different numbers/types of independent observations to explore the 3-D deformations of this earthquake. The results demonstrate that the type of incorporated observations can significantly dominate the accuracy of the 3-D deformations compared to the number of observations, which can provide an important reference for relevant studies that estimate 3-D deformations. Furthermore, the proposed methods and conclusions are beneficial for estimating 3-D surface deformations associated with other geophysical processes, such as volcanic eruptions.

Automated summary

The proposed SMAD method aims to improve the accuracy of 3-D deformations estimated by the SM-VCE method, especially near the surface rupture area. Additionally, the study investigates the impact of the number and type of independent observations on the accuracy of 3-D deformations, introducing the concept of deformation dilution of precision. The results suggest that the type of observations incorporated can significantly influence the accuracy of 3-D deformations compared to the number of observations.