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Euler solution selecting method based on the damping factor

Qiang Liu, Changli Yao, Yao Luo, Junjun Yang, Zelin Li

Acta Geophysica

2022

Vol. 70, no 4

1551--1564

We present a method, named the variable damping factor selecting method, to select reliable Euler solutions. Our method considers the influence of small perturbations on the movement of Euler solutions as a selection criterion. Small perturbations have little influence on the least-squares solution generated from a stable matrix with large eigenvalues and in the projection area of the source position in the observational data. It is found that the matrix is stable and the solutions are reliable. By using the damped least square method to calculate the Euler solutions, our method can automatically estimate whether a solution can be saved. The saved solution, which is considered to be reliable, is not sensitive to any changes of the damping factor and is usually generated within a sliding window located in the projection area. In our work, the damping factor is chosen from the eigenvalue of the sliding window. Tests on synthetic and real data showed that our method is simple and easy to conduct, and can successfully outline causative bodies and singular point sources.