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Euler solution selecting method based on the damping factor


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.

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(modified from Sherrod et al. (2008)). The purple rectangle shows the study area. EB—Everett basin, SB—Seattle basin, SU—Seattle uplift, S—Seattle, SF—Seattle fault, TF—Tacoma fault, T—Tacoma, TB—Tacoma basin, PT—Port Townsend, WI—Whidbey Island, CRBF—Coast Range boundary fault, OF—Olympia fault, RMF—Rattlesnake Mountain fault, SWIF—Southern Whidbey Island fault, UPF—Utsalady Point fault

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We thank the Society of Exploration Geophysicists and USGS for providing the data. This work was supported by National High Technology Research and Development Project of China (No. 2014AA06A613), National Natural Science Foundation of China (No. 42004121, No. 42006197), and Natural Science Foundation of Hebei Province (D2020402009). We would like to thank the Associate Editor Prof. T. Grabowska and two anonymous reviewers for their constructive comments that have helped improve the quality of the manuscript.

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Correspondence to Liu Qiang.

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On behalf of all authors, the corresponding author states that there is no conflict of interest.

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Edited by Prof. Teresa Grabowska (ASSOCIATE EDITOR) / Prof. Michał Malinowski (CO-EDITOR-IN-CHIEF).

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Qiang, L., Changli, Y., Yao, L. et al. Euler solution selecting method based on the damping factor. Acta Geophys. 70, 1551–1564 (2022).

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  • Potential field
  • Euler deconvolution
  • Damped least square method
  • Damping factor
  • Filter Euler solution