基于SVD-TLS算法的非预测欧拉反褶积

针对地下有多个异常源时，单一预测构造指数难于表征多个异常源。采用非预测欧拉反褶积以避免可能错误确定构造指数使得欧拉解过度发散的问题；同时针对欧拉反褶积超定方程组的条件数很大，致使欧拉反褶积解集中良解占优率低等解的非唯一性和解的不稳定性等局限性，采用奇异值分解总体最小二乘法（SVD-TLS算法），以降低由于奇异值分析不当造成计算欧拉解非唯一性和解的不稳定性的问题，并利用SVD-TLS的截断误差构造阈值函数对解集进行过滤。数值结果表明了算法的有效性和可靠性。

Euler deconvolution based on SVD-TLS

It is difficult to characterize complicated anomaly sources with the single prescribed structure index and to determine structural index when these types of causative sources are unknown, and solutions of Euler deconvolution with divergent trend caused by error set or wrongly estimated structural index. Pathological equations of Euler deconvolution results in good solution. In this paper, we use SVD-TLS algorithm to reduce instability and non-uniqueness of Euler solution due to improper singular value analysis, then use truncation error of SVD-TLS to construct threshold function to filter the erroneous solutions. The proposed method is verified by one numerical example and results show that the approach is effective.