Details of the Abstract
| Title of paper | The use of L-curve criteria in non-linear inverse problem |
| List of authors | H. Song, Y. Usui, T. Koyama, D. Diba, M. Uyeshima, K. Baba, P. Yu, B. Yang |
| Affiliation(s) |
State Key Laboratory of Marine Geology, Tongji University, Earthquake Research Institute, the University of Tokyo, Earthquake Research Institute, the University of Tokyo, Earthquake Research Institute, the University of Tokyo, Earthquake Research Institute, the University of Tokyo, Earthquake Research Institute, the University of Tokyo, State Key Laboratory of Marine Geology, Tongji University, Key Laboratory of Ocean and Marginal Sea Geology, South China Sea Institute of Oceanology, Chinese Academy of Sciences, Guangzhou, China |
| Summary | Since the ill-posed nature intrinsically exists in almost all kinds of geophysical inverse problems, the regularization stabilizing the inversion process plays a crucial role in the current deterministic inversion framework. One important issue still open question is which philosophy we should adhere to and how to find the 'optimal' trade-off parameter to balance data fitting and regularization. Currently, there exists the data-fitting-oriented discrepancy principle, represented as OCCAM. This approach is popular within the EM community. However, it carries a risk of over-fitting when the data uncertainty is not accurately estimated. Another well-known approach is the cooling approach. Its underlying philosophy seems very geologically meaningful. However, when one really starts inversion homework, this philosophy can sometimes become a prejudice, as many settings –– such as the initial trade-off parameter, the corresponding decreasing rate, and the data decreasing threshold –– lack a reasonable quantitative explanation. Here, we advocate for the L-curve criteria. This approach is well-validated in mathematics. However, it's important to note that the L-curve was originally designed for linear inverse problems in which the quality (e.g. distribution of singular values) of the forward matrix is fixed. Using it in nonlinear scenarios, such as 3D MT inversion, the nonlinearity of MT should be considered. In this work, through three simulated cases and the USArray data application, we will show (1) the potential risks when the nonlinearity of inversion is not considered, (2) the merits of L-curve criteria when it is correctly used, (3) the underlying connection between L-curve and cooling in nonlinear problems. |
| Session Keyword | 2.0 EM theory, modelling and Inversion |
| File upload |
2.0_the_use_of_l-curve_criter_song_04.pdf
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