[S-EM14] 電気伝導度・地殻活動電磁気学

[SEM14-P05] L1-TV1正則化を用いた磁気構造インバージョン手法について

*宇津木 充¹ (1.京都大学大学院理学研究科附属地球熱学研究施設火山研究センター)

キーワード：3次元スパース磁気インバージョン、L1正則及び全変動、交互方向乗算法

Magnetic inversion is a popular method to obtain information about subsurface structures. However, this method has a serious limitation in that the linear equations to be solved become ill-posed and under-determined, and therefore, the uniqueness of the solution is not guaranteed. Consequently, several different models fit the observed data with the same accuracy. Conventional studies introduced a regularization technique based on a quadratic solution norm to reduce this non-uniqueness of the problem. However, these regularization methods impose a certain level of smoothness into the model, which cause the resultant model to be blurred. Sparse regularization was introduced in many recent magnetic inversion studies to obtain a focused model; some studies investigated methods to recover the blocky feature of subsurface structures with their sharp boundaries to facilitate model interpretation. To this end, this study attempts to use the combination of the L1 norm and total variation (TV) penalty. The TV penalty is widely used in geophysical inversion studies. Although this penalty is written by the L1 norm of the model differentiation, most conventional studies replace this penalty with an alternative quadratic penalty to make it easy to solve the penalized inversion problem. However, in this study, TV1, the original TV penalty written by the L1 norm, is directly incorporated into the inversion method to derive a model that emphasizes the structural boundaries [1]. To solve this L1-TV1 penalized problem, alternating direction method of multipliers (ADMM) is used, which is one of the simple, and efficient algorithm to solve a problem with multi-type L1 penalty terms. In this paper, a scheme of this L1-TV1 penalized magnetic inversion method is proposed, and its effectiveness and the improvements to computational efficiency are discussed. Further, the proposed inversion scheme was applied to a real aeromagnetic data aquired over the Sakainokami pluton of the North Kitakami belt in Tohoku area, northeast Japan, which is a granite plutonic body intruded on Early Cretaceous, and attempted to obtain subsurface magnetic susceptibility model. For this real data test, a part of the aeromagnetic data of the aeromagnetic survey database (AMSurvDB) [2], was used.

[1] Utsugi, M., 2021. Magnetic inversion method to recover the subsurface block structures based on L1-TV1 regularization, G.J.I.(submitted)
[2] Okuma, S. & Nakatsuka, T., 2005. Aeromagnetic Anomalies Database of Japan, Digital Geoscience Maps, 6, Geological Survey of Japan, AIST.