High-precision magnetization vector inversion: application to magnetic data in the presence of significant remanent magnetization

Abstract

Magnetization vector inversion is essential for obtaining magnetization vector information from subsurface rocks. To obtain focused inversion results that better match the true magnetization distributions, sparse constraints are considered to constrain the objective function. A compact magnetization vector inversion method is proposed that can provide accurate inversion results for magnetic data with significant remanent magnetization. Considering the sparse constraint and the correlation between the three magnetization components with different directions, the L1-norm is modified and introduced into the inversion algorithm to obtain compact results. Furthermore, to reduce the computational cost, a randomized singular value decomposition is used to replace the traditional singular value decomposition and iteratively minimize the proposed objective function. Two synthetic models with different magnetization directions are developed to verify the performance of the proposed method. The results of magnetization vectors obtained by the proposed method are focused and accurate. Finally, the proposed method is applied to igneous rocks with strong remanent magnetization in the Haba River area of northwestern China. The distributions, directions of total magnetization and remanent magnetization of the medium-base igneous rocks are revealed by the sparse magnetization vector inversion method, which provides a wealth of information about the concealed deposits in the area.

Predicting Magnetization Directions Using Convolutional Neural Networks

“…Conventional means of magnetic data processing and modeling assumes that the induced magnetization is the sole factor that contributes to the magnetic field. However, as argued by Li (2017), the occurrence of remanent magnetization is almost ubiquitous; therefore, ignoring remanence could lead to false interpretations in many cases, as evidenced by previous works (e.g., Lelièvre & Oldenburg, 2009;Pratt et al, 2014). from −180°to 180°with an eastward deviation of the magnetic field from the geographic north being positive.…”

“…These methods all have their pros and cons and typically involve 3-D inversions that are either procedurally or computationally complex. We refer readers to Li (2017) for an overview of these methods. In this study, we propose a machine learning-based approach for predicting the magnetization direction of a compact source body based on a magnetic map, with no wavenumber domain conversions or RTP involved.…”

Determination of the magnetization direction via correlation between reduced‐to‐the‐pole magnetic anomalies and total gradient of the magnetic potential with vertical magnetization

“…To solve Equation (), the objective function $${P^\alpha }({\bf{m}})$$ is defined and minimized to estimate the parameter $${\bf{m}}$$: $$$$\begin{equation} \def\eqcellsep{&}\begin{array}{l} {\bf{m}} = \arg \mathop {\min }\limits_{\bf{m}} \{ {P^\alpha }({\bf{m}})\} \\ \mathop {}\nolimits = \arg \mathop {\min }\limits_{\bf{m}} \left\{ {\left\| {{\bf{Gm}} - {{\bf{d}}_{{\mathrm{obs}}}}} \right\|_2^2 + {\alpha ^2}\left\| {{\bf{Wm}}} \right\|_2^2} \right\} \end{array} ,\end{equation}$$$$where $${{\bf{d}}_{{\mathrm{obs}}}}$$ is the observed total field anomaly and α is the regularization parameter. $${\bf{W}}$$ is a diagonal matrix involving depth weighting (Liu et al., 2017) and sparse constraints (Li et al., 2022) applied to the inversion model to obtain a more compact distribution of magnetic sources. The boundary limitation of magnetization intensity in inversion process is set as 0–2.5 A/m.…”

“…Magnetization vector inversions (Fournier et al, 2020;Ghalehnoee & Ansari, 2022;Li et al, 2022;Liu et al, 2013Liu et al, , 2017Sun & Li, 2018) are conducted for the above anomalies to recover a three-dimensional (3D) distribution of the magnetization vector. The inversion process involves regular discretization, where the subsurface is partitioned into cuboid cells, each assumed to be magnetized by a homogeneous total magnetization vector.…”

Unique reconstruction of simple magnetizations from their magnetic potential

“…A fairly recent overview is provided, e.g. in [43]. The underlying models often distinguish explicitly between remanent and induced magnetizations and aim at including geological constraints, while we consider a more general setup.…”