Downward Continuation and Transformation of Total‐Field Magnetic Anomalies Into Magnetic Gradient Tensors Between Arbitrary Surfaces Using Multilayer Equivalent Sources

Abstract

The equivalent source method offers a potential means for continuing and manipulating magnetic data between arbitrary surfaces. However, it ultimately suffers from a limited continuation distance and significant errors, which restrict its applicability in practice. To address this problem, we reformulate the equivalent source method with a partial differential equation framework. A multilayer equivalent susceptibility method is innovatively derived based on this approach. The location of equivalent sources is designed for adaptive estimation through the inverse procedure. We introduce nonlinear optimization, regularization, and constraining technologies in inversion to improve the stability and accuracy of the solution. Synthetic, real airborne, and ground data are tested in experiments. The results show that the new method significantly improves the capability and accuracy of the downward continuation and transformation of irregularly located data between arbitrary undulating surfaces.

Low-latitude reduction-to-the-pole and upward continuation between arbitrary surfaces based on the partial differential equation framework

“…In eq. ( 4), F(•) is the forward modelling operator in the PDE solution corresponding to d obs , which can predict one of three types of magnetic data, for example total magnetic anomaly data, magnetic three-component vector data and magnetic gradient tensor data (Lelièvre & Oldenburg 2006;Zuo et al 2019Zuo et al , 2020. Therefore, the proposed method can be utilized to interpret these types of magnetic data.…”

“…These studies demonstrated that the PDE non-linear inverse framework exhibits stable performance under complex magnetization conditions. We also proposed downward-continuing and transforming total-field magnetic anomalies into a gradient tensor using the PDE framework (Zuo et al 2020). As these studies show, the PDE framework exhibits some desirable characteristics, such as a continued inversemesh region and an all-natural sparse matrix while accounting for self-demagnetization.…”

Can Targeted Source Information Be Extracted From Superimposed Magnetic Anomalies?

“…Identification of rocks in the source interference case (2) discussed above is also necessary for appropriate interpretation. Methods such as downward continuation and derivative analysis have thus been proposed to evaluate the horizontal positions of sources with similar depths (Zhang et al., 2018; Zuo et al., 2020). Local separation methods based on 3‐D susceptibility imaging (Li & Oldenburg, 1998) and equivalent sources (Zhang et al., 2021) are used to obtain the magnetic anomaly caused by the target source.…”

3‐D Magnetic Unstructured Inversion

“…3‐D magnetic inversion plays an important role in acquiring information about the subsurface distribution of magnetic susceptibility and has been employed in various survey applications (Blakely, 1996), such as mineral exploration (Leão‐Santos et al., 2015; Sayyed et al., 2018), planetary geophysics (Langlais et al., 2004, Moore & Bloxham, 2017), and geological and tectonic research (Bouligand et al., 2020; Naeim & Ebbing, 2018; Noble et al., 2020). The 3‐D magnetic inversion technique has also been used to continue and manipulate geomagnetic data by using inverted intermediate equivalent sources (Li et al., 2014; Oliveira et al., 2017; Yang et al., 2020; Zuo et al., 2020, 2021). The classic 3‐D magnetic structured inversion scheme was originally presented by Li and Oldenburg (1996).…”

“…However, due to the differences among these grids and modeling approaches, the results of tesseroid and block-oriented approaches exhibit evident disparities (Heck & Seitz, 2007;Ren et al, 2017), increasing the ambiguities of data interpretation. Third, existing structured grid-based PDE magnetic methods exhibit stable performance in 3-D magnetic inversion and continuation (Lelièvre & Oldenburg, 2006;Zuo et al, 2019Zuo et al, , 2020, but these methods encounter natural limitations during the gridding process, and the free space needs to be finely distinguished. Although the free space between the topography and the airborne draping surface or the satellite observation surface is not contained within the inverse model, it still needs to be considered in forward modeling, which inevitably increases the cost of forward modeling.…”