3D sharp-boundary inversion of potential-field data with an adjustable exponential stabilizing functional

Abstract

Potential-field sharp-boundary inversion will allow us to identify the sharp petrophysical deposit boundaries inside the host rocks. With the purpose to find a more simple and convenient way to achieve a sharp-boundary and well-focused image for 3D focusing inversion, we analyze and discuss the influence of the focusing parameter in several commonly used stabilizing functionals, such as minimum support (MS), minimum gradient support (MGS), modified total variation ([Formula: see text]TV) stabilizing functional, etc. Then, we evaluate an adjustable exponential stabilizing (AES) functional, the focus of which is adjustable by the base and the exponent of the exponential functional, and we apply it to 3D density and magnetic susceptibility inversion for synthetic and field data. Compared with MS, MGS, [Formula: see text]TV, and other stabilizers, the proposed stabilizer can generate well-focused images and provide sharp boundaries. We also determine that sharp-boundary images produced by the proposed AES stabilizer have a weak dependence on the focusing parameter. Furthermore, we can obtain a stable and focused result by controlling the focusing parameter in the exponent of AES adaptively increasing with the iterations. The model tests and inversion of field data verify the flexibility and stability of this adjustable stabilizer.

Supplemental Material: Phanerozoic cratonization by plume welding

“…We employ the three-dimensional (3D) regularization inversion (Hu et al, 2019;Zhao et al, 2020) to image the plume-derived mafic-originated magnetic structure (Figs. S3 and S4), in which the total-field magnetic anomaly intensity (ΔT) dataset is transformed to the UTM projection of WGS84 ellipsoid with a central meridian of 81° E. It is assumed that the crustal magnetic anomaly is a function of the volume and extent of mafic material in the crust, such that bulk crust-scale magnetization primarily depends on the total content of mafic material (Saltus et al, 1999).…”

Integrated Geophysical Evidence for the Middle-Lower Crust Melting of the Songpan-Aba Terrain, NE Tibetan Plateau

“…The depth weighting of this regularization method depends on the selection of the regularization factor, α. The adaptive regularization factor selection method proposed by Hu et al (2019) was applied in this study. We followed Li and Oldenburg (1996), using the reciprocal of the vertical surface component of the total magnetic anomaly data as the dataweighting factor.…”

“…We followed Li and Oldenburg (1996), using the reciprocal of the vertical surface component of the total magnetic anomaly data as the dataweighting factor. If the model sensitivity matrix is directly incorporated into data-fitting (Zhdanov, 2002;Hu et al, 2019;Zhao et al, 2020), this problem can be solved. After model weighting, the total sensitivities of the weighted model parameter of all grid cells are equal, and the contribution of observed data is essentially identical.…”

Undersea Target Reconstruction Based on Coupled Laplacian-of-Gaussian and Minimum Gradient Support Regularizations

“…S(σ ) is a diagonal matrix containing the conductivity values. The discretized potential distribution u can be obtained by solving the linear system (2). However, in the inversion process, we obtain the voltages d only from the subset of u using a projection matrix Q.…”