Year: 2026
Type: preprint
Abstract: The main difficulty in 3D gravity inversion is that surface observations lack vertical wavenumber information, making the problem underdetermined and depth resolution poor. Building on the author's spectral-domain pseudo-inverse theory for unitary diagonalizable systems, this paper presents a true 3D inversion method. Surface data are analytically continued upward via Laplace's equation to form a 3D data volume, providing the vertical wavenumber sampling for the 3D Fourier transform. A general analytical expression for the half-space spectrum is derived, separating the horizontal spectrum from the vertical propagation kernel. The Green's function of the 3D Poisson equation is unitarily diagonalized, yielding the forward spectral response $λ(\kk) = -i 4πG k_z / K^2$, and a stable inverse filter $q_α(λ) = \barλ/(|λ|^2 + α)$ is constructed. This filter is proved to have bounded stability and consistency (reducing to the exact inverse as $α\to 0^+$). Validation with a homogeneous sphere model shows correct recovery of the anomaly location and singular behavior at the source. The contributions are twofold: (1) upward continuation constructs a 3D volume from 2D surface data, which does not add physical observations but unfolds the 3D spatial variation information (data innovation) derived through the governing physical equation; (2) the inversion is reduced to one forward 3D Fourier transform, one spectral scaling, and one inverse transform. The framework extends to any linear potential-field inverse problem with a translation-invariant forward operator, including magnetic inversion.
Source: arXiv (Cornell University)
Author: Chen, Shengchang
Institution: Zhejiang University
Language: English
Subfield: Geophysics
Field: Earth and Planetary Sciences
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7202281974