arXiv subjects

Shengchang Chen

Publications and source records attributed to Shengchang Chen.

3 recordsLinked to original sources

arXiv2026

PSDWII: Physical-Structure-Driven Waveform Inversion Imaging

This paper proposes a Physical-Structure-Driven Waveform Inversion Imaging framework (PSDWII), grounded in the recognition that surface-recorded seismic data are directly related to subsurface virtual sources rather than to the model parameters themselves. Based on this recognition, we decompose seismic wave propagation into a three-step physical process: source excitation and incident wave propagation; interaction of the incident wave with heterogeneities, which generates virtual sources with distinct radiation patterns and excites secondary waves; and propagation and reception of the secondary waves. The adjoint of the propagation operator (reverse-time extrapolation) is then used to formulate a linear inversion projection for the virtual sources. By distinguishing different virtual-source expressions and their underlying physical mechanisms, we establish a unified mathematical representation for three inversion tasks: Full Waveform Inversion(FWI), stratigraphic physical properties imaging, and stratigraphic structures imaging. Deconvolution and linear inversion are respectively adopted to achieve multi-parameter decoupling in FWI and in angle-domain common-image gather inversion for stratigraphic physical properties imaging. The PSDWII framework shifts the conventional ``mathematical optimization driven'' paradigm of waveform inversion to a ``physical-structure-driven'' one. It neither constructs objective functions nor computes their gradients or Hessian inverses. Within this framework, we develop three specific methods: physical-structure-driven FWI (PSDFWI), physical-structure-driven stratigraphic physical properties imaging with angle-domain common-image gather inversion (PSDSI), and physical-structure-driven stratigraphic structures imaging (PSDMig).

physics.geo-ph↗

arXiv2026

A Spectral-Domain Pseudo-Inverse Method for True 3D Gravity Inversion

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 $\lambda(\kk) = -i 4\pi G k_z / K^2$, and a stable inverse filter $q_\alpha(\lambda) = \bar{\lambda}/(|\lambda|^2 + \alpha)$ is constructed. This filter is proved to have bounded stability and consistency (reducing to the exact inverse as $\alpha \to 0^+$). 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, mitigating underdetermination; (2) the inversion is reduced to one forward 3D Fourier transform, one spectral scaling, and one inverse transform.The proposed framework is not limited to gravity; it applies to any linear potential-field inverse problem with a translation-invariant forward operator, including magnetic inversion.

physics.geo-ph↗

arXiv2026

A Spectral-Domain Pseudo-Inverse Construction Method for Unitary Diagonalizable Linear Inverse Problems

Linear inverse problems are prevalent in geophysics, signal processing, image restoration, and medical imaging. Mathematically, they can be formulated as $Gm = d$. When $G$ is ill-conditioned or singular, the problem becomes ill-posed and requires regularization methods or generalized inverse methods for a stable solution. However, both types of methods encounter significant computational difficulties for large-scale linear inverse problems. In this paper, we establish a spectral-domain pseudo-inverse construction method for a class of linear inverse problems that can be diagonalized by unitary matrices. The core idea is to construct a stable pseudo-inverse operator directly in the transform domain, starting from the unitary diagonalization structure of the matrix. We first provide the analytic Singular Value Decomposition (SVD) of this class of matrices, clarifying the correspondence between spectral decomposition and SVD. On this basis, we define spectral-domain regularization filtering factors, construct a stable spectral-domain pseudo-inverse operator, and prove its bounded stability as well as its consistency in converging to the Moore--Penrose generalized inverse. This construction is numerically equivalent to zeroth-order Tikhonov regularization and converges to the Moore--Penrose generalized inverse as $\alpha \to 0^+$, but its methodological path differs from both. This paper reveals that the stable generalized inverse of a class of structured matrices can be directly constructed from their spectral decomposition, providing an efficient solution method for large-scale structured inverse problems. The Fourier transform case is a special instance of this method when the unitary matrix is taken as the discrete Fourier transform matrix.

math.NA↗