在离散势理论中求重力线性反问题的稳定近似解：一个局部版本

IF 1 4区地球科学 Q4 GEOCHEMISTRY & GEOPHYSICS

Izvestiya, Physics of the Solid Earth Pub Date : 2025-07-18 DOI:10.1134/S1069351325700089

I. E. Stepanova, I. I. Kolotov, A. N. Levashov, A. V. Gorbachev

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引用次数: 0

摘要

摘要：本文在局部版本的离散势理论框架下，研究了求解重力测量线性逆问题的算法。主要的焦点是如何在三维（3D）空间中找到笛卡尔坐标下拉普拉斯方程基本解的离散模拟。利用矩阵扫描法在规则三维网格节点上重建了拉普拉斯方程基本解的网格模拟。然后求解线性代数方程组（SLAE），从已知的网格引力势值在某些节点子集上求出同一网格节点上的重力质量分布。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

On Finding Stable Approximate Solutions of Linear Inverse Problems of Gravimetry in the Discrete Potential Theory: A Local Version

查看原文本刊更多论文

On Finding Stable Approximate Solutions of Linear Inverse Problems of Gravimetry in the Discrete Potential Theory: A Local Version

Abstract—We consider the algorithms for solving linear inverse problems of gravimetry in the framework of discrete potential theory in the local version. The main focus is on ways to find a discrete analog of the fundamental solution of the Laplace equation in Cartesian coordinates in a three-dimensional (3D) space. The grid analog of the fundamental solution of the Laplace equation is reconstructed at the nodes of a regular 3D grid using the matrix sweep method. A system of linear algebraic equations (SLAE) is then solved to find the distribution of gravitating masses at the nodes of the same grid from the values of the grid gravitational potential known on some subset of nodes.

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来源期刊

Izvestiya, Physics of the Solid Earth 地学-地球化学与地球物理

CiteScore

1.60

自引率

30.00%

发文量

审稿时长

6-12 weeks

期刊介绍： Izvestiya, Physics of the Solid Earth is an international peer reviewed journal that publishes results of original theoretical and experimental research in relevant areas of the physics of the Earth''s interior and applied geophysics. The journal welcomes manuscripts from all countries in the English or Russian language.