Scholarlink

<p><b>Abstract</b>—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.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

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

  • 期刊论文

  • 发表日期：

    2025年2月1日

查看全文
  • I. E. Stepanova,
  • I. I. Kolotov,
  • A. N. Levashov,
  • A. V. Gorbachev

摘要

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.