资源勘探中的反问题的数学理论与算法

项目名称： 资源勘探中的反问题的数学理论与算法

项目编号： No.11331004

项目类型： 重点项目

立项/批准年度： 2014

项目学科： 数理科学和化学

项目作者： 程晋

作者单位： 复旦大学

项目金额： 240万元

中文摘要： 本项目为解决资源勘探中的粘弹性介质的反演和背景噪声反演的难点问题，与应用数学领域的随机微分方程解的性质和数值解法的热点研究方向相结合，开展应用数学领域大家普遍关心的数学物理反问题研究，为加快资源勘探突破提供理论上的支持和可行的反演算法。本项目将针对资源勘探中不同地质构造环境，研究粘弹性数学模型的构建和基于偏微分方程的反问题的理论和算法；研究含随机源的随机偏微分方程，利用随机微分方程解的统计性质和边界上的观测资料，提取和重构偏微分方程解的Green函数，研究由Green函数重构偏微分方程系数的反问题的唯一性、条件稳定性、快速算法以及数值实现问题。研究成果将应用于解决一二个资源勘探中的实际问题，为地球物理领域的研究者提供一些新的思路和新的方法。

中文关键词： 反问题;粘弹性;背景噪声;数学模型;反演算法

英文摘要： The target of this project is to find the new methods for solving the key problems in reversion of the viscoelastic and image reversion by ambient noises in the resource exploration. By studying properties of the solutions of stochastic differential equations and numerical methods, which are the hot topics in the applied mathematics studies, we will study the inverse problems of mathematical physics, which are interesting topics for many researchers. In this project, we will study the suitable mathematical models for the different underground viscoelastic geological structures, the inverse problems based on the partial differential equations and reversion algorithms. The researches include that the stochastic differential equation with the random sources. By the stochastic properties of the stochastic differential equations and measurements on the boundary, the Green functions of the partial differential equations can be extracted and reconstructed. Moreover, the uniqueness, conditional stability, fast algorithms and numerical simulations will be studied for the inverse problems of reconstructing the coefficients in the partial differential equations. The results will be applied to solve one or two real problems in the resource exploration. We hope our research will provide some new ideas and new technology for the researchers in the fields of geophysics.

英文关键词： inverse problems;viscoelastic;seismic ambient noise;mathematical model;inversion algorithms