基于面向对象思想的正演反演统一框架结构

The framework designing of geophysical Modeling and Inversion base on object-oriented method

运用面向对象思想分析地球物理正演与反演问题,提出了一种基于有限单元正演与正则化非线性最小二乘反演的统一框架结构.该框架采用稀疏线性系统求解作为正演的基础类;分别建立一维、二维、三维的几何模型类,用于完成模型的剖分与有限单元钢度矩阵的生成,其中与单元物质属性相关的计算采用纯虚函数的形式,在具体解问题中实现;以正则化非线性最小二乘最优化算法作为反演基础类,反演中有关模型的正演数据计算及Fréchet矩阵求解等采用纯虚函数的形式,在具体问题中进行计算.框架结构的建立提高了代码的重用性与程序开发速度;对地质单元采用统一的空间剖分,有利于开展联合反演程序设计.

We analyze the problem of geophysical modeling and inversion using obiect-oriented method, then a framework using finite element numerical simulation and regularized nonlinear least square method were proposed. The base class of numerical simulation were designed that processing sparse linear system. Designed one dimension, two dimension and three dimension geometry modeling class aim to discrete geometry model and calculate steal matrix. The virtual function were applied to calculate the physical properties of discrete element when calculate steel matrix, because the element physical properties were conformed only at special modeling problem. The base classes of inversion were designed as solving optimum problem using regularized gradient type methods. The function of calculate numerical data and Fr6chet matrix were designed as virtual functions, because there are conformed by special modeling problem. We can reuse codes and shorten the development cycle when applied this framework. Other benefit of using this framework is easy to designed joint inversion of different geophysical methods because the geometry model was discrete using the same elements.