重力反演边界元法

GRAVITY INVERSION BY BOUNDARY ELEMENT METHOD

由高斯定理,可将沿密度体的体积分化为沿该体表面的面积分,由此提出一个新的重力反演方法称为表面积分法。将密度体的表面参数化,并将反问题线性化,可以导出一个线性方程组,可用Levenberg-Marquardt方法,奇异值分解方法和代数重建技术求解,文中引入一些理论计算例子用以说明这个反问题过程是稳定的。本法适用于确定密度体的边界,特别是地下密度界面的起伏。文中还引入一个实际计算例子。

Based on Gauss's theorem, a new gravity inversion method, called boundary element method, has been developed. By parameterization of the boundary and linearization, the inverse problem is formulated to a linear equation system. The modified Levenberg-Marquardt method, the singular value decomposition method and algebraic reconstruction techniques are used in an iterative procedure to solve the inverse problem. Some theoretical examples are presented to prove the inversion process stable. This method is suitable to determine the boundary of density inhomogeneities, especially interface topography. A practical example is included.