重力异常界面反演的Gauss-Newton方法及其隐式迭代实现

Gauss Newton Method Using Implicit Iterative Increments for the Inversion of Gravity Anomalies

首先根据重力异常积分公式及重力异常实测数据将确定异常源的密度界面问题归结为求非线性泛函极小化的变分问题，并在Ｈｉｌｂｅｒｔ空间中应用Ｇａｕｓｓ－Ｎｅｗｔｏｎ迭代方法进行求解．在实际计算中采用有限维试验函数空间对模型进行离散，每次迭代的增量由隐式迭代方法给出。

A variational equation of nonlinear functional minimizing for the surface inversion of gravity anomalies is first derived, and then the equation is discribed in a finite dimension Hilbert space. We resolve the equation with Gauss Newton method. For the sake of the stability of its solution, the increment of each step is given by the implicit iteration method.