重力异常稳健迭代密度界面反演研究

重力异常界面反演是重力勘探中的一个重要研究课题,它是一个求解第一类Fredholm非线性积分方程问题,目前情况下直接求解比较困难,只能采用拟合法或逐步线性化办法实现反演计算.在计算过程中,由于反演的不适定性,往往不能很好地获得反演解.我们从二度体重力异常正演公式出发,导出地下界面迭代反演的计算公式;然后利用广义似然函数对模型参数进行优化选择,从而获得模型参数修正量迭代计算方法,实现二度体单一密度界面的稳健迭代(最小二乘加权迭代)反演.模型计算表明方法可以很好地反演出地下界面.

Robust iterative inversion of density interface based on gravity anomaly

Inversion of density interface by using gravity anomaly is an important research subject in gravity prospecting,which is a problem of answering the first Fredholm nonlinear integral equation.At the moment it is difficult to solve the problem directly,so generally fitting process and gradual linearizing process were utilized to inverse the interface.In computational processes,it is difficult to obtain good inversion results due to ill-posed problems.We first deduced the iterative inversion formula from gravity anomaly formula of 2-D density interface,and then optimized the model parameter by using generalized likelihood function.Thus,the iterative method for computing correction value of the model parameter was obtained,and robust iterative inversion(least square weighting iterative inversion) of 2-D density interface was achieved.Model computation shows that the interface could be inversed well.