用一种简明的共轭梯度算法对局部地层进行波阻抗反演

A brief conjugate gradient method for local layer impedance inversion

1. 地矿部石油物探研究所, 南京210014;2. 西北石油地质局地球物理研究所, 乌鲁木齐830011

Researeh Institute of Geophysieal Prospecting for Petroleum, Nanjing 210014

经典的共轭梯度迭代方法对线性反演问题是有效的。但是地球物理反演一般是非线性的,那未经典的方法得到的反演解法往往是无法控制的,又不能产生最大似然反演,更不会得到可重复的反演结果。本文提出了一种简明的反演算法,该算法在迭代过程中只需计算误差函数对各个反射系数变元的一阶梯度值,而无需进行复杂的矩阵运算和求逆,是一种简单明了且易于实现的快速算法。理论记录和实际记录处理表明,本文提供的方法具有可重复性和较快的收敛速度。

For linear inversion problem, the classic conjugate gradient iteration method is effictive, but geophysical inversion is usually nonlinear, so the result of the classic method can not be controlled and repeated.The method presented in this paper only calculates the first order gradient of error function with respect to each reflectivity variable. It doesn’t calculate the complex matrix and its inverse matrix, so it is easy and fast. Theoretical and praetieal results show that this method is repeatable and has good eonvergence.