稳健估计算法求取AVO截距和梯度

Computation of AVO intercept and gradient by robust estimation algorithm.

准确地求取截距(A)和梯度(B)对于AVO分析具有重要意义。在实际应用中,不同类型地震噪声的存在给截距和梯度的可靠估计带来了很大困难。本文针对地震记录存在异常噪声时用传统的最小二乘算法求取的截距和梯度不可靠这一问题,提出了一种应用稳健估计算法来计算AVO截距和梯度的方法。最小二乘法是基于数据的测量误差呈正态分布,而稳健估计算法可适用于数据的测量误差呈尾部外露的柯西分布。实际模型的估算结果表明:当局部异常噪声使得AVO响应特征发生严重畸变时,利用假设噪声具有高斯分布特征的最小二乘回归算法很难得到截距和梯度的合理估计,而稳健估计算法则可以给出比较精确的计算结果。因此,本文给出的计算方法对于多参数AVO反演及其他一些地球物理反演有一定的借鉴意义。

Correct computation of intercept ( A) and gradient (B) has important meaning for AVO anal- ysis. In practice, the existence of different types of seismic noises causes significant difficulties to reliably estimate intercept and gradient. In view of the issue that abnormal noises existed in seismic data made the intercept and gradient, computed by traditional least square method, unreliable, the paper presented the method using robust estimation algorithm to compute the AVO intercept and gradient. The least square method is on the basis of normal distribution of measured data errors,but robust estimation algorithm is suitable for Cauchy distribution that the tail of measured data errors exposed outside. The estimated results of practical model showed that, when the AVO response was seriously distorted by local abnormal noises, using the least square regression method that supposes the noises is Gauss distribution is difficult to estimate the intercept and gradient, while the robust estimation algorithm can give more precious computational results. Therefore, the algorithm presented in the paper has some referent meaning for multi-parameters AVO inversion and other geophysical inversions.