最大似然估计和子波处理在拟速度测井中的应用

MAXIMVM LIKELIHOOD ESTIMATION AND THE APPLICATION OF WAVELET PROCESSING TO SEISLOGGING

武汉地质学院北京研究生部

在拟速度测井中,地震子波是根据信号检测理论的最大似然估计方法来估算的。当假设干扰是均值为零的高斯白噪音时,最大似然准则等效于最小均方误差准则,求取地震子波的最大似然估计值就是求解一个托布里兹方程组。在假设干扰为其它情况时,可引出另外的方程组。本文仅讨论了最简单的均值为零的高斯白噪干扰情况。子波处理是将地震记录中既非零相又非最小相位的子波处理为零相子波,进而处理为最小相位子波。这样可提高记录的讯噪比,使拟速度测井结果更为精确。其中间结果(零相子波记录)在地震解释中极为有用。

In seislogging, seismic wavelet is estimated by the maximum likelihood estimation technique of signal detection theory. The maximum likelihood criterion is equivalent to the minimum root-mean-square error criterion when the supposed noise is Gaussian white noise of average value of zero. The solution of Toeplitz coupled equations, therefore, is the maximum likelihood estimating value of the seismic wavelet. Other coupled equations can be derived from when the supposed noise is something else. Inthis paper, the simplest case is merely discussed-the average value ofGaussian white noise is zero.The wavelet processing means to make neither zero-phase nor minimum-phase wavelets from seismograms be zero-phase wavelets and, then be minimum-phase wavelets during further processing. In so doing, the signal-to-noise ratio can be improved, making the results of seislog more precise. The intermediate data (zero-phase wavelet data) are extremely useful in seismic interpretation.