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反滤波用于地震数据以消除子波效应和获得反射序列的估计。在许多情况下,子波是未知的,而仅能估算出子波的自相关函数(ACF)。求解Yule-Walker方程能获得符合最小延迟子波的反滤波器。当子波是混合延迟时,这个反滤波器产生的结果较差。 通过求解滤波器方程组的主对角线上ACF的延迟量为α的扩展Yule-Walker方程组,可将反滤波器分解为一个有限长度的滤波器与一个无限长度滤波器的褶积。我们在先前的一篇论文中曾提出,在一个混合延迟的反滤波器中,有限长度滤波器是最大延迟的,而无限长度滤波器则是最小延迟的。 本文通过分析有限长度滤波器的Z变换多项式的根改进了上述方法。通过改变混合延迟反滤波器单位圆内根的数目,可获得最多2~α个不同的滤波器。将每个滤波器应用于小的数据集(如一个CMP道集),并选择使得输出结果具有最大L~p(p=5)范数的滤波器为最佳滤波器。这是通过提高α的值来获得最终最佳滤波器。从这一最佳滤波器出发,可以很容易构造出反子波,它可作为地震子波的一个估计来使用。 新的算法已用于合成子波和气枪子波以检验其性能和验证重构的子波与初始子波的接近程度。本算法还用于海上叠前地震数据,与用最小延迟滤波器的处理结果比较,本方法改善了叠加剖面。
The inverse filter is used for seismic data to eliminate the wavelet effect and obtain an estimate of the reflection sequence. In many cases, the wavelet is unknown and only the auto-correlation function (ACF) of the wavelet can be estimated. Solving the Yule-Walker equation yields an inverse filter that meets the minimum delay wavelet. This inverse filter produces poorer results when the wavelet is a hybrid delay. The inverse filter can be decomposed into a convolution of a finite-length filter and an infinite-length filter by solving the extended Yule-Walker equations for which the delay of the ACF on the main diagonal of the filter system is α. In a previous paper, we proposed that in a mixed-delay inverse filter, the finite-length filter is the maximum delay and the infinite-length filter is the least delayed. This paper improves the above method by analyzing the roots of Z-transform polynomials of finite-length filters. By changing the number of roots in the unit circle of the hybrid delay-inverse filter, up to 2 to α different filters can be obtained. Apply each filter to a small dataset (such as a CMP gobble) and select the filter that makes the output result have a maximum norm of L ~ p (p = 5) as the best filter. This is achieved by increasing the value of α to get the final best filter. Starting from this optimal filter, it is easy to construct a trans-wave, which can be used as an estimate of the seismic wavelet. The new algorithm has been used to synthesize wavelet and airgun wavelet to test its performance and verify the reconstructed wavelet close to the initial wavelet. The algorithm is also used for prestack seismic data over the sea. Compared with the processing results of the least delay filter, this method improves the superimposed profile.