用于地震资料分析的小波函数构造及其应用/Wavelet Construction and Its Applicaiton in Seismic Signal A

2018-08-11 05:54:55

signal 小波 processing wavelet seismic



石油的勘探开发是石油开采的重要前提和保证,而地震信号处理是石油勘探开发的一个重要环节。针对传统的地震信号处理中的一些不足的地方,本文通过引入近代数字信号处理中的时频分析方法来得到更加令人满意的效果。主要工作是针对具体研究的物理问题,寻找恰当的小波函数,并以这些函数为基本小波,解决地震信号处理中的问题。在整个硕士学位攻读期间,主要从事了两种小波的研究:给定信号的最佳匹配小波的构造以及多重小波(即Slepian小波)的算法。最后,把这两种小波应用于地震信号处理中。
第一部分仔细研究了美国斯坦福大学的J.O Chapa提出的小波构造方法,这种方法是在最小均方误差标准下计算给定信号的最佳匹配小波,并从连续和离散两个方面给出了从给定信号的谱直接推导最佳匹配小波谱的表达式。本文的主要工作是熟悉地震信号处理的一般流程和地震专业软件strata,尤其是掌握其中地震子波提取的相关知识和应用。然后根据J.O Chapa的小波构造方法,实现了地震子波的最佳匹配小波算法,最后把这种最佳匹配小波应用于相应的实际地震记录,取得了去除噪声及压制面波干扰的较好的结果。
第二部分主要研究了Jonathan M.Lilly和Jeffrey Park等人提出的多重小波变换。本文的主要工作是把多重小波变换与其他已知的变换相比较,得出了其在保持一般小波变换的性能的同时,还具有了低方差的谱估计的优良特性。最后,初步探索这种多重小波变换在地震数据极化分析中的应用。

Seismic signal processing is significant step in oil exploration and development. Based on time-frequency domain analysis from modern signal processing, this thesis improves the performance in traditional seismic signal processing, and obtains satisfied effects. Focusing on concrete physical research, we try to seek proper wavelet to solve problems in seismic signal processing. During my school time, I study two wavelets: wavelet to match a specified signal and Slepian wavelet, and use them in seismic signal processing.

This thesis includes two parts. In part one, I study a method of wavelet construction presented by J.O Chapa from Stanford University, and in his method, two sets of equations are developed that allow us to design the wavelet directly from the signal of interest. Both sets impose bandlimitedness, resulting in closed form solutions. The first set derives expressions for continuous matched wavelet spectrum amplitudes. The second set of equations provides a direct discrete algorithm for calculating close approximations to the optimal complex wavelet spectrum. The discrete solution for the matched wavelet spectrum amplitude is identical to that of the continuous solution at the sampled frequencies. After familiar with flows of seismic signal processing and seismic professional software strata, the knowledge of seismic wavelet and its application are mastered. According to J.O Chapa’s method of wavelet construction, I present algorithm of wavelet to match seismic wavelet, then apply the wavelet in seismic data processing, and achieve the effect of de-noise and suppressing surface wave.
In part two, I study the multi-wavelet presented by Jonathan M.Lilly and Jeffrey Park. Compared with other wavelet transform, multi-wavelet has an spectrum evaluation with low variance when keeping the performance of other wavelets. Finally, we discuss multi-wavelet application in seismic data polarization analysis.