中文摘要：

数学形态学是一门新兴科学，它建立在严格的数学理论基础之上，是研究数字信号（图像）形态结构特征及其快速并行处理方法的理论，已经成功应用于图像处理、医学信号处理和语音信号处理等领域．地震信号去噪处理和裂缝检测的研究一直都是地质学家和油气藏工程学家感兴趣的问题．本文将数学形态学与地震信号处理相结合，重点探讨了数学形态学在地震信号处理中的应用，针对地震信号的特点，设计了形态滤波器，应用于合成地震资料，得到了理想的结果．在此基础上，本文研究并构造了形态学边缘检测算子，通过理论和实际资料检验，该方法具有良好适用性．以上研究表明，基于形态学的地震信号处理是可行的，具有推广应用前景．

英文摘要：

Mathematical morphology is a new developing science. It is based on strict mathematical theory, and provides a systematic approach to analyze the geometric characteristics of signals or images. And it has been applied widely to many fields such as image processing, medical signal processing, speech signal processing and so on. Seismic signal filtering and fracture detection are important to geologists and oil reservoir engineers. Thus, this paper attempts to introduce mathematical morphology in the seismic exploration field, and mainly discusses applications of mathematical morphology to seismic signal processing. Then according to the characteristics of the seismic signal, we construct and design a morphological filter, which is applied to the filtering of synthetical seismic sections, yielding a satisfied result. On this basis, the paper studies and constructs an operator of morphological edge detection, which is applied to the seismic fracture detection with a good result. The result of research indicates it is feasible to process seismic signals based on mathematical morphology. And it has a prospect of popularizing and applying.