几种波动方程叠前深度偏移方法对比研究

针对不同的叠前深度偏移算法在成像效果和计算效率方面存在差异问题，采用理论解析和模型实验等方法，对有限差分法、相移法、分步傅里叶和傅里叶有限差分等几种叠前深度偏移方法进行了对比研究，介绍了几种偏移方法的基本原理，分析了波场延拓存在的相对误差，通过模型数据进行了成像测试。结果表明，有限差分法叠前深度偏移具有较高的成像分辨率，但计算量较大；频率—波数域偏移方法具有较高的计算效率，其中相移偏移适用于水平层状介质成像，傅里叶有限差分偏移对复杂构造适应性好，是成像效果最好的方法；在波动方程叠前深度偏移计算中，波场延拓步长和边界吸收条件是影响成像效果的最重要因素。研究分析了几种偏移方法的特点，可为波动方程叠前深度偏移方法的应用选择提供参考。

Study on comparison of several methods for wave equation prestack depth migration

Aiming at the difference of imaging result and computational efficiency of different prestack depth migration algorithms，this paper used theoretical analysis and model experiments to compare several prestack depth migration methods，such as finite difference method，phase shift method，step fourier and fourier finite difference method.The basic principles of several migration methods were introduced，and the relative errors of wave field continuation were analyzed.The imaging test was carried out by model data.The results showed that the finite difference method has high imaging resolution but large computational cost，and the frequency- wavenumber domain migration method has high computational efficiency，in which the phase shift migration is suitable for horizontal layered medium imaging，and the fourier finite difference migration is the best method for complex structure.In wave equation prestack depth migration calculation，wave field extension step size and boundary absorption condition are the most important factors affecting imaging effect.In this paper，the characteristics of several migration methods were analyzed，which provides a reference for the application and selection of wave equation prestack depth migration method.