三维波动方程正演及模型应用研究

The application of 3D wave equation forward and modeling

（成都理工大学油气藏地质与开发工程国家重点实验室，四川成都 610059）

State Key Lab. of Oil and Gas Reservoir Geology and Exploration, Chengdu University of Technology, Chengdu 610059, China

为了真实准确地反映三维地质体的波场特征，在频率-波数域将二维波场延拓算子推广到三维空间，采用三维波动方程延拓方法实现了三维地质模型的快速叠后正演。该方法可以采用相位移加插值方法处理一定的横向变速情况，可以更加灵活方便地模拟地下复杂的三维地质体。首先进行了三维French模型数值模拟，得到了和实际物理模型实验结果相一致的正演记录，并对比分析了三维偏移剖面和二维偏移剖面的偏移效果；然后进行了三维缝洞地质模型的正演计算，得到了高信噪比的正演记录。模拟结果验证了三维正演和偏移方法的正确性，以及利用该方法进行缝洞地质体识别和研究的可行性。

To correctly study the characters of 3-D seismic wave field, the paper extends 2-D wave field continuation operator to 3-D space in F-K domain, and applies 3-D wave equation to realize fast poststack forward modeling of 3-D geologic body. The method has fast calculating efficiency by FFT, stabile algorithm and can handle variable velocity in landscape orientation by PSPI, so it provides a new effective tool for convenient simulating complex 3-D underground geologic body. As the examples, the paper firstly simulates 3-D French model, which can get the same results as practical physical model, and tests its correctness and applicability by contrastively analyzing the migrated data of 3-D and 2-D. Then the paper simulates the 3-D geological fractured model and gets its seismic data with high S/N, which is helpful for us to recognize and explain the characters of the model’s seismic wave-field.