特征高斯波包叠前深度偏移方法

高斯波包（Gaussian packet）传播算子可在局部时空域高效地计算局部波包的传播.高斯波包叠前深度偏移的基础是在Gabor变换域描述观测数据，再利用高斯波包传播算子计算炮点波场和检波点波场，两者相关即可得到偏移结果.利用炮道集的局部τ-p特征在Gabor变换域表达观测数据，可以仅关注部分高斯波包框架函数上的数据投影，这样既实现了波场的压缩存储，同时可利用高斯波包传播算子反传框架函数以实现整个炮道集的快速反传.这些综合了观测数据局部τ-p特征的高斯波包函数称为特征高斯波包（characteristic Gaussian packet，CGP），相应的波场反传称为特征高斯波包反传.理论及数值分析证明了上述特征高斯波包反传方法是有效且快速的.炮点正传波场也利用高斯波包传播算子模拟.利用互相关成像条件可实现特征高斯波包叠前深度偏移（characteristic Gaussian packet pre-stack depth migration，CGPM）.由于高斯波包传播算子描述了局部方向及局部空间的波场，所以CGPM可以自然地提取角度域成像道集（ADCIG），并易于实现面向目标叠前深度偏移，从而作为偏移引擎为偏移速度分析（MVA）服务.数值实验证明了CGPM和面向目标CGPM的有效性和实用性.

Efficient pre-stack depth migration method using characteristic Gaussian packets

A Gabor domain seismic data sparse expression method is presented in this paper. To express seismic data sparsely in Gabor domain, the travel-times and the propagation directions of local plane waves from the seismic signals are selected. Seismic traces are then characterized by those parameters in Gabor domain, and we name the corresponding frame functions as characteristic Gaussian packets (CGP). Due to the sparse expression of seismic data in Gabor domain, back-propagation is much more efficient than the conventional method. Consequently, the characteristic Gaussian packets migration (CGPM) can be implemented efficiently by cross-correlating the Gabor-domain forward and backward propagated Gaussian packets. Besides, target-oriented imaging and angle-domain CIG outputting can be carried out naturally, because of the Gaussian packet's local orientation and the local spatial character. Numerical example shows that the back-propagated Gaussian packets are comparable with the back-propagated wavefield produced by the RTM (Reverse Time Migration) method, the target-oriented CGPM and the target-body CGPM are practically useful.