时-空局域化地震波传播方法:Dreamlet叠前深度偏移

提出了一种在时间和空间上完全局域化的波场分解和传播算法─dreamlet偏移方法.Dreamlet是一种脉冲-小波束形式的波场分解原子,它利用多维局部分解变换,把时空域波场映射到局部时间-频率-空间-波数相空间,并用局部相空间的传播算子(dreamlet算子)沿深度延拓.本文利用多维局部余弦变换实现dreamlet算法,分解后的波场系数和传播算子不仅有很好的稀疏性,且均为实数,也即波的传播和成像过程完全在实数域实现.文中推导了局部余弦基dreamlet波场分解和传播算子理论公式并将其应用于叠前深度偏移.在dreamlet相空间波的传播过程为稀疏矩阵相乘,而且延拓后的地表数据波场的有效时间长度随深度的增加不断减小,从而可以减少需要传播的波场系数.二维SEG/EAGE盐丘和SIGSBEE模型算例验证了理论推导的正确性,成像结果显示该方法在横向速度变化剧烈情况下有很好的精度.

Time-space localized seismic wave propagation: Dreamlet prestack depth migration

We propose a complete time-space localized seismic wavefield decomposition and propagation method─dreamlet migration. The time-space wavefield is projected to the time-frequency-space-wavenumber domain by the local cosine transform, and the wavefield is extrapolated to next depth by the local phase space dreamlet one-way propagator. The wavefield and propagator after decomposition are very sparse and most importantly, they stay in the real data domain, which means the process of propagation and imaging complete in the real data domain. In this paper, we derive the formulas of the wavefield decomposition and phase-space dreamlet one-way propagator. The dreamlet domain wave propagation is sparse matrix multiplication, and the valid time length of the receiver wavefield is shrinking as the depth increasing. Numerical examples and tests on the synthetic two dimensional SEG/EAGE salt model and SIGSBEE model demonstrate the validity of this method. Migration results show that this method has good imaging quality in laterally high contrast heterogeneous media.