基于时空局域化dreamlet单程波算子的观测系统沉降法偏移

Survey sinking migration using the time-space localized dreamlet one-way propagator

Dreamlet偏移成像目的是探索一类能够对地震波场和单程波传播算子同时分解和压缩的理论和方法,也即实现在压缩域的传播与成像、地震数据在时间和空间的非平稳性质,决定了要实现地震数据的有效稀疏表示,分解方法必须在时间和空间上同时具有局域化性质.Dreamlet由时间和空间局部分解原子的张量积构成,可以看作一种脉冲-小波束形式的波场分解原子.时空局域化的dreamlet单程波传播算子在对波场沿深度方向延拓时,地震数据在时间轴上总是向同一方向流动.随着深度的增加,部分用于成像浅层结构的数据归位至其空间位置后被dreamlet算子丢弃,波场的有效记录时间变短,每一步用于波场延拓的计算量也相应下降.为了充分发挥这一优势,本文介绍dreamlet传播算子与观测系统沉降法偏移相结合的理论与方法.观测系统沉降法偏移每一步都将记录到的所有数据向下延拓,沉降后的波场等效于把源和检波器都放置在目标深度所能接收的反射数据.Dreamlet观测系统沉降过程只保留用于成像观测系统下部地质结构的有效数据,自动丢弃已经用于成像观测系统上部而对下部成像没有贡献的信号.本文通过二维SEG/EAGE叠后和Marmousi叠前数据算例展示了dreamlet传播算子应用于观测系统沉降法偏移的这一特点.数值算例结果显示,在不影响成像质量的前提下,该偏移方法能够有效减少传播数据量,为发展一种快速高效的偏移方法提供了新的思路.

The dreamlet seismic imaging method is seeking to develop the theory and algorithm for the decomposition and compression of seismic wavefields and the one-way wave equation operator, that is, wave propagation and imaging in the compressed domain. Due to the temporal and spatial non-stationary property of the seismic signal, the decomposition must be localized both in time and space in order to achieve sparse representation. The dreamlet is generated by the tensor product of the time and space localized atoms, and can be taken as impulse-beamlet wave atoms. During migration, the time-space localized dreamlet one-way propagator downward continues the wavefield in depth and the seismic signal propagates in one direction along the time axis. With depth increasing, part of data used to image the shallow structures is abandoned after reaching its depth location, therefore, the valid time length of the seismogram is shorter and the computation cost is decreased for the wavefield depth stepping. In order to fully take advantage of this property, in this paper, we introduce the theory and method of combining the dreamlet propagation with survey sinking migration. Survey sinking migration downward continues the entire surface received data simultaneously. The sunk wavefield is equivalent to the data acquired by deploying sources and receivers at that depth. In dreamlet survey sinking migration, it only keeps the data for imaging the structures beneath the sinking survey system and gets rid of the data already used to image structures above it. Numerical tests on the two dimensional SEG/EAGE post-stack and Marmousi prestack data demonstrate properties of the dreamlet survey sinking. The numerical results show that the combination of dreamlet migration and survey sinking imaging can drastically reduce the data to be propagated without giving for the image quality. It has the potential to be developed as a highly efficient migration method.