地震成像中的Born近似与Rytov近似比较

A COMPARISON BETWEEN THE BORN AND RYTOV APPROXIMATIONS FOR SEISMIC IMAGING

地震波散射理论中的Born近似和Rytov近似是目前地震数据波动方程叠前深度偏移成像技术和波场模拟技术中最为常用的两种近似。利用波场传播散射理论中的局部Born近似和局部Rytov近似,分别导出了单程波方程的稳定的Born近似波场传播算子和稳定的Rytov近似波场传播算子,然后从理论和实践上比较了它们在地震数据波动方程叠前深度偏移成像中的应用效果。基于相位扰动的稳定的Rytov近似波场传播算子对速度变化引起的波场相位变化的适应性要比基于波场扰动的稳定的Born近似波场传播算子好,稳定的Born近似波场传播算子可视为稳定的Rytov近似波场传播算子的一阶近似,因此,对于主要基于地震数据相位信息的地震数据构造偏移成像,Rytov近似在理论上要优于Born近似。此外,还用国际标准模型———Marmousi模型地震数据的偏移成像,从实践上证明了Rytov近似要优于Born近似。

The Born and Rytov approximations of seismic wave scattering theory are the most common two approximation methods for prestack depth migration imaging of wave equation and wave-field simulation. The stable wave-field propagators of one-way wave equation for Born and Rytov approximations are derived by using the local Born and local Rytov approximation methods in the scatter theory of wave-field propagation, and their application effects in prestack depth migration imaging of wave equation are compared theoretically and practically. The phase-perturbation-based stable Rytov approximation wave-field propagator is better than the wave-field-based stable Born approximation wave-field propagator in its adaptability to wave-field phase change resulted from velocity variation, and the latter can be viewed as the first order approximation of the former. Therefore, for seismic migration imaging based on the phase information of seismic data, the Rytov approximation is theoretically superior to the Born approximation. In addition, the seismic migration imaging results with the Marmousi model, which is an international normative model, verify the superiority of the Rytov approximation to the Born approximation.