基于插值原理的检查点技术波场重构与叠前逆时偏移

叠前逆时偏移等基于波场互相关原理的地球物理方法存在极大的计算与存储需求，因此采用合适的波场重构方法显得尤为重要.常规的随机边界法容易产生成像噪声，而有效边界法在三维情况仍难以实现，检查点技术具有内存要求小的特点，但存在较高的重算率，因此本文提出了插值原理的检查点技术波场重构方法.在满足Nyquist采样定理的前提下对相邻检查点间的波场进行规则抽样，将抽样波场作为插值节点，运用多项式插值算法重构任意时刻的波场，从而避免优化检查点技术反复递推造成的计算效率问题.数值实验表明：插值检查点重构算法能有效的恢复波场，其中三次样条插值重构精度最高，而牛顿法插值法计算代价较小适合于快速重构.经Sigsbee模型的叠前逆时偏移证明了插值算法的可行性，并且极大的提高了波场重构的计算效率.三维模型分析得出在增加少量存储的情况下插值重构法的重算率大幅度降低，存储量减少为有效边界法的7.1%，对于三维尺度的叠前逆时偏移有实际意义.

A checkpoint-assisted interpolation algorithm of wave field reconstruction and prestack reverse time migration

Pre-stack reverse time migration and other geophysical methods based on wave field correlation principles have great computational and storage requirements, so it is very important to adopt appropriate wave field reconstruction methods capable of improving these two effects.Conventional reconstruction methods, such as the random boundary, is easy to produce imaging noise, and the effective boundary method is still difficult to work well in three-dimensional situations; the checkpoint method characteristically computes faster but has a high recalculation ratio.Therefore, this paper proposes a checkpoint-assisted interpolation algorithm to reconstruct the wavefield.In this method, the wavefield is sampled using the Nyquist sampling theory, making it possible to easily reconstruct the wavefield at any time which is reconstructed by polynomial interpolation between sampling wavefields, smartly handling the repetitive recursion that is a bane of computational efficiency.Numerical analysis shows that the interpolation algorithm can effectively reconstruct the wavefield and circumvent the problem of computational efficiency often caused by repeated recursion of the checkpoint technology.The experiments demonstrate that the accuracy of the cubic spline interpolation is quite high, and the Newton method is less computationally expensive and suitable for fast wavefield reconstruction.The feasibility of the interpolation algorithm is proved by the pre-stack reverse time migration of the Sigsbee model, resulting in a highly improved the computational efficiency of the wavefield reconstruction.Applying this method to a 3D model shows that the recomputation ratio of the interpolation reconstruction method is greatly reduced in the case of a small increase in storage.Compared with the efficient boundary condition method, the storage capacity is reduced by 7.1%, thereby making it a practically significant tool to achieve the 3D prestack reverse time migration.