变阶数有限差分法及逆时偏移有效边界存储最优化策略

Variable order finite difference method and optimization strategy of efficient boundary storage for reverse time migration

地震资料逆时偏移方法在计算过程中需要保存大量的波场信息,这种巨大的存储需求限制了该方法的实际应用.因此,研究能够显著降低波场存储量的存储策略对于推进逆时偏移方法的实用化具有重要的理论意义和实际价值.本文分别从时间和空间的角度提出了相应的波场存储策略:(1)提出变阶数有限差分算子,在计算波场左、右和下边界处时,将差分阶数由高阶递减至二阶,结合有效边界存储策略,可在不损失波场重建精度的同时大幅降低波场存储量;(2)借鉴checkpoint策略和缓冲区思想,提出了基于拉格朗日乘子法的参数最优化方案,在时间方向上压缩波场存储量.通过对二维盐丘模型进行震源波场重建和逆时偏移存储量测试,结果表明:本文方法可实现对震源波场的高精度重建,与传统方法相比,在不损失成像精度的前提下,新的存储策略可大幅降低逆时偏移方法的波场存储需求.

A huge amount of wavefield information needs to be saved in the process of reverse-time migration,which limits the practical application of the method. The research of efficient boundary saving strategy,that can reduce the requirement of storage dramatically,is of important theoretical significance and practical value in promoting practical application. In this paper,from the perspective of time and space, two strategies are proposed respectively：（ 1） The variable order finite difference method is presented,the high order operator is gradually reduced to second order when calculating the wavefield boundaries except the upper side,so the wavefields can be reconstructed with high accuracy under a lower cost;（ 2） Drawing lessons from the checkpoint technology and the buffer zone,the Lagrange multiplier method based optimization strategy is proposed,it can compress wavefield storage in the time direction. We tested the reconstruction of the source wavefield and the storage requirement of reverse-time migration with 2D salt model,the results show that the approach proposed in this article can achieve high-precision reconstruction of the source wavefield,compared to the tradition method,the storage requirements for reverse-time migration are greatly reduced without loss of imaging resolution.