基于PML边界的变网格高阶有限差分声波方程逆时偏移

叠前逆时深度偏移采用全声波方程求解,不受介质横向速度变化和高陡倾角的影响,具有成像精度高、相位准确、实现回转波成像等优点。逆时偏移利用双程波动方程构造波场延拓算子,正向延拓时间域震源点波场,逆时反向外推时间域检波点波场,然后利用互相关成像条件实现成像,因此正演模拟技术是其成功与否的关键。当浅层为海水或者低速层时,常规的有限差分方法必须采用小网格才能有效压制频散,得到高质量的波场记录,从而保证成像精度。但是若对整个区域都用小网格和小的时间采样间隔进行波场计算,势必造成计算量的增加。本文给出了声波方程变网格算法的差分格式,推导了基于PML边界条件的变网格高阶有限差分方程,将可变网格和可变时间步长算法应用于逆时偏移的波场外推,既保证了波场外推计算的精度和最终逆时偏移的成像效果,同时又提高了计算效率,并通过数值算例试算和逆时偏移成像的应用,说明了该方法的有效性和可行性。

High-order finite difference method in reverse-time migration with variable grids based on PML boundary condition

The reverse-time migration solves two-way acoustic wave equation without equation decomposition.This migration method has the advantages of high precision,accurate phase and better rotating wave imaging without influences of lateral velocity changes and high angle.Reverse-time migration builds wavefield continuation operator by two-way wave equation.It performs forward continuation to obtain source wavefield in time domain,and reverse extrapolation to obtain receiver wavefield in time domain.Then it uses cross-correlation imaging condition to complete the migration.So numerical modeling is the key process for reverse-time migration.If the shallow layer is seawater or low velocity zone,smaller spatial grid size must be used for finite difference method to effectively suppress dispersion,and to ensure the precision of the simulated wavefield.But if small spatial grid size and small time sample interval are applied to the whole region,extremely great computer time and large memory space will be needed.So this paper derives the high-order finite-difference algorithm based on PML boundary condition with variable spatial grid size and variable time sample interval for wavefield extrapolation,which can ensure the accuracy of the simulated wavefield and the precision of the finial reverse time imaging results,and also can save computer time.The numerical data experiments demonstrate that the method is effective and feasible.