一种基于新差分模板和无穷范数的震源波场重建方法

Source wavefield reconstruction based on a new finite-difference stencil and infinity norm

伴随状态法广泛应用于偏移成像和全波形反演中。模型的像或梯度可通过震源波场和伴随波场之间的相互运算得到。但两种波场分别沿时间正向和反向传播,无法同时访问。为避免对震源波场进行存储,可采用边界波场逆向重建震源波场。但现有的重建方法仍无法平衡精度和存储需求。为此,发展了一种新的交错网格有限差分震源波场重建方法。新方法通过存储边界区域的N层波场和M-N层波场的线性组合来重建内部区域的震源波场(M为差分算子长度参数,0≤N≤M)。推导了基于新差分模板的频散关系,构建了无穷范数型目标函数,采用Remez交换算法优化了重建系数。详细分析了所提方法的精度和稳定性,并将其应用于声波逆时偏移和弹性波全波形反演。数值结果表明:新方法可以获得足够精确的重建波场、偏移剖面和反演结果;其内存需求仅为传统方法的(N+1)/M。

The adjoint-state method is widely used in migration imaging and full waveform inversion.The image or gradient of the model can be obtained by the interaction between source and adjoint wavefields.The two wavefields,however,propagate in forward and backward time directions,respectively,and cannot be accessed at the same time.To avoid the storage of the source wavefield,we can use boundary wavefields to reconstruct the source wavefield in the backward time direction,but the existing reconstruction methods still cannot balance the requirements of accuracy and storage.Hence,this paper develops a new staggered-grid finitedifference(FD)source wavefield reconstruction method.The method stores the N-layer wavefields and a linear combination of(M-N)-layer wavefields in the boundary area to reconstruct the internal source wavefield,where M denotes the length parameter of the FD operator,and 0≤N≤M.On the basis of the new FD stencil,we derive the dispersion relation,construct an infinite-norm-type objective function,and optimize the reconstruction coefficients by the Remez exchange algorithm.Moreover,we analyze the accuracy and stability of the proposed method and apply it to acoustic reverse time migration and elastic full waveform inversion.Numerical results reveal that the new method can obtain sufficiently accurate reconstructed wavefields,migration profiles,and inversion results,and its memory usage is only(N+1)/M of that of the traditional method.