Source wavefield reconstruction using a linear combination of the boundary wavefield in reverse time migration

Abstract

We have developed a new scheme with high accuracy and parsimonious memory requirements to reconstruct the source wavefield in reverse time migration (RTM). This scheme used a linear combination of the boundary wavefield in several layers to reconstruct the wavefield in the imaging domain. The value of the linear combination was stored in one buffer, making the computer memory requirement of our method equal to that of a method that only stored one layer of the boundary wavefield. The coefficients for the linear combination were determined by an optimization technique that minimized the finite difference error in the Fourier domain. The optimal coefficients were presented for finite-difference (FD) stencils of 5–15 grid points. The numerical error of our scheme was analyzed and compared with that of standard FD stencils, representing the conventional method that used multiple layers of boundary wavefield to back propagate the source wavefield. The accuracy of our method is only less accurate than the conventional method in theoretical analysis. However, the storage requirement of our method is merely 1/N of the conventional method if a 2N+1 grid-point FD stencil is used in the space. We have also extended the comparison to two other methods, a one-layer method and an extrapolation method, beyond the conventional method. The numerical results demonstrated that our method can accurately generate high-accuracy images in RTM.

An efficient source wavefield reconstruction scheme using single boundary layer values for the spectral element method

“…In general, this reconstruction method shares similar ideas with the method proposed by Liu SL et al () in teleseismic wavefield modeling using the hybrid method. The storage cost is comparable to that of the method proposed by Liu SL et al () using the FD method. However, unlike the latter, our reconstruction method does not involve any optimization of coefficients as in the method by Liu SL et al (), nor does it require an extrapolation step as described by Tan SR and Huang LJ () and Yang PL et al ().…”

“…The storage cost is comparable to that of the method proposed by Liu SL et al () using the FD method. However, unlike the latter, our reconstruction method does not involve any optimization of coefficients as in the method by Liu SL et al (), nor does it require an extrapolation step as described by Tan SR and Huang LJ () and Yang PL et al (). We then use the Marmousi model to demonstrate its effectiveness and analyze its accuracy and efficiency.…”

“…This method makes full use of the elementwise global property of the Laplace operator in the SEM. The memory requirements are equivalent to those needed in the FD scheme (Liu SL et al, ; Vasmel and Robertsson, ). In comparison with the FD approach, the new method is algorithmically simpler because it does not involve any extra operations.…”

“…It is able to offer high accuracy with fewer storage requirements than the standard method, although it still needs to store several layers of wavefield values depending on the length of the FD stencil. To further reduce the storage demand, Liu SL et al () proposed a source wavefield reconstruction method that stores only one wavefield value as a linear combination of wavefields in the boundary region. They used an optimization technique in the Fourier domain to obtain the coefficients for this linear combination, and they presented an implementation for a regular grid.…”

“…They used an optimization technique in the Fourier domain to obtain the coefficients for this linear combination, and they presented an implementation for a regular grid. This method, which is less accurate than the standard method (Liu SL et al, ), essentially adopts an asymmetric FD operator, that is, a longer operator toward the PMLs domain and a shorter operator toward the computational domain. Recently, Vasmel and Robertsson () presented an alternative scheme that adopts the method of multiple point sources.…”