Seismic imaging is a major challenge in geophysics with broad applications. It involves solving wave propagation equations with absorbing boundary conditions (ABC) multiple times. This drives the need for accurate and efficient numerical methods. This study examines a collection of exponential integration methods, known for their good numerical properties on wave representation, to investigate their efficacy in solving the wave equation with ABC. The purpose of this research is to assess the performance of these methods. We compare a recently proposed Exponential Integration based on Faber polynomials with well-established Krylov exponential methods alongside a high-order Runge-Kutta scheme and low-order classical methods. Through our analysis, we found that the exponential integrator based on the Krylov subspace exhibits the best convergence results among the high-order methods. We also discovered that high-order methods can achieve computational efficiency similar to lower-order methods while allowing for considerably larger time steps. Most importantly, the possibility of undertaking large time steps could be used for important memory savings in full waveform inversion imaging problems.

翻译：地震成像是地球物理学中的重大挑战，具有广泛的应用前景。该方法需要多次求解含吸收边界条件（ABC）的波传播方程，这推动了对高精度高效数值方法的需求。本研究考察了一组在波场模拟中具有优良数值特性的指数积分方法，探讨其在求解含吸收边界条件的波动方程时的有效性，旨在评估这些方法的性能。我们对比了近期提出的基于Faber多项式的指数积分方法、成熟的Krylov指数方法、高阶Runge-Kutta格式以及低阶经典方法。通过分析发现，基于Krylov子空间的指数积分器在高阶方法中表现出最优的收敛特性。同时，高阶方法在允许使用显著更大时间步长的前提下，能够达到与低阶方法相似的计算效率。最重要的是，采用大时间步长的可能性可为全波形反演成像问题节省大量内存资源。