Full waveform inversion (FWI) entails the ill-posed reconstruction of material parameters (such as sound speed and attenuation) from measurements of complete wave fields (full seismograms). In this paper we present a novel framework for FWI in the visco-acoustic regime. The new framework is based on a new elegant derivation of the system of state and adjoint PDEs which are approximated by the discontinuous Galerkin (DG) method. The inverse problem is then solved by the well established regularization scheme CG-REGINN which has not yet been applied in the context of FWI. For the DG discretization we provide a preconditioner for the efficient computation of the time steps by GMRES which yields optimal convergence estimates in space and time and which is confirmed by numerical tests. The inverse solver expresses the required Fréchet derivative and its adjoint in the DG setting. Successful reconstructions in a simplified cross-well setting serve as a proof of concept for our framework and demonstrate the applicability of our new combination of DG method and inverse solver. Some of the inversion experiments use seismograms generated by an independent finite difference time domain forward solver to avoid inverse crime.

全波形反演 (FWI) 需要根据完整波场（全地震图）的测量对材料参数（例如声速和衰减）进行不适定重建。在本文中，我们提出了粘声系统中 FWI 的新框架。新框架基于状态系统和伴随偏微分方程的新优雅推导，这些系统由不连续伽辽金 (DG) 方法逼近。然后通过完善的正则化方案CG-REGINN解决逆问题尚未在 FWI 的背景下应用。对于 DG 离散化，我们为 GMRES 的时间步长的有效计算提供了一个预处理器，它产生了空间和时间上的最佳收敛估计，并通过数值测试得到了证实。逆求解器在 DG 设置中表达所需的 Fréchet 导数及其伴随。在简化的井间设置中成功重建作为我们框架的概念证明，并证明了我们新的 DG 方法和逆求解器组合的适用性。一些反演实验使用由独立有限差分时域正向求解器生成的地震图来避免逆向犯罪。