Abstract
Full-Waveform Inversion seeks to achieve a high-resolution model of the subsurface through the application of multi-variate optimization to the seismic inverse problem. Although now a mature technology, FWI has limitations related to the choice of the appropriate solver for the forward problem in challenging environments requiring complex assumptions, and very wide angle and multi-azimuth data necessary for full reconstruction are often not available. Deep Learning techniques have emerged as excellent optimization frameworks. Data-driven methods do not impose a wave propagation model and are not exposed to modelling errors. On the contrary, deterministic models are governed by the laws of physics. Seismic FWI has recently started to be investigated as a Deep Learning framework. Focus has been on the time-domain, while the pseudo-spectral domain has not been yet explored. However, classical FWI experienced major breakthroughs when pseudo-spectral approaches were employed. This work addresses the lacuna that exists in incorporating the pseudo-spectral approach within Deep Learning. This has been done by re-formulating the pseudo-spectral FWI problem as a Deep Learning algorithm for a theory-driven pseudo-spectral approach. A novel Recurrent Neural Network framework is proposed. This is qualitatively assessed on synthetic data, applied to a two-dimensional Marmousi dataset and evaluated against deterministic and time-based approaches. Pseudo-spectral theory-guided FWI using RNN was shown to be more accurate than classical FWI with only 0.05 error tolerance and 1.45\% relative percent-age error. Indeed, this provides more stable convergence, able to identify faults better and has more low frequency content than classical FWI. Moreover, RNN was more suited than classical FWI at edge detection in the shallow and deep sections due to cleaner receiver residuals.
Abstract (translated)
全波形反演（Full-Waveform Inversion，FWI）旨在通过多变量优化方法解决地震逆问题，从而获得地下高分辨率的模型。尽管FWI现在是一项成熟的技术，但在复杂环境中选择合适的正向问题求解器时仍存在局限性，并且需要非常宽的角度和多方位的数据才能进行完整的重建，而这些数据通常不可用。深度学习技术已经作为优秀的优化框架出现。数据驱动的方法不依赖于波传播模型，因此不受建模误差的影响。相反，确定性的模型受物理定律的约束。最近，地震FWI开始被研究为一种深度学习框架。目前的研究主要集中在时间域上，而伪谱域尚未得到探索。然而，传统的FWI在采用伪谱方法时取得了重大突破。 这项工作旨在填补将伪谱方法整合到深度学习中的空白。通过重新表述基于理论的伪谱FWI问题为深度学习算法，实现了这一目标，并提出了一种新的递归神经网络框架。该方案已在合成数据上进行了定性评估，并应用于二维Marmousi数据集，同时与确定性和时间基方法进行了对比。结果表明，在仅0.05误差容限和1.45%相对百分比误差的情况下，使用RNN的伪谱理论指导下的FWI比传统FWI更准确。此外，这种方法能够提供更为稳定的收敛性，更好地识别断层，并且具有比传统FWI更多的低频成分。更重要的是，在浅层和深层区域边缘检测方面，RNN方法的表现优于传统FWI，这得益于接收器残差的清洁度。 总之，该研究展示了将深度学习技术应用于地震全波形反演中的伪谱理论指导策略的有效性，并为未来的相关应用提供了新的可能性。
URL
https://arxiv.org/abs/2502.17624
