Data-Driven and Theory-Guided Pseudo-Spectral Seismic Imaging Using Deep Neural Network Architectures

TL;DR

The study tackles the limitations of traditional Full Waveform Inversion by integrating data-driven and theory-guided neural networks with a pseudo-spectral formulation. It develops two complementary frameworks: a data-driven DNN to learn direct inversions and a theory-guided RNN that emulates wave propagation within a learned forward model, both evaluated on synthetic data and the Marmousi model. Results show that the data-driven DNN provides superior velocity-contrast recovery in deep/over-thrust regions, while the theory-guided RNN yields sharper edges and better stability, with RNNs exhibiting computational efficiency. The work demonstrates the potential of combining data-driven and physics-informed neural nets to enhance seismic imaging, and outlines pathways for extending these frameworks to real data and broader DL approaches.

Abstract

Full Waveform Inversion (FWI) reconstructs high-resolution subsurface models via multi-variate optimization but faces challenges with solver selection and data availability. Deep Learning (DL) offers a promising alternative, bridging data-driven and physics-based methods. While FWI in DL has been explored in the time domain, the pseudo-spectral approach remains underutilized, despite its success in classical FWI. This thesis integrates pseudo-spectral FWI into DL, formulating both data-driven and theory-guided approaches using Deep Neural Networks (DNNs) and Recurrent Neural Networks (RNNs). These methods were theoretically derived, tested on synthetic and Marmousi datasets, and compared with deterministic and time-domain approaches. Results show that data-driven pseudo-spectral DNNs outperform classical FWI in deeper and over-thrust regions due to their global approximation capability. Theory-guided RNNs yield greater accuracy, with lower error and better fault identification. While DNNs excel in velocity contrast recovery, RNNs provide superior edge definition and stability in shallow and deep sections. Beyond enhancing FWI performance, this research identifies broader applications of DL-based inversion and outlines future directions for these frameworks.

Figures (91)

• Figure 1: Horizontal slices though the Samson Dome in the Barent Sea at 1350m showing the uplift in imaging obtained through FWI. Axis indicated extend of the horizontal slice were not present in the original image from Morgan2013.
• Figure 2: Limitations of FWI due to poor illumination. From Shin2010.
• Figure 3: First practical application of FWI using the Marmousi model. This shows significant improvements for the FWI results as presented by Bunks1995.
• Figure 4: Improvements in velocity model and pre-stack depth migrated images obtained through FWI over the Valhall field. The FWI updated velocity model demonstrated a network of shallow high-velocity channels and a gas-filled fracture extension from a gas cloud which was not previously identifiable in conventional tomography. The impact is evident in the migrated sections, which show more continues events in otherwise poorly illuminated area. Adapted from Sirgue2009 and Sirgue2010.
• Figure 5: Imaging improvements obtained through orthorhombic imaging. This produces sharp truncations and clearer faults as highlighted by the red dashed ovals, as well as better focussed gathers. Adapted from Xie2017.