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Inversion-DeepONet: A Novel DeepONet-Based Network with Encoder-Decoder for Full Waveform Inversion

Zekai Guo, Lihui Chai, Shengjun Huang, Ye Li

TL;DR

This paper addresses the brittleness of data-driven FWI under fixed-source configurations by introducing enhanced OpenFWI-based datasets with varying source frequencies and locations. It then presents Inversion-DeepONet, an encoder–decoder DeepONet that incorporates source-parameter inputs into the trunk net to enable parameter-aware inversion, and uses a decoder to improve velocity-model reconstruction. Across FWI-F, FWI-L, and FWI-FL, the method demonstrates higher accuracy and better generalization than InversionNet and Fourier-DeepONet, particularly under frequency and location variability. The work provides both dataset augmentation and a robust operator-learning approach, with practical implications for more reliable subsurface imaging in real-world scenarios. Overall, Inversion-DeepONet advances full waveform inversion by combining enhanced data diversity with a more expressive encoder–decoder architecture for seismic velocity reconstruction.

Abstract

Full waveform inversion (FWI) plays a crucial role in the field of geophysics. There has been lots of research about applying deep learning (DL) methods to FWI. The success of DL-FWI relies significantly on the quantity and diversity of the datasets. Nevertheless, existing FWI datasets, like OpenFWI, where sources have fixed locations or identical frequencies, provide limited information and do not represent the complex real-world scene. For instance, low frequencies help in resolving larger-scale structures. High frequencies allow for a more detailed subsurface features. %A single source frequency is insufficient to describe subsurface structural properties. We consider that simultaneously using sources with different frequencies, instead of performing inversion using low frequencies data and then gradually introducing higher frequencies data, has rationale and potential advantages. Hence, we develop three enhanced datasets based on OpenFWI where each source have varying locations, frequencies or both. Moreover, we propose a novel deep operator network (DeepONet) architecture Inversion-DeepONet for FWI. We utilize convolutional neural network (CNN) to extract the features from seismic data in branch net. Source parameters, such as locations and frequencies, are fed to trunk net. Then another CNN is employed as the decoder of DeepONet to reconstruct the velocity models more effectively. Through experiments, we confirm the superior performance on accuracy and generalization ability of our network, compared with existing data-driven FWI methods.

Inversion-DeepONet: A Novel DeepONet-Based Network with Encoder-Decoder for Full Waveform Inversion

TL;DR

This paper addresses the brittleness of data-driven FWI under fixed-source configurations by introducing enhanced OpenFWI-based datasets with varying source frequencies and locations. It then presents Inversion-DeepONet, an encoder–decoder DeepONet that incorporates source-parameter inputs into the trunk net to enable parameter-aware inversion, and uses a decoder to improve velocity-model reconstruction. Across FWI-F, FWI-L, and FWI-FL, the method demonstrates higher accuracy and better generalization than InversionNet and Fourier-DeepONet, particularly under frequency and location variability. The work provides both dataset augmentation and a robust operator-learning approach, with practical implications for more reliable subsurface imaging in real-world scenarios. Overall, Inversion-DeepONet advances full waveform inversion by combining enhanced data diversity with a more expressive encoder–decoder architecture for seismic velocity reconstruction.

Abstract

Full waveform inversion (FWI) plays a crucial role in the field of geophysics. There has been lots of research about applying deep learning (DL) methods to FWI. The success of DL-FWI relies significantly on the quantity and diversity of the datasets. Nevertheless, existing FWI datasets, like OpenFWI, where sources have fixed locations or identical frequencies, provide limited information and do not represent the complex real-world scene. For instance, low frequencies help in resolving larger-scale structures. High frequencies allow for a more detailed subsurface features. %A single source frequency is insufficient to describe subsurface structural properties. We consider that simultaneously using sources with different frequencies, instead of performing inversion using low frequencies data and then gradually introducing higher frequencies data, has rationale and potential advantages. Hence, we develop three enhanced datasets based on OpenFWI where each source have varying locations, frequencies or both. Moreover, we propose a novel deep operator network (DeepONet) architecture Inversion-DeepONet for FWI. We utilize convolutional neural network (CNN) to extract the features from seismic data in branch net. Source parameters, such as locations and frequencies, are fed to trunk net. Then another CNN is employed as the decoder of DeepONet to reconstruct the velocity models more effectively. Through experiments, we confirm the superior performance on accuracy and generalization ability of our network, compared with existing data-driven FWI methods.
Paper Structure (29 sections, 6 equations, 11 figures, 7 tables)

This paper contains 29 sections, 6 equations, 11 figures, 7 tables.

Table of Contents

  1. Introduction
  2. Contributions
  3. Related Work
  4. Pure Physics-Driven Methods.
  5. Pure Data-Driven Methods.
  6. Hybrid Data-Driven and Physics-Driven Methods.
  7. Preliminaries
  8. Full waveform inversion
  9. Dataset
  10. Methodology
  11. The limitations of vanilla DeepONet
  12. Inversion-DeepONet
  13. Experiments
  14. Implementation details
  15. Data description.
  16. ...and 14 more sections

Figures (11)

  • Figure 1: Forward modeling and data-driven FWI. Red stars represent five seismic sources placed on the ground surface to generate waves. Velocity model indicates the distribution of seismic wave speeds in the subsurface medium. Seismic data is obtained from receivers placed on the ground surface.
  • Figure 2: (a) Ground Truth. The predicted velocity models of InversionNet tested on seismic data where the frequencies of five sources are: (b) all 15 Hz. (c) 14, 15, 16, 15 and 14 Hz. (We use the InversionNet model trained on OpenFWI which has fixed source frequency at 15 Hz.)
  • Figure 3: Architecture of Inversion-DeepONet to learn the inversion mapping from seismic data to velocity model. The detailed configuration of this architecture is shown in Table \ref{['table:componets']}.
  • Figure 4: The predictions of three models tested on FlatFault-B in FWI-F. For this example, the five source locations are 0, 172.5, 345.0, 517.5.2 and 690.0 m (red stars in ground truth). The five source frequencies are 17.3, 10.9, 15.4, 5.3 and 5.5 Hz.
  • Figure 5: The predictions of three models tested on FlatVel-B in FWI-L. For this example, the five source locations are 33.8, 140.7, 314.9, 480.2 and 649.8 m (red stars in ground truth). And the five source frequencies are all 15 Hz.
  • ...and 6 more figures