Skip to main content Skip to secondary navigation

Full waveform inversion by model extension SEP-188 (2022)


Table of contents

  • Chapter 1: Introduction
  • Chapter 2: Seismic modeling operators
  • Chapter 3: Theory and design
  • Chapter 4: Optimization: A model-space multi-scale approach
  • Chapter 5: Applying FWIME to realistic 2D synthetic examples
  • Chapter 6: 3D field-data application
  • Chapter 7: Conclusions
  • Appendix A: FWIME and FWI share the same global minimum
  • Appendix B: Convergence of FWIME towards conventional FWI
  • Appendix C: Derivation of the FWIME gradient
  • Appendix D: High-performance computing implementation for 3D applications
  • Bibliography


Seismic imaging is an effective method to produce accurate maps of the Earth’s subsurface, and has been employed for decades in global seismology, hydrocarbon exploration, geothermal energy production, and more recently CO2 sequestration and monitoring. In complex geological settings, the quality of such maps highly depends on having a reliable seismic velocity model, which can be difficult to obtain. In this thesis, I develop a novel method, namely full waveform inversion by model extension (FWIME), designed to produce accurate acoustic velocity models of the subsurface from seismic recordings when conventional methods fail. I leverage the robust convergence properties of wave-equation migration velocity analysis (WEMVA) with the accuracy and high-resolution nature of acoustic full waveform inversion (FWI) by combining these techniques into a compact, mathematically consistent, and user-friendly workflow. By doing so, I mitigate the need for accurate initial models and the presence of coherent long-offset and/or low-frequency energy within the recorded data, which are difficult and costly to acquire but often necessary for conventional methods to succeed. The novelty of my method resides in the design of a custom loss function and the optimization strategy I develop to pair WEMVA with FWI, which is more efficient and powerful than simply applying each method separately or sequentially. My new objective function contains two components. In the first one, I modify the forward mapping of the FWI problem by adding a data-correcting term computed with an extended demigration operator, whose goal is to ensure phase matching between predicted and observed data, even when the initial model is inaccurate. The second component, which is a modified WEMVA cost function, allows me to progressively remove the contributions of the data-correcting term throughout the inversion process. The coupling between the two components is automatically and seamlessly handled by the variable projection method, which also reduces the number of adjustable hyper-parameters, thereby making my solution simple to use. For the optimization process, I devise a model-space multi-scale approach based on model reduction using spline interpolation to control and gradually increase the spatial resolution of the velocity model updates. Unlike conventional methods, FWIME simultaneously inverts the full dataset and bandwidth from the start and does not require tedious data filtering/selection. I illustrate the potential of my proposed method by accurately inverting datasets generated by iv realistic 2D benchmark models which simulate complex and challenging geological scenarios encountered in field applications. In each scenario, the dataset lacks low-frequency energy and the initial velocity model is inaccurate, which prevents conventional methods from recovering useful solutions. I develop an efficient 3D numerical implementation of FWIME with the use of generalpurpose graphics processing units (GPU) to handle 3D field datasets containing tens of terabytes of information, and to recover billions of unknown parameters. I successfully apply FWIME to a 3D ocean-bottom-node dataset acquired by Shell in the Gulf of Mexico. I show that my method outperforms conventional FWI and manages to improve the velocity model and the resulting subsurface image quality.

Reproducibility and source codes

This thesis has been tested for reproducibility. The source codes are made available for download (password required).


Defense presentation

Guillaume Barnier
Publication Date
May, 2022

Related Topics