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Full Waveform Inversion


Part 1: Devito (Python DSL)

This section includes examples that showcase the use of Devito for computational geophysics tasks, focusing on symbolic expressions, stencil computations, and forward modeling.

  • Symbolic Mathematics with SymPy: Automatically generate symbolic expressions for wave equations.
  • Stencil Computations: Leverage Devito's finite-difference capabilities for wave propagation.
  • Forward Modeling: Simulate seismic wave propagation for various velocity models to create synthetic seismic data.
  • Basic Examples:
    • 2D and 3D Acoustic wave modeling
    • 2D Elastic wave modeling

Part 2: JUDI (Julia Framework)

This section focuses on utilizing the JUDI framework for seismic inversion. JUDI is a Julia-based framework for large-scale seismic modeling and inversion, combining the power of Julia with performance-optimized linear algebra and parallel computing libraries.

JUDI Overview:

  • Seismic Inversion with Julia: High-performance tools for Full Waveform Inversion (FWI) in Julia.
  • Efficient and Scalable: Designed to handle industrial-scale seismic data using parallelization and memory-efficient algorithms.
  • Integration with Devito: JUDI leverages Devito for discretization of the wave equation, allowing seamless integration for forward and adjoint modeling tasks.

Key Features:

  • Custom Objective Functions: Easily define and modify objective functions for FWI problems.
  • Field Data Processing: Comprehensive tools for working with real-world seismic data, including pre-processing and inversion.
  • Adjoint-State Methods: JUDI provides efficient implementations of adjoint-state methods, making gradient computation for FWI fast and scalable.

Example Workflows:

  1. FWI Setup: Initialize and run inversion problems using the JUDI interface.
  2. Field Data Inversion: Load field seismic data and apply inversion workflows.
  3. Custom Objective Functions: Implement custom loss functions tailored to specific inversion problems.

License

This project is licensed under the MIT License - see the LICENSE file for details.


References