Full Waveform Inversion

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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

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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.

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License

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

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References

• Devito Documentation
  Learn more about Devito for symbolic computations and stencil-based modeling.
• JUDI.jl Documentation
  For further reading on JUDI's capabilities and architecture.