FWI-LS Project

Solver for Full Waveform Inversion (FWI) using Level Set in the frequency domain. This software is part of a project for my masters' degree in Mechanical Engineering (UFSC, 2019) - The Dissertation is available here.

This software is implemented using the Finite Element Method (FEM) with 2d linear quadrilateral elements for spatial discretization. Parallelization on the frequency domain, with options to parallel linear solver configurations and parallel shots (per source).

Project uses conda to manage it's Python dependencies. cmake and a C++ compiler are also necessary in order to compile the C++ code used to improve Python performance in specific contexts. The C++ bindings are compiled and placed on src/cpp/build. This path must be on PYTHONPATH.

Level Set Evolution Algorithm

A Level Set function is used to approximate the solution. For each optimization step, the Level Set evolution direction is calculated using an "evolution velocity", which is determined using the Diffusion-Reaction equation, which depends on information from the sensibility analysis. The step, on the other hand, must be guessed by the user. Based on this guess, the algorithm will then search for a more suitable step, to guarantee that the objective function from the optimization procedure is decreased.

Useful tools

• inv compile Compiles the project using cmake and gcc
• inv clean Cleanup compilation artifacts
• inv run-fwi-case Runs FWI case from database of cases. Options:
  • --case-name (required) which case to run
  • --iterations Number of iterations to run (default=10)
  • --threads Number of parallel shots (default=1)
  • --no-plot Disable output plots
  • --ignore-LS-V-at-sponge If set, will not generate inclusions in the sponge area (When using sponge absorbing layers)
  • --min-obj-function-ratio-change Set the minimum change between optimization steps (Values lower than this will assume the optimization has converged)
  • Level Set Evolution options (See Level Set Evolution section on this file for more information)
    • initial-evolution-step Initial guess for dtheta on the LS evolution algorithm
    • min-evolution-step Minimum step size for dtheta on the LS evolution
• inv run-fwd-case Runs forward case from database of cases. Options:
  • --case-name (required) which case to run
  • --omega Frequency to run, in rad/s (default=5.0)
  • --size Mesh size (size == nx == ny) (default=80)
  • --threads Number of threads for the linear solver (default=1)