Isogeometric Multi-Resolution Full Waveform Inversion based on the Finite Cell Method

Abstract

Full waveform inversion (FWI) is an iterative identification process that serves to minimize the misfit of model-based simulated and experimentally measured wave field data, with the goal of identifying a field of parameters for a given physical object. The inverse optimization process of FWI is based on forward and backward solutions of the (elastic or acoustic) eave equation. In a previous paper [1], we explored opportunities of using the finite cell method (FCM) as the wave field solver to incorporate highly complex geometric models. Furthermore, we demonstrated that the identification of the model's density outperforms that of the velocity -- particularly in cases where unknown voids characterized by homogeneous Neumann boundary conditions need to be detected. The paper at hand extends this previous study: The isogeometric finite cell analysis (IGA-FCM) -- a combination of isogeometric analysis (IGA) and FCM -- is applied for the wave field solver, with the advantage that the polynomial degree and subsequently also the sampling frequency of the wave field can be increased quite easily. Since the inversion efficiency strongly depends on the accuracy of the forward and backward wave field solution and of the gradient of the functional, consistent and lumped mass matrix discretization are compared. The resolution of the grid describing the unknown material density is the decouple from the knot span grid. Finally, we propose an adaptive multi-resolution algorithm that refines the material grid only locally using an image processing-based refinement indicator. The developed inversion framework allows fast and memory-efficient wave simulation and object identification. While we study the general behavior of the proposed approach on 2D benchmark problems, a final 3D problem shows that it can also be used to identify voids in geometrically complex spatial structures.

19 pages, 14 figures

References in corpus (5)

• A mathematical theory for mass lumping and its generalization with applications to isogeometric analysis
• On the Use of Neural Networks for Full Waveform Inversion
• Towards higher-order accurate mass lumping in explicit isogeometric analysis for structural dynamics
• Immersed boundary parametrizations for full waveform inversion
• Critical time-step size analysis and mass scaling by ghost-penalty for immersogeometric explicit dynamics

Cited by in corpus (5)

• On the Use of Neural Networks for Full Waveform Inversion
• Quantitative Comparison of the Total Focusing Method, Reverse Time Migration, and Full Waveform Inversion for Ultrasonic Imaging
• Implicit-Explicit Time Integration for the Immersed Wave Equation
• On the efficiency of explicit and semi-explicit immersed boundary finite element methods for wave propagation problems
• A Memory Efficient Adjoint Method to Enable Billion Parameter Optimization on a Single GPU in Dynamic Problems