Immersed boundary parametrizations for full waveform inversion

Abstract

Full Waveform Inversion (FWI) is a successful and well-established inverse method for reconstructing material models from measured wave signals. In the field of seismic exploration, FWI has proven particularly successful in the reconstruction of smoothly varying material deviations. In contrast, non-destructive testing (NDT) often requires the detection and specification of sharp defects in a specimen. If the contrast between materials is low, FWI can be successfully applied to these problems as well. However, so far the method is not fully suitable to image defects such as voids, which are characterized by a high contrast in the material parameters. In this paper, we introduce a dimensionless scaling function $\gamma$ to model voids in the forward and inverse scalar wave equation problem. Depending on which material parameters this function $\gamma$ scales, different modeling approaches are presented, leading to three formulations of mono-parameter FWI and one formulation of two-parameter FWI. The resulting problems are solved by first-order optimization, where the gradient is computed by an ajdoint state method. The corresponding Fréchet kernels are derived for each approach and the associated minimization is performed using an L-BFGS algorithm. A comparison between the different approaches shows that scaling the density with $\gamma$ is most promising for parameterizing voids in the forward and inverse problem. Finally, in order to consider arbitrary complex geometries known a priori, this approach is combined with an immersed boundary method, the finite cell method (FCM).

23 pages, 21 figures

Cited by in corpus (8)

• On the Use of Neural Networks for Full Waveform Inversion
• Isogeometric Multi-Resolution Full Waveform Inversion based on the Finite Cell Method
• 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
• Vibroacoustic simulations of acoustic damping materials using a fictitious domain approach
• On the efficiency of explicit and semi-explicit immersed boundary finite element methods for wave propagation problems
• A CFL condition for the finite cell method
• A Memory Efficient Adjoint Method to Enable Billion Parameter Optimization on a Single GPU in Dynamic Problems