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May 27, 2026Computer Methods in Applied Mechanics and Engineering0 citationsOpen Access

Full waveform inversion with an adjoint scheme for time-dependent inverse wave problems in nonlinear media

DGDan GivoliTechnion – Israel Institute of Technology DRDaniel RabinovichTechnion – Israel Institute of Technology ETEli TurkelTel Aviv University

Key Points

The study aims to solve time-dependent inverse wave problems in nonlinear media using Full Waveform Inversion.
Employs Full Waveform Inversion with adjoint method for gradient calculation.
Presents a semi-discrete formulation for analysis of nonlinear material behavior.
Evaluates performance through numerical experiments with specific models.
The adjoint method effectively identifies nonlinear material parameters in both models tested.
Numerical experiments show improved accuracy despite the presence of measurement noise.
Performance varies based on model characteristics, indicating adaptability of the method.

Abstract

The solution of time-dependent inverse wave problems in nonlinear media is considered, using Full Waveform Inversion (FWI). The goal is the identification of parameters related to the nonlinear material behavior. The adjoint method is employed for the efficient calculation of the functional gradient. A general formulation of the method at the semi-discrete level is presented. Two specific models are used to experiment with this formulation: a miniature model that lacks physical meaning, and a model of the deflection of a membrane made of a softening material. The method is specialized to these two models, and numerical experiments demonstrate its performance in each case. Computational aspects that are considered include assessing the success of the identification, and evaluating the performance of the method in the presence of measurement noise.

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