Optimal Transport-Based Full Waveform Inversion for Nondestructive Evaluation using Ultrasonic Arrays

Abstract Full Waveform Inversion (FWI) is a state-of-the-art family of methods for seismic imaging. These methods are based on optimization algorithms and allow for the reconstruction of maps of certain material properties (e.g. sound speed) with high resolution, providing a powerful tool for the assessment of reservoirs of oil and gas. The Nondestructive Evaluation (NDE) literature contains some attempts to apply FWI methods using ultrasonic data. One problem that limits this application is the oscillatory nature of ultrasonic signals, which tends to generate local minima in optimization problems formulated with the L2 norm as a measure of data fidelity. This problem is already well documented in seismic imaging and is referred to as cycle skipping. On the other hand, Optimal Transport (OT) optimization methods have been demonstrated to be robust to cycle skipping when used in lieu of the traditional L2 residual minimization for FWI of seismic data, motivating an assessment of their applicability to ultrasound FWI. This work presents an OT-FWI method for the reconstruction of speed maps of metallic structures from signals acquired with ultrasonic arrays. Synthetic data were generated on a finite difference-based acoustic simulator and represent two arrays with 64 elements each and 1MHz center frequency. Results obtained from the simulated data show the robustness of the method with relation to cycle skipping as well as its capacity to reconstruct complex geometries hidden inside structures. All source codes for the implementation of the method using Python 3.12 and CUDA are provided, as well as the simulated data.