Ultrasonic Travel-Time Tomography for Approximating the Local Elastic Tensor in Complex Media

Ultrasonic non-destructive evaluation (UNDE) is vital for assessing the structural integrity of safety-critical infrastructure. However, accurate defect detection and characterisation using UNDE is particularly challenging in complex materials like austenitic steel welds, as the heterogeneous and locally anisotropic grain structures distort wave paths, causing traditional imaging methods based on homogeneous and isotropic assumptions to fail. We present a probabilistic framework to reconstruct spatially varying elastic tensor information from ultrasonic travel-time data using stochastic Stein Variational Gradient Descent. Unlike prior approaches, our method relaxes assumptions of uniformity of material properties across the domain and considers uncertainty induced by limited prior knowledge. We show that travel-time data alone cannot fully constrain high-dimensional domains, and accurate imaging requires informed priors on a series of anisotropy parameters we use as a proxy for the stiffness tensor - scale, strength, and orientation.