A Numerical Study of Cross-Weld Virtual-Array Coda-Wave Tomography for Volumetric Imaging of Weld Defects in Steel Plates

Ultrasonic inspection of welded steel components remains challenging due to weld-scale material gradients, local anisotropy, attenuation, and aperture limitations. These factors severely distort both the first-arrival wavefield and the late-arriving scattered wavefield. To address this, this study presents a numerical proof of concept for three-dimensional cross-weld virtual-array coda-wave tomography (VACWT). The “virtual array” utilizes a synthetic aperture created by re-indexing sequential source–receiver records from two opposing line scans into midpoint–angle–depth coordinates. This approach enables line-based data acquisition to achieve multi-angle volumetric coverage without requiring a two-dimensional matrix array. A parameterized welded-solid benchmark model was developed, incorporating effective longitudinal and shear wave velocities, attenuation, and out-of-plane tilt fields. Four defect scenarios were evaluated: a cylindrical void, a lack-of-fusion ribbon, a porosity cluster, and an interference case. For each source–receiver path, four observables were extracted from the synthetic records: first-arrival travel time perturbations, coda wave stretching, coda decorrelation, and late-window energy ratios. These observables were then coupled into a volumetric inverse problem to separate smooth slowness variations, distributed scattering strength, and compact defect occupancy. Under the current simulation conditions, VACWT achieved smaller recovered support volumes and higher volumetric overlap compared to the delay-and-sum total focusing method (DAS-TFM), background-corrected TFM, and reverse time migration (RTM). In the interference case, applying a fixed defect-free calibration threshold yielded a centroid error of 0.48 mm, a volumetric intersection over union (IoU) of 0.856, and a false-positive volume fraction of 0.0%. While these findings serve as benchmark results rather than generalized experimental validation, the study demonstrates that late scattered wave observables provide valuable constraints for volumetric support recovery in a controlled welded-solid model. Future experimental verification on welded steel specimens with known defects remains necessary.