Drilled shaft imaging with 3D ultrasonic full waveform inversion of cross-hole sonic logging (CSL) data

Accurate integrity assessment of drilled shafts is essential for ensuring the stability and long-term performance of heavily loaded infrastructures. Conventional non-destructive testing (NDT) methods often lack the resolution needed to delineate as-built shaft boundaries and detect defects, particularly beyond the rebar cage. We present a novel three-dimensional ultrasonic full-waveform inversion (3D UFWI) method based on the solution of 3D acoustic wave equations and the adjoint-state optimisation. Forward modelling of the acoustic wavefield is performed using a k-space method, enhanced with perfectly matched layers (PML) to suppress artificial boundary reflections. To preserve sharp velocity contrasts at the shaft boundary and reduce inversion artefacts, we employ a matrix-free Tikhonov – Total Variation regularisation scheme and an approximate Hessian-based scaling matrix to improve gradient accuracy, emphasising regions beyond the rebar cage. Synthetic tests demonstrate that 3D UFWI resolves shaft geometry, boundary contrasts, and internal defects without prior knowledge of shaft diameter. We further demonstrate field performance on a full-scale drilled shaft (2.4 m diameter, 21.3 m length) using standard cross-hole sonic logging data acquired with co-depth transmitters and receivers. The resulting 3D P-wave velocity model accurately captures the shaft boundary and surrounding region, providing an improved tool for drilled-shaft integrity evaluation.