ToFD probe delay and velocity from lateral wave and backwall

The lateral wave and the backwall give two equations in the two quantities a ToFD setup cannot measure directly: the material compression velocity and the total delay through the two wedges. Both signals pass through the same wedges, so subtracting the two arrival times removes the delay and leaves t_BW - t_LW = (2*sqrt(S^2 + T^2) - PCS)/c, which gives the velocity. The delay then follows from the lateral wave alone, t_delay = t_LW - PCS/c.

This is the routine way to set up a ToFD depth scale. It needs only a piece of the parent material of known thickness, often the component itself away from the weld, and it calibrates velocity and delay in the same geometry, at the same temperature, with the same wedges and couplant that will be used for the scan. No side-drilled holes and no separate calibration block are required for depth linearity, although a reference block is still needed to demonstrate sensitivity.

Always sanity-check the result. A velocity far from about 5900 m/s in ferritic steel almost always means the PCS or the thickness used is wrong, not that the material is unusual. A delay that drifts between checks means wedge wear, a temperature change or a probe holder that has moved, and any depths measured in between are suspect. Repeat the check at the end of the scan and record both results.

The velocity solved here is the compression velocity, because both the lateral wave and the first backwall arrival are longitudinal. Entering shear-wave times or a shear velocity anywhere in this calculation is a category error and will produce nonsense depths.

S = PCS / 2
path difference = 2 × √(S² + T²) − PCS
c = path difference / (t_BW − t_LW)
t_delay = t_LW − PCS / c
delay per probe = t_delay / 2