TCG point gain

A time corrected gain curve equalises the response of the same reflector at different sound paths. Two effects have to be undone. Beam spreading makes the echo fall off as a power of range that depends on the reflector shape: a large flat back wall behaves as 1/z, a side drilled hole as 1/z^1.5 and a disc or flat bottomed hole as 1/z². In decibels that is 20·k·log10(z/z_ref) with k equal to 1, 1.5 or 2.

The second effect is material attenuation, which is linear in path length rather than logarithmic: 2·α·(z − z_ref) for the round trip. Over short paths spreading dominates; in coarse grained or austenitic material attenuation quickly becomes the larger term, and it is the one that varies most from part to part.

The sum of the two is the extra gain the TCG point needs. Add it to the reference gain and compare with what the instrument can deliver: running out of gain at the far TCG points is common on thick sections and shows up as a curve that flattens at the end. When that happens the fix is a lower frequency, a larger aperture or a different reflector depth, not more electronic gain on an already saturated receiver.

Attenuation should be measured on the part or on a block of the same material, not taken from a table. The reflector exponents are geometry and are reliable; α is metallurgy and is not.

ΔG = 20·k·log10(z / z_ref) + 2·α·(z − z_ref)
k = 1 back wall, 1.5 side drilled hole, 2 flat bottomed hole
gain at the point = reference gain + ΔG
TCG point time = 2 · z / c