Resolution near the far surface is limited in the same way as near the scanning surface, but by the backwall reflection instead of the lateral wave. A tip close to the backwall diffracts a signal that arrives only slightly before the backwall echo, and if that gap is shorter than the pulse duration the two cannot be separated.

Setting the time difference equal to the pulse duration gives the deepest resolvable tip: d_max = sqrt((sqrt(S^2 + T^2) - c*tau/2)^2 - S^2). The dead zone is what remains of the wall, T – d_max. It is normally much thinner than the near-surface dead zone because the arrival-time curve is steep at that depth, but it is real, and mode-converted signals that follow the backwall make it worse in practice than the geometry alone suggests.

Root defects therefore need a complementary technique. In practice the backwall itself carries most of the useful information: a root-breaking flaw locally removes, delays or phase-reverses the backwall, and that behaviour is usually more reliable than searching for a separate tip signal a fraction of a microsecond ahead of it.

Compression wave

Worked example

Probe centre separation	70 mm
Wall thickness	25 mm
Probe centre frequency	5 MHz
Cycles in the pulse	2
Compression velocity	5900 m/s
Half separation	35 mm
Pulse duration	0.4 µs
Half backwall path	43.01 mm
Deepest resolvable tip	22.91 mm
Backwall dead zone height	2.09 mm

S = 35 mm, c = 5.9 mm/us, tau = 2/5 = 0.400 us so c*tau/2 = 1.18 mm. R = sqrt(1225 + 625) = sqrt(1850) = 43.0116 mm (43.01). R - 1.18 = 41.8316 mm, squared = 1749.8850, minus S^2 = 524.8850, and the square root is 22.9104 mm, so d_max = 22.91 mm. Dead zone = 25 - 22.9104 = 2.0896 mm, that is 2.09 mm.