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Ultrasonic waves are mechanical waves which can spread in solid, liquid and gas mediums. They may be differently attenuated when propagating in different mediums, and also have different velocities in different mediums. The velocity and the attenuation are the two most important parameters in ultrasonic testing.

For the ultrasonic testing of stone, the favourable frequency range is 20 kHz–1000 kHz. The velocity and attenuation of ultrasonic waves in stone depend among other factors on the density, water content and cracks. The amplitude and velocity of the first wave received are positively correlated to the mechanical strength of the stone, and the mechanical strength directly responds to the weathering condition of the stone.

Therefore ultrasonic testing is an appropriate method to detect the position and trend of weathered zones and cracks inside a stone.

There are many situations for cracks, crazings, and splits on the surface and in the interior of stone sculptures. Ultrasonic waves may go directly through a crack if the fracture surfaces are still in contact with each other with little effect on the velocity but with a distinct attenuation of the amplitude. For the situation that the fracture surfaces are completely apart from each other, the waves bypass the crack and the transit time increases. Due to the open split that runs through the stone, the wave will not be received on the other side.

For evaluating the stone weathering level, we use the P-wave velocity V normalized with respect to the velocity of an unweathered sample V₀ as shown in table 1, which is normally used by conservators. For the Fangshan Hanbaiyu marble V₀ is about 4,500 m/s.

175Table 1: Normalized velocity ratios for the definition of stone weathering levels.

Weathering Level	Vi / V0
Not Weathered	≥ 0.9
Void ratio increased	0.75–0.9
Floor level of weathering	0.75
Slightly waethered	0.5–0.75
Moderately weathered	0.25–0.5
Severly weathered	≤ 0.25