Ultrasonic P-wave to ascertain the mean grain diameter of D’Euville limestone

In this paper, ultrasonic P-wave is used to ascertain the mean grain diameter of heterogeneous D’Euville limestone. A previous model of P-wave is used to yield phase velocity ( V p ) and the quality factor due to viscous squirt ( Q ps ) in the ultrasonic band, for the limestone saturated with water. As the limestone has grain diameter ( d ) ranging from 400 to 1000 μm, we set the mean d to be 800, 600 and 400 μm in turn. V p is fitted precisely as possible between the model and ultrasonic measurement. The emission frequency was 500 kHz. With the mean d of 800 μm, the model yields Q ps agreeing with the measurement not very accurately and the average frequency (between emission and receiving) is inverted as 251 kHz (which is too low). With the mean d of 600 μm, the model yields Q ps agreeing with the measurement surprisingly well and the average frequency is inverted as 355 kHz (which is very reasonable). With the mean d of 400 μm, neither V p nor Q ps fits well between the model and measurement and the average frequency is inverted as 631 kHz (which is unreasonable). It is concluded that the mean d of D’Euville limestone is 600 μm.