Elastic wave attenuation and velocity of Berea sandstone measured in the frequency domain

P. A. Johnson, T. M. Hopson, and T. J. Shankland,
J. Acoust. Soc. Am., 92, 2842-2850 (1992).

ABSTRACT

This paper describes a frequency domain travel time (FDTT) method for measurement of direct and reflected travel times of sound waves based on the change in phase with frequency between a reference signal and a transmitted wave. An ordinary (linear) source can be used for shorter path lengths and a parametric array (nonlinear) source can be used for longer path lengths. In the single source measurement a reference signal is electronically multiplied with a signal that is time delayed by propagation through a rock sample. As frequency is incremented stepwise, the relative phase difference generates a corresponding stepwise DC output from the multiplier. For any travel path within the sample, there is a characteristic cycle of the DC signal whose reciprocal is proportional to the group time delay along the path. If more than one arrival exists, characteristic cycles are superposed. Thus, a inverse Fourier transform of the frequency signal gives the discrete arrival times for each path. In the parametric measurement a second electronic multiplier is used to create an electronic difference frequency signal for phase comparison with a wave at the difference frequency created by nonlinear elastic interaction in the material. The FDTT method should be applicable to ultrasonic investigation of material properties, nondestructive evaluation, seismology, sonar, and architectural acoustics