1965 Paper I-A

ULTRASONIC PULSED-BEAM TRANSMISSION AND REFLECTION METHODS FOR MEASURING ROCK PROPERTIES - SOME THEORETICAL AND EXPERIMENTAL RESULTS

by

A. R. Gregory

Gulf Research & Development Company Pittsburgh, Pennsylvania

ABSTRACT

This paper is a progress report on the development of laboratory apparatus designed to determine dilatational and shear wave velocities of rock samples by critical angle measurements using both transmission and reflection methods. The methods require accurate measurements of the amplitude of sound pulses reflected from and transmitted through a solid layer immersed in a liquid medium. It is pointed out that the character of a wave train is influenced by numerous interacting factors including the transducer spacing, pulse length, pulse shape, frequency, impedance ratios, and sample thickness. The practical significance of these factors and their relationship to the propagation of wave trains in rocks is discussed.

A computer program is used to determine the energy ratios, amplitude ratios and phase angles at the interfaces for a sound beam in transit across the sample along the PPP and PSP wave paths. Angles of incidence are varied from zero to the second critical angle in increments of 0.09 degree. The pulses which emerge after traversing the sample via the PPP and PSP paths are combined using the principle of superposition to from a synthetic wave train. The results of laboratory measurements are found to be in good agreement with theory Numerical examples are given for Solenhofen limestone and for three different sandstones.

From the reflection technique useful relationships are found between the reflection coefficient and the ratios of impedance, velocity and density of two media at their interface. It is pointed out that most of the important physical properties of rocks including their porosity and elastic constants can be deduced from measurements of the reflection coefficient at some angle near normal incidence. Some applications of the principles of elastic wave propagation to the interpretation of acoustic logs are discussed.