Abstract:
An ultrasonic immersion procedure for determining third-order elastic coefficients of rock via measurements of harmonic generation was described recently by Plona et al. [ J. Acoust. Soc. Am. 98, 2886(A) (1995)]. Here an accurate quasilinear model is presented for second harmonic generation in a sound beam transmitted through an isotropic solid immersed in liquid. With the primary beam represented as an angular spectrum, analytic solutions were derived for second harmonic generation by all pairs of plane waves in both the liquid and the solid. Numerical superposition of the analytic solutions, followed by Fourier transformation, yields the second harmonic field anywhere in the solid or liquid. There are no restrictions on geometry or orientation of the sound source, and all combinations of compression and shear wave interactions are taken into account. At the previous meeting the accuracy of this model for the case of reflection near the Rayleigh angle was demonstrated [J. Acoust. Soc. Am. 99, 2538(A) (1996)]. Reported here are comparisons with second harmonic diffraction patterns that were measured in a 1-MHz beam radiated by a 1.2-cm radius source and transmitted through a 10-cm-thick block of lucite immersed in water. [Work supported by ONR, NSF, and Schlumberger Foundation.]