P -wave ray velocities and the inverse acoustic problem for anisotropic media
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ICAL PROPERTIES OF CRYSTALS
P-Wave Ray Velocities and the Inverse Acoustic Problem for Anisotropic Media I. Yu. Zela, b, T. I. Ivankinaa, D. M. Levinb, and T. Lokajicekc a Frank
Laboratory of Neutron Physics, Joint Institute for Nuclear Research, ul. Joliot-Curie 6, Dubna, Moscow oblast, 141980 Russia b Tula State University, pr. Lenina 92, Tula, 300600 Russia c Institute of Geology, Academy of Sciences of the Czech Republic, Rozvojova 269, 16500 Praha 6 – Lysolaje, Czech Republic e-mail: [email protected] Received June 1, 2015
Abstract—The specific features of the calculation of ray velocities of quasi-longitudinal waves in anisotropic media have been considered. A technique for calculating elastic constants using P-wave ray velocities measured in an ultrasonic experiment on spherical samples is presented. It is shown by an example of tabular data that elastic constants С11, С22, and С33 and combinations of constants (С12 + 2С66), (С13 + 2С55), (С23 + 2С44), (С14 + 2С56), (С25 + 2С46), and (С36 + 2С45) can be calculated most accurately for the general case of anisotropic media with elastic properties of arbitrary symmetry. Since the determining system of equations is illconditioned, the values of elastic constants entering these combinations depend on the choosed initial approximation. DOI: 10.1134/S106377451604026X
INTRODUCTION The study of the anisotropy of elastic properties of different materials is an urgent problem. The results of this study are widely applied in materials science (for example, when studying structurally inhomogeneous, heterogeneous, composite, etc., materials), different fields of geophysics (from seismic sounding to earthquake physics), and crystal physics. An important feature of elastic wave propagation in anisotropic media is the dependence of the phase and ray velocities of quasi-longitudinal and quasi-transverse waves on the wave-propagation direction. Experimentally measured velocities of elastic waves with different propagation directions and polarizations can be used to solve the inverse problem of determining elastic constants of anisotropic material [1, 2]. A method for measuring longitudinal-wave velocities on spherical samples was proposed in [3, 4] to study the anisotropy of elastic properties of geological samples. The method is based on the application of ultrasonic transducer for generating and receiving elastic pulses, a system of two-dimensional stepwise sample rotation, and the corresponding sample environment (high-pressure chamber). When measuring the ultrasound transmission velocity, acoustic transducers are brought into point contact with the sample surface to measure the ray velocities of quasi-longitudinal elastic waves.
The experimental values of quasi-longitudinal Pwave velocities were considered in [5] phase velocities and used, jointly with the velocities of quasi-transverse S waves, to calculate the elasticity tensor components. This approach was substantiated by the fact that the samples under study exhibited a weak anisotropy of elastic properties,
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