The results of the GS + EC theory are compared with the experimental measurement data on of phase velocity and attenuation taken from the open sources. According to the GS + EC theory, significant sound speed dispersion and deviations of the attenuation frequency dependence upon the linear law in the mid-frequency range occur due to a change of the medium compressibility.
Substitution of the equation of state into the wave equation results in a quadratic dispersion relation whose roots yield the wave numbers of two types of the waves, namely the fast and slow ones (Grain Shearing + Effective Compressibility or GS + EC theory). Then, a new two-phase equation of state is deduced, where a part of the fluid is considered to be associated with a solid phase and another part is mobile. The wave equation and the dispersion relation including the internal friction only are deduced using the mathematical apparatus of the fractional derivatives. The medium in a dry state is represented as a generalized Kelvin-Voigt element consisting of a spring and a springpot that is an element combining the spring conservative properties and the dashpot dissipative properties. Whereas in the saturated media, the deviations from this law are noted whence it follows that there are two physical loss mechanisms: the internal and viscous friction.ĭata and methods. It is shown experimentally that the in dry granular media, the attenuation coefficient is directly proportional to frequency. The phase velocities, the attenuation coefficients and their frequency dependences are the acoustic properties of these waves. The longitudinal and shear waves can propagate in marine sediments. Sevastopol State University, Sevastopol, Russian Federation e-mail: The quasi-two-phase theory of propagation of an elastic wave in the unconsolidated marine sediments is represented. Generalized Rheological Model of the Unconsolidated Marine Sediments with Internal Friction and Effective Compressibility At high frequencies, the granules and the fluid oscillate together, and attenuation in the medium arises due to the forces of the internal friction.
Viscous dissipation is manifested at the medium frequencies, when the fluid is still mobile and the viscous forces are rather significant. It is shown that at low frequencies, the unconsolidated medium is of greater compressibility than at high ones that is a result of the fluid displacement from the pore space narrowing. Whereas in the saturated media, the deviations from this law are noted whence it follows that there are two physical loss mechanisms: the internal and viscous friction.
The quasi-two-phase theory of propagation of an elastic wave in the unconsolidated marine sediments is represented.
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