Простая акустическая модель неконсолидированных морских осадков с внутренним и вязким трением

Abstract

The main object of research in the shallow water acoustics is the sea floor and marine sediments. An unconsolidated, saturated marine sediment consists of a more or less loose assemblage of mineral grains in contact, with seawater in the pores. In the layer of unconsolidated marine sediments, elastic waves of two types can propagate: longitudinal and shear. The acoustic properties of these waves are phase velocities, attenuation coefficients and their frequency dependences. It has been shown experimentally that in dry granular media the attenuation coefficient is directly proportional to the frequency. In saturated media, deviations from this law are noted, whence it follows that there are two physical mechanisms of dissipation - internal friction and viscous dissipation. In the article, marine sediments are considered as an environment in which there are no elastic bonds between the granules. The propagation and attenuation of the longitudinal and transverse waves is explained by a special intergranular interaction, nonlinear at the microscopic level. The model of the elementary volume of such a medium in the dry state is represented as a generalized Kelvin-Voigt element, consisting of a spring and a springpot, an element combining the conservative properties of the spring and the dissipative properties of the dashpot. Applying the mathematical apparatus of fractional derivatives, we derive a generalized wave equation describing the elementary volume of the medium. Harmonic substitution leads to a dispersion relation for the longitudinal and shear waves. The resulting dispersion relation includes only internal friction. Then, the equations of motion for the longitudinal and transverse waves are corrected, so that the motion of the solid phase and fluid is considered separately. In this case, part of the fluid is considered to be coupled with the solid phase, and some - mobile. The term "percolation porosity" is defined. Harmonic substitution in new, two-phase wave equations gives new dispersion relation, including internal friction and viscous dissipation. The presented theory is called "GS+ED". The results of the GS+ED theory are compared with the experimental data taken from the open sources. It is shown that the GS+ED theory gives a best fit, compared to the theories of GS and Biot-Stoll. An estimate is made of the contribution of internal friction and viscous dissipation to the total attenuation in the propagation of longitudinal and transverse waves. Frequency ranges are defined in which internal or viscous friction is manifested. Evaluation is given for two cases - when the medium represents dense marine sediments and when the medium is a suspension.