Generally, marine sediments, soils, and sedimentary rocks are porous media. Such media are composed of a framework made up of interlocking solid particles. The voids, or pores, between the particles may be filled with a fluid or a gas. As a wave propagates through such a medium, the pore fluid or gas may move in relation to the solid particles. Sound propagation in such materials is of great importance in underwater acoustics and seismic exploration and also important for many other acoustical applications, such as in material science and fabrication of acoustic damping elements for buildings.
In porous media, sound speed and attenuation of a propagating wave are functions of the physical properties of the fluid and solid constituents—that is, functions of both porosity and framework rigidity. Because these functional dependencies are complex, and since the acoustic properties of marine sediments are difficult to determine theoretically, sound speeds and attenuations in marine sediments and soils are generally considered empirical quantities whose values can be found only by measurement. Hamilton (1980, 1987) provides very useful references about established values of sound speeds and attenuations within composite porous media. In order to make use of such information, it is necessary to have a broad understanding of the physical processes that are involved when sound is propagating in composite porous media. In this chapter, we discuss the common physical models, with emphasis on models for sound speed and attenuation in marine sediments. First we derive the Gassmann model of propagation in porous media, which can be considered an extension of the Wood’s equation that we derived in chapter 3; the extension is to include the frame rigidity. In addition, we present some of the conventional viscous models, also known as “dashpot models,” which are commonly used to describe attenuation of sound in sediments and rocks.
However, the major part of this chapter is spent on discussion of the Biot theory as it relates to sound propagation in porous media. This theory, which is a further extension of the Gassmann model, also takes into consideration the movement of pore fluid in relation to the framework. The Biot theory’s importance lies in its prediction of three kinds of body waves in porous material: two types of pressure or compressional waves, plus a shear wave. The Biot model’s shear wave and first type of pressure wave are very similar to those we already know from ordinary elastic wave theory; however, Biot’s second pressure wave is a highly attenuated wave, which is significant mainly because it pulls energy away from the first, or ordinary, compressional wave, thereby increasing absorption significantly.