A theory of compressional and shear wave propagation in consolidated porous
media (rocks) is developed by extending ideas already introduced in: conne
ction with unconsolidated marine sediments. The consolidated material is tr
eated as an elastic medium which exhibits a specific form of stress relaxat
ion associated with grain boundaries and microcracks. The stress relaxation
, which is linear in the sense that it obeys superposition, shows hysteresi
s, as characterized by a material response function. Two linear wave equati
ons are derived, one for compressional and the second for shear waves, from
which expressions for the wave speeds and attenuations are established. In
both cases, the attenuation is found to scale with the first power of freq
uency, consistent with many observations of attenuation in sandstones, lime
stones, and shales; the wave speeds show weak logarithmic dispersion. These
expressions for the wave speeds and attenuations satisfy the Kronig-Kramer
s dispersion relationships, as they must if the response of the medium to d
isturbances is to be causal. Some comments are offered on the nature of the
material response, notably that it appears to be primarily associated with
grain-boundary interactions: occurring at a molecular level, rather than b
eing related to the macroscopic properties of the material, such as density
or porosity. (C) 1999 Acoustical Society of America. America. [S0001-4966(
99)02106-2].