Theory of compressional and transverse wave propagation in consolidated porous media
نویسنده
چکیده
A theory of compressional and shear wave propagation in consolidated porous media ~rocks! is developed by extending ideas already introduced in connection with unconsolidated marine sediments. The consolidated material is treated as an elastic medium which exhibits a specific form of stress relaxation associated with grain boundaries and microcracks. The stress relaxation, which is linear in the sense that it obeys superposition, shows hysteresis, as characterized by a material response function. Two linear wave equations 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 frequency, consistent with many observations of attenuation in sandstones, limestones, and shales; the wave speeds show weak logarithmic dispersion. These expressions for the wave speeds and attenuations satisfy the Kronig– Kramers dispersion relationships, as they must if the response of the medium to disturbances 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 being related to the macroscopic properties of the material, such as density or porosity. © 1999 Acoustical Society of America. @S0001-4966~99!02106-2#
منابع مشابه
Body waves in poroelastic media saturated by two immiscible fluids
A study of body waves in elastic porous media saturated by two immiscible Newtonianfluids is presented. We analytically show the existence of three compressionalwaves and one rotationalwave in an infinite porous medium. The first and second compressional waves are analogousto the fast and slow compressionalwaves in Biot's theory. The third compressionalwave is associated with the pressure diffe...
متن کاملSpectral-element simulations of wave propagation in porous media
S U M M A R Y We present a derivation of the equations describing wave propagation in porous media based upon an averaging technique which accommodates the transition from the microscopic to the macroscopic scale. We demonstrate that the governing macroscopic equations determined by Biot remain valid for media with gradients in porosity. In such media, the well-known expression for the change i...
متن کاملVariational Principle and Plane Wave Propagation in Thermoelastic Medium with Double Porosity Under Lord-Shulman Theory
The present study is concerned with the variational principle and plane wave propagation in double porous thermoelastic infinite medium. Lord-Shulman theory [2] of thermoelasticity with one relaxation time has been used to investigate the problem. It is found that for two dimensional model, there exists four coupled longitudinal waves namely longitudinal wave (P), longitudinal thermal wave (T),...
متن کاملElastic Wave Propagation at Imperfect Boundary of Micropolar Elastic Solid and Fluid Saturated Porous Solid Half-Space
This paper deals with the reflection and transmission of elastic waves from imperfect interface separating a micropolar elastic solid half-space and a fluid saturated porous solid half-space. Longitudinal and transverse waves impinge obliquely at the interface. Amplitude ratios of various reflected and transmitted waves are obtained and computed numerically for a specific model and results obta...
متن کاملTime domain numerical modeling of wave propagation in 2D heterogeneous porous media
This paper deals with the numerical modeling of wave propagation in porous media described by Biot’s theory. The viscous efforts between the fluid and the elastic skeleton are assumed to be a linear function of the relative velocity, which is valid in the low-frequency range. The coexistence of propagating fast compressional wave and shear wave, and of a diffusive slow compressional wave, makes...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 1999