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acoustic amplitude analyzed angle of incidence angular frequency attenuation behavior Berea sandstone Biot Biot's theory Bourbie bulk modulus Chapter complex complex modulus compressional wave confining pressure considered Constant Q model corresponding curves decreases defined density depends displacement dissipation effective pressure elastic elastic modulus energy equation example experimental Fontainebleau sandstone function geometry given granite group velocity hence homogeneous increase interface intergranular linear liquid macroscopic Massillon sandstone matrix mechanisms method non-wetting fluid normal observed obtained P2 wave parameters phase velocity plane Plona Poisson's ratio pore pressure pore space porosity porous medium problem quality factor Rayleigh wave reflection coefficient resonant bar rock sample saturated porous saturating fluid Section seismic prospecting shear wave shows signal slow wave solid Stoneley wave strain temperature tensor tortuosity transmission ultrasonic measurements variations vector velocities and attenuations viscoelastic viscosity water saturation wave propagation wave velocity wavelength zero