This study attempts to validate a mathematical formalism of introducing attenuation into Schoenberg's linear slip model. This formalism is based on replacing the real-valued weaknesses by complex-valued ones. During an ultrasonic experiment, performed at a central frequency of 100 kHz on a plate-stack model with 1-mm-thick Plexiglas™ plates, the velocity and attenuation ͑inverse of the quality factor Q͒ of P-, SH-, and SV-waves are measured in directions from 25°to 90°with the symmetry axis for dry and oil-saturated models and loading uniaxial pressures of 2 and 4 MPa. The velocity and attenuation data are fitted by the derived theoretical functions. The values of the real and imaginary parts of the complex-valued weaknesses are estimated. The real parts of the weaknesses, which have a clear physical meaning ͑they affect the weakening of the material͒, are three times larger for the dry model than for the oil-saturated one. The imaginary parts of the weaknesses are responsible for attenuation; their values are an order of magnitude smaller than the real parts. The derived expressions for angle-dependent velocities and attenuations can be used to distinguish between dry and oil-saturated fractures. In particular, the P-wave attenuation function in the symmetry-axis direction ͑normal to fracture planes͒ is different in dry and saturated media. The experiment shows that the platestack model is inhomogeneous because of the nonuniform pressure distribution, which degrades the experimental results and creates difficulties in the inversion for the complex-valued weaknesses -particularly in joint inversion of P-and S-wave data.

A ballistic gravimeter has been constructed using a laser interferometer to measure the vertical distance traversed by a free-falling body and a rubidium frequency standard to measure elapsed time. The error in distance and time measurement are estimated to be less than 2 x 10(-8) and 2 x 10(-11) respectively. The systematic error in measuring gravitational acceleration, after corrections have been made, does not exceed 0.02 mgal.

We perform an ultrasonic experiment on anisotropy of wave propagation in the model constructed from plexiglas plates, with oil saturation and without any saturation. We determine the directional dependencies of P-and S-waves attenuations and velocities and estimate Thomsen-style parameters for attenuation Q ε , Q δ , and Q γ as well asThomsen's velocity parameters. We develop a theory that predicts certain relationship between anisotropies of P-, SH-and SV-wave attenuation and velocity in transversely isotropic (TI) media due to aligned fracture set. Taking into account the interplay of the velocity and attenuation anisotropies, we develop the effective TI model of the attenuative fractured medium fitted to the experimental data. We derive formulas for the parameters Q ε , Q δ , and Q γ in terms of complex-valued weaknesses that relates these parameters to fractured medium parameters. We found out that the ratio of the symmetry-axis P-and S-wave attenuations S P Q Q / and the parameter Q δ are interlinked and strongly dependent of the fluid type in cracks that is confirmed by the experiment. The value of Q δ is much greater for dry-crack medium than for wet-crack medium, that is correlated with the S P Q Q / -ratio, which is on the contrary larger in wet-crack medium and smaller in drycrack medium. This is in accordance with laboratory measurements at ultrasonic frequencies of P-and S-wave quality factors.

We propose a mathematical formalism of introducing attenuation in Schoenberg's Linear Slip model. This formalism consists in replacing the real-valued weaknesses, normal and tangential, entering in the stiffness matrix by the complex-valued quantities. To test the validity of this procedure, an ultrasonic experiment was performed with the use of a plate-stack model made from plexiglass plates. We measured velocities and attenuations of P-, SH-and SV-wave versus the angle between the ray and the symmetry axis of TI model for air-filled and oil-saturated state of the model under uniaxial pressure of 2 and 4 MPa. The data on velocities and attenuations were fitted by the derived theoretical functions. We have estimated the values of the imaginary and real parts of the complex-valued weaknesses. The real parts of the weaknesses are threefold for the air-filled model in comparison with the oil-saturated one. The imaginary parts of the weaknesses, responsible for attenuation, are one order of magnitude less than the values of the real parts of the weaknesses. Both P-wave anisotropies, the velocity anisotropy and the attenuation anisotropy, are greater in the air-filled model than in the oil-saturated one. Besides, in the air-filled model, the symmetry-axis attenuation of the P-wave is much greater than the S-wave symmetry-axis attenuation, whereas in the oil-saturated model these attenuations are similar.