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 [Formula: see text] on a plate-stack model with [Formula: see text]-thick Plexiglas™ plates, the velocity and attenuation (inverse of the quality factor [Formula: see text]) 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 [Formula: see text]. 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. Thereal parts of the weaknesses, which have a clear physical meaning (they affect the weakening of the material), 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 planes) is different in dry and saturated media. The experiment shows that the plate-stack 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.

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.

To find out the nature of gyrotropic properties of sedimentary rocks, physical modelling has been applied to test some hypotheses on possible causes for seismic gyrotropy. The objects of investigation are artificial models of sedimentary rocks, constructed on the principle of "azimuthal turn plus translation", which, from Curie's symmetry principle, creates the preconditions for elastic gyrotropy, namely such a property as the ability to rotate the polarization plane of shear waves. This ability, referred to in optics and acoustics as natural activity, its occurrence or absence, was checked. For laboratory experiments, we used piezoceramic transducers with a frequency of 100 kHz as source and two-component receivers. Polarization of shear waves propagating along a symmetry axis in the models of VTI symmetry was studied with the use of the following three models: the cement block with embedded turning sand strips, the cement block with embedded aluminum-foil turning strips, and a collection of turning fiber-glass plastic plates glued together. All three models appear to be gyrotropic. The polarizational processing of the two-component records has shown a turn of polarization plane of shear waves, and the turn value, at prevailing frequencies of spectra, was proportional to the frequencies of oscillations; besides, the rotation was right-handed at right-hand turning of strips, and it was left-handed at left-hand turning. The determined quantitative characteristics of gyrotropy appeared to be in good agreement with the expected ones.

We have developed a theory of attenuation anisotropy in transversely isotropic (TI) medium due to a single set of parallel fractures, and carried out an ultrasonic laboratory experiment on wave propagation in a thin-layered synthetic medium (dry and oil-saturated), that imitates the fractured medium. The theory predicts that Q-anisotropy is linked to velocity anisotropy. We study the directional behavior of P- and S-wave attenuation as a function of wave-propagation angle a from symmetry axis, and found out that it is similar to the behavior of the corresponding velocities. The theory also predicts a certain ratio between P-wave attenuations and velocities in two principal symmetry directions of TI medium (normal and parallel to fracture planes), as well as a certain relationship between SH- and SV-wave attenuations, and P- and SV-wave attenuations. We have compared the experimental data with the theory-predicted data and have obtained good confirmation of the theory. We have developed a methodology for estimating anisotropy parameters for the transversely isotropic attenuative medium, using joint inversion of all data on attenuations and velocities of the three wave types (P, SH and SV). We take into account the interrelationship of P- and S-waves attenuations which depend on the same quantities - complex moduli of the stiffness matrix which include complex weaknesses characterizing fractures. In the result, for the experimental data, the complex weaknesses have. been reconstructed, as well as Thomsen-style parameters for attenuation epsilon(Q), delta(Q), and gamma(Q). We found out that epsilon(Q) is independent of fracture properties, it is a simple function of the V-P/V-S-ratio. However, the parameter delta(Q) may be meaningful for fracture characterization, because it is defined by the Q(P)/Q(S)-ratio, where Q(S)(-1) and Q(P)(-1) are the S-wave and P-wave attenuations in the direction orthogonal to the fracture plane. The sign of delta(Q) may serve as an indicator of the crack-fill fluid; if delta(Q) < 0 then Q(P)/Q(S) < 1, which corresponds to the case of gas-filled cracks, and vice versa if delta(Q) > 0, then it's the case of liquid-filled cracks for which Q(P)/Q(S) > 1.

A precise τ lepton mass measurement performed at the VEPP-4M collider with the KEDR detector is reported. The mass value is evaluated from the τ + τ − cross section behavior around the production threshold. The result based on 6.7 pb −1 of data is m τ = 1776.81 −0.23 +0.25 ± 0.15 MeV. Using 0.8 pb −1 of data collected at the ψ′ peak, we have also determined that Γ ee B ττ (ψ′) = 9.0 ± 2.6 eV.

The objective of the given work was the study of rocks anisotropy, which was considered as a consequence of the directed dry and impregnated (with oil, water and even melted magma at the big depths) fractures.