A new regional tectonic map of the consolidated crystalline basement of sedimentary basins and near-surface fold structures of the Ural region

A new approach to the tectonic zoning of the consolidated crystalline basement and near-surface fold structures, taking into account the specific features of the structure of the Earth’s crust is suggested. As a result, a new regional tectonic map of these complexes of the Ural region was created.     

A Hamiltonian approach to asymptotic seismic reflection and diffraction modelling

A model-independent Hamiltonian formulation of paraxial and diffracted ray-tracing equations is presented. It is applied to asymptotic Green's function computations. The medium can have an arbitrary number of interfaces, possibly intersecting at diffracting edges and vertices. Continuously varying model parameters and anisotropy are allowed. The algorithm for elastic waves, involving accuracy control and amplitude computation, is implemented in a platform-independent object-orientated C++ package. Numerical tests and modelling examples are presented.     

Prestack depth imaging via model-independent stacking

Most seismic reflection imaging methods are confronted with the difficulty of accurately knowing input velocity information. To eliminate this, we develop a special prestack depth migration technique which avoids the necessity of constructing a macro-velocity model. It is based upon the weighted Kirchhoff-type migration formula expressed in terms of model-independent stacking velocity and arrival angle. This formula is applied to synthetic sub-basaltic data. Numerical results show that the method can be used to successfully image beneath basalts.     

Nonlinear ray perturbation theory with its applications to ray tracing and inversion in anisotropic media

A comprehensive approach, based on the general nonlinear ray perturbation theory (Druzhinin, 1991), is proposed for both a fast and accurate uniform asymptotic solution of forward and inverse kinematic problems in anisotropic media. It has been developed to modify the standard ray linearization procedures when they become inconsistent, by providing a predictable truncation error of ray perturbation series. The theoretical background consists in a set of recurrent expressions for the perturbations of all orders for calculating approximately the body wave phase and group velocities, polarization, travel times, ray trajectories, paraxial rays and also the slowness vectors or reflected/transmitted waves in terms of elastic tensor perturbations. We assume that any elastic medium can be used as an unperturbed medium. A total 2-D numerical testing of these expressions has been established within the transverse isotropy to verify the accuracy and convergence of perturbation series when the elastic constants are perturbed. Seismological applications to determine crack-induced anisotropy parameters on VSP travel times for the different wave types in homogeneous and horizontally layered, transversally isotropic and orthorhombic structures are also presented. A number of numerical tests shows that this method is in general stable with respect to the choice of the reference model and the errors in the input data. A proof of uniqueness is provided by an interactive analysis of the sensitivity functions, which are also used for choosing optimum source/receiver locations. Finally, software has been developed for a desktop computer and applied to interpreting specific real VSP observations as well as explaining the results of physical modelling for a 3-D crack model with the estimation of crack parameters.     

Separation of Variables Applied to the Wave Equation in Laterally Inhomogeneous Media

--The new eigenfunction expansion formula based upon the method of separation of variables is derived. The method gives the exact transport equation and the generalized eikonal equation without the need of asymptotic series expansions. The generalized eikonal equation extends the classical eikonal equation to a rapidly varying medium. It governs the wave propagation with dispersive phase velocity depending upon the amplitude. Both equations are separated by making use of conventional phase-ray coordinates. The solution is expressed in terms of the elementary Sturm-Liouville eigenfunctions or modes for the vibrating string. The generalized eikonal equation is solved by employing the modified Hamiltonian formalism. This results in frequency-dependent phase-ray trajectories associated with the energy flux vector field.     

Atmospheric boundary layer over steep surface waves

Turbulent air-sea interactions coupled with the surface wave dynamics remain a challenging problem. The needs to include this kind of interaction into the coupled environmental, weather and climate models motivate the development of a simplified approximation of the complex and strongly nonlinear interaction processes. This study proposes a quasi-linear model of wind-wave coupling. It formulates the approach and derives the model equations. The model is verified through a set of laboratory (direct measurements of an airflow by the particle image velocimetry (PIV) technique) and numerical (a direct numerical simulation (DNS) technique) experiments. The experiments support the central model assumption that the flow velocity field averaged over an ensemble of turbulent fluctuations is smooth and does not demonstrate flow separation from the crests of the waves. The proposed quasi-linear model correctly recovers the measured characteristics of the turbulent boundary layer over the waved water surface.     

Distribution of radioactive isotopes in rock and ore of Arkhangelskaya pipe from the Arkhangelsk diamond province

The contents of radioactive elements and the uranium isotopic composition of kimberlite in the Arkhangelskaya pipe at the M.V. Lomonosov deposit and of nearby country rocks have been studied. A surplus of ²³⁴U isotope has been established in rocks from the near-pipe space. The high γ = ²³⁴U/²³⁸U ratio is controlled by the geological structure of the near-pipe space. A nonequilibrium uranium halo reaches two pipe diameters in size and can be regarded as a local ore guide for kimberlite discovery. The rocks in the nearpipe space are also characterized by elevated or anomalous U, Th, and K contents with respect to the background.     

Laboratory, numerical, and theoretical modeling of the flow in a far wake in a stratified fluid

The far-wake flow past a sphere towed in a fluid with high Reynolds and Froude numbers and with a pycnocline-form salt-density stratification is studied in a laboratory experiment based on particle image velocimetry and in numerical and theoretical modeling. In the configuration under consideration, the axis of sphere towing is located under a pycnocline. Flow parameters, the profiles of density and average velocity, and the initial field of velocity fluctuation in numerical modeling are specified from the data of the laboratory experiment. The fields of fluid velocity at different times and the time dependences of integral parameters of wake flow, such as the average velocity at the axis and the transverse width of the flow, are obtained. The results of numerical modeling are in good qualitative and quantitative agreement with the data of the laboratory experiment. The results of the laboratory experiment and numerical modeling are compared to the predictions of a quasi-linear and quasi-two-dimensional theoretical model. The time evolution of both the average velocity at the axis and the transverse width of the wake is obtained with the model and is in good agreement with the experimental data. The results of numerical modeling also show that, under the effect of velocity fluctuation in the wake, internal waves whose spatial period is equal to the characteristic period of the wake’s vortex structure are excited efficiently in the pycnocline.