Prediction of sweet spots in tight sandstone reservoirs based on anisotropic frequency-dependent AVO inversion

The frequency-dependent amplitude-versus-offset (FAVO) method has become a practical method for fluid detection in sand reservoirs. At present, most FAVO inversions are based on the assumption that reservoirs are isotropy, but the application effect is not satisfactory for fractured reservoirs. Hence, we analyse the frequency variation characteristics of anisotropy parameters in tight sandstone reservoirs based on a new petrophysical model, and propose a stepwise anisotropic FAVO inversion method to extract frequency-dependent attributes from prestack seismic field data. First, we combine the improved Brie's law with the fine-fracture model to analyse frequency-dependent characteristics of velocities and Thomsen anisotropy parameters at different gas saturations and fracture densities. Then, we derive an anisotropic FAVO inversion algorithm based on Rüger's approximation formula and propose a stepwise anisotropic FAVO inversion method to obtain the dispersions of anisotropy parameters. Finally, we propose a method that combines the inversion spectral decomposition with the stepwise anisotropy FAVO inversion and apply it to tight sand reservoirs in the Xinchang area. We use P-wave velocity dispersion and anisotropy parameter ε dispersion to optimise favourable areas. Numerical analysis results show that velocity dispersion of the P-wave is sensitive to fracture density, which can be used for fracture prediction in fractured reservoirs. In contrast, anisotropic parameter dispersion is sensitive to gas saturation and can be used for fluid detection. The seismic data inversion results show that velocity dispersion of the P-wave and anisotropic parameter dispersion are sensitive to fractured reservoirs in the second member of Xujiahe Group, which is consistent with logging interpretation results.

Anisotropic frequency-dependent characteristics of PP- and PS-waves in partially saturated double-porosity rocks

Most frequency-dependent AVO inversions are currently based on an approximate equation derived using an isotropic medium. However, actual reservoirs usually show anisotropy, such as shale reservoirs, tight sandstone reservoirs and fractured reservoirs. We propose a joint frequency-dependent AVO (JFAVO) inversion in an anisotropic medium based on a periodic layered double-porosity medium. This JFAVO will allow us to quantitatively study the influence of fluids on the dispersion of PP- and PS-wave velocities and anisotropic parameters. First, we used a double-porosity medium to analyse the frequency-dependent characteristics of velocities and anisotropy parameters. We found that the anisotropic parameters show obvious dispersions, similar to those of velocities. Then, we derived the JFAVO inversion based on Rüger's equation to extract the dispersion of velocities and anisotropic parameters. Finally, we analysed the stability and applicability of the inversion algorithm, and used three sets of models to analyse the sensitivity of dispersion properties to fluids. The numerical analysis results show that PP-wave velocity dispersion and anisotropic parameter δ dispersion are sensitive to fluids, whereas, the velocity dispersion of the PS-wave is not. When saturation exceeds 80%, the velocity dispersion and anisotropic parameter dispersion properties are not sensitive to fluids.

Anisotropic diffusivities' effects in rotating magnetoconvection and geodynamo problems

<p>There are many examples which show how the anisotropic diffusive coefficients crucially influence geophysical and astrophysical flows and in particular flows in the Earth’s outer core. Thus, many models concerning rotating magnetoconvection with anisotropy in the viscosity, thermal and magnetic diffusivities have been developed.  </p><p>Different models correspond to different cases of anisotropic diffusivities. For example, we consider several anisotropic models: one with anisotropy in all diffusivities and other models with various combinations of anisotropic and isotropic diffusivities.  </p><p>Firstly, all kind of anisotropies are reminded and described. Then, a thorough comparison of these anisotropies, especially of the physical differences among them is done. All physical systems with the above mentioned anisotropies are prone to the occurrence of convection and other instabilities. We show how different types of anisotropy cause a different convection and a different balance among the main forces in the Earth’s Outer Core (Magnetic, Archimedean, Coriolis).  </p><p>As usually, to study instabilities in such systems, we use analysis in term of normal modes and search for preferred modes. In all our models, only marginal modes with zero growth rate have so far been studied. Now, we present the bravest modes, i.e. the ones with maximum growth rate. The comparison of the modes dependent on basic input parameters - Prandtl numbers, anisotropic parameter, Ekman and Elsasser numbers - is made mainly for values corresponding to the Earth’s outer core. In all our models the anisotropic diffusive coefficients are represented as diagonal tensors with two equal components different from the third one giving the chance to define simply the anisotropic parameter.  </p><p>We stress how magnetoconvection problems with the anisotropy included, became more and more important among the geodynamo problems in the last years; indeed, the origin of flows necessary for dynamo action, as studied in magnetoconvection with resulting instabilities, is important, as well as the problem of the origin of magnetic fields.  </p>

EMT simulation and effect of TTI anisotropic media in EMT signal

An axisymmetric finite difference method is employed for the simulations of electromagnetic telemetry in the homogeneous and layered underground formation. In this method, we defined the anisotropy property using extensive 2D conductivity tensor and solved it in the transverse magnetic mode. Significant simplification arises in the decoupling of the anisotropic parameter. The developed method is cost-efficient, more straightforward in modeling anisotropic media, and easy to be implemented. In addition, we solved the integral operation in the estimation of measured surface voltage using Gaussian quadrature technique. We performed a series of numerical modeling of EM telemetry signals in both isotropic and anisotropic models. Experiment with 2D tilt transverse isotropic media characterized by the tilt axis and anisotropy parameters shows an increase in the EMT signal with an increase in the angle of tilt of the principal axis for a moderate coefficient of anisotropy. We show that the effect of the tilt of the subsurface medium can be observed with sufficient accuracy and that it is an order of magnitude of 5 over the tilt of 90 degrees. Lastly, consistent results with existing field data were obtained by employing the Gaussian quadrature rule for the computation of surface measured signal.

Formulation of Anisotropic Strength Criterion for Geotechnical Materials

A new nonlinear unified strength (NUS) criterion is obtained based on the spatially mobilized plane (SMP) criterion and Mises criterion. New criterion is a series of smooth curves between SMP curved triangle and Mises circle in the π plane and thereby unifies the strength criteria. The new criterion can reflect the effect of the intermediate principal stress and consider the strength nonlinearity of a material. Based on the fabric tensor, the anisotropic parameter A is defined, and the anisotropic equation is proposed and introduced into the NUS criterion to form a nonlinear unified anisotropic strength criterion. The new criterion can be used to predict the strength variation of granular materials and cohesive materials under three-dimensional stress and can present the strength anisotropy of the geomaterials. The validity of the new criterion was checked using rock and soil materials. It is shown that the prediction results for the criterion agree well with the test data.

An anisotropic model for stars

A stellar model with anisotropic pressure is constructed and analyzed, the metric components that describe the geometry and the source of matter satisfy Einstein’s equations and both are finite inside the star. In addition, density and pressure are decreasing monotone functions of the radial distance. The speed of sound is positive and less than the speed of light, furthermore the model is potentially stable. The model allows describing compact objects with compactness of [Formula: see text] and as a result of the anisotropic value there is a range of values of the central density, in particular for the maximum value of compactness a star with [Formula: see text] and a value of anisotropic parameter [Formula: see text] we get a stellar radius of [Formula: see text] and a central density [Formula: see text]. The above makes the solution a physically realistic model that can be used to describe dense objects such as neutron stars whose characteristic density is of the order of nuclear density.