Velocity Anisotropy Parameter Research Articles

The influence of lamination and fracture on the velocity anisotropy of tectonic coals

The elastic anisotropy of coal formations is important for the prediction of unconventional coalbed methane reservoir performance and hydraulic fracturing. Although essential for a number of geophysical applications, the elastic anisotropy of coals is still poorly understood. Therefore, three sets of cylindrical coal samples are drilled parallel and perpendicular to the bedding plane, and the ultrasonic velocities under different confining pressures are measured in the laboratory. We combine experimental observations and modeling analysis to evaluate the elastic anisotropy of the coals. The results suggest that the velocity of coals parallel to the bedding plane is less sensitive to the confining pressure than that perpendicular to the bedding plane. The fracture densities of coals parallel to the bedding plane are much lower than those perpendicular to the bedding plane, and most of the fractures are closed when the pressure is higher than 15 MPa. The organic matter and clay content and their preferred orientation play dominant roles in the velocity anisotropy, and the fracture effect can significantly enhance it. Velocity anisotropy parameters of coals are positively correlated with the organic matter and clay content, and the preferred orientation of organic matter and clay plays a significant role in coal anisotropy. The results in this study are helpful in the characterization of fractures of coals and can provide an important rock physics basis for microseismic fracture monitoring and reservoir prediction.

Effects of background elastic and permeability anisotropy on dynamic seismic signatures of a fluid-saturated porous rock with aligned fractures

Seismic dispersion, attenuation, and frequency-dependent anisotropy due to wave-induced fluid flow (WIFF) in fluid-saturated porous and fractured rocks have been widely studied. However, most of these studies do not consider the effects of background elastic and permeability anisotropy. In this work, we study such effects by considering a fluid-saturated porous rock with penny-shaped fractures embedded in the isotropic plane of a transversely isotropic (TI) background. Starting with P-waves propagating perpendicularly to the fracture plane, we obtain the wavefields in the fluid-saturated porous TI background scattered from a single fracture. This allows for the calculation of effective P-wavenumber through the Foldy approximation and the derivation of a frequency-dependent fracture compliance matrix. The angle-dependent seismic dispersion and attenuation, as well as frequency-dependent anisotropy, can thus be calculated. Using this model, we study a fractured tight sandstone with a TI background. The results show that the background elastic anisotropy primarily affects the seismic frequency-dependent anisotropy, while the background permeability anisotropy not only affects seismic frequency-dependent anisotropy but also influences seismic dispersion and attenuation. In particular, the background permeability anisotropy alters the rate of change in seismic velocities and velocity anisotropy parameters with frequencies and the peaks of seismic attenuation and attenuation anisotropy parameters. By comparing the theoretical predictions of our model to other theories and also to two sets of experimental data, our model is validated. Our model can be applied to characterize the fractured, layered earth.

A new highly accurate and efficient pure visco‐acoustic wave equation for tilted transversely isotropic attenuating media

AbstractThe propagation of seismic waves in attenuating anisotropic media exhibits amplitude dissipation and phase dispersion. To describe its effects, the fractional Laplacian pure visco‐acoustic wave equations capable of producing stable and noise‐free wavefields have been derived. However, except for acoustic approximation, previous wave equations utilize the approximations with lower accuracy in simplifying the denominator of the approximate complex‐valued dispersion relation, resulting in reduced accuracy. To address this concern, we use a combination of complex stiffness coefficients to replace the denominator term of the approximate complex‐valued dispersion relation. This approximation effectively reduces the loss of accuracy caused by ignoring the influence of the velocity anisotropy parameter ε and the attenuation anisotropy parameter εQ in the denominator term, leading to a wave equation with high accuracy in media with large anisotropic parameters ε and δ. In addition, the new wave equation only contains two high‐order spatial partial derivatives and has high computational efficiency. Theoretical analysis and numerical examples demonstrate that the proposed pure visco‐acoustic tilted transversely isotropic wave equation outperforms the previous pure visco‐acoustic wave equation in terms of simulation accuracy. The newly developed wave equation is well suited for the application of Q‐compensated reverse time migration and full waveform inversion in attenuating anisotropic media.

An anisotropic rock physics modeling for the coalbed methane reservoirs and its applications in anisotropy parameter prediction

The elastic properties and anisotropy of coalbed methane reservoirs are still poorly understood due to the complicated pore structure and the existing state of the coalbed methane. Therefore, an anisotropic rock physics model for the coalbed methane reservoirs is proposed based on the related effective medium theories, which focuses on the equivalent calculation of the elastic properties for adsorbed coalbed methane and the characterization of the multiple pore structure. Many factors related to the elastic properties of coal are considered, including the composition, pore structure, adsorbed gas content and pore fluid. The measured ultrasonic and well-logging data demonstrate that the proposed physics model is effective in predicting the elastic constants and velocity anisotropy parameters. The results suggest that the elastic constants increase with the increase of adsorbed gas content to some extent, and the effect of porosity on the elastic constants is much more obvious than that of adsorbed gas content. The velocity anisotropy parameters increase with the aligned fracture porosity and the fracture aspect ratio, and the P-wave anisotropy is more sensitive to these two factors. With increasing organic matter and clay content and porosity, Young's modulus and brittleness index decrease while the Poisson's ratio increases, and the impact of the porosity on the brittleness index is more significant than that of organic matter and clay content. The results are helpful in establishing the relationship between reservoir physics parameters and seismic response and can provide a basis for coalbed methane reservoir prediction and hydraulic fracturing.

Predicting the scaling relations between the dark matter halo mass and observables from generalised profiles I: Kinematic tracers

Abstract We investigate the relationship between a dark matter halo’s mass profile and measures of the velocity dispersion of kinematic tracers within its gravitational potential. By predicting the scaling relation of the halo mass with the aperture velocity dispersion, $M_\mathrm{vir} - \unicode{x03C3}_\mathrm{ap}$ , we present the expected form and dependence of this halo mass tracer on physical parameters within our analytic halo model: parameterised by the halo’s negative inner logarithmic density slope, $\unicode{x03B1}$ , its concentration parameter, c, and its velocity anisotropy parameter, $\unicode{x03B2}$ . For these idealised halos, we obtain a general solution to the Jeans equation, which is projected over the line of sight and averaged within an aperture to form the corresponding aperture velocity dispersion profile. Through dimensional analysis, the $M_\mathrm{vir} - \unicode{x03C3}_\mathrm{ap}$ scaling relation is devised explicitly in terms of analytical bounds for these aperture velocity dispersion profiles: allowing constraints to be placed on this relation for motivated parameter choices. We predict the $M_{200} - \unicode{x03C3}_\mathrm{ap}$ and $M_{500} - \unicode{x03C3}_\mathrm{ap}$ scaling relations, each with an uncertainty of $60.5\%$ and $56.2\%$ , respectively. These halo mass estimates are found to be weakly sensitive to the halo’s concentration and mass scale, and most sensitive to the size of the aperture radius in which the aperture velocity dispersion is measured, the maximum value for the halo’s inner slope, and the minimum and maximum values of the velocity anisotropy. Our results show that a halo’s structural and kinematic profiles impose only a minor uncertainty in estimating its mass. Consequently, spectroscopic surveys aimed at constraining the halo mass using kinematic tracers can focus on characterising other, more complex sources of uncertainty and observational systematics.

Near-Surface Radial Anisotropy Tomography of Geothermal Reservoir Using Dense Seismic Nodal Array

The development and utilization of geothermal energy has become an indispensable part in the process of urbanization in China. Near-surface tomographic imaging based on ambient noise is increasingly widely used in geothermal exploration. To construct the subsurface structure of Shear-wave velocity in Andi town, Zhejiang Province, recordings of ambient noise data of 4.7 days were recorded by a dense seismic array composed of 192 stations with an aperture of about 5 km. Analysis of array beamforming in high-frequency bands indicated the approximately uniformly distributed of noise sources. We applied seismic interferometry to retrieve both Rayleigh and Love waves. We used two-station analysis to obtain dispersion images and the corresponding high-quality dispersion curves were extracted by automated codes. 3-D tomographic results down to a depth of 1.6 km of S-wave velocity structure and radial anisotropy parameters were obtained using direct surface wave radial anisotropy tomography method. The anomalies of S-wave velocity and radial anisotropy parameters were combined to infer the storage of geothermal reservoir in Andi town. Furthermore, the accuracy of our results was verified by the borehole data.

The investigation of multiple factors on elastic anisotropy of artificial shale based on the orthogonal experiment

Elastic anisotropy of shales is critical to accurate constraints for rock physical models, quantitative interpretation and hydraulic fracturing. However, the causes of elastic anisotropy of shales are very complicated, and the understanding of how multiple influence factors affect the elastic anisotropy of shales is still not clear. Hence, the orthogonal experiment, as an effective multiple factors experimental method, is adopted in this study to analyze the effect of multiple factors for shale elastic anisotropy. Three factors, clay content, organic matter (OM) content and compaction stress are selected as independent variables, the orthogonal test table L16(43) with four levels for each factor is adopted. According to the designed orthogonal table, sixteen artificial shales are constructed based on the cold-pressing method, and all the dry artificial shales are measured by the ultrasonic measurements. The influence of each factor on the elastic anisotropy and the sensitivity orders of three factors are obtained using the range analysis. The orders of sensitivity for selected factors follow the sequence clay content > compaction stress > OM content for velocity anisotropy parameters. The compaction mechanism of artificial shales is also discussed by the compaction factor, which are positively correlated with the velocity anisotropy parameters. The clay platelets orientation distribution function (ODF) of samples is evaluated by a theoretical model, the ODF coefficients are significantly affected by the clay content and compaction stress, and W200 are much more sensitive to these factors than W400. The results can provide a critical rock physics basis for quantitative interpretation and reservoir prediction of the low-maturity or maturity shale reservoir.

Dynamics of dwarf galaxies in f(R) gravity

ABSTRACT We use the kinematic data of the stars in eight dwarf spheroidal galaxies to assess whether f(R) gravity can fit the observed profiles of the line-of-sight velocity dispersion of these systems without resorting to dark matter. Our model assumes that each galaxy is spherically symmetric and has a constant velocity anisotropy parameter β and constant mass-to-light ratio consistent with stellar population synthesis models. We solve the spherical Jeans equation that includes the Yukawa-like gravitational potential appearing in the weak field limit of f(R) gravity, and a Plummer density profile for the stellar distribution. The f(R) velocity dispersion profiles depends on two parameters: the scale length ξ−1, below which the Yukawa term is negligible, and the boost of the gravitational field δ > −1. δ and ξ are not universal parameters, but their variation within the same class of objects is expected to be limited. The f(R) velocity dispersion profiles fit the data with a value $\xi ^{-1}= 1.2^{+18.6}_{-0.9}$ Mpc for the entire galaxy sample. On the contrary, the values of δ show a bimodal distribution that picks at $\overline{\delta }=-0.986\pm 0.002$ and $\overline{\delta }=-0.92\pm 0.01$. These two values disagree at 6σ and suggest a severe tension for f(R) gravity. It remains to be seen whether an improved model of the dwarf galaxies or additional constraints provided by the proper motions of stars measured by future astrometric space missions can return consistent δ’s for the entire sample and remove this tension.

Regulation Mechanism of the Shock Waves in a Pentamode Lattice-Ring Structure Subjected to Collision

This paper hopes to explore the application potential of pentamode materials in the field of shock protection. Hammer percussion tests revealed that the peak strain of the inner-ring front shock surface of the pentamode lattice-ring structure is 103.9% of that of the inner-ring rear shock surface. According to the simulation results, for a solid ring of equal mass made of the same base material, the ratio mentioned above reaches 3385.7%. Compared with the solid ring of equal mass made of the same base material, the pentamode lattice-ring structure saw a decline of 65.5% in the peak strain of its inner-ring front shock surface. The distribution laws of the group velocity characterizing energy-flow characteristics were discovered by calculating cell dispersion curves in various layers of the pentamode lattice-ring structure. The laws governing the effects of cellular structure parameters on group velocity anisotropy and pentamode characteristic parameters were also revealed. It was found that the deflection angle of the energy-flow vector is positively correlated with group velocity anisotropy and that the effects of pentamode characteristic parameters π and μ on the deflection angle of the energy-flow vector vary greatly in different value ranges. The deflection angle of the energy-flow vector has a decisive effect on the protection performance of the pentamode lattice-ring structure. The conclusions of this study can provide some theoretical support for the shock protection of submarine structures.

Probing the Galactic halo with RR lyrae stars − III. The chemical and kinematic properties of the stellar halo

ABSTRACT Based on a large spectroscopic sample of ∼4300 RR Lyrae stars with metallicity, systemic radial velocity, and distance measurements, we present a detailed analysis of the chemical and kinematic properties of the Galactic halo. Using this sample, the metallicity distribution function (MDF) as a function of r and the velocity anisotropy parameter β profiles (for different metallicity populations) are derived for the stellar halo. Both the chemical and kinematic results suggest that the Galactic halo is composed of two distinct parts, the inner halo and outer halo. The cutoff radius (∼30 kpc) is similar to the previous break radius found in the density distribution of the stellar halo. We find that the inner part is dominated by a metal-rich population with extremely radial anisotropy (β ∼ 0.9). These features are in accordance with those of ‘Gaia-Enceladus-Sausage’ (GES) and we attribute this inner halo component as being dominantly composed of stars deposited from this ancient merged satellite. We find that GES probably has a slightly negative metallicity gradient. The metal-poor populations in the inner halo are characterized as a long tail in MDF with an anisotropy of β ∼ 0.5, which is similar to that of the outer part. The MDF for the outer halo is very broad with several weak peaks and the value of β is around 0.5 for all metallicities.

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

Abstract 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.

N-body Self-consistent Stellar-halo Modeling of the Fornax Dwarf Galaxy

Abstract We present nearly self-consistent stellar-halo models of the Fornax dwarf spheroidal galaxy associated with the Milky Way galaxy. Such galaxies are dominated by dark matter and have almost no gas in the system. Therefore, they are excellent objects for N-body modeling that takes into account visible and dark matter halo components. In order to model the dark matter halo inferred from the analysis of the measured velocities of Fornax's stars, we constructed several self-consistent quasi-equilibrium models based on two source code sets. One of them (GalactICS Software, NEMO) deals with the self-consistent distribution function modeling that depends on the energy E and vertical component of the angular momentum L z . The other is included in the AGAMA framework and is based on Schwarzschild's calculation of orbits. It can reproduce the nonspherical self-consistent structure of Fornax as the weighted sum of orbit contributions to the galactic density even though the inferred dark halo parameters come from Jeans analysis, which does not require that any distribution functions be positive. To guess the parameters that make the N-body models close to the visible object, we use the stellar dark matter model of the Fornax galaxy based on hydrodynamic axisymmetric Jeans equations taking into account the velocity anisotropy parameter. Then, we studied the evolution of the models by performing N-body simulations with the falcON code in order to test their stability. The variability of the model parameters over time was obtained during simulations. The AGAMA models show the best agreement of the resulting velocity dispersion profiles with the observed data.

The elastic properties and anisotropy of artificial compacted clay samples

Clay minerals are a major component of hydrocarbon reservoir rocks, and they are known to play important roles in the physical and elastic properties of rocks. However, it is difficult to directly measure these properties of single-crystal clays due to their small particle size. Therefore, we have constructed three sets of artificial clay samples with different compaction stresses to investigate the effect of the compaction stress and clay mineralogy on their elastic properties and anisotropy. All of the dry samples are measured by the pulse-transmission method. The results indicate that the compaction stress and clay mineralogy have a significant influence on the physical and elastic properties of the clay samples. The microstructures of clay samples indicate that the clay platelets are aligned almost perpendicularly to the direction of compaction stress, and the ultrasonic velocity analysis validates the assumption of transverse isotropy of our clay samples. The velocities increase with the compaction stress, especially at low stress, which corresponds to the rapid porosity reduction at low stress levels. Velocity anisotropy parameters increase with increasing of compaction stress due to the increase of texture sharpness for clay minerals during the compaction process. The elastic moduli of the clay samples display a significant stress sensitivity and a strong directional dependence, with the Young’s moduli increasing and the Poisson’s ratios decreasing with the compaction stress. A simple theoretical template is used to quantify the orientation distribution functions (ODFs) of clay platelets, and the generalized Legendre coefficients of ODF increase with the increase of compaction stress, especially at low stress. Further, the compressional-wave (P-wave) and shear-wave anisotropy increase with the ODF coefficients [Formula: see text] and [Formula: see text], especially P-wave anisotropy.

Anisotropy of random motions of gas in Messier 33

Context. The ellipsoid of random motions of the gaseous medium in galactic disks is often considered isotropic, as appropriate if the gas is highly collisional. However, the collisional or collisionless behavior of the gas is a subject of debate. If the gas is clumpy with a low collision rate, then the often observed asymmetries in the gas velocity dispersion could be hints of anisotropic motions in a gaseous collisionless medium. Aims. We study the properties of anisotropic and axisymmetric velocity ellipsoids from maps of the gas velocity dispersion in nearby galaxies. This data allow us to measure the azimuthal-to-radial axis ratio of gas velocity ellipsoids, which is a useful tool to study the structure of gaseous orbits in the disk. We also present the first estimates of perturbations in gas velocity dispersion maps by applying an alternative model that considers isotropic and asymmetric random motions. Methods. High-quality velocity dispersion maps of the atomic medium at various angular resolutions of the nearby spiral galaxy Messier 33, are used to test the anisotropic and isotropic velocity models. The velocity dispersions of hundreds of individual molecular clouds are also analyzed. Results. The HI velocity dispersion of M 33 is systematically larger along the minor axis, and lower along the major axis. Isotropy is only possible if asymmetric motions are considered. Fourier transforms of the H I velocity dispersions reveal a bisymmetric mode which is mostly stronger than other asymmetric motions and aligned with the minor axis of the galaxy. Within the anisotropic and axisymmetric velocity model, the stronger bisymmetry is explained by a radial component that is larger than the azimuthal component of the ellipsoid of random motions, thus by gaseous orbits that are dominantly radial. The azimuthal anisotropy parameter is not strongly dependent on the choice of the vertical dispersion. The velocity anisotropy parameter of the molecular clouds is observed highly scattered. Conclusions. Perturbations such as HI spiral-like arms could be at the origin of the gas velocity anisotropy in M 33. Further work is necessary to assess whether anisotropic velocity ellispsoids can also be invoked to explain the asymmetric gas random motions of other galaxies.

Frequency-dependent P-wave anisotropy due to scattering in rocks with aligned fractures

Frequency-dependent P-wave anisotropy due to scattering often occurs in fractured formations, whereas the corresponding theoretical study is lacking. Hence, based on a newly developed P-wave scattering model, we have studied the frequency-dependent P-wave scattering anisotropy in rocks with aligned fractures. To describe P-wave scattering anisotropy, we develop the corresponding anisotropy parameters similar to those for elastic anisotropy. Our results indicate that the P-wave velocity anisotropy parameters [Formula: see text] and [Formula: see text] do not change with frequency monotonically, which is different from that caused by wave-induced fluid flow. Fluid saturation in fractures can greatly decrease the P-wave velocity anisotropy, whose effects depend on the ratio of the fluid bulk modulus to the fracture aspect ratio. The P-wave exhibits elliptical anisotropy for the dry fracture case at low frequencies, but anelliptical anisotropy for the case with fluid-filled fractures. The P-wave attenuation anisotropy parameters [Formula: see text] and [Formula: see text] vanish in the low- and high-frequency limits but reach their maxima at the characteristic frequency when the P-wavelength is close to the fracture length. The influence of fluid on the P-wave attenuation anisotropy is similar to that on the velocity anisotropy. To further analyze frequency-dependent P-wave scattering anisotropy, theoretical predictions are compared with experimental results, which indicate reasonable agreement between them.

Local Group Analogs in ΛCDM Cosmological Simulations

Abstract We use semi-analytic galaxy catalogs based on two high-resolution cosmological N-body simulations, Millennium-WMAP7 and Millennium-II, to investigate the formation of Local Group (LG) analogs. Unlike previous studies, we use the observed stellar masses to select the LG member (Milky Way (MW) and M31) analogs, and then impose constraints using the observed separation, isolation, and kinematics of the two main member galaxies. By comparing radial and low-ellipticity orbits between the MW and M31, we find higher tangential velocity results in higher total mass, which are 10 and 10 for radial and low-ellipticity orbits. The orbits also influence the individual mass distribution of MW and M31 analogs. For radial orbits, typical host halo masses of the MW and M31 are 10 and 10 for low-ellipticity orbits, the masses are 10 and 10 . The LG is located primarily in filaments with tails extending toward higher densities up to . The dark matter velocity anisotropy parameters β of both the MW and M31 analogs are close to zero in the center, increasing to 0.2–0.3 at 50–80 kpc and decreasing slowly outward. The slope is much flatter than computed from the MW satellites, and the amplitude is smaller than traced by halo stars. Values of β from different tracers agree at ∼120 kpc where β ∼ 0.2. We also find that model predictions agree broadly with observations in the radial distribution and luminosity function of satellites around the MW and M31.

Measurements Combination of Elastic Anisotropy and Anisotropy of Magnetic Susceptibility on Case Study in Igneous Rock of Lava Flow Type from Ijen Volcanic Complex, East Java

Research about the anisotropy parameters of rock is important for geophysical investigations. This research was a preliminary study which aims to find the relationship between elastic anisotropy and anisotropy of magnetic susceptibility in igneous rock of lava flow type with MR1 code and to interpret preferred orientation in MR1 sample based on the integration of anisotropy measurement results with the supported results from micro-computed tomography (μCT) analysis, petrography analysis and geological data analysis. This research has never been done before. This study was divided into several main stages consist of elastic anisotropy measurements on a cube-shaped specimen to determine the direction of maximum velocity and elastic anisotropy parameter values, anisotropy of magnetic susceptibility measurements on six cylindrical specimens to determine the direction of maximum susceptibility (magnetic mineral orientation) and AMS parameter values, petrography analysis on the all sides of the cube in order to observe preferred orientation in mineral and μCT analysis in a cylindrical specimen to determine the pore trend of rock. This study showed the relationship between AMS and elastic anisotropy in MR1 sample which indicated by positive correlation between the direction of maximum susceptibility and maximum velocity. Based on the results, MR1 sample has elastic anisotropy degree ranges from 2,6 % - 6,6 % for P waves and 2,2 % - 4 % for S waves and anisotropy of magnetic susceptibility degree around 2,6 % - 5,4 %. The integration of all measurement results including the direction of maximum velocity, direction of maximum susceptibility, preferred orientation in mineral, pore trend, and dip direction of sheeting joint indicate preferred orientation in MR1 sample towards NE-SW. One possible cause of such preferred orientation is the direction of the lava flow. Further studies in this topic are needed to support this hypothesis.

Velocity anisotropy analysis for shale lithology of the complex geological section in Jaisalmer sub-basin, India

Measurement of velocity anisotropy is an essential parameter for capturing the heterogeneity of sub-surface geology to characterise the hydrocarbon-bearing reservoir. The incorporation of velocity anisotropy parameters during the preparation of the 3D velocity model represents a robust result in a challenging geological set-up during interpretation. Generally, we can observe that the shale formation is more sensitive to velocity anisotropy response in comparison with other formations such as sandstone, siltstone for clastic reservoir or limestone and dolomite for carbonate reservoir. This study was performed mostly in the high amount shale section mixed with limestone and claystone of the Jaisalmer sub-basin area which lies in the western part of India. The preparation of the velocity model for frequent changes of lithology in the clastic and carbonate reservoir is challenging due to several changes of velocity which show a limitation in the result of the gridded velocity model. The objective of this study is to capture the changes of compressional and shear wave velocity in mixed lithology of the significant shale formation. The idea was due to the inclusion of the anisotropy incorporated changed velocity during the preparation of the gridded velocity model for correctly identified lithology. The shale formation which is the zone of investigation of the current study is situated over a carbonate sequence, and an estimated velocity anisotropy factor of this shale formation will contribute significantly during the cumulative study of velocity modelling of all formation. The current study shows that shale formation shows the character of orthorhombic anisotropy; however, this study was performed based on significant changes of well log data and related effects of vertically transverse isotropic parameters of the shale formation. The fundamental Thomsen anisotropy parameters were estimated by capturing the deviation of five independent stiffness coefficients. Significant changes in evaluated shale velocity were observed after the incorporation of the estimated Thomsen parameter in velocity values.

The MASSIVE Survey XIII. Spatially Resolved Stellar Kinematics in the Central 1 kpc of 20 Massive Elliptical Galaxies with the GMOS-North Integral Field Spectrograph

Abstract We use observations from the GEMINI-N/GMOS integral field spectrograph (IFS) to obtain spatially resolved stellar kinematics of the central ∼1 kpc of 20 early-type galaxies (ETGs) with stellar masses greater than 1011.7 M ⊙ in the MASSIVE survey. Together with observations from the wide-field Mitchell IFS at McDonald Observatory in our earlier work, we obtain unprecedentedly detailed kinematic maps of local massive ETGs, covering a scale of ∼0.1–30 kpc. The high (∼120) signal-to-noise ratio of the GMOS spectra enables us to obtain two-dimensional maps of the line-of-sight velocity and velocity dispersion σ, as well as the skewness h 3 and kurtosis h 4 of the stellar velocity distributions. All but one galaxy in the sample have σ(R) profiles that increase toward the center, whereas the slope of σ(R) at one effective radius (R e ) can be of either sign. The h 4 is generally positive, with 14 of the 20 galaxies having positive h 4 within the GMOS aperture and 18 having positive h 4 within 1R e . The positive h 4 and rising σ(R) toward small radii are indicative of a central black hole and velocity anisotropy. We demonstrate the constraining power of the data on the mass distributions in ETGs by applying Jeans anisotropic modeling (JAM) to NGC 1453, the most regular fast rotator in the sample. Despite the limitations of JAM, we obtain a clear χ 2 minimum in black hole mass, stellar mass-to-light ratio, velocity anisotropy parameters, and circular velocity of the dark matter halo.

Can Globular Clusters in the Galaxy Be Classified by the Velocity Anisotropy Parameter?

Classification problems of globular star clusters in the Galaxy have been briefly discussed. The values of the velocity anisotropy parameter are calculated for 36 globular clusters, by using relatively new data for their apparent surface density. Those values are grouped into three classes. The correlation of the examined parameter with other parameters of globular clusters is analyzed.