Velocity Anisotropy Research Articles

Modelling elastic properties of partially saturated porous rocks with aligned fractures

SUMMARY A simple but rigorous extension to anisotropy of the isotropic theory for partially saturated rocks is developed to model the variations of the P-wave velocities with angle of incidence and water saturation in partially saturated fractured rocks. The theory is developed to match ultrasonic measurements on a synthetic sandstone samples with a regular distribution of aligned, penny-shaped fractures. The velocity anisotropy in the dry fractured sample is well described with a set of standard anisotropic effective medium theory for penny-shaped cracks. The saturation dependence of the velocities is modelled by a combination of four mechanisms (squirt flow, uniform saturation, patchy saturation and full water saturation) and described by four corresponding theoretical models (squirt-flow relaxation model, anisotropic Gassmann–Wood equations, Backus average and anisotropic Gassmann equations). At ultrasonic frequencies, this simple but rigorous combination of poroelastic models can describe angle and saturation dependency of velocities and moduli in a partially saturated fractured and porous rock reasonably well.

Optical absorption in two-dimensional materials with tilted Dirac cones

The interband optical absorption of linearly polarized light by two-dimensional (2D) semimetals hosting tilted and anisotropic Dirac cones in the band structure is analysed theoretically. Supercritically tilted (type-II) Dirac cones are characterized by an absorption that is highly dependent on the incident photon polarization and frequency and is tunable by changing the Fermi level with a back-gate voltage. Type-II Dirac cones exhibit open Fermi surfaces and large regions of the Brillouin zone where the valence and conduction bands sit either above or below the Fermi level. As a consequence, unlike their subcritically tilted (type-I) counterparts, type-II Dirac cones have many states that are Pauli blocked even when the Fermi level is tuned to the level crossing point. We analyze the interplay of the tilt parameter with the Fermi velocity anisotropy, demonstrating that the optical response of a Dirac cone cannot be described by its tilt alone. As a special case of our general theory, we discuss the proposed 2D type-I semimetal 8-$Pmmn$ borophene. Guided by our in-depth analytics, we develop an optical recipe to fully characterize the tilt and Fermi velocity anisotropy of any 2D tilted Dirac cone solely from its absorption spectrum. We expect our paper to encourage Dirac cone engineering as a major route to create gate-tunable thin-film polarizers.

Non-resonant relaxation of anisotropic globular clusters

ABSTRACT Globular clusters are dense stellar systems whose core slowly contracts under the effect of self-gravity. The rate of this process was recently found to be directly linked to the initial amount of velocity anisotropy: tangentially anisotropic clusters contract faster than radially anisotropic ones. Furthermore, initially anisotropic clusters are found to generically tend towards more isotropic distributions during the onset of contraction. Chandrasekhar’s ‘non-resonant’ (NR) theory of diffusion describes this relaxation as being driven by a sequence of local two-body deflections along each star’s orbit. We explicitly tailor this NR prediction to anisotropic clusters, and compare it with N-body realizations of Plummer spheres with varying degrees of anisotropy. The NR theory is shown to recover remarkably well the detailed shape of the orbital diffusion and the associated initial isotropization, up to a global multiplicative prefactor which increases with anisotropy. Strikingly, a simple effective isotropic prescription provides almost as good a fit, as long as the cluster’s anisotropy is not too strong. For these more extreme clusters, accounting for long-range resonant relaxation may be necessary to capture these clusters’ long-term evolution.

Early-type galaxy density profiles from IllustrisTNG – III. Effects on outer kinematic structure

ABSTRACT Early-type galaxies (ETGs) possess total density profiles close to isothermal, which can lead to non-Gaussian line-of-sight velocity dispersion (LOSVD) under anisotropic stellar orbits. However, recent observations of local ETGs in the MASSIVE Survey reveal outer kinematic structures at 1.5Reff (effective radius) that are inconsistent with fixed isothermal density profiles; the authors proposed varying density profiles as an explanation. We aim to verify this conjecture and understand the influence of stellar assembly on these kinematic features through mock ETGs in IllustrisTNG. We create mock Integral-Field-Unit observations to extract projected stellar kinematic features for 207 ETGs with stellar mass $M_{\ast }\geqslant 10^{11} \, \mathrm{M_{\odot}}$ in TNG100-1. The mock observations reproduce the key outer (1.5Reff) kinematic structures in the MASSIVE ETGs, including the puzzling positive correlation between velocity dispersion profile outer slope γouter and the kurtosis h4’s gradient. We find that h4 is uncorrelated with stellar orbital anisotropy beyond Reff; instead, we find that the variations in γouter and outer h4 (a good proxy for h4 gradient) are both driven by variations of the density profile at the outskirts across different ETGs. These findings corroborate the proposed conjecture and rule out velocity anisotropy as the origin of non-Gaussian outer kinematic structure in ETGs. We also find that the outer kurtosis and anisotropy correlate with different stellar assembly components, with the former related to minor mergers or flyby interactions while the latter is mainly driven by major mergers, suggesting distinct stellar assembly origins that decorrelates the two quantities.

Modeling of pure visco-qP-wave propagation in attenuating tilted transversely isotropic media based on decoupled fractional Laplacians

The pseudoviscoacoustic anisotropic wave equation is widely used in the oil and gas industry for modeling wavefields in attenuating anisotropic media. Compared to the full viscoelastic anisotropic wave equation, it can greatly reduce the computational cost of wavefield modeling while maintaining the visco-qP-wave kinematics very well. However, even if we place the source in a thin isotropic layer, there will be some unwanted S-wave artifacts in the qP wavefield simulated by the pseudoviscoacoustic anisotropic wave equation due to the stepped approximation of inclined layer interfaces. Furthermore, the wavefield simulated by the pseudoviscoacoustic anisotropic wave equation may suffer from numerical instabilities when the anisotropy parameter epsilon is less than delta. To overcome these problems, we derive a pure-viscoacoustic tilted transversely isotropic (TTI) wave equation in media with anisotropy in velocity and attenuation based on the exact complex-valued phase velocity formula. The pure-viscoacoustic TTI wave equation has decoupled amplitude dissipation and phase dispersion terms, which is suitable for further reverse time migration with Q compensation. For numerical simulations, we adopt the second-order Taylor series expansion to replace the mixed-domain spatially variable fractional Laplacian operator, which guarantees the decoupling of the wavenumber from the space-related fractional order. Then, we use an efficient and stable hybrid finite-difference and pseudospectral method (HFDPSM) to solve the pure-viscoacoustic TTI wave equation. Numerical tests indicate that the simulation results of the newly derived pure-viscoacoustic TTI wave equation are stable, free from S-wave artifacts, and accurate. We further demonstrate that HFDPSM outperforms the pseudospectral method in terms of numerical simulation stability and computing efficiency.

An anisotropic equation of state for high-pressure, high-temperature applications

SUMMARY This paper presents a strategy for extending scalar (P–V–T) equations of state to self-consistently model anisotropic materials over a wide range of pressures and temperatures under nearly hydrostatic conditions. The method involves defining a conventional scalar equation of state (V(P, T) or P(V, T)) and a fourth-rank tensor state variable $\boldsymbol {\Psi }(V,T)$ whose derivatives can be used to determine the anisotropic properties of materials of arbitrary symmetry. This paper proposes two functional forms for $\boldsymbol {\Psi }(V,T)$ and provides expressions describing the relationship between $\boldsymbol {\Psi }$ and physical properties including the deformation gradient tensor, the lattice parameters, the isothermal elastic compliance tensor and thermal expansivity tensor. The isothermal and isentropic stiffness tensors, the Grüneisen tensor and anisotropic seismic velocities can be derived from these properties. To illustrate the use of the formulations, anisotropic models are parametrized using numerical simulations of cubic periclase and experimental data on orthorhombic San Carlos olivine.

Annular Creep Barrier Evaluation and Qualification Using Ultrasonic Measurements

Summary It is well-known that formations that exhibit active creep behavior under downhole conditions, such as reactive shales and mobile salts, can form annular barriers across uncemented or poorly cemented annular sections behind casing strings. Such creep barriers can simplify well abandonments, particularly in high-cost offshore environments. Evaluation and qualification of creep barriers in the field, however, have proven challenging and labor-intensive when casing is perforated, and annular rock material is pressure-tested to verify its sealing ability. This work seeks to eliminate the need for pressure testing by allowing the barrier to be qualified using only casedhole log measurements. Sophisticated rock mechanical laboratory experiments under realistic downhole conditions were conducted to investigate the formation of creep barriers by North Sea Lark shale. The experiments evaluated barrier formation while varying annular fluid chemistry and temperature. Measurement parameters included creep rate, pressure transmission across newly formed barriers, pressure breakthrough through the newly formed barriers as well as ultrasonic responses by the shale. It was found that the Lark/Horda shale has a distinct anisotropic ultrasonic wave velocity profile that uniquely characterizes it. This can be used to identify its presence in an annular space when contacting the casing. A main conclusion is that a Lark shale barrier can be qualified through casedhole sonic and ultrasonic logging alone without the need for pressure testing if (1) the magnitude of the wave propagation velocity of the shale behind casing can be confirmed (2077 m/s for Lark shale); (2) the characteristic velocity anisotropy profile, unique to the shale (~10.1% for Lark shale), can be verified; (3) good contact with/bonding to the casing is observed; and optionally (4) anisotropy in the time behavior of the shale contacting the pipe is observed when the barrier is stimulated artificially. If these conditions are met, then our experiments show that the barrier will have excellent hydraulic sealing ability, with a permeability of a few microdarcies at most and a breakthrough pressure that approaches the minimum horizontal effective stress value. Additional findings are that shale heating will accelerate barrier formation but may damage the shale formation in the process. Extraordinary fast annular closure and barrier formation with evident shale rehealing was observed by using a concentrated KCl solution as pore fluid, showing the merits of barrier stimulation by chemical means. This result can be explained by considering the effect of solutes on shale hydration forces.

The SAMI Galaxy Survey: The Internal Orbital Structure and Mass Distribution of Passive Galaxies from Triaxial Orbit-superposition Schwarzschild Models

Dynamical models are crucial for uncovering the internal dynamics of galaxies; however, most of the results to date assume axisymmetry, which is not representative of a significant fraction of massive galaxies. Here, we build triaxial Schwarzschild orbit-superposition models of galaxies taken from the SAMI Galaxy Survey, in order to reconstruct their inner orbital structure and mass distribution. The sample consists of 161 passive galaxies with total stellar masses in the range 109.5–1012 M ⊙. We find that the changes in internal structures within 1R e are correlated with the total stellar mass of the individual galaxies. The majority of the galaxies in the sample (73% ± 3%) are oblate, while 19% ± 3% are mildly triaxial and 8% ± 2% have triaxial/prolate shape. Galaxies with are more likely to be non-oblate. We find a mean dark matter fraction of f DM = 0.28 ± 0.20, within 1R e. Galaxies with higher intrinsic ellipticity (flatter) are found to have more negative velocity anisotropy β r (tangential anisotropy). β r also shows an anticorrelation with the edge-on spin parameter , so that β r decreases with increasing , reflecting the contribution from disk-like orbits in flat, fast-rotating galaxies. We see evidence of an increasing fraction of hot orbits with increasing stellar mass, while warm and cold orbits show a decreasing trend. We also find that galaxies with different (V/σ – h 3) kinematic signatures have distinct combinations of orbits. These results are in agreement with a formation scenario in which slow- and fast-rotating galaxies form through two main channels.

Experimental and theoretical studies of the fluid elasticity on the motion of macroscopic models of active helical swimmers

This work presents experimental and theoretical studies on the locomotion of helical artificial swimmers at low Reynolds number in both Newtonian and viscoelastic ambient liquids. We examine the effect of fluid elasticity on the propulsive force and torque on the body and speed velocity of the swimmer in terms of two physical parameters: Deborah number (De) and Strouhal number (Sh). For this end, some experiments with prototype microorganisms in creeping flow motion are conducted. In the experiments, a macroscopic swimmer that propels itself by mimicking helical flagella are developed and tested. Three swimming models propelled by a helical tail with different wavelengths are investigated, and their motions examined for both cases: when the ambient solvent is a pure Newtonian viscous fluid and when the base fluid is an elastic polymeric solution. In addition, we also apply the slender body theory and the method of regularized Stokeslet in order to calculate theoretically the force and torque, as function of the Strouhal number (Sh), produced by the helical swimmer moving in a Newtonian fluid. The theoretical results are compared with experimental data, and a very good agreement is observed especially for higher values of Sh within the error bars of the experimental data. In the case of a non-Newtonian base fluid, the flow problem of an Oldroyd-B elastic fluid is solved numerically using a computational code based on a finite element method. The helical swimmer propulsive velocity is calculated in terms of the elastic parameter Deborah number and also compared with the experimental observation when the base fluid is non-Newtonian. It is shown experimentally that the swimming speed increases as the elastic effect in the base fluid increases until a critical Deborah number O(1), when the velocity saturates for a constant value within the experimental error bars. The velocity anisotropy measured experimentally by the ratio of the swimmer speed in two different directions is insensitive to the elastic effect in the base fluids. We complete our discussion on the helical swimmers motion in creeping flow by presenting a comparison between predictions of the speed velocity given by finite elements simulations using an Oldroyd-B model for the base elastic fluid and experimental data. The agreement between the two sets of results is very good within the experimental error bars for the elastic parameter varying from 0 to 2. It may be remarked, however, that while the experimental data tend to saturate at larger De, the simulations results seem to have a continuous increase according to the constitutive model used to describe the base elastic liquid.

Experimental study of the anisotropic behaviour of the Naparima Hill argillite

Argillite rocks are often anisotropic due to the presence of microfractures , clay minerals, laminations , and bedding planes . Understanding the anisotropic behaviour of organic-rich argillite rocks is critical for their successful exploitation as unconventional reservoirs. In this study, the anisotropic rock properties of the argillite in the Naparima Hill Formation, Trinidad, an unconventional reservoir, was studied in laboratory experiments. A series of laboratory measurements including permeability, P- and S-wave velocities, and compressive strength were conducted at effective pressures of up to 130 MPa. The rock samples tested were collected from the Naparima Hill outcrop described by three lithofacies : siliceous calcareous mudstones , calcareous mudstone, and siliceous mudstones. The anisotropy of the argillite was determined by the ratio of the rock property measured perpendicular to the outcrop bedding to the rock property measured parallel to the outcrop bedding. For all the studied argillites, the permeability anisotropy ratios is about 2, while the P- and S-wave velocities anisotropy ratios, and compressive strength anisotropy ratios are close to 1, indicating that the rocks are fairly anisotropic. With increasing effective pressure, the permeability, velocities, and strength anisotropy ratios all decreased marginally. A comparison analysis reveals that the anisotropies of permeability and strength, anisotropies of P-velocity and permeability and anisotropies of S-velocity and permeability are all unrelated. However, anisotropies of P-wave velocity and strength, anisotropies of S-wave velocity and strength, and anisotropies of P-wave velocity and S-wave velocity anisotropy all have a 1:1 relationship. Overall, the results of the study suggest that the Naparima Hill argillite is weak to fairly anisotropic, which can be attributed to the low clay content, poor laminations, lack of foliation and few microfractures in the rocks.

Vertical confinement effects on a fully developed turbulent shear layer

The effects of vertical confinement on a turbulent shear layer are investigated with large-eddy simulations of a freely developing shear layer (FSL) and a wall-confined shear layer (WSL) that develops between two horizontal walls. In the case of the WSL, the growth of the shear layer is inhibited by the walls. Once the walls prevent the development of the shear layer, highly anisotropic velocity fluctuations become prominent in the flow. These anisotropic velocity fluctuations are recognized as elongated large-scale structures (ELSS), whose streamwise length is much larger than the length scales in the other directions. Spectral analysis confirms that the turbulent kinetic energy is dominated by the ELSS, whose streamwise length grows continuously. A proper orthogonal decomposition can effectively extract a velocity component associated with the ELSS. The isotropy of the Reynolds stress tensor is changed by the presence of the ELSS. These changes in flow characteristics due to the ELSS are not observed in the FSL, where the shear layer thickness increases continuously. These behaviors of the WSL are consistent with those of stably stratified shear layers (SSSLs), where flow structures similar to ELSS also develop when the vertical flow development is confined by the stable stratification. The vertical confinement by the walls or stable stratification strengthens mean shear effects. The flow behavior at large scales in the WSL and SSSL is consistent with rapid distortion theory for turbulence subject to mean shear, suggesting that the development of ELSS is caused by the mean shear.

Flapwise and chordwise free vibration analysis of a rotating laminated composite beam

In this paper, the flapwise and chordwise free vibrations of a rotating laminated composite beam are studied. To determine the potential energy of the rotating system, two different approaches are presented to evaluate the centrifugal force. Using Hamilton’s principle, the governing differential equations of motion for the rotating system are obtained. In order to solve these equations for the free vibration problem, the finite element method is utilized. The effects of some parameters, such as the hub radius, angular velocity, layups configuration, and material anisotropy, on the vibrational characteristics are investigated in detail. It is anticipated that the results of this paper can be utilized for a more accurate prediction of the free vibration response of rotating composite beams.

Acoustoelastic FD Simulation of Elastic Wave Propagation in Prestressed Media

Insights into wave propagation in prestressed media are important in geophysical applications such as monitoring changes in geo-pressure and tectonic stress. This can be addressed by acoustoelasticity theory, which accounts for nonlinear strain responses due to stresses of finite magnitude. In this study, a rotated staggered grid finite-difference (RSG-FD) method with an unsplit convolutional perfectly matched layer absorbing boundary is used to solve the relevant acoustoelastic equations with third-order elastic constants for elastic wave propagation in prestressed media. We partially verify our numerical simulations by the plane-wave theoretical solution. Comparisons of theoretical and calculated wave velocities are conducted for both P-wave and S-wave as a function of hydrostatic prestresses. We discuss several aspects of the numerical implementation. Numerical acoustoelasticity simulations for wave propagation in single- and double-layer models are carried out under four states of prestresses, confining, uniaxial, pure-shear, and simple-shear. The results display the effective anisotropy of elastic wave propagation in acoustoelastic media, illustrating that the prestress-induced velocity anisotropy is of orthotropic features strongly related to the orientation of prestresses. These examples demonstrate the significant impact of prestressed conditions on seismic responses in both phase and amplitude.

Elastic, electronic, optical and thermoelectric properties of the novel Zintl-phase Ba2ZnP2

We report and discuss the results of a detailed first-principles calculations of the structural, elastic, electronic, optical and thermoelectric properties of the new Zintl phase dibarium zinc diphosphide Ba2ZnP2. The calculated structural parameters using the GGA-PBEsol functional are in excellent agreement with the available experimental counterparts. From the monocrystalline elastic constants numerically estimated through the stress-strain technique, a set of related properties, viz., mechanical stability, elastic anisotropy, brittle/ductile character, anisotropic sound velocities, polycrystalline elastic moduli, including isotropic bulk modulus, shear modulus, Young's modulus, Poisson's ratio, average sound velocity and Debye temperature, are deduced. The electronic and optical properties are investigated through the state-of-the art FP-(L)APW + lo method with the accurate TB-mBJ potential. Ba2ZnP2 is an indirect semiconductor with a gap of 1.24 eV. The charge-carrier effective masses are calculated. The valence band maximum is less dispersive than the conduction band minimum. The microscopic origins of the electronic states composing the energy bands are determined via the PDOS diagrams. Topological analysis of the charge density shows that a covalent character is dominantly ruling the Zn–P bond inside the block ZnP4, while an ionic bonding is mainly ruling the bond between the cation Ba and the polyanion ZnP4. Frequency-dependent macroscopic linear optical functions are predicted in a wide energy range 0–30 eV. Within the visible spectra, the calculated magnitude of the absorption coefficient, reflectivity and refractive index are in the ranges ∼4−35×104cm−1, 29−36% and 3.18−3.47, respectively. The semi-classical Boltzmann transport theory within the constant relaxation time approximation is used to study the thermoelectric properties. The title compound has a figure of merit of ∼1.77 at 300 K, which makes it a potential candidate for thermoelectric applications.

P-wave velocity anisotropy in Hamra Quartzites reservoir, Hassi Messaoud oil field in Algeria

P-wave velocity anisotropy in Hamra Quartzites reservoir, Hassi Messaoud oil field in Algeria

Nematic Quantum Criticality in Dirac Systems.

We investigate nematic quantum phase transitions in two different Dirac fermion models. The models feature twofold and fourfold, respectively, lattice rotational symmetries that are spontaneously broken in the ordered phase. Using negative-sign-free quantum MonteCarlo simulations and an ε-expansion renormalization group analysis, we show that both models exhibit continuous phase transitions. In contrast to generic Gross-Neveu dynamical mass generation, the quantum critical regime is characterized by large velocity anisotropies, with fixed-point values being approached very slowly. Both experimental and numerical investigations will not be representative of the infrared fixed point, but of a quasiuniversal regime where the drift of the exponents tracks the velocity anisotropy.

Effect of pressure on anisotropy in elasticity, sound velocity, and thermal conductivity of vanadium borides

Effect of pressure on anisotropy in elasticity, sound velocity, and thermal conductivity of vanadium borides

Infrasound propagation through the atmosphere with mesoscale wind velocity and temperature fluctuations

Some results on modeling and observation of infrasound propagation in the atmosphere in a presence of mesoscale and anisotropic wind velocity and temperature fluctuations are presented. The theoretical model of infrasound scattering from anisotropic wind velocity and temperature inhomogeneities of the atmosphere is developed. With this model, the appearance of the stratospheric, mesospheric, and thermospheric arrivals of the infrasound signals in the acoustic shadow zones is explained. The analytic relation between the wave field of the scattered infrasound signal and the vertical profile of the effective sound speed fluctuations is obtained. Using this relation, the vertical profiles of the fluctuations within the upper stratosphere (25–55 km) and the lower thermosphere (105–140 km) were retrieved from the waveforms and travel times of the signals recorded in the acoustic shadow zones. The theoretical frequency spectrum of the infrasound wavefield reflected from the fine-scale layered structure of the atmosphere is obtained and compared with the spectra of the observed stratospheric arrivals.

Propagating Seismic Waves in VTI Attenuating Media Using Fractional Viscoelastic Wave Equation

AbstractSeismic velocity and attenuation anisotropy are ubiquitous in the crust and upper mantle, significantly modulating the characteristics of seismic wave propagation in the Earth's interior. Accurate seismic wave modeling of velocity and attenuation anisotropy is essential for the understanding of wave propagation in the Earth's interior as well as constructing global and region‐scale seismic full waveform tomography. Here, we derive a decoupled fractional Laplacian (DFL) viscoelastic wave equation to characterize the Earth's frequency‐independent Q behavior in the vertical transversely isotropic (VTI) media. We verify the accuracy of the proposed viscoelastic wave equation by 2D synthetic examples; to show its applicability in crustal‐scale seismic modeling, we present an example of 3D seismic wave propagation in the realistic Salton Trough model. Through extensive numerical tests, we conclude that the proposed viscoelastic wave equation is superior in four aspects. First, the viscoelastic wave equation takes VTI anisotropy of both velocity and attenuation into account and can describe the strong direction‐dependent attenuation. Second, our derivation contains spatially independent Laplacians, and thus the proposed wave equation enjoys higher simulation accuracy for heterogeneous Q media. Third, the new viscoelastic wave equation can decouple the amplitude decay and the phase distortion, which is appealing for improving the resolution in seismic imaging and inversion. Lastly, compared to viscoelastic wave equations with time‐fractional operators, our scheme has higher computational efficiency by avoiding substantial wavefield storage.

Velocity Anisotropy in Self-gravitating Molecular Clouds. II. Observation

Abstract The view on velocity structures in molecular clouds and their relationship with magnetic fields (B field) has evolved during the past decade from almost no correlation to highly parallel. Our numerical simulations suggest a more nuanced picture: Depending on whether the self-gravity is dynamically dominant, the velocity field can be governed by either contraction (at high densities) or turbulence (at low densities), and their anisotropies will tend to be either perpendicular or parallel, respectively, to the B fields. High-density regions are always embedded in the low-density fore/background, so the velocity behaviors from lines of sight (LOSs) with high column densities will be a mixture of orthogonal anisotropies, which can be hard to interpret and necessitates zooming in onto certain LOS scales to better characterize localized behaviors. We tested and confirmed the above prediction with CO observations of the Taurus molecular cloud.