Azimuthal Variation Research Articles

Azimuthal Prestack Seismic Anisotropic Inversion on a Deep and Tight Carbonate Reservoir From the North Potwar Basin of Pakistan

Summary Quantitative characterization of deep, tight, and heterogeneous reservoirs plays an important role in identifying hydrocarbon pathways for effective and optimal reservoir field development. In this case study, we used an azimuthal prestack seismic anisotropic inversion approach to estimate attributes of horizontal transverse isotropy (HTI) caused by a set of vertical fractures, oriented cracks, and stress. Anisotropic inversion facilitated the conversion of interface properties to the corresponding layer-based properties, which led to the quantitative interpretation of reservoir properties related to azimuthal variation in seismic amplitudes. To estimate the anisotropy magnitude and the direction of the isotropy axis in HTI media, elastic properties (P-impedance and Vp/Vs) obtained from prestack seismic inversion (using six azimuth × four angle stack) served as inputs. The isotropic low-frequency model (LFM) is used as the foundation of the inversion for all azimuths, and the anisotropy effects are later added by updating the model along the azimuths. The direction of the isotropy plane resulting from the anisotropic inversion is determined by using the maximum horizontal stress as a prior constraint, which eliminates any inherent uncertainty. The workflow used effectively characterized the orientation and density of fractures from the recently discovered oilfield reservoirs of the Paleocene (Lockhart) formation located in Pakistan’s north Potwar Basin. It also helped improve the prediction accuracy for fractures in the study area. According to the observations (fractures) from the exploratory drilled well (D1) in the tight carbonate (Lockhart) reservoir, a significant amount of anisotropy magnitude is observed. This provides the basis for hydrocarbon exploration, field development, and reliable drilling decisions.

Drift phase resolved diffusive radiation belt model: 1. Theoretical framework

Most physics-based models provide a coarse three-dimensional representation of radiation belt dynamics at low time resolution, of the order of a few drift periods. The description of the effect of trapped particle transport on radiation belt intensity is based on the random phase approximation, and it is in one dimension only: the third adiabatic invariant coordinate, akin to a phase-averaged radial distance. This means that these radiation belt models do not resolve the drift phase or, equivalently, the magnetic local time. Yet, in situ measurements suggest that radiation belt intensity frequently depends on magnetic local time, at least transiently, such as during active times. To include processes generating azimuthal variations in trapped particle fluxes and to quantify their relative importance in radiation belt energization, an improvement in the spatiotemporal resolution of the radiation belt models is required. The objective of this study is to pave the way for a new generation of diffusive radiation belt models capable of retaining drift phase information. Specifically, we highlight a two-dimensional equation for the effects of trapped particle transport on radiation belt intensity. With a theoretical framework that goes beyond the radial diffusion paradigm, the effects of trapped particle bulk motion, as well as diffusion, are quantified in terms of Euler potentials, α,β, quantities akin to the radial and azimuthal directions. This work provides the theoretical foundations underlying the drift phase resolved transport equation for radiation belt dynamics. It also brings forward the concept of azimuthal diffusion as a phase-mixing agent.

SO and SiS Emission Tracing an Embedded Planet and Compact 12CO and 13CO Counterparts in the HD 169142 Disk

Planets form in dusty, gas-rich disks around young stars, while at the same time, the planet formation process alters the physical and chemical structure of the disk itself. Embedded planets will locally heat the disk and sublimate volatile-rich ices, or in extreme cases, result in shocks that sputter heavy atoms such as Si from dust grains. This should cause chemical asymmetries detectable in molecular gas observations. Using high-angular-resolution ALMA archival data of the HD 169142 disk, we identify compact SO J = 88 − 77 and SiS J = 19 − 18 emission coincident with the position of a ∼ 2 M Jup planet seen as a localized, Keplerian NIR feature within a gas-depleted, annular dust gap at ≈38 au. The SiS emission is located along an azimuthal arc and has a morphology similar to that of a known 12CO kinematic excess. This is the first tentative detection of SiS emission in a protoplanetary disk and suggests that the planet is driving sufficiently strong shocks to produce gas-phase SiS. We also report the discovery of compact 12CO and 13CO J = 3 − 2 emission coincident with the planet location. Taken together, a planet-driven outflow provides the best explanation for the properties of the observed chemical asymmetries. We also resolve a bright, azimuthally asymmetric SO ring at ≈24 au. While most of this SO emission originates from ice sublimation, its asymmetric distribution implies azimuthal temperature variations driven by a misaligned inner disk or planet–disk interactions. Overall, the HD 169142 disk shows several distinct chemical signatures related to giant planet formation and presents a powerful template for future searches of planet-related chemical asymmetries in protoplanetary disks.

Shock wave propagation in a rotational axisymmetric dusty gas for adiabatic flow using group invariance method

The main purpose of this investigation is to discuss the entire class of similarity solutions for adiabatic flow behind the cylindrical shock wave in a dusty gas (a mixture of non-ideal gas and small solid particles) using the Lie group invariance method. The group invariance method is used to derive the similarity transformations and the similarity variable, which transforms the set of partial differential equations into a set of ordinary differential equations. The obtained set of ordinary differential equations is solved numerically using the Runge–Kutta method of fourth order in Mathematica software. It is found that the shock wave decays with the variation of the gas non-idealness parameter. Also, the shock strength enhanced with an increase in the ratio of the specific heat of the solid particles to the specific heat of the gas at constant volume or the initial azimuthal velocity variation exponent or the ratio of the density of solid particles to the initial density of the gas. The behavior of the flow variables behind the shock wave is analyzed graphically. This study may be helpful in understanding the astrophysical phenomena such as supernovae explosion, in a dusty gas environment.

Terahertz Bessel Beams Formed by Binary and Holographic Axicons

The characteristics of high-power vortex Bessel beams in the terahertz range (λ=141 μm) obtained with the use of diffractive axicons (DAs) illuminated by a Gaussian beam of the Novosibirsk free-electron laser were studied. Two of the three possible types of DA recently described in our previous paper, namely, binary spiral silicon axicons (BAs), forming beams with a topological charge l equal to 0–4 and 9, and a diamond “holographic” axicon (HA), forming a beam with l=9, were used in the experiments. These axicons formed beams whose cross sections in the region of inner Bessel rings were close to those of ideal Bessel beams, but their intensities varied in azimuth with a frequency of l and 2l for the BAs and HA, respectively. However, in the case of the BAs, the beams had a pronounced helical structure at the periphery, whereas for the HA, the beam was axisymmetric. By focusing these beams with a lens, we studied the structure of the so-called “perfect” beams (PBs). While an ideal Bessel beam exhibits a PB as a thin ring, in the case of the BAs, we observed a broadened ring structure consisting of 2l short spirals, and for the HA, we observed a narrow ring with 2l maxima in azimuth. A comparison of the numerical calculations and experiments showed that the observed azimuthal intensity variations can be attributed to inaccuracies in the preparation of the axicon relief and/or discrepancies between the calculated and actual wavelengths, within a few percent. The results of this work enable the establishment of quality requirements for axicon manufacture and the appropriate selection of the axicon type in accordance with the requirements for the beam.

Sap flow responses in pioneer and late-successional tree species in secondary tropical montane forests of Eastern Himalaya, India.

The interactive role of life-history traits and environmental forcing on plant-water relations is crucial for understanding species response to climate change but remains poorly understood in secondary tropical montane forests (TMFs). Comparing contrasting life-history traits (pioneer vs late-successional species) in a biodiverse Eastern Himalayan secondary TMF, we investigated sap flow responses in co-occurring pioneer species, Symplocos racemosa (n=5) and Eurya acuminata (n=5), and late-successional species, Castanopsis hystrix (n=3), using modified Granier's Thermal Dissipation probes. The fast-growing pioneers S. racemosa and E. acuminata) had 2.1- and 1.6-times higher sap flux density than the late-successional C. hystrix, respectively, and exhibited characteristics of long-lived pioneer species. Significant radial and azimuthal variability in sap flow (V) between species was observed and attributed to life history traits and the canopy's access to sunlight. Nocturnal V (1800-0500hr) was 13.8 % of daily V and is attributed to stem recharge for evening V (1800-2300hr) and to endogenous stomatal controls for pre-dawn V (0000-0500hr). Both the shallow-rooted pioneer species exhibited midday depression in V attributed to photosensitivity and diel moisture stress response. In contrast, deep-rooted C. hystrix transpired unaffected across the dry season likely accessing groundwater. Thus, the secondary broadleaved TMFs, with the dominance of shallow-rooted pioneers, are more prone to the negative impacts of drier and warmer winters than primary forests, which are dominated by deep-rooted species. The study provides an empirical understanding of life-history traits and microclimate modulating plant-water use in widely distributed secondary TMFs in Eastern Himalaya and highlights their vulnerability against warmer winters and reduced snowfall due to climate change.

Performance Comparison Of Three Antennas With Passive Reflecting Walls For Wireless Power Transmission

This paper presents a novel wireless power transmission system through reflecting walls for enhancing received signal strength. The study has been conducted with an objective to achieve a novel system for the energy harvesting and subsequent wireless power transmission for mobile phone charging applications. The work is carried out at the well-known RF frequency range from 469.5 MHz to 773.5 MHz. We have employed three different antennas for the proposed system. Multiple changes in antenna orientations have also been accounted for including azimuthal variations. The results show substantial enhancement in the received signal strength (RSS) due to use of these reflecting walls

Crustal anisotropy of the South China block and tectonic implications

Exploiting the teleseismic waveform data from permanent seismic stations distributed in the South China block, we obtained the crustal anisotropy parameters at 51 stations by fitting the azimuthal variations of arrival times of the PMs converted wave of radial receiver functions. The results show the dominant direction of fast wave polarity in the South China block is NW–SE, which is basically consistent with the absolute plate motion direction. Combining the shear wave splitting and GPS results, we speculated that the tectonic extension of the Paleo-Pacific plate subduction dominates the crust–mantle anisotropy, which reflects the large-scale tectonic stress setting of the South China block. The fast wave directions of NE–SW and E–W calculated by a few stations might represent a local complex tectonic environment, and the crustal anisotropy of NE–SW is well related to the tectonic deformation in Paleozoic. The delay time of slow waves caused by crustal anisotropy ranges from 0.14 s to 0.71 s, with an average of 0.33 s. The delay time of Jiangnan orogenic belt, which located in the southeast of Yangtze block, is particularly large, which reflects the complex and intense intra-continental tectonic movements since Neoproterozoic. The crustal anisotropy along the southeast coast can be contributed to the local lithosphere underplating caused by the upwelling of asthenosphere in Cretaceous.

Effect of Perceptual Training with Sound-Guided and Kinesthetic Feedback on Human 3D Sound Localization Capabilities.

In this paper, we experimentally investigate how the 3D sound localization capabilities of the blind can improve through perceptual training. To this end, we develop a novel perceptual training method with sound-guided feedback and kinesthetic assistance to evaluate its effectiveness compared to conventional training methods. In perceptual training, we exclude visual perception by blindfolding the subjects to apply the proposed method to the visually impaired. Subjects used a specially designed pointing stick to generate a sound at the tip, indicating localization error and tip position. The proposed perceptual training aims to evaluate the training effect on 3D sound localization, including variations in azimuth, elevation, and distance. The six days of training based on six subjects resulted in the following outcomes: (1) In general, accuracy in full 3D sound localization can be improved based on training. (2) Training based on relative error feedback is more effective than absolute error feedback. (3) Subjects tend to underestimate distance when the sound source is near, less than 1000 mm, or larger than 15° to the left, and overestimate the elevation when the sound source is near or in the center, and within ±15° in azimuth estimations.

Estimating two groups of fracture weaknesses using azimuthal differences in partially incidence-angle-stacked seismic amplitudes

Geophysical and geologic data, e.g., results obtained using rock cores, outcrops, and borehole images, reveal the presence of multiple sets of fractures in rock. To analyze how fracture interactions affect seismic anisotropy and dispersion, we consider an effective model that contains two sets of orthogonal fractures. In seismic amplitude analysis, we focus on the case of subsurface target zones containing a fracture network composed of primary and secondary fracture sets. Focusing on gas-bearing rocks with small fracture densities, we formulate simplified stiffness parameters in terms of two groups of fracture weaknesses, which are related to the primary and secondary fractures, respectively. Using the simplified stiffness parameters, we derive the PP-wave reflection coefficient and the azimuthal elastic impedance (AEI) as functions of the two groups of normal and tangential fracture weaknesses. Based on the derived PP-wave reflection coefficient and AEI, we propose a method and workflow in which the azimuthal variations of the partial incidence-angle-stacked seismic data are used to estimate the AEI and differences in AEI (which we refer to as DEI) is input to a nonlinear inversion for two groups of fracture weaknesses. In the nonlinear inversion, the initial values of fracture weaknesses are obtained based on a two-term approximation of the PP-wave reflection coefficient. First- and second-order derivatives of DEI with respect to fracture weakness parameters are calculated to generate the update in the unknown parameter vector. Synthetic seismic gathers with varying signal-to-noise ratios are used to validate the robustness of the estimation. Applying the inversion method to a real data set, we obtain what we interpret to be reliable fracture weakness estimates that produce azimuthal amplitude differences matching those extracted from real seismic data. The results provide a potential tool for determining if two sets of fractures have developed in a reservoir.

Single-point dispersion measurement of surface waves combining translation, rotation and strain in weakly anisotropic media: theory

SUMMARY A new approach is proposed for measuring the dispersion relation of surface waves in weakly anisotropic media using a single station, which consists of translational displacement and rotation or strain. The azimuth-dependent surface wave dispersion curve can be directly obtained by using the amplitude ratio of translational displacement to rotation or strain. Using observations from earthquakes from a variety of azimuths allows us to characterize the anisotropy of subsurface media. The amplitude ratio gives the localized azimuth-dependent dispersion relations of the formation beneath a receiver without requiring knowledge of the source or structure along the path. The theory shows that in anisotropic media the coupled quasi-Rayleigh wave and quasi-Love wave will result in elliptically polarized rotational motions. In addition, rotational motion information allows the determination of backazimuth even in general anisotropic media. We carry out numerical experiments, investigate the effects of noise and degree of anisotropy and demonstrate the potential for field studies.

Testing observables for teleseismic shear-wave splitting inversions: ambiguities of intensities, parameters, and waveforms

We assess the capabilities of different observables for the inversion of core-refracted shear waves (XKS phases) to uniquely resolve the anisotropic structure of the upper mantle. For this purpose, we perform full-waveform calculations for relatively simple, canonical models of upper-mantle anisotropy. The models are characterized by two and four domains of different anisotropic properties. Specifically, we assume hexagonal symmetry with arbitrarily chosen strength of the anisotropy and orientation of the horizontal fast axis. XKS waveforms, generated from plane-wave initial conditions, traverse through anisotropic models and are recorded at the surface by a single station (in case of vertical variations) and by a dense station profile across the laterally and vertically varying structure. In addition to waveforms, we consider the effects of anisotropic variations on apparent splitting parameters and splitting intensity. The results show that, generally, it is not possible to fully resolve the anisotropic parameters of a given model, even if complete waveforms (under noisefree conditions and for the complete azimuthal range) are considered. This is because waveforms for significantly different anisotropic models can be indistinguishable. However, inversions of both waveforms and apparent splitting parameters lead to similar models that exhibit systematic variations of anisotropic parameters. These characteristics may be exploited to better constrain the inversions. The results also show that splitting intensity holds some significant drawbacks: First, even from measurements over a wide range of back-azimuth, there is no characteristic signature that would indicate depth variations of anisotropy. Secondly, identical azimuthal variations of splitting intensity for different anisotropic structures do not imply that the corresponding split waveforms are also similar. Thus, fitting of observed and calculated splitting intensities could lead to anisotropic models that are incompatible with the observed waveforms. We conclude that (bandlimited) XKS-splitting inversions and related tomographic schemes, even if based on complete waveforms, are not sufficient to fully resolve the heterogeneous anisotropic structures of the upper mantle and that combinations with alternative methods, based on e.g., receiver-function splitting, P-wave travel-time deviations, or surface waves, are required.

Large-Eddy Simulation of airborne wind energy systems wakes

Wind energy is usually harnessed using wind turbines but it is not the only way of collecting this energy. In this paper, Airborne Wind Energy Systems (AWES) are considered. The understanding of the wake shed by such devices is of primary importance when considering farms, yet it has not been much studied so far, and even less so when considering kites with soft curved wing. In this work, LES is used to analyse the wake of AWES. Two types of wings are considered: a straight wing, modelling the reference rigid wing AWES and a curved wing accounting for leading edge inflatable kites. Both types of wings are modelled using actuator lines. The wake analysis reveals that the wake of curved wings tends to be stronger and to recover faster. For the case of the tilted trajectory, asymmetries in the wake are also noted. The difference is explained by the azimuthal variation of the circulation distribution on the wing. It also relates to some wakes characteristics for tilted wind turbines. The wake of the curved wing is also more sensitive to the variation of the loading when it flies tilted trajectory, due to the varying loading on its tips.

Chemical cartography with LAMOST and Gaia reveal azimuthal and spiral structure in the Galactic disc

ABSTRACT Chemical Cartography, or mapping, of our Galaxy has the potential to fully transform our view of its structure and formation. In this work, we use chemical cartography to explore the metallicity distribution of OBAF-type disc stars from the LAMOST survey and a complementary sample of disc giant stars from Gaia DR3. We use these samples to constrain the radial and vertical metallicity gradients across the Galactic disc. We also explore whether there are detectable azimuthal variations in the metallicity distribution on top of the radial gradient. For the OBAF-type star sample from LAMOST, we find a radial metallicity gradient of Δ[Fe/H]/ΔR ∼−0.078 ± 0.001 dex kpc−1 in the plane of the disc and a vertical metallicity gradient of Δ[Fe/H]/ΔZ ∼−0.15 ± 0.01 dex kpc−1 in the solar neighbourhood. The radial gradient becomes shallower with increasing vertical height, while the vertical gradient becomes shallower with increasing Galactocentric radius, consistent with other studies. We also find detectable spatially dependent azimuthal variations on top of the radial metallicity gradient at the level of ∼0.10 dex. Interestingly, the azimuthal variations appear be close to the Galactic spiral arms in one data set (Gaia DR3) but not the other (LAMOST). These results suggest that there is azimuthal structure in the Galactic metallicity distribution and that in some cases it is co-located with spiral arms.

Azimuthal C/O variations in a planet-forming disk

AbstractThe elemental carbon-to-oxygen ratio (C/O) in the atmosphere of a giant planet is a promising diagnostic of that planet’s formation history in a protoplanetary disk. Alongside efforts in the exoplanet community to measure the C/O ratio in planetary atmospheres, observational and theoretical studies of disks are increasingly focused on understanding how the gas-phase C/O ratio varies both with radial location and between disks. This is mostly tied to the icelines of major volatile carriers such as CO and H2O. Using ALMA observations of CS and SO, we have found evidence for an entirely unexpected type of C/O variation in the protoplanetary disk around HD 100546: an azimuthal variation from a typical, oxygen-dominated ratio (C/O ≈ 0.5) to a carbon-dominated ratio (C/O ≳ 1.0). We show that the spatial distribution and peculiar line kinematics of both CS and SO molecules can be well explained by azimuthal variations in the C/O ratio. We propose a shadowing mechanism that could lead to such a chemical dichotomy. Our results imply that tracing the formation history of giant exoplanets using their atmospheric C/O ratios will need to take into account time-dependent azimuthal C/O variations in a planet’s accretion zone.

Alignment scheme optimization when gyro accuracy inconsistency for inertial navigation system

Rotation modulation technology can average out constant errors in fiber optic gyro (FOG) rotational inertial navigation system (RINS). As a result, angle random walk (ARW) of FOGs plays a significant role in the precision of initial alignment. Using different gyros as horizontal gyros gradually transitioned from theory to practical application with the advancement of design philosophy. The theoretical formula between azimuth alignment accuracy and random walk coefficients (RWCs) of two horizontal gyros is deduced in this paper. A completely new multiple rotations and stationary alignment scheme is suggested. A recursive least-squares filter with azimuth variation in body reference frame and accelerometer outputs in navigation frame as measurements is constructed. The efficiency of this method is demonstrated through simulation and experimentation. The findings demonstrate that using this formula and alignment scheme, azimuth alignment accuracy could be greatly increased, which can be improved by 10.85% compared to common continuous rotation alignment scheme.

New experimental evidence for pervasive dynamics in proteins.

There is ample computational, but only sparse experimental data suggesting that pico-ns motions with 1 Å amplitude are pervasive in proteins in solution. Such motions, if present in reality, must deeply affect protein function and protein entropy. Several NMR relaxation experiments have provided insights into motions of proteins in solution, but they primarily report on azimuthal angle variations of vectors of covalently-linked atoms. As such, these measurements are not sensitive to distance fluctuations, and cannot but under-represent the dynamical properties of proteins. Here we analyze a novel NMR relaxation experiment to measure amide proton transverse relaxation rates in uniformly 15 N labeled proteins, and present results for protein domain GB1 at 283 and 303 K. These relaxation rates depend on fluctuations of dipolar interactions between 1 HN and many nearby protons on both the backbone and sidechains. Importantly, they also report on fluctuations in the distances between these protons. We obtained a large mismatch between rates computed from the crystal structure of GB1 and the experimental rates. But when the relaxation rates were calculated from a 200 ns molecular dynamics trajectory using a novel program suite, we obtained a substantial improvement in the correspondence of experimental and theoretical rates. As such, this work provides novel experimental evidence of widespread motions in proteins. Since the improvements are substantial, but not sufficient, this approach may also present a new benchmark to help improve the theoretical forcefields underlying the molecular dynamics calculations.

Slip model with supershear rupture velocity and stress drop for an M4.5 aftershock of the 2019 Ridgecrest, California, earthquake sequence

SUMMARY We use records from 24 stations with epicentral distances under 50 km to invert for slip and rupture time of an M4.5 aftershock of the 2019 Ridgecrest, California, earthquake sequence. Slip was determined by inverting source time functions (STFs), which were obtained at each station by decomposing a main shock, in this case an M4.5 aftershock, into a series of subevents using an empirical Green's function (eGf) as a template. The technique is iterative in the time domain with a positivity constraint. The STFs are characterized by a single pulse with durations that were longer in the southeast direction (about 1.0 s) and shorter in the northwest direction (about 0.6 s) suggesting rupture directivity to the northwest. We inverted the STFs for slip using a tomographic algorithm from that uses a high-frequency approximation to ray theory for the forward problem. The tomographic algorithm solves for slip and rupture time on a grid of points, which provides a better strategy for elucidating directivity than a model that uses subfaults. We solve for the strike-slip intensity on a near-vertical plane striking northwest, similar to the M7.1. After nine iterations, the slip model reduces the chi-squared estimate of fit by 68 per cent. Most of the slip is to the northwest, with a narrow well-defined peak in slip about 0.3 km NW of the origin. The peak is fairly symmetrical and about 1.5 km across its base. The model shows significant directivity to the northwest as suggested by the azimuthal variation of the STF pulse widths. Rupture velocity increases from nucleation to the peak in slip, becomes supershear, and then slows to about 3.2 km s−1, but there is little slip beyond 0.8 s contour in the forward direction. It appears that the peak in slip contributed stress to accelerate the rupture to the northwest. Low-level, parabolic-shaped slip patterns are seen to the northwest, which could be where the rupture front is dying out. Similar, but fainter curves facing the southeast suggests some bilateral rupture but the rupture to the northwest was stronger. Static stress drop was calculated using a formula for an elastic half-space giving a maximum of 35 bars at the peak in slip, but smoothing controls the absolute value. The average over a presumed fault plane is about 1.4 bars, much less than the peak. Slip and stress drop are highly heterogeneous.

Dipolarization Events With Inductive, Radial Electric Fields Observed by Van Allen Probes

AbstractDipolarization events with inductive, radial electric fields are examined, using Van Allen Probes data between 2012 and 2019. Two cases are studied, followed by statistical analyses. These events were observed between evening and premidnight magnetic local times (MLTs) under moderate geomagnetic activities. Radial electric field variations, azimuthal magnetic field variations, and energetic protons were often observed when horizontal magnetic fields started to decrease in the dip region. Magnetic field lines were stretched with their motion similar to the gradient B/curvature drift velocities of energetic protons. Signs of electric fields changed when horizontal magnetic fields started to increase in the dipolarization front (DF). Electric field and magnetic field variations were correlated and in quadrature regarding the phase relation. Among other explanations, we interpret these observations in terms of energetic proton structures drifting toward the probe locations, while being accompanied by standing waves.

PP-wave reflection coefficient for vertically cracked media: Single set of aligned cracks

The main goal is to analyze the influence of cracks on the azimuthal variations of amplitude. We restrict our investigation to a single set of vertical, circular, and flat cavities aligned along a horizontal axis. Such cracks are embedded in either transversely isotropic background with a vertical symmetry axis (VTI) or isotropic surroundings. We employ the effective medium theory to obtain either orthotropic or VTI homogenised medium, respectively. To consider the amplitudes, we focus on a Vavrycuk-Psencik approximation of the PP-wave reflection coefficient. We assume that cracks are situated in one of the halfspaces only.Azimuthal variations depend on the background stiffnesses, incidence angle, and crack density parameter. Upon analytical analysis, we indicate which factors (such as background’s saturation) cause the reflection coefficient to have maximum absolute value in the direction parallel or perpendicular to cracks. We discuss the irregular cases, where such extreme values appear in the other than the aforementioned directions.Due to the support of numerical simulations, we propose graphic patterns of two-dimensional amplitude variations with azimuth. The patterns consist of a series of shapes that change with the increasing value of the crack density parameter. Schemes appear to differ depending on the incidence angle and the saturation. Finally, we extract these shapes that are characteristic of gas-bearing rocks. They may be treated as gas indicators. We support the findings and verify our patterns using real values of stiffnesses extracted from the sedimentary rocks’ samples.