Statistical Anisotropy Research Articles

Gas Reservoir Identification Based on Nonstationary and Anisotropic FFT-MA Stochastic Modeling

Summary High-resolution reservoir modeling is a crucial technique for the precise identification of gas reservoirs, holding significant importance in guiding natural gas development. However, the nonstationarity and statistical anisotropy of subsurface media present immense challenges to the reliable implementation of high-resolution reservoir modeling. In response to the nonstationarity and anisotropy of complex reservoirs, we propose a novel stochastic modeling method based on fast Fourier transform moving average (FFT-MA). In this method, variational mode decomposition (VMD) is introduced to decompose logging curves into a series of sparse components with specific center frequencies and narrow bandwidths. Subsequently, the autocorrelation functions of each component are computed and synthesized, thereby inferring the nonstationary vertical autocorrelation functions of logging curves. In addition, to characterize the anisotropic and lateral nonstationary features of the reservoir, angle parameters and lateral autocorrelation functions are extracted from seismic records. Lastly, considering the high sensitivity of Lamé constants (λ and μ) and their density-combined counterparts (λρ and μρ) to gas-bearing reservoirs, FFT-MA stochastic modeling is applied to λρ, μρ, and ρ. Gas identification is then performed based on the joint probability distribution extracted from logging data. The proposed method is tested in the sand-shale reservoirs of the Yinggehai Basin, China. The results indicate that the stochastic models for λρ, μρ, and ρ effectively characterize the nonstationary and anisotropic features of complex reservoirs, significantly enhancing the resolution and accuracy of gas identification.

Statistical Anisotropy of Primordial Gravitational Waves from Generalized δN Formalism.

In this Letter, we demonstrate how to use the generalized δN formalism, which enables us to compute the evolution of all the large-scale fluctuations, including gravitational waves, solely by solving the evolution of the background homogeneous Universe. Using the Noether charge density, we derive an analytic formula which describes the mapping between the fluctuations at the horizon crossing and the sourced gravitational waves at the end of inflation. This formula can apply also to an inflation model with an anisotropic background. Using this formula, we discuss the condition for the nonvanishing linear polarization and the qualitative difference between single- and multigauge field models.

Misalignment production of vector boson dark matter from axion-SU(2) inflation

We present a new mechanism to generate a coherently oscillating dark vector field from axion-SU(2) gauge field dynamics during inflation. The SU(2) gauge field acquires a nonzero background sourced by an axion during inflation, and it acquires a mass through spontaneous symmetry breaking after inflation. We find that the coherent oscillation of the dark vector field can account for dark matter in the mass range of 10-13 – 1 eV in a minimal setup. In a more involved scenario, the range can be wider down to the fuzzy dark matter region. One of the dark vector fields can be identified as the dark photon, in which case this mechanism evades the notorious constraints for isocurvature perturbation, statistical anisotropy, and the absence of ghosts that exist in the usual misalignment production scenarios. Phenomenological implications are discussed.

Passive scalar small-scale anisotropy and mixing characteristics in magnetohydrodynamic turbulent channel flow

In wall-bounded turbulent flows, both velocity and scalar fluctuations exhibit inhomogeneity and anisotropy. This study investigates the statistical properties of the small-scale scalar fluctuations in a turbulent channel flow at Reτ≈585 using direct numerical simulations with and without a magnetic field. The influence of the Hartmann, Ha, and Prandtl, Pr, numbers on turbulent velocity and passive scalar fields is examined at Ha=0, 20, and 40 and Pr=0.7 and 1.4. Small-scale dynamics of the passive scalar and velocity fields are studied, analyzing their probability density functions and higher-order moments, as well as their gradients. We observed that the magnetic field substantially changes flow dynamics such as the typical cliff-and-ramp type structures. The presence of the magnetic field led to statistical anisotropy, even at small-scale gradient fields. The findings reveal that the skewness of the normal derivative of scalar fluctuations remains at the order of 2. We investigated mixing characteristics by analyzing scalar dissipation rates. Scalar dissipation rates near the wall remain close to unity and decrease sharply toward the channel center, reaching a minimum value. Moreover, an increase in scalar dissipation rates leads to a decrease in the corresponding mixing timescale of the flow. This could suggest a connection between an increase in the Lorentz force and potential adjustments in the mixing timescale, potentially contributing to enhance overall mixing. Additionally, we argue that combined effects of strong intermittency and persistency of anisotropy at small scales can influence the mixing characteristics of magnetohydrodynamic turbulent flow.

Nearby active galactic nuclei and starburst galaxies as sources of the measured UHECRs anisotropy signal

The Pierre Auger and the Telescope Array observatories have measured independent and statistical significant anisotropy in the arrival direction of ultra-high-energy cosmic rays (UHECR). Three hotspot regions with relative excess of events and a dipole signal have been identified in different regions of the sky and energy ranges. In this paper, we investigate the conditions under which these anisotropy signal could be generated by nearby (<23 Mpc) active galactic nuclei (AGN) and/or starburst galaxies (SBG). We studied a wide range of possibilities including injected nuclei (p, He, N, Si, and Fe), three UHECR luminosity proxies and three extragalactic magnetic field models. The results shows that both local AGN and SBG are needed to describe all the anisotropy signal. The contribution of AGN to hotspots and to the generation of the dipole is dominant in most cases. SBG is required only to explain the hotspot measured by the Telescope Array Observatory.

Detection of Dipole Modulation in CMB Temperature Anisotropy Maps from WMAP and Planck using Artificial Intelligence

Breakdown of rotational invariance of the primordial power spectrum manifests in the statistical anisotropy of the observed Cosmic Microwave Background (CMB) radiation. Hemispherical power asymmetry in the CMB may be caused due to a dipolar modulation, indicating the presence of a preferred direction. Appropriately rescaled local variance maps of the CMB temperature anisotropy data effectively encapsulate this dipolar pattern. As a first-of-its-kind method, we train Artificial Neural Networks (ANNs) with such local variances as input features to distinguish statistically isotropic CMB maps from dipole-modulated ones. Our trained ANNs are able to predict components of the amplitude times the unit vector of the preferred direction for mixed sets of modulated and unmodulated maps, with goodness-of-fit (R 2) scores >0.97 for full sky and >0.96 for partial sky coverage. On all observed foreground-cleaned CMB maps, the ANNs detect the dipolar modulation signal with overall consistent values of amplitudes and directions. This detection is significant at 97.21%–99.38% C.L. for all full sky maps, and at 98.34%–100% C.L. for all partial sky maps. Robustness of the signal holds across full and partial skies, various foreground cleaning methods, inpainting algorithms, instruments, and all the different periods of observation for Planck and WMAP satellites. The significant and robust detection of the signal, in addition to the consistency of values of amplitude and directions, as found independent of any preexisting methods, further mitigates the criticisms of look-elsewhere effects and a posteriori inferences for the preferred dipole direction in the CMB.

Anisotropic warm inflation

Anisotropic inflation is a model that succeeded in explaining statistical anisotropy. Warm inflation is a model that succeeded in providing a mechanism of reheating during inflation. We study anisotropic warm inflation focusing on the cosmic no-hair conjecture. In the anisotropic warm inflation, the condition for making anisotropy survive is clarified. By assuming a constant value for the dissipation ratio, we find exact solutions of power-law anisotropic warm inflation, and investigate the phase space structure of general solutions. It turns out that whether the anisotropy during inflation survives or not depends on the competition of the potential that drives anisotropic inflation against dissipation of an inflaton field. Anisotropic warm inflation will be realized if the decaying process is not efficient.

Antipodal angular correlations of inflationary stochastic gravitational wave background

The measurement of the inflationary stochastic gravitational-wave background (SGWB) is one of the main goals of future GW experiments. In direct GW experiments, an obstacle to achieving it is the isolation of the inflationary SGWB from the other types of SGWB. In this paper, as a distinguishable signature of the inflationary SGWB, we argue the detectability of its universal property: antipodal correlations, i.e., correlations of GWs from the opposite directions, as a consequence of the horizon re-entry. A phase-coherent method has been known to be of no use for detecting the angular correlations in SGWB due to a problematic phase factor that erases the signal. We thus investigate whether we can construct a phase-incoherent estimator of the antipodal correlations in the intensity map. We found that the conclusion depends on whether the inflationary GWs have statistical isotropy or not. In the standard inflationary models with statistical homogeneity and isotropy, there is no estimator that is sensitive to the antipodal correlations but does not suffer from the problematic phase factor. On the other hand, it is possible to find a non-vanishing estimator of the antipodal correlations for inflationary models with statistical anisotropy. SGWB from anisotropic inflation is distinguishable from the other components.

Forecasting Pulsar Timing Array Sensitivity to Anisotropy in the Stochastic Gravitational Wave Background

Statistical anisotropy in the nanohertz-frequency gravitational wave background (GWB) is expected to be detected by pulsar timing arrays (PTAs) in the near future. By developing a frequentist statistical framework that intrinsically restricts the GWB power to be positive, we establish scaling relations for multipole-dependent anisotropy decision thresholds that are a function of the noise properties, timing baselines, and cadences of the pulsars in a PTA. We verify that (i) a larger number of pulsars, and (ii) factors that lead to lower uncertainty on spatial cross-correlation measurements between pulsars, lead to a higher overall GWB signal-to-noise ratio, and lower anisotropy decision thresholds with which to reject the null hypothesis of isotropy. Using conservative simulations of realistic NANOGrav data sets, we predict that an anisotropic GWB with angular power C l=1 > 0.3C l=0 may be sufficient to produce tension with isotropy at the p = 3 × 10−3 (∼3σ) level in near-future NANOGrav data with a 20 yr baseline. We present ready-to-use scaling relationships that can map these thresholds to any number of pulsars, configuration of pulsar noise properties, or sky coverage. We discuss how PTAs can improve the detection prospects for anisotropy, as well as how our methods can be adapted for more versatile searches.

Induced gravitational waves from statistically anisotropic scalar perturbations

Scalar-induced gravitational waves (SIGWs) are attracting growing attention for probing extremely short-scale scalar perturbations via gravitational wave measurements. In this paper, we investigate the SIGWs from statistically anisotropic scalar perturbations, which are motivated in inflationary scenarios in the presence of, e.g., a vector field. While the ensemble average of the SIGW energy spectrum is isotropic for the standard statistically isotropic scalar perturbations, the statistical anisotropy in the source introduces the multipole moments of the differential SIGW energy spectrum. We consider quadrupole anisotropy in the scalar power spectrum and show that the SIGW spectrum has anisotropies up to $\ensuremath{\ell}=4$. We present generic formulas of the multipole moments and then apply them to the delta-function-like and log-normal source spectra. We find analytic expressions for the former case and show that the infrared scalings of the multipole moments are the same as the isotropic SIGWs. Interestingly, the monopole has an additional local minimum in the high-$k$ tail, a key feature to distinguish from the isotropic SIGWs. The latter log-normal case is analytic for the narrow-peak source, and we perform the numerical calculation for the broad peak. As one expects, the multipole moments become broader with increasing source width. Our results are helpful to test the isotropy of primordial density perturbations at extremely small scales through SIGWs.

Constraints on τ NL from Planck temperature and polarization

We update constraints on the amplitude of the primordial trispectrum, using the final Planck mission temperature and polarization data. In the squeezed limit, a cosmological local trispectrum would be observed as a spatial modulation of small-scale power on the CMB sky. We reconstruct this signal as a source of statistical anisotropy via quadratic estimator techniques. We systematically demonstrate how the estimated power spectrum of a reconstructed modulation field can be translated into a constraint on τ NL via likelihood methods, demonstrating the procedures effectiveness by inferring known τ NL signal(s) from simulations. Our baseline results constrain τ NL < 1700 at the 95% confidence level, providing the most stringent constraints to date.

Aquifer heterogeneity controls to quality monitoring network performance for the protection of groundwater production wells

A groundwater monitoring network surrounding a pumping well (such as a public water supply) allows for early contaminant detection and mitigation where possible contaminant source locations are often unknown. This numerical study investigates how the contaminant detection probability of a hypothetical sentinel-well monitoring network consisting of one to four monitoring wells is affected by aquifer spatial heterogeneity and dispersion characteristics, where the contaminant source location is randomized. This is achieved through a stochastic framework using a Monte Carlo approach. A single production well is considered that results in converging non-uniform flow close to the well. Optimal network arrangements are obtained by maximizing a weighted risk function that considers true and false positive detection rates, sampling frequency, early detection, and contaminant travel time uncertainty. Aquifer dispersivity is found to be the dominant parameter for the quantification of network performance. For the range of parameters considered, a single monitoring well screening the full aquifer thickness is expected to correctly and timely identify at least 12% of all incidents resulting in contaminants reaching the production well. This proportion increases to a global maximum of 96% for a network consisting of four wells and very dispersive transport conditions. Irrespective of network size and sampling frequency, more dispersive transport conditions result in higher detection rates. Increasing aquifer heterogeneity and decreasing aquifer spatial continuity also lead to higher detection rates, though these effects are diminished for networks of 3 or more wells. Statistical anisotropy has no effect on the network performance. Earlier detection, which is critical for remedial action and supply safety, comes with a significant cost in terms of detection rate, and should be carefully considered when a monitoring network is being designed.

Effect of Statistically Anisotropic Undrained Shear Strength on the Probability of Slope Failure

Due to large-scale geological deposition processes, slope structures are often stratified, which means that the spatial distribution of the parameters involved in slope reliability evaluation is statistically anisotropic. This paper studies the effect of the statistical anisotropy of undrained shear strength on the probability of slope failure (pf) based on the Monte Carlo simulation. The results show that for the horizontally layered slope, the larger the horizontal correlation scale of undrained shear strength (λx) is, the larger pf is, especially when λx is smaller than the slope length; for the vertically layered slope, the larger the vertical correlation scale (λy) is, the smaller pf is, especially when λy is smaller than the slope height. Additionally, the mechanism of the above results is discussed by analyzing the displacement distribution at different correlation scales. The findings indicate that in the reliability evaluation of undrained slopes in stratified structures, either underestimation of λx or overestimation of λy leads to an unconservative estimate of pf, resulting in an overestimation of the slope stability.

Model-independent Estimators for the Statistical Anisotropy of the Cosmic Microwave Background

We construct estimators for testing the statistical anisotropy of the cosmic microwave background arising due to a quadrupolescale-independent anisotropy in the primordial power spectrum. The estimators do not require the knowledge of basic cosmological parameters. We determine the sensitivity of the constructed estimators to the magnitude of the statistical anisotropy and perform test simulations that confirm our theoretical estimates.

Primordial tensor bispectra in μ-CMB cross-correlations

Cross-correlations between Cosmic Microwave Background (CMB) temperature and polarization anisotropies and μ-spectral distortions have been considered to measure (squeezed) primordial scalar bispectra in a range of scales inaccessible to primary CMB bispectra. In this work we address whether it is possible to constrain tensor non-Gaussianities with these cross-correlations. We find that only primordial tensor bispectra with statistical anisotropies leave distinct signatures, while isotropic tensor bispectra leave either vanishing or highly suppressed signatures. We discuss how the angular dependence of squeezed bispectra in terms of the short and long momenta determine the non-zero cross-correlations. We also discuss how these non-vanishing configurations are affected by the way in which primordial bispectra transform under parity. By employing the so-called BipoSH formalism to capture the observational effects of statistical anisotropies, we make Fisher-forecasts to assess the detection prospects from μ T, μ E and μ B cross-correlations. Observing statistical anisotropies in squeezed ⟨γγγ⟩ and ⟨γγζ⟩ bispectra is going to be challenging as the imprint of tensor perturbations on μ-distortions is subdominant to scalar perturbations, therefore requiring a large, independent amplification of the effect of tensor perturbations in the μ-epoch. In absence of such a mechanism, statistical anisotropies in squeezed ⟨ζζγ⟩ bispectrum are the most relevant sources of μ T, μ E and μ B cross-correlations. In particular, we point out that in anisotropic inflationary models where ⟨ζζζ⟩ leaves potentially observable signatures in μ T and μ E, the detection prospects of ⟨ζζγ⟩ from μ B are enhanced.

Stochastic reconstruction of 3D microstructures from 2D cross-sectional images using machine learning-based characterization

The availability of high-quality three-dimensional (3D) microstructures is an essential prerequisite to understanding the macroscopic behaviours of heterogeneous media. Considering the high cost of 3D microscopy imaging, it is an economical way to derive large numbers of virtual 3D microstructures from limited morphological information of 2D cross-sectional images. This paper presents an efficient method that incorporates machine learning-based characterization of 2D images to statistically reconstruct 3D microstructures. The latent stochasticity of 2D images is mastered by fitting supervised machine learning models, which essentially characterize the local morphological statistics. A morphology integration scheme is developed to project the 2D morphological statistics into the 3D space, and new equivalent 3D microstructures can then be synthesized by sequentially generating voxel values from probability sampling. The new method is tested on a series of heterogeneous media with distinct morphologies, and it is also compared with two classical methods (i.e. stochastic optimization-based reconstruction and Gaussian random field transformation) in terms of reconstruction accuracy and efficiency. Besides, various microstructural descriptors are used to quantify the discrepancies between the reconstructed and target microstructures. The results confirm that the proposed method provides a highly cost-effective and widely applicable way to reproduce 3D realizations that precisely preserve the statistical characteristics, geometrical irregularities, long-distance connectivity and anisotropy that exist in 2D cross-sectional images.

Bayesian estimation of our local motion from the Planck-2018 CMB temperature map

The largest fluctuation in the CMB sky is the CMB dipole, which is believed to be caused by the motion of our observation frame with respect to the CMB rest frame. This motion accounts for the known motion of the Solar System barycentre with a best-fit amplitude of 369 km/s, in the direction (ℓ= 264°, b=48°) in galactic coordinates. Along with the CMB dipole signal, this motion also causes an inevitable signature of statistical anisotropy in the higher multipoles due to the modulation and aberration of the CMB temperature and polarization fields. This leads to a correlation between adjacent CMB multipoles causing a non-zero value of the off-diagonal terms in the covariance matrix which can be captured in terms of the dipolar spectra of the bipolar spherical harmonics (BipoSH). In our work, we jointly infer the CMB power spectrum and the BipoSH spectrum in a Bayesian framework using the Planck-2018 SMICA temperature map. We detect amplitude and direction of the local motion consistent with the canonical value v=369 km/s inferred from CMB dipole with a statistical significance of 4.54σ, 4.97σ and 5.23σ respectively from the masked temperature map with the available sky fraction 40.1%, 59.1%, and 72.2%, confirming the common origin of both the signals. The Bayes factor in favor of the canonical value is between 7 to 8 depending on the choice of mask. But it strongly disagrees (by a value of the Bayes factor about 10-10–10-11) with a higher value of local motion which one can infer from the amplitude of the dipole signal obtained from the CatWISE2020 quasar catalog using the WISE and NEOWISE data set.

Explaining cosmological anisotropy: evidence for causal horizons from CMB data

ABSTRACT The origin of power asymmetry and other measures of statistical anisotropy on the largest scales of the universe, as manifested in cosmic microwave background (CMB) and large-scale structure data, is a long-standing open question in cosmology. In this paper, we analyse the Planck Legacy temperature anisotropy data and find strong evidence for a violation of the Cosmological principle of isotropy, with a probability of being a statistical fluctuation of the order of ∼10−9. The detected anisotropy is related to large-scale directional ΛCDM cosmological parameter variations across the CMB sky, which are sourced by three distinct patches in the maps with circularly averaged sizes between 40° and 70° in radius. We discuss the robustness of our findings to different foreground separation methods and analysis choices, and find consistent results from WMAP data when limiting the analysis to the same scales. We argue that these well-defined regions within the cosmological parameter maps may reflect finite and casually disjoint horizons across the observable universe. In particular, we show that the observed relation between horizon size and mean dark energy density within a given horizon is in good agreement with expectations from a recently proposed model of the universe that explains cosmic acceleration and cosmological parameter tensions between the high- and low-redshift universe from the existence of casual horizons within our universe.

Minimum variance estimation of statistical anisotropy via galaxy survey

We consider the benefits of measuring cosmic statistical anisotropy from redshift-space correlators of the galaxy number density fluctuation and the peculiar velocity field without adopting the plane-parallel (PP) approximation. Since the correlators are decomposed using the general tripolar spherical harmonic (TripoSH) basis, we can deal with wide-angle contributions untreatable by the PP approximation, and at the same time, target anisotropic signatures can be cleanly extracted. We, for the first time, compute the covariance of the TripoSH decomposition coefficient and the Fisher matrix to forecast the detectability of statistical anisotropy. The resultant expression of the covariance is free from nontrivial mixings between each multipole moment caused by the PP approximation and hence the detectability is fully optimized. Compared with the analysis under the PP approximation, the superiority in detectability is always confirmed, and it is highlighted, especially in the cases that the shot noise level is large and that target statistical anisotropy has a blue-tilted shape in Fourier space. The application of the TripoSH-based analysis to forthcoming all-sky survey data could result in constraints on anisotropy comparable to or tighter than the current cosmic microwave background ones.

Statistically-anisotropic tensor bispectrum from inflation

We develop a possibility of generating tensor non-Gaussianity in a kind of anisotropic inflation, where a (1) gauge field is kinetically coupled to a spectator scalar field.Owing to this coupling, the coherent mode of the electric field appears and softly breaks the isotropy of the Universe.We compute the bispectrum of linearly-polarized tensor perturbations sourced by the gauge field and find that it is strongly red-tiltedand has distinctive statistical anisotropies including higher-order multipole moments.Interestingly, the tensor bispectra with the specific combinations of linear polarization modes are dominant, and their amplitudes depend on the different sets of multipole moments.This new type of statistically-anisotropic tensor non-Gaussianity can be potentially testable with the upcoming cosmic microwave background B-mode polarization experiments.