A novel algorithm for evaluating cement azimuthal density based on perturbation theory in horizontal well

Cement density monitoring plays a vital role in evaluating the quality of cementing projects,which is of great significance to the development of oil and gas.However,the presence of inhomogeneous cement distribution and casing eccentricity in horizontal wells often complicates the accurate evaluation of cement azimuthal density.In this regard,this paper proposes an algorithm to calculate the cement azimuthal density in horizontal wells using a multi-detector gamma-ray detection system.The spatial dynamic response functions are simulated to obtain the influence of cement density on gamma-ray counts by the perturbation theory,and the contribution of cement density in six sectors to the gamma-ray recorded by different detectors is obtained by integrating the spatial dynamic response functions.Combined with the relationship between gamma-ray counts and cement density,a multi-parameter calculation equation system is established,and the regularized Newton iteration method is employed to invert casing eccentricity and cement azimuthal density.This approach ensures the stability of the inversion process while simultaneously achieving an accuracy of 0.05 g/cm^(3) for the cement azimuthal density.This accuracy level is ten times higher compared to density accuracy calculated using calibration equations.Overall,this algorithm enhances the accuracy of cement azimuthal density evaluation,provides valuable technical support for the monitoring of cement azimuthal density in the oil and gas industry.

Effect of variations in the polar and azimuthal angles of coarse particles on the structure of drainage channels in thickened beds

The 3D reconstruction and quantitative characterization of drainage channels and coarse tailings particles in a bed were conducted in this study.The influence of variations in the azimuthal angle(θ)and polar angle(φ)of coarse particles on drainage channel structure was analyzed,and the drainage mechanism of the bed was studied.Results showed that water discharge in the bed reduced the size of pores and throat channels,increasing slurry concentration.The throat channel structure was a key component of the drainage process.Theφandθof particles changed predominantly along the length direction.The changes inφhad a cumulative plugging effect on the drainage channel and increased the difficulty of water discharge.The rake and rod formed a shear ring in the tailings bed with shear,and theθdistribution of particles changed from disorderly to orderly during the rotation process.The drainage channel was squeezed during the shearing process with the change inθ,which broke the channel structure,encouraged water discharge in the bed,and facilitated a further increase in slurry concentration.The findings of this work are expected to offer theoretical guidance for preparing high-concentration underflow in the tailings thickening process.

An Investigation of Purely Azimuthal Passive Localization and Position Adjustment in Attempted UAV Formation Flights

When a cluster of unmanned aerial vehicles (UAVs) is flying in formation, it is crucial to maintain the formation and not to be interfered by external electromagnetic wave signals. In order to maintain the formation, this paper proposes to use pure azimuth passive positioning to adjust the position of UAVs, i.e., certain UAVs in the formation transmit signals, the rest of the UAVs receive the signals passively, and extract the orientation information from them to adjust the position of the UAVs [1] [2] [3]. In this paper, the position adjustment problem of UAVs in “circular” formation flight under three models is investigated. To address the problem of “how to obtain the position of the receiving UAV when there are two UAVs with known numbers and evenly distributed on the circumference in addition to the UAV transmitting at the known center of the circle, and the rest of the UAVs with slight deviations in their positions are receiving the signals”, two purely mathematical geometric methods, namely, triangular localization method and polar co-ordinate method, are proposed respectively. We have determined the position of the receiving UAV;we have used the exhaustive method and the construction and disproof method to solve the problem of “how many UAVs are needed to transmit signals in order to realize the effective positioning of the UAVs when it is known that a certain UAV with a slight deviation in its position receives the signals emitted by two UAVs at the same time”, and the results show that: in addition to the known signals emitted by two UAVs, it is also necessary to transmit the signals emitted by two UAVs. The results show that in addition to the known two UAVs transmitting signals, two additional UAVs are required to transmit signals for precise po-sitioning. When the position of UAVs has deviation at the initial moment, the ideal approximation method and the target delimitation method are pro-posed, and the target of nine UAVs uniformly distributed on a circle of a spe-cific radius is achieved through several adjustments, after which the ad-vantages and disadvantages of each model are analyzed, and suggestions for improvement are put forward. The purely azimuthal passive localization method and the constructed model approach proposed in this paper can be extended to other fields, such as spacecraft formations in space and battle-ship formations at sea, as well as other formation flight position adjustment problems.

GRB 200612A:An Ultralong Gamma-Ray Burst Powered by Magnetar Spinning Down

GRB 200612A could be classified as an ultralong gamma-ray burst due to its prompt emission lasting up to~1020 s and the true timescale of the central engine activity t_(burst)≥4×10^(4) s.The late X-ray light curve with a decay index ofα=7.53 is steeper than the steepest possible decay from an external shock model.We propose that this X-ray afterglow can be driven by dipolar radiation from the magnetar spindown during its early stage,while the magnetar collapsed into the black hole before its spindown,resulting in a very steep decay of the late X-ray light curve.The optical data show that the light curve is still rising after 1.1 ks,suggesting a late onset.We show that GRB 200612A’s optical afterglow light curve is fitted with the forward shock model by Gaussian structured off-axis jet.This is a special case among GRBs,as it may be an ultralong gamma-ray burst powered by a magnetar in an off-axis observation scenario.

First Digit Distributions of Gamma-Ray Bursts

The occurrence of the first significant digits from real world sources is usually not equally distributed,but is consistent with a logarithmic distribution instead,known as Benford’s law.In this work,we perform a comprehensive investigation on the first digit distributions of the duration,fluence,and energy flux of gamma-ray bursts (GRBs) for the first time.For a complete GRB sample detected by the Fermi satellite,we find that the first digits of the duration and fluence adhere to Benford’s law.However,the energy flux shows a significant departure from this law,which may be due to the fact that a considerable part of the energy flux measurements is restricted by lack of spectral information.Based on the conventional duration classification scheme,we also check if the durations and fluences of long and short GRBs (with duration T_(90)>2 s and T_(90)≤2 s,respectively) obey Benford’s law.We find that the fluences of both long and short GRBs still agree with the Benford distribution,but their durations do not follow Benford’s law.Our results hint that the long–short GRB classification scheme does not directly represent the intrinsic physical classification scheme.

Time-resolved Spectral Properties of Fermi-GBM Bright Long Gamma-Ray Bursts

The prompt emission mechanism of gamma-ray bursts(GRBs)is still unclear,and the time-resolved spectral analysis of GRBs is a powerful tool for studying their underlying physical processes.We performed a detailed time-resolved spectral analysis of 78 bright long GRB samples detected by Fermi/Gamma-ray Burst Monitor.A total of 1490 spectra were obtained and their properties were studied using a typical Band-shape model.First,the parameter distributions of the time-resolved spectrum are given as follows:the low-energy spectral indexα~-0.72,high-energy spectral indexβ~2.42,the peak energy E_(p)~221.69 keV,and the energy flux F~7.49×10^(-6)erg cm^(-2)s^(-1).More than 80%of the bursts exhibit the hardest low-energy spectral indexα_(max),exceeding the synchrotron limit(-2/3).Second,the evolution patterns of a and E_(p)were statistically analyzed.The results show that for multi-pulse GRBs the intensity-tracking pattern is more common than the hard-to-soft pattern in the evolution of both E_(p)andα.The hard-to-soft pattern is generally shown in single-pulse GRBs or in the initial pulse of multi-pulse GRBs.Finally,we found a significant positive correlation between F and E_(p),with half of the samples exhibiting a positive correlation between F andα.We discussed the spectral evolution of different radiation models.The diversity of spectral evolution patterns indicates that there may be more than one radiation mechanism occurring in the GRB radiation process,including photo spheric radiation and synchrotron radiation.However,it may also involve only one radiation mechanism,but more complicated physical details need to be considered.

Probing the Gamma-Ray Emission Region of Five TeV Flat Spectrum Radio Quasars

The location ofγ-ray emission of blazars remains a contested topic,inspiring the development of numerous investigative techniques to address this issue.In this work,we analyzed Fermiγ-ray light curves in the GeV and MeV bands,employing the discrete cross-correlation function method to discern time lags between the two bands.For 4C+21.35,Ton 599,B21420+32,and PKS 1510-089,we identified a time lag spanning several days,while for PKS 1441+25,the time lag was not statistically found.The results imply that the soft photons necessary for inverse Compton scattering predominantly originate from the dusty torus in the first four sources,whereas for PKS1441+25,they seem to be sourced mainly from the broad-line region.Further analysis of the opacity(τγγ)and the GeV spectra study supports the conclusion that the location of the dissipation region must be beyond the BLR to avoid significant absorption.Notably,for PKS 1441+25,the emission region is also posited to lie outside yet proximate to the BLR.The parameters of describing the emission region were obtained by fitting broadband spectral energy distribution with contemporaneous observation data.Our findings suggest that for the five TeV FSRQs,during Te V flaring events,the jet appears to maintain an equilibrium between the energy density of the magnetic field and that of the particles for all investigated sources,with the exceptions of 4C+21.35 and PKS1441+25.In terms of the overall jet power,particle energy is the dominant contributor,and the observed blazar radiation cannot be solely attributed to the magnetic field,except in the case of 4C+21.35.Consequently,magnetic reconnection is unlikely to be the primary mechanism behind particle acceleration in these systems.

Refinement of the Proposed Gamma-Ray Burst Time Delay Model

This paper is the second instalment in our study of the observed time delay in the arrival times of radio photons emanating from Gamma Ray Bursts (GRBs). The mundane assumption in contemporary physics as to the cause of these pondersome time delays is that they are a result of the photon being endowed with a non-zero mass. While we do not rule out the possibility of a non-zero mass for the photon, our working assumption is that the major cause of these time delays may very well be that these photons are travelling in a rarefied cosmic plasma in which the medium’s electrons interact with the electric component of the Photon, thus generating tiny currents that lead to dispersion, hence, a frequency-dependent speed of Light (FDSL). In the present instalment, we “improve” on the model presented in the first instalment by dropping the assumption that the resultant pairs of these radio photons leave the shock front simultaneously. The new assumption of a non-simultaneous— albeit systematic—emission of these photon pairs allows us to obtain a much more convincing and stronger correlation in the time delay. This new correlation allows us to build a unified model for the four GRBs in our sample using a relative distance correction mechanism. The new unified model allows us to obtain as our most significant result a value for the frequency equivalence of the interstellar medium (ISM)’s conductance ν* ~ 1.500 ± 0.009 Hzand also an independent distance measure to the GRBs where we obtain for our four GRB samples an average distance of: ~69.40 ± 0.10, 40.00 ± 0.00, 58.40 ± 0.40, and 86.00 ± 1.00 Mpc, for GRB 030329, 980425, 000418 and 021004 respectively.

Crustal anisotropy of Taihang Mountain Range using azimuthal variation of receiver functions

摘要探讨了利用接收函数方位变化研究各向异性复杂地区速度结构的可能性。详细介绍了具有任意对称轴方向的横向各向同性系统中介质响应的计算过程，并将利用接收函数方位变化研究地壳各向异性的方法应用于华北太行山地区。结果表明，研究台站下方地壳具有明显的各向异性特征，其中地表盖层表现为8％-15％的慢轴型各向异性；深部地壳各向异性略小，表现为3％-5％的快轴型各向异性特征,不同台站获得的各向异性对称轴的方向及深度分布不具有明显的一致性,区域构造环境的变化可能是导致地壳各向异性存在的原斟。

Azimuthal elastic impedance-based Fourier coefficient variation with angle inversion for fracture weakness

Quantitative inversion of fracture weakness plays an important role in fracture prediction.Considering reservoirs with a set of vertical fractures as horizontal transversely isotropic media,the logarithmic normalized azimuthal elastic impedance(EI)is rewritten in terms of Fourier coefficients(FCs),the 90°ambiguity in the azimuth estimation of the symmetry axis is resolved by judging the sign of the second FC,and we choose the FCs with the highest sensitivity to fracture weakness and present a feasible inversion workflow for fracture weakness,which involves:(1)the inversion for azimuthal EI datasets from observed azimuthal angle gathers;(2)the prediction for the second FCs and azimuth of the symmetry axis from the estimated azimuthal EI datasets;and(3)the estimation of fracture weakness combining the extracted second FCs and azimuth of the symmetry axis iteratively,which is constrained utilizing the Cauchy sparse regularization and the low-frequency regularization in a Bayesian framework.Tests on synthetic and field data demonstrate that the 90°ambiguity in the azimuth estimation of the symmetry axis has been removed,and reliable fracture weakness can be obtained when the estimated azimuth of the symmetry axis deviates less than 30°,which can guide the prediction of fractured reservoirs.

A method for inversion of layered shear wavespeed azimuthal anisotropy from Rayleigh wave dispersion using the Neighborhood Algorithm

Seismic anisotropy provides important constraints on deformation patterns of Earth＇s material. Rayleigh wave dispersion data with azimuthal anisotropy can be used to invert for depth-dependent shear wavespeed azimuthal anisotropy, therefore reflecting depth-varying deformation patterns in the crust and upper mantle. In this study, we propose a two-step method that uses the Neighborhood Algorithm （NA） for the point-wise inversion of depth-dependent shear wavespeeds and azimuthal anisotropy from Rayleigh wave azimuthally anisotropic dispersion data. The first step employs the NA to estimate depth- dependent Vsv （or the elastic parameter L） as well as their uncertainties from the isotropic part Rayleigh wave dispersion data. In the second step, we first adopt a difference scheme to compute approximate Rayleigh-wave phase velocity sensitivity kernels to azimuthally anisotropic parameters with respect to the velocity model obtained in the first step. Then we perform the NA to estimate the azimuthally anisotropic parameters Gc/L and Gs/L at depths separately from the corresponding cosine and sine terms of the azimuthally anisotropic dispersion data. Finally, we compute the depth-dependent magnitude and fast polariza- tion azimuth of shear wavespeed azimuthal anisotropy. The use of the global search NA and Bayesian analysis allows for more reliable estimates of depth-dependent shear wavespeeds and azimuthal anisotropy as well as their uncertainties.We illustrate the inversion method using the azimuthally anisotropic dispersion data in SE Tibet, where we find apparent changes of fast axes of shear wavespeed azimuthal anisotropy between the crust and uppermost mantle.

Improvement of the axial trapping effect using azimuthally polarised trapping beam

A dual optical tweezers system, which consists of a doughnut mode optical tweezer （DMOT） with the azimuthally polarised trapping beam and a solid mode optical tweezer （SMOT） with the Gauss trapping beam was constructed to compare the axial trapping effect of DMOT and SMOT. The long-distance axial trapping of ST68 microbubbles （MBs） achieved by DMOT was more stable than that of SMOT. Moreover the axial trapping force measured using the viscous drag method, was depended on the diameter of the particle, the laser power, and the numerical aperture （NA） of the objective lens. The measurement of the axial trapping force and the acquisition of CCD images of trapping effect confirmed that the DMOT showed excellent axial trapping ability than SMOT. A simple and effective method is developed to improve axial trapping effect using the azimuthally polarized beam as trapping beam. This is helpful for the long-distance manipulating of particles especially polarised biological objects in axial direction.

Azimuthal distributions of final-state particles and fragments and transverse structure of emission source in high-energy nucleus-nucleus collisions

The azimuthal distributions of final-state particles and fragments produced in high-energy nucleus-nucleus collisions are described by a modified multisource ideal gas model which contains the expansions and movements of the emission sources. The transverse structures of the sources are given in the transverse plane by momentum components Px and Py, and described by parameters in the model. The results of the azimuthal distributions, calculated by the Monte Carlo method, are in good agreement with the experimental data in nucleus-nucleus collisions at high energies.

Numerical simulation of high-resolution azimuthal resistivity laterolog response in fractured reservoirs

The high-resolution azimuthal resistivity laterolog response in a fractured formation was numerically simulated using a three-dimensional finite element method. Simulation results show that the azimuthal resistivity is determined by fracture dipping as well as dipping direction, while the amplitude differences between deep and shallow laterolog resistivities are mainly controlled by the former. A linear relationship exists between the corrected apparent conductivities and fracture aperture. With the same fracture aperture, the deep and shallow laterolog resistivities present small values with negative separations for low-angle fractures, while azimuthal resistivities have large variations with positive separations for high-angle fractures that intersect the borehole. For dipping fractures, the variation of the azimuthal resistivity becomes larger when the fracture aperture increases. In addition, for high-angle fractures far from the borehole, a negative separation between the deep and shallow resistivities exists when fracture aperture is large as well as high resistivity contrast exists between bedrock and fracture fluid. The decreasing amplitude of dual laterolog resistivity can indicate the aperture of low-angle fractures, and the variation of the deep azimuthal resistivity can give information of the aperture of high-angle fractures and their position relative to the borehole.

Azimuthal anchoring of a nematic liquid crystal on a grooved interface with anisotropic polar anchoring

Zhang Y J et al.[Zhang Y J,Zhang Z D,Zhu L Z and Xuan L 2011 Liquid Cryst.38 355] investigated the effects of finite polar anchoring on the azimuthal anchoring energy at a grooved interface,in which polar anchoring was isotropic in the local tangent plane of the surface.In this paper,we investigate the effects of both isotropic and anisotropic polar anchoring on the surface anchoring energy in the frame of Fukuda et al.’s theory.The results show that anisotropic polar anchoring strengthens the azimuthal anchoring of grooved surfaces.In the one-elastic-constant approximation（K11 = K22 = K33 = K）,the surface-groove-induced azimuthal anchoring energy is entirely consistent with the result of Faetti,and it reduces to the original result of Berreman with an increase in polar anchoring.Moreover,the contribution of the surface-like elastic term to the Rapini-Papoular anchoring energy is zero.

Detection performance and inversion processing of logging-while-drilling extra-deep azimuthal resistivity measurements

We present systematic investigations on the physics,detection performance and inversion of logging-while-drilling extradeep azimuthal resistivity measurements(EDARM).First,the definitions of EDRAM measurements are discussed,followed by the derivation of the attenuation and phase-shift geometrical factors to illustrate the relative contributions of formation units to the observed signals.Then,a new definition of detection depth,which considers the uncertainty of inversion results caused by the data noise,is proposed to quantify the detection capability of ED ARM.Finally,the B ayesian theory associated with Markov chain Monte Carlo sampling is introduced for fast processing of EDARM data.Numerical results show that ED ARM is capable of detecting the azimuth and distance of remote bed boundaries,and the detection capability increases with increasing spacing and resistivity contrast.The EDARM tool can accommodate a large range of formation resistivity and is able to provide the resistivity anisotropy at arbitrary relative dipping angles.In addition,multiple bed boundaries and reservoir images near the borehole are readily obtained by using the Bayesian inversion.

Estimation of fracture density and orientation from azimuthal elastic impedance difference through singular value decomposition

Accurate estimation of fracture density and orientation is of great significance for seismic characterization of fractured reservoirs.Here,we propose a novel methodology to estimate fracture density and orientation from azimuthal elastic impedance(AEI)difference using singular value decomposition(SVD).Based on Hudson's model,we first derive the AEI equation containing fracture density in HTI media,and then obtain basis functions and singular values from the normalized AEI difference utilizing SVD.Analysis shows that the basis function changing with azimuth is related to fracture orientation,fracture density is the linearly weighted sum of singular values,and the first singular value contributes the most to fracture density.Thus,we develop an SVD-based fracture density and orientation inversion approach constrained by smooth prior elastic parameters.Synthetic example shows that fracture density and orientation can be stably estimated,and the correlation coefficient between the true value and the estimated fracture density is above 0.85 even when an S/N ratio of 2.Field data example shows that the estimated fracture orientation is consistent with the interpretation of image log data,and the estimated fracture density reliably indicates fractured gas-bearing reservoir,which could help to guide the exploration and development of fractured reservoirs.

Study of a background reconstruction method for the measurement of D-meson azimuthal angular correlations

We studied experimental background reconstruction methods for the measurement of the D-D correlation using PYTHIA simulation.The like-sign(LS)and side-band(SB)background methods,which are widely used in the experimental measurements of single D-meson production yields,were deployed for correlation study.It was found that the LS method,which describes the combinatorial background of single D^(0) meson yields,fails to reproduce the correlated background in the D^(0)-D^(0) correlation measurement,while the SB background method yields a good description of the background for both single D^(0) yields and the correlated background of the D^(0)-D^(0) correlation measurement.We further examined the validity of the correlation methods under different signal-to-background ratios,providing direct references for experimental measurements.

Forecasting Fractures in Coal Seams by Using Azimuthal Anisotropy from P-Wave Seismic Data

If the thickness of coal seams and the lithology of both roofs and floors of coal seams have not changed at all or only a little, then it is thought that the elastic anisotropy of coal seams depends mainly on fractures and obeys the horizontally symmetric model of an azimuth anisotropy. For a fixed offset, the amplitude A of the reflection P-wave and the cosine of 2φ has an approximately linear relation, (φ is the source-detector azimuth with respect to the fracture strike. Based on this relationship, many things can be done, such as the extraction of macro bins, the correction of residual normal moveout, the formation of azimuth gather, the transformation and normalization of azimuth gathers and the extraction of reflection wave amplitudes of coal seams. The least squares method was used to inverse theoretically the direction and density of fractures of coal seams. The result is in good agreement with the regional geological structure, indicating that the azimuth anisotropic analysis of the P-wave is feasible in evaluating the density and direction of fractures in coal seams.

Occam Inversion of Transient Electromagnetic Data in a Layered Medium with Azimuthal Anisotropy

In recent years, the anisotropic study has become a hot topic in the field of electromagnetics. Currently, inversion technologies of transient electromagnetic sounding data are mainly based on the case of an isotropic medium. However, the actual underground electrical structure tends to be complicated and anisotropic. It is often found that the isotropic inversion technologies do not lead to good results for field transient electromagnetic sounding data. We have developed an algorithm for calculating the transient electromagnetic response in a layered medium with azimuthal anisotropy. An occam inversion algorithm has also been implemented to invert the transient electromagnetic data induced by a grounded horizontal electric dipole in a layered medium with azimuthal anisotropy. Synthetic examples demonstrate the stability and validity of the inversion algorithm. Experimental results show different data for inverting have great influence on the inversion results.