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.

Component azimuths of the CEArray stations estimated from P-wave particle motion

The recently built China Digital Seismic Network consists of the China National Digital Seismic Network （CNDSN）, 31 regional seismic networks and several small aperture arrays with more than 1 000 stations including 850＋ broadband stations. It forms a gigantic seismic array that provides an unprecedented opportunity to study the Earth＇s deep interior besides its routine task of seismic monitoring. Many modern seismic studies rely on rotation of vertical and horizontal components in order to separate different types of seismic waves. Knowledge of the orientations of the two horizontal components thus is important to perform a correction rotation. We analyzed particle motions of teleseismic P waves recorded by the network and used them to estimate the northcomponent azimuth of each station. An SNR-weighted-multi-event method was introduced to obtain component azimuths that best explain the P-wave particle motions of all the events recorded at a station. The method provides robust estimates including a measurement error calculated from background noise levels. We found that about one third of the stations have some sort of problems, including misorientation of the two horizontal components, mislabeling and polarity reversal in one or more components. These problems need to be taken into account for any rotation based seismic studies.

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.

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。

P-wave fracture prediction algorithm using pre-stack data with limited azimuth distribution:A case study in the TZ45 area,Tarim Basin,China

Fractured reservoirs always show anisotropic amplitude features,i.e.the reflection amplitude of seismic waves varies with offset and azimuth （AVOZ）.A noise attenuation fracture inversion algorithm is presented for fracture detection based on P-wave AVOZ.The conventional inversion method always fails when applied to limited azimuth data because of the existence of noise.In our inversion algorithm,special attention is paid to suppressing the noise during inversion,to overcome the limitation of the conventional inversion method on limited azimuth data.Numerical models are employed to illustrate the effectiveness of the method.The inversion algorithm is then applied to Tazhong 45 area field data which is acquired under limited azimuth distribution.Compared with cores and fullbore formation microimage （FMI）,the inverted results （fracture density and orientation） are reasonable,suggesting that the inversion algorithm is feasible for fracture prediction in the Tarim Basin.

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.

Wide/narrow azimuth acquisition footprints and their effects on seismic imaging

Acquisition footprint is a new concept to describe the seismic noise in three-dimensional seismic exploration and it is closely related to geometry and observation shuttering. At present, the study on acquisition footprints has become a hot spot. In partnership with the Dagang Oilfield, we used the channel sand body seismic physical model to study the characteristics of wide/narrow azimuth acquisition footprints and analyzed and compared the two types of footprints and their effects on target imaging. In addition, the footprints caused by data processing of the normal moveout offset （NMO） stretching aberration were discussed. These footprints are located only in the shallow or middle layer in the time slice, and possibly affect the imaging of shallow target layers, and have no influence on deep target imaging. Seismic physical modeling has its advantages in the study of acquisition footprints.

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.

PERFORMANCE ANALYSIS OF AZIMUTH ELECTRONIC BEAM STEERING MODE SPACEBORNE SAR

Pointing angle and pattern of the antenna can be changed swiftly to actualize the azimuth beam scanning by using electronic beam steering, which makes the Synthetic Aperture Radar (SAR) system more flexible and achieve a high resolution or cover a long strip within short time span. When the pointing angle is steered away from boresight, some aberrations may appear on the antenna pattern, e.g., the grating lobe appears, the main lobe gain decrease, and antenna pattern broadens, e.g., the aberrations result in the worsening of system performance, and complicate the corresponding performance analysis method. Conventional computation methods of performance parameters do not account for the rapid change of the antenna pattern. It introduces remarkable errors when the scanning angle is large. In this paper, a method of calculating performance parameters is proposed for the beam steering mode, which achieves the parameters by the energy accumulation in time domain. Actually, the proposed method simulates the working process of SAR and obtains accurate performance parameters. Furthermore, we analyze the effects of the grating lobe on the Azimuth Ambiguity to Signal Ratio (AASR), and present the generic Pulse Repetition Frequency (PRF) choosing principle which can also prevent the ambiguous area from weighting by the grating lobe. Finally, the effect of the antenna configuration on the performance parameters is analyzed by a system example.

Azimuth space-variant properties of BiSAR with nonequal velocities

Bistatic SAR possesses characteristic of the azimuth space-variant when the velocities of transmitter and receiver are not equal. The geometric model of BiSAR with the parallel trajectories and the nonequal platform velocities is presented. Analyzing the motion relationship of transmitter and receiver, the formula of azimuth spacevariant is derived in time domain. Via Taylor polynomial expansions, the azimuth space-variant is factorized by four terms： zero-order, first-order, second-order, and third-order term. And, their impacts on impulse response are illuminated. Some characteristics about azimuth space-variant of airborne BiSAR case are exhibited by simulation experiments, and these simulated results are coincident with the formulae of azimuth space-variant.

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.

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.

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.

Significant wave height estimation using azimuth cutoff of C-band RADARSAT-2 single-polarization SAR images

This paper proposes two simple models, look-up table（LUT） model and empirical model, to directly retrieve significant wave height（Hs） using synthetic aperture radar（SAR） azimuth cutoff（λc）. Both models aim at C-band VV, HH, VH, and HV single-polarization SAR images. The LUT model relates Hs to λc, while the empirical model relates Hs to both λc and SAR range-to-velocity（β）. The LUT model coefficients are derived by simulation under different sea states and observation conditions, which depend on incidence angle（θ）, wave direction（dw）, and βbut are independent of polarization. The empirical model coefficients are obtained by fitting the collocated data,which only depend on polarization. To fit empirical model coefficients and validate the two models, C-band RADARSAT-2 fine quad-polarization（VV＋HH＋VH＋HV） single-look complex（SLC） SAR images and collocated buoy data are collected. Retrieved Hs, using Yang model and the two models proposed in this paper from four kinds of polarization SAR data, are compared with buoy Hs. Results show that both LUT and empirical models have the capacity of retrieving Hs from C-band RADARSAT-2 co-polarization SAR data, while Yang model is not suitable for these kinds of SAR data. Moreover, the empirical model is also valid for cross-polarization SAR data showing clear ocean wave stripes.

Effect of uneven noise source and/or station distribution on estimating the azimuth anisotropy of surface waves

With the development of the dense array,the surface wave velocity and azimuthal anisotropy under the array can be directly obtained by beamforming the noise cross-correlation functions(NCFs). However, the retrieval of the Green’s function by cross-correlating the seismic noise requires that the noise source has a uniform distribution. For the case with uneven noise source, the azimuthal dependence on the sources in the expression for the spatial coherence function, which corresponds to the NCF in the time domain,has the same form as the azimuthal dependence of the surface wave velocity in weakly anisotropic media. Therefore, the uneven noise source will affect the surface wave anisotropy extraction. In this study, three passive seismic methods, i.e.,beamforming, SPAC(spatial autocorrelation), and NCF, are compared to demonstrate that an uneven source distribution and uneven station distribution have equivalent effects on the outcome from each method. A beamforming method is proposed to directly extract the velocity and azimuthal anisotropy of surface waves. The effect of uneven noise source and/or station distribution on estimating the azimuth anisotropy of surface waves was investigated using data from the ChinArray Phase Ⅱ. A method for correcting the apparent anisotropy in beamforming results caused by an uneven station distribution is suggested.

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.

ANALYSIS OF METHOD FOR DETERMINING AZIMUTH OF PRINCIPAL AXIS OF INERTIA BASED ON DYNAMIC BALANCE MEASUREMENT

The dynamic balance quality of a rotating object is an important factor to maintain the stability and accuracy for motion. The azimuth of the principal axis of inertia is a major sign of dynamic balance. A usual method is measuring moment of inertia matrix relative to some base coordinates on a rotary inertia machine so as to calculate the azimuth of principal axis of inertia, By using the measured unbalance results on the two trimmed planes on a vertical hard bearing double-plane dynamic balancing machine, the dimension and direction of couple unbalance can be found. An azimuth angle formula for the principal axis of inertia is derived and is solved by using unbalance quantities. The experiments indicate that method based on dynamic balancing measurement is proved rational and effective and has a fine precision.