Azimuthal Measurements Research Articles

Robust Azimuth Measurement Method Based on Polarimetric Imaging for Bionic Polarization Navigation

Azimuth information obtained from a polarization pattern in the sky provides many organisms like insects and birds, with the ability to navigate. The aim of this article is to investigate the azimuth method to measure the solar meridian from the pattern of the Angle of E (AOE) vector when it is partially obscured and disturbed. The model of the sky polarization pattern projected onto an imaging sensor is analyzed. The projection characteristic of the solar meridian is proved to be a straight line passing through the principal point, which is composed of pixels with the E-vector orientation 90° in the AOE map. Based on the mutation feature of the gradient amplitude of E-vector orientation 90° and occlusion without mutation on the solar meridian, a robust gradient amplitude and binary integration (GABI) azimuth method for a polarization imaging sensor is proposed. Then, the feasibility and robustness of this method are verified via numerical simulation and outdoor experiments, and the results show that when branches and buildings shield more than 80% of the AOE map, the azimuth measurement method remains effective. The accuracy of azimuth is 0.417° ( $\sigma$ ). This indicates that the azimuth can be effectively measured, even in the presence of occlusion and interference.

Assessing Error in Locations of Conspicuous Wildlife Using Handheld GPS Units and Location Offset Methods

ABSTRACTCollecting spatially explicit locations of individual animals often is an important part of the study of habitat use. Obtaining accurate locations without disturbing an individual can be difficult for small species and may be limited for species of conservation concern, such as piping plover (Charadrius melodus), where a close approach is undesirable because of the potential for disturbance. To reduce disturbance while estimating an animal's location, an observer can collect their location using Global Positioning System (GPS) and offset that position using a distance and azimuth. Typically, error is not considered when these locations are determined, despite the potential effects of inaccuracy on habitat association results. Therefore, our objectives were to quantify potential error using the offset method and then evaluate how that error may manifest. During the plover breeding season in 2017 (Apr through Sep), we tested the error of Trimble GPS units compared with benchmark locations to assess the accuracy of locations derived from these units. We then assessed the error associated with offset locations of a small target using Trimble GPS units, laser rangefinders, and 2 compass types. Finally, we determined the potential consequence of unaccounted error in our system by comparing the difference between point locations and land‐cover data using our estimated error as a point buffer. Average error of the GPS units at benchmark locations was 0.95 m. The mean error of the offset locations increased with increasing observer distance from the decoy location (from = 2.9 m to 7.6 m at distances of 20 m and 100 m, respectively). Error also increased with increasing error in the distance and azimuth measurements, and was greater using a digital GPS compass as compared with a handheld magnetic compass corrected for magnetic declination. In addition, potential misclassification of land‐cover type increased with increasing potential location error. When modeling animal locations, the error of point locations using this method, especially for land‐cover at the point location, should be accounted for using appropriately sized position buffers. Using this location collection method, we can increase our knowledge and study of conspicuous species to ensure that we consider habitats used throughout the species' life stages. © 2020 The Wildlife Society.

Data Fusion by a Supervised Learning Method for Orientation Estimation Using Multi-Sensor Configuration Under Conditions of Magnetic Distortion and Shock Impact

Accurate subsurface sensing during directional drilling is critical in the mining and energy extraction industries. One challenge is to measure the azimuth accurately. Azimuth measurements are hindered by magnetic disturbances such as iron debris, especially when magnetometers are used. Moreover, gyroscopes are susceptible to shocks during drilling surveys. To overcome these challenges, we developed a supervised learning filter (SLF) using a multi-sensor configuration (MSC) to accurately estimate the azimuth. The MSC consists of micro-electro-mechanical systems (MEMS) based magnetometers, gyroscopes, and accelerometers into two set of sensors, and the groups are separated by a known distance D to acquire additional rotational information using a dual acceleration difference (DAD) method. Also, D can reduce the negative effect of magnetic disturbances. A Kalman filter (KF) with known a priori noise information removes white noise; however, it is difficult to deal with unknown magnetic and shock disturbances. To reduce the effect of unknown magnetic and shock disturbances, we use the SLF to estimate orientation information. First, the SLF employs an adaptive neuro network fuzzy inference system (ANFIS) to build error models of each sensor; then the SLF calculates the proper weights of the sensors using the error models. Lab-scale experiments are performed on a test rig where the SLF is evaluated using one case with training and verified using two cases without training. The results showed an improvement in azimuth estimation.

Calculation of Tilted Coil Voltage in Cylindrically Multilayered Medium for Well-Logging Applications

In cylindrical multilayered medium, we develop two tool models for electromagnetic (EM) well logging: a metal mandrel winding with a co-axial (tilted) transmitter coil and a tilted (coaxial) receiver coil. The voltages on receivers in those two models are proven to be the same and only zero-order harmonic of EM field need to be considered for voltage calculation. To calculate the voltage, two pseudo-analytical formulae are presented by using the integral of electrical field in spatial and wavenumber domain, respectively. Those two alternative pseudo-analytical formulae can be used to verify calculation accuracy of each other in some scenarios when other numerical methods do not work well. Furthermore, the reflection coefficients of EM fields, consisting of the ratios of the cylindrical functions, are introduced to avoid overflow problems in the numerical integral. Numerical examples corroborate the correctness and stability of the proposed formulae. These formulae help advance the forward modeling and inversion of logging-while-drilling (LWD) azimuthal resistivity measurements and new extra-deep azimuthal resistivity tools (EDAR).

Numerical and experimental simulations of multiarray azimuthal laterolog sonde responses in fractured reservoirs

The occurrence, orientation, and development of fractures are key parameters in the evaluation of carbonate and volcanic reservoirs. We have used a 3D finite-element method to numerically simulate the logging responses of a newly proposed multiarray azimuthal laterolog sonde (MALS) in a fractured formation. More importantly, a physical simulation performed with a scaled-down 3D resistivity apparatus was developed to verify the numerical simulation results. Comparative analysis indicated that the laterolog resistivity curves are controlled by the fracture dip angles. High-angle fractures normally correspond to positive differences in the array laterolog curves, whereas fractures with low dip angles consistently result in a negative difference. The MALS tool also provides an azimuthal resistivity measurement that can be used to determine the fracture dipping direction. The sine-wave trend in the 2D imaging of azimuthal resistivity displays the fracture occurrence. In addition, MALS can be used to identify vertical fractures around a borehole within a certain distance. In addition, combined with laterolog data, the fracture occurrence and extension length can be evaluated.

Accuracy Check and Comparative Analysis of Horizontal Fiber-Optic Gyro Inclinometer in Freezing Hole

Based on the principle of fiber-optic gyro inclinometer, the characteristics of horizontal freezing hole and the working conditions, it is analyzed that the horizontal hole fiber-optic gyroscope tilting technology for freezing holes is one of the most reliable methods. In order to verify the azimuth measurement error of the horizontal fiber optic-gyro inclinometer, the simulation test under the 1:1 working condition was carried out with the actual working conditions on site. Compared with the total station measurement data, it was concluded that 85.2% of the data is in measurement error within ±2°, 55.6% of the data is within ±1°, which verifies the reliability of the measurement data of the horizontal fiber-optic gyro inclinometer. At the test level of α=0.05, the azimuth test error accords with the normal distribution of μ=0.54 and σ=0.73. In the actual use process, the algorithm can be used to optimize the measurement data by taking multiple measurements and taking the average value in combination with the field conditions, so that the data can be closer to the true value.

A Novel Method for Estimating Pitch and Yaw of Rotating Projectiles Based on Dynamic Constraints.

This paper addresses the difficult problem of measuring the attitude of a high-spinning projectile and presents a novel method for estimating the pitch and yaw angles of the projectile in flight. The method is based on analysis of the external moment of the rotating projectile during flight and theoretical derivations obtained from the dynamics’ equations. First, the principle of zero-crossing method is introduced, which explains the process of geomagnetic azimuth and roll measurements by the non-orthogonal geomagnetic sensor combination. Then, the dynamics constraint equations between the Euler angles and flight-path angle, trajectory deflection angle of the projectile are derived using the dynamics equations of the projectile rotating around the centroid, and analysis of the flight characteristics of the projectile in stable flight. Next, the spatial orientation relationship between pitch, yaw angles and magnetic azimuth is established based on the physical principle of geomagnetic azimuth. Finally, the pitch and yaw angles are estimated using the unscented Kalman filter (UKF), with the dynamics constraint equations serving as the driving equations. In the UKF prediction stage, the Runge-Kutta method is used to discretize the state equation that improves the prediction accuracy. Simulation results show that the proposed method can be used to accurately calculate the pitch and yaw angles, and results of experimental data processing also verify the feasibility of the proposed method for real-world applications.

Method to determine initial aiming azimuth accuracy using acceleration, gyroscope, and geomagnetic sensors

Abstract Initial aiming azimuth measurement using a geomagnetic sensor is very common, but difficult to use, because the accuracy cannot be determined even in places where geomagnetic disturbance can be compensated. In this letter, we propose a novel algorithm that employs acceleration, gyroscope, and geomagnetic sensor data to determine the accuracy of the initial oriented azimuth. Decision accuracy is 75% for various experiment locations. In the case of a false alarm, it is necessary to move to another location and remeasure, and ultimately the decision accuracy could reach 100%.

Influence of the Anode of a Non-Self-Sustained Glow Discharge with a Hollow Cathode on the Spatial Distribution of Plasma Concentration

The results of investigation of the influence of geometrical dimensions, shape and position of the anode of a high-current non-self-sustained glow discharge with a hollow cathode at low (≈1 Pa) pressure with the current up to 100 A on the degree of inhomogeneity of azimuthal plasma-concentration distributions are presented. The azimuthal measurements demonstrate that upon injection of an electron flow with the current exceeding that of the electrons, formed as a result of the secondary ion-electron emission, the value of the average path length L of electrons before their escape to the anode is much lower than that in a self-sustained discharge burning mode. It is determined that in the case of injection of an electron flow into the hollow-cathode glow discharge the anode position considerably affects the degree of plasma concentration inhomogeneity. It is shown that placing the annular anode in the site preventing the line-of-site between the electron injection and anode surface directions allows achieving the minimum inhomogeneity coefficient value.

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 extra-deep 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 EDARM. Finally, the Bayesian theory associated with Markov chain Monte Carlo sampling is introduced for fast processing of EDARM data. Numerical results show that EDARM 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.

An Iteratively Reweighted Instrumental-Variable Estimator for Robust 3-D AOA Localization in Impulsive Noise

This paper considers the problem of robust three-dimensional (3-D) angle-of-arrival (AOA) source localization in the presence of impulsive α-stable noise based on the I <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</sub> -norm minimization criterion. The iteratively reweighted least-squares algorithm (IRLS) is a well-known technique for solving I <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</sub> -norm minimization with the desirable global convergence property. Adopting the IRLS for 3-D AOA localization requires nonlinear-to-pseudolinear transformation of azimuth and elevation angle measurement equations, thus resulting in a new variant of the IRLS, called the iteratively reweighted pseudolinear least-squares estimator (IRPLE). Unfortunately, there exists correlation between the measurement matrix and noise vector in the pseudolinear measurement equations, which consequently makes the IRPLE biased. To counter the bias problem of the IRPLE, a new iteratively reweighted instrumental-variable estimator (IRIVE) is proposed based on the exploitation of instrumental variables. The IRIVE is analytically shown to achieve the theoretical covariance of the general least I <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</sub> -norm estimation. Extensive simulation studies are presented to demonstrate the performance advantages of the IRIVE over the IRPLE as well as other existing least-squares and least I <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</sub> -norm estimators. The IRIVE is observed to produce nearly unbiased estimates with mean squared error performance very close to the Cramér-Rao lower bound.

Numerical simulation of acoustic reflection logging while drilling based on a cylindrical phased array acoustic receiver station

With the increase of drilling activities, improving the azimuth measurement capability of acoustic logging while drilling (LWD) tools has been an urgent requirement for the petroleum exploration. In this study, a novel acoustic reflection LWD scheme is developed based on a cylindrical phased array (CPA) acoustic receiver station, which is composed of several arcuate phased array (APA) acoustic receiver stations arranged uniformly along the tool axis. The azimuthal performance of the APA and CPA acoustic receiver stations in acoustic reflection LWD with one or two formation interfaces away from the borehole are studied using the finite-difference time-domain method. The simulation results show that the amplitude distribution of reflected waves received by different azimuthal receiver elements is helpful for determining the azimuth angles of formation interfaces. Compared with the individual-reception mode, the azimuth measurement accuracy of the APA acoustic receiver station is greatly improved when working in the scanning-reception mode. Compared with the APA scanning-reception scheme, the CPA scanning-reception scheme performs better in simultaneously measuring the azimuth angles of two reflectors outside the borehole.

Investigation of borehole effects on azimuthal resistivity measurements using novel pseudo‐analytic formulas

ABSTRACTDownhole resistivity measurements provide valuable information for geosteering and formation evaluation. It is important to understand and correct the environmental effects, such as the borehole, the tool eccentricity and the resistivity anisotropy effects, of the measurements based on fast and accurate modelling methods. A new pseudo‐analytic solution for eccentric coaxial and tilted‐coil antennas in the cylindrically multilayered medium with transverse isotropic conductivity was developed. This method can take the eccentric tool, the borehole, the mud invasion and the resistivity anisotropy into account. These formulas enable us to simulate the responses of the downhole induction logging tools, including induction wireline and azimuthal propagation logging‐while‐drilling measurements. Instead of using the prior fictitious boundary, the generalized reflection coefficients are proposed to construct the linear matrix functions to deal with the tool eccentricity. The cylindrical functions are reorganized and presented in forms of ratios. Thus, the proposed formulas obviate the overflow issue in the computation and are more stable and efficient. The proposed approach is compared and validated with other well‐established methods. Simulations and case studies show that: (1) the responses of azimuthal resistivity logging‐while‐drilling tool are affected by the tool's eccentricity in both isotropic and anisotropic medium; (2) sine curve behaviours exist for the phase difference and amplitude ratio of azimuthal resistivity measurements along with different eccentricity azimuth.

Noniterative Three-Dimensional Location Estimation Using Azimuth and Elevation Measurements at Multiple Locations

Closed-form expression of three-dimensional emitter location estimation using azimuth and elevation measurements at multiple locations is presented in this paper. The three-dimensional location estimate is obtained from three-dimensional sensor locations and the azimuth and elevation measurements at each sensor location. Since the formulation is not iterative, it is not computationally intensive and does not need initial location estimate. Numerical results are presented to show the validity of the proposed scheme.

Azimuthal shear-wave anisotropy measurement in a borehole: Physical modeling and dipole acoustic verification.

An anisotropic physical model is constructed to evaluate the anisotropy measurement. The model consists of a series of equally spaced thin limestone slab sheets cemented with concrete, resulting in a transversely isotropic medium. For the anisotropy measurement evaluation, the borehole model is tested by a standard multipole acoustic tool. The measurement finds an S-wave anisotropy magnitude about 20% and determines the fast S-wave polarization along the alignment direction of the slab sheets. The results of the work not only validate the borehole measurement technology, but also provide a testing facility for calibrating the measurement acoustic tool.

Noncollinear effective anisotropies in exchange coupled NiFe/IrMn bilayers

Abstract The influence of noncollinearity between unidirectional and uniaxial anisotropies on asymmetric magnetization reversal of NiFe/IrMn bilayers has been investigated. The experimental findings show that a noncollinear effective anisotropies originates from the competition among the applied magnetic field, magnetic anisotropy and exchange coupling, and the presence of magnetic frustration at NiFe/IrMn interfaces. Azimuthal measurements of the exchange bias suggest that the degree of effective interfacial anisotropies, which can be quantified by the angle ( γ ) between the uniaxial and unidirectional anisotropies, plays a crucial role in determining magnetization reversal. For a variable thickness of antiferromagnet layers, the experimental findings suggest a non-monotonic correlation between the magnitude of γ and the degree of interfacial roughness. Numerical analysis has been performed by considering the magnetic frustration present at the ferromagnet/antiferromagnet interfaces, suggesting a good agreement with experimental findings.

How To Manage Geomagnetic-Field Disturbances in the Northern Auroral Zone To Improve the Accuracy of Magnetic Measurement-While-Drilling Directional Surveys

Summary The auroral zone is the region surrounding the geomagnetic North and South Poles, and it is where the largest and most frequent disturbances in the Earth's magnetic field are experienced. Because geomagnetic disturbances affect the accuracy of magnetic measurement-while-drilling (MWD) directional data, surveying wells in the auroral zone is challenging. Development of industry practices to enable accurate surveying and safe operations in these areas is important. The objective of this study was to investigate how magnetic disturbances in the auroral zone influence the geomagnetic-field parameters of declination, dip angle, and total magnetic-field intensity. This investigation analyzed the statistical properties of data from 20 land-based magnetic observatories and variometer stations in Scandinavia, Greenland, and Alaska—all located in the auroral zone. The results were used to estimate magnetic-field-disturbance covariations as a function of distance and direction. Additionally, methods to reduce azimuth uncertainty using data from distant monitoring stations were studied. Uncritical use of data obtained from monitoring stations can result in uncertain azimuth measurements. In cases where data from more than one nearby monitoring station are available, the challenge is often to identify which stations are providing the most-accurate corrections. Important criteria for the selection of monitoring stations are not limited to directions and distances, but also include the location of the ionospheric current relative to the rig location. Procedures and methods for predicting the location of ionospheric currents were tested. The data sets analyzed in this study contain measured deviations from the quiet mean for periods with low, moderate, and high geomagnetic activity. Station pairs with mutual distances ranging from 150 to 850 km were considered. The general trends of the magnetic data from station pairs located along the east/west direction are more correlated than in the north/south direction, and the differences in magnetic fluctuations between station pairs are lower in the east/west direction than in the north/south direction. This holds true for all distances, directions, and disturbance levels.

Analysis and comparison of azimuthal resistivity measurement modes for laterolog tool

Though proposed previously, the azimuthal focusing modes applied to laterolog tool still need to be researched. A three-dimensional numerical simulation process is first applied to analyze the azimuthal resistivity measurement of deep measurement of dual laterolog tool adopting four modes, i.e., independent current-emitting mode, passive equipotential mode, independent current-adjusting mode and potential-measuring mode. Afterwards, three typical formation models, i.e., a formation model with a resistivity anomaly contacting the borehole wall, a formation model with a resistivity anomaly non-contacting the borehole wall and a formation model with asymmetrical horizontal or downward mud invasion in horizontal well, are developed to test the four modes and the integrated performances of the four modes are revealed. Two tests are carried out to test the independent current-adjusting mode. It has been demonstrated that overall the potential-measuring mode manifests the least ideal measured results, and it only possesses slightly qualitative measurement in the formation model with a resistivity anomaly non-contacting the borehole wall. The independent current-emitting mode can realize qualitative measurement in all the three formation models, but the measured azimuthal difference is indistinctive especially in the case of asymmetrical mud invasion in horizontal well. The passive equipotential mode exhibits an indigent effect, nevertheless it can quantitatively characterize the electrical difference in the formation model with a resistivity anomaly contacting borehole wall. The independent adjustable current mode is the optimum choice because it possesses the relatively perfect performance in all the three cases, especially in the extremely common asymmetrical mud invasion occurring in horizontal well. It has a relative measured error changing from 0.10% to 4.09% and can be adopted to uncover formation characteristics, and it should be the best azimuthal focusing mode employed by the laterolog tool for the azimuthal resistivity measurement.

Single Space Based Sensor Bias Estimation Using a Single Target of Opportunity

Sensor registration refers to the estimation/compensation of systematic (bias) errors, in contrast to the random errors from sensor noise. Various methods have been proposed for bias estimation of multiple optical sensors using common targets of opportunity. However, the proposed solutions required the use of multiple (two or more) optical sensors and the need to solve the data association problem arising from the fusion of measurements from multiple sensors. In order to remove these constraints, we provide in this paper a new methodology using a single exoatmospheric target of opportunity seen in a single satellite borne sensor's field of view to estimate the sensor's biases simultaneously with the state of the target. The satellite-based sensor sees the target from a changing direction as a function of its position, allowing the target in this nonlinear tracking system to be observable. The sensor provides the line of sight (LOS) measurements of azimuth and elevation to the target. Sensor pointing calibration is the key precondition for accurate tracking of a target in a space-based system. Statistical tests on the results of simulations, and the evaluation of the Cramer–Rao lower bound (CRLB) on the covariance of the bias estimates show that this method is statistically efficient.

Fast inversion of logging-while-drilling azimuthal resistivity measurements for geosteering and formation evaluation

We developed an efficient parametric inversion method for the determination of the distances to boundaries (DTBs), dip angle, and formation anisotropic resistivities from logging-while-drilling (LWD) azimuthal resistivity measurements (ARM) in real time. To increase the efficiency, the development employed a depth window, which will slide along the well trajectory during data processing. The local structure inside the depth window can be regarded as one-dimensional (1D) layered formation. A three-layer model (one transverse isotropic (TI) layer embedded between two isotropic shoulder layers) is assumed in the inversion to rebuild the formation structure. Then, the inversion problem is solved using a regularized Levenberg-Marquardt minimization approach. Multiple initial guesses are employed in order to avoid local minima and to find the global solution. Synthetic experiments show that the developed algorithm, which is capable of handling a large subset of the complex 3D conditions and arbitrary well trajectory, is robust and efficient. Discussions are also made to further demonstrate the advantages and limitations of ARM and the inversion processing in geosteering and formation evaluation.