Minimum Curvature Method Research Articles

Noise suppression of airborne transient electromagnetic data with minimum curvature

The airborne transient electromagnetic (ATEM) method is a geophysical exploration technique that offers several advantages, including rapid exploration, minimal interference from complex terrains, dense data sampling, and environmental friendliness. However, the full-frequency time-domain secondary field signal acquisition of the ATEM data is susceptible to various electromagnetic interferences, resulting in noise in the collected data. This noise complicates subsequent processing and interpretation. To address this issue, we have developed a 1D minimum-curvature difference equation with unequal spacing based on minimum-curvature differential equations. Through research, we develop an ATEM noise-suppression method based on multiple single-step and multiple superposition-step implicit iterative formats. In addition, we have investigated the convergence of explicit and implicit iterative schemes via Fourier spectrum analysis and proven that the implicit iterative schemes converge. This method effectively suppresses noise in synthetic and real ATEM data during processing. Our results show that the minimum-curvature method is particularly effective in suppressing sferic and Gaussian noises in ATEM data. As a result, our method provides high-quality and reliable ATEM data for further data processing and interpretation. Moreover, the minimum-curvature method is also capable of suppressing noise in ground and ground-space transient electromagnetic data, as well as magnetotelluric data noise. Therefore, this method exhibits a wide range of potential applications.

The improvements to the minimum curvature race line optimization

Motorsports is gaining increasingly large and broad attention and simulations using modern information technology on race performance are in demand. This paper focuses on the improvements of the minimum curvature method on optimal racing lines for a race car. The key contribution of the improvements is to generate a more realistic optimal racing line, therefore getting a better description of the car and driver performance. The improvements contain the introduction of the kerb of the track and the late apex technique applied by drivers during the race. The effect of two improvements is verified in the simulation racing software Assetto Corsa and the result shows that the introduction of the kerb raises the lap time accuracy by 90% and the late apex trajectory is matched with the actual path.

Application of long short-term memory network for wellbore trajectory prediction

For improving the accuracy of wellbore trajectory prediction, especially in the build section, a new prediction model based on long short-term memory (LSTM) network was proposed. At the same time, the model was built by Python language and TensorFlow library. The well inclination and azimuth angle were predicted by the LSTM model. Moreover, the prediction accuracy of the LSTM was compared with that of the minimum curvature method. The results show that the average prediction error of the LSTM is much 50% lower than the minimum curvature method, and the proposed model in this article is more consistent with the actual drilling data. This method does not rely on any assumption of the path shapes and geometries. In addition, the model proposed in this article is easy to use and convenient for the engineering field application without the derivation of mathematical formulas.

Directional Drilling Design Using Computer Model

The number of directionally drilled wells in Sudan is progressively increasing. Directional drilling calculations when done manually or through Microsoft Excel are tedious, susceptible to mistakes and take long time. The software prescribed in this paper is designed to treat these problems. This paper describes Software called CDD which stands for Computerized Directional Drilling. It is employing the minimum curvature method using visual basic (VB.NET) as a programming language to achieve calculations and minimize the uncertainty and risks related to achieve a predetermined target. The Software is capable of calculating the survey data of the well trajectory for all types of directional drilling wells. In addition, the CDD computes the actual coordinates along the planned trajectory at regular or irregular intervals and designs plots to show the well trajectory in 2D charts in top and side views. It also gives 3D graph for more visual representation of the well trajectory. The CDD enables the user to compare different well trajectories and show them in the same chart. The input data could be saved in the database section and the output results could be exported into various formats. Based on applying the CDD on the Case Studies, this Software gives accurate results and can be used in planning of CDD with error of less than 1%.

Quantitative Precipitation Estimation (QPE) Rainfall from Meteorology Radar over Chi Basin

This study of the Quantitative Estimation Precipitation (QEP) of rainfall, detected by two Meteorology Radars over Chi Basin, North-east Thailand, used data from the Thai Meteorological Department (TMD). The rainfall data from 129 rain gauge stations in the Chi Basin area, covering a period of two years, was also used. The study methodology consists of: firstly, deriving the QPE between radar and rainfall based on meteorological observations using the Marshall Palmer Stratiform, the Summer Deep Convection, and Regression Model and calibrating with rain gauge station data; secondly, Bias Correction using statistical method; thirdly, determining spatial variation using three methods, namely Kriging, Inverse Distance Weight (IDW), and the Minimum Curvature Method. The results of the study demonstrated the accuracy of estimating precipitation using meteorological radar. Estimated precipitation compared against an equivalent of 2 years of rain station measurement had a probability of detection (POD) of 0.927, where a value of 1 indicated perfect agreement, demonstrating the effectiveness of the method used to calibrate the radar data. The bias correction method gave high accuracy compared with measured rainfall. Furthermore, of the spatial estimation of rainfall methods, the Kriging methodology showed the best fit between estimation of rainfall distribution and measured rainfall distribution. Therefore, the results of this study showed that the rainfall estimation, using data from a meteorology radar, has good accuracy and can be useful, especially in areas where it is not possible to install and operate rainfall measurement stations, such as in heavily forested areas and/or in steep terrain. Additionally, good accuracy rainfall data derived from radar data can be integrated with other data used for water management and natural disasters for applications to reduce economic losses, as well as losses of life and property.

Analysis of Regional and Residual Gravity Disturbance of Major Fault Belts in the Tarim Basin, Western China

Large fault belts often influence the paleo-geomorphic changes in basins and control hydrocarbon accumulation and distribution in basins. Based on the gravity field model European Improved Gravity model of the Earth via New techniques (EIGEN)-6C4, this study calculated the residual Bouguer gravity disturbance of the Tarim Basin by using the minimum curvature method and analyzed gravitational characteristics of major fault belts of the Tarim Basin. The residual Bouguer disturbance exhibits linear residual Bouguer disturbance zones in the Tianshan Mountains, West Kunlun, and the Altyn region, which is consistent with the spatial distribution of their related fault belts. The regional Bouguer disturbance is related to crust–mantle boundary depth, which can be used to roughly estimate crust thickness. Thus, we suggest that the crust–mantle boundary depth order of major faults from deep to shallow is the Altyn region, West Kunlun, and Tianshan Mountains. There is a discontinuity in the residual Bouguer disturbance of West Kunlun, which compares well with the fault belt of West Kunlun. Furthermore, the residual Bouguer disturbance of the Tarim Basin has a series of elliptical areas with a central positive disturbance located within the Bachu uplift and other uplift structures. The residual Bouguer disturbance also reflects the position and distribution of the major fault belts and the boundary of the Tarim Basin, which can provide guidance for dynamic evolution analysis of large basins.

An enhancing precision method for downward continuation of gravity anomalies

Downward continuation of the gravity field observed on the surface is a method applied to calculate the anomalous field below the surface close to deep sources. However, the downward continuation is mathematically incomplete and uncertain, and its accuracy depends on the sampling rate and coverage of the gravity data. To improve the accuracy of the downward continuation of gravity anomalies, we constructed a quasi-neural network that is made up of multiple layers of neurons. Each of the neurons analyzes the attributes of the input data to determine the best control parameters for the downstream output of the current layer, and to judge whether the results of the downstream extension are close to the main anomalous sources. We define the singularity statistic parameter and singular probability of the signal to characterize the singularity attribute of each-layer's continuation results. If the continuation data contain large singularity, they are corrected by the minimum curvature method to weaken the influence of the interference of shallow random sources. Numerical simulation tests showed that the proposed method can effectively weaken the interference of shallow random sources, and obtain more accurate information on deep-sources. A real-world example demonstrated that the method successfully delineate deep geological structures.

Seismic Drill-Bit Tracking for Improved Well Positioning

Summary The lateral well position uncertainty of magnetic/gyro measurement-while-drilling (MWD) measurements can often exceed the requirements regarding anticollision, for optimal placement of infill wells between existing producers, or for hitting targets with limited geological extent. The positional uncertainty can be significantly reduced by implementing high-precision drill-bit localization using passive seismic data. Consequently, not only drilling risks can be reduced, but optimal reservoir drainage is ensured as well. By using passive seismic recordings from the seafloor, we can “listen” to the noise generated by the bottomhole assembly (BHA) while drilling. Despite various noise sources in the vicinity (e.g., vessels and rigs), advanced data processing and the combination of hundreds of seafloor receivers spread above the ongoing drilling enable us to detect the drilling signal and locate the drill bit. Whereas the magnetic and gyro MWD tools have errors that accumulate with measured depth (MD), each bit position derived from seismic (usually every 90 seconds) is completely independent. For horizontal sections, the error does not increase with MD and hence can provide improved lateral accuracy. No additional BHA tool is required, and the measurements are neither dependent on the magnetic nor gravitational field. Moreover, the passive seismic measurements can be used to obtain an improved lateral well position estimate. This is done by optimizing the azimuth information of the well trajectory in the minimum curvature method. A lateral uncertainty measure can be derived from the residuals between the passive measurements and the updated well path. Since 2018, we have used the continuous stream of passive data from permanent seafloor sensors at the Grane Field, with its reservoir depth of around 1800 m true vertical depth subsea (TVDSS) to follow all wells with this drill-bit tracking scheme. Lateral deviations from the official well path based on magnetic/gyro measurements are mostly within ±30 m. The lateral position uncertainty can be as low as a couple of meters under optimal conditions.

Potential field data interpolation by Taylor series expansion

Data interpolation is critical in the analysis of geophysical data when some data are missing or inaccessible. We interpolate irregular or missing potential field data using the relation between adjacent data points inspired by the Taylor series expansion (TSE). The TSE method first finds the derivatives of a given point near the query point using data from neighboring points and then uses the Taylor series to obtain the value at the query point. The TSE method works by extracting local features represented as derivatives from the original data for interpolation in the area of data vacancy. Compared with other interpolation methods, the TSE provides a complete description of potential field data. Specifically, the remainder in TSE can measure local fitting errors and help obtain accurate results. Implementation of the TSE method involves two critical parameters — the order of the Taylor series and the number of neighbors used in the calculation of derivatives. We find that the first parameter must be carefully chosen to balance between the accuracy and numerical stability when data contain noise. The second parameter can help us build an over-determined system for improved robustness against noise. Methods of selecting neighbors around the given point using an azimuthally uniform distribution or the nearest-distance principle are also presented. Our approach is first illustrated by a synthetic gravity data set from a single survey line, and then it is generalized to the case over a survey grid. In both numerical experiments, the TSE method demonstrates an improved interpolation accuracy in comparison with the minimum curvature method. Finally, we apply the TSE method to a ground gravity data set from the Abitibi Greenstone Belt, Canada, and an airborne gravity gradient data set from the Vinton Dome, Louisiana, USA.

A Generalized Solution to the Point-to-Target Problem Using the Minimum Curvature Method

Summary An explicit solution to the general 3D point-to-target problem based on the minimum curvature method has been sought for more than four decades. The general case involves the trajectory's start and target points connected by two circular arcs joined by a straight line with the position and direction defined at both ends. It is known that the solutions are multivalued, and efficient iterative schemes to find the principal root have been established. This construction is an essential component of all major trajectory construction packages. However, convergence issues have been reported in cases where the intermediate tangent section is either small or vanishes and rigorous mathematical conditions under which solutions are both possible and are guaranteed to converge have not been published. An implicit expression has now been determined that enables all the roots to be identified and permits either exact or polynomial-type solution methods to be used. Most historical attempts at solving the problem have been purely algebraic, but a geometric interpretation of related problems has been attempted, showing that a single circular arc and a tangent section can be encapsulated in the surface of a horn torus. These ideas have now been extended, revealing that the solution to the general 3D point-to-target problem can be represented as a 10th-order self-intersecting geometric surface, characterized by the trajectory's start and end points, the radii of the two arcs, and the length of the tangent section. An outline of the solution's derivation is provided in the paper together with complete details of the general expression and its various degenerate forms so that readers can implement the algorithms for practical application. Most of the degenerate conditions reduce the order of the governing equation. Full details of the critical and degenerate conditions are also provided, and together these indicate the most convenient solution method for each case. In the presence of a tangent section, the principal root is still most easily obtained using an iterative scheme, but the mathematical constraints are now known. It is also shown that all other cases degenerate to quadratic forms that can be solved using conventional methods. It is shown how the general expression for the general point-to-target problem can be modified to give the known solutions to the 3D landing problem and how the example in the published works on this subject is much simplified by the geometric, rather than algebraic treatment.

Design and Calculation of Complex Directional-Well Trajectories on the Basis of the Minimum-Curvature Method

Summary The vector-algebra method and the minimum-curvature method were used to solve the trajectory design challenge for intersecting two wells. In accordance with known parameters, we expressed algorithms for intersecting a horizontal well. The geometrical shape of the target area was extended to attain the algorithms needed for landing on spherical and cylindrical surfaces. Combined with the expression for calculating the tool-face angle, the algorithms needed for calculating the closest distance to an existing well and landing surface were also proposed. The algorithms presented here provide a theoretical basis for the design and control of complex directional-well trajectories.

Automated Real-Time Torque-and-Drag Analysis Improves Drilling Performance

This article, written by JPT Technology Editor Chris Carpenter, contains highlights of paper SPE 191426, “Implementation of a Fully Automated Real-Time Torque-and-Drag Model for Improving Drilling Performance: Case Study,” by Mojtaba Shahri, SPE, Timothy Wilson, Taylor Thetford, SPE, Brian Nelson, SPE, and Michael Behounek, SPE, Apache, and Adrian Ambrus, John D’Angelo, and Pradeepkumar Ashok, SPE, Intellicess, prepared for the 2018 SPE Annual Technical Conference and Exhibition, Dallas, 24–26 September. The paper has not been peer reviewed. Significant progress has been made on physics-based torque-and-drag (T&D) models that can run either offline or in real time. Despite its numerous benefits, real-time T&D analysis is not prevalent because it requires merging real-time and contextual data of dissimilar frequency and quality, along with repeated calibration, the results of which are not easily accessible to the user. In this paper, the application of a real-time T&D model is demonstrated. The process of T&D analysis was automated, and the time and cost required to run physical models offline was reduced or, in some cases, eliminated. Introduction Traditional electronic drilling recorders (EDRs) are third-party systems that collect rig-sensor data. Major limitations in the operator’s ability to fully leverage the potential of this data exist, including issues with rig-sensor-measurement quality and rigsite data-aggregation methods, relatively slow data-sampling rates, and limited interoperability. To this end, the operator initiated a project to use drilling data better, focusing on improving data quality by building on previous work validating rig-sensor data. Rig-Based T&D Advisory System T&D Modeling. Onshore US operators are investing heavily in unconventional horizontal plays. In these wells, excessive T&D is a critical limiting factor in exposure to productive formations. Predictive T&D computer models were developed as early as 1984. An initial model assumed that T&D are both caused by sliding friction on the wellbore, using the product of the normal force and friction coefficient to yield values for T&D. Later, the model was put in standard differential form and made to include the effects of mud pressure. These models (now termed soft-string) treat tubulars like a rope, ignoring bending moments and assuming continuous contact with the wellbore. Conversely, the stiff-string model was designed to account for borehole-assembly stiffness and radial clearances but requires more-complex numerical techniques such as finite-element analysis. Many researchers have focused efforts on increasing accuracy of the stiff-string model and decreasing the required time and computing power. Other researchers have focused on obtaining analytical solutions for T&D calculations. A major weakness of the standard T&D model is the use of the minimum-curvature method in calculating well-bore trajectory, because the bending moment is discontinuous at survey points and a smooth curved wellbore is assumed between these points. The soft-string model is used currently as the industry standard for routine T&D analysis. Accordingly, a 3D soft-string T&D model has been developed by the authors.

A Reduced Inertial Sensor System Based on MEMS for Wellbore Continuous Surveying While Horizontal Drilling

This research introduces a low cost, small size directional solution for the rotary steerable system installed directly behind the drilling bit. The proposed solution employs a reduced inertial sensor system (RISS) to provide the 3-D navigation solution for wellbore continuous surveying while horizontal drilling. The RISS consists of one micro-electromechanical systems (MEMS) gyroscope and three-axis MEMS accelerometers. The azimuth angle is obtained using a single gyro. The inclination and the toolface angle are derived from the measurements of the three-axis accelerometers together with an accurate earth gravity model. With the attitude information, velocities of the drilling bit are determined by the penetration rate of the drill bit, which is continuously available by using the information of the drill pipe length and drilling time. To limit the long-term growth of the surveying errors, a Kalman filter relying on the minimum curvature method position was developed to estimate the position errors. The proposed method is examined by conducting a drilling simulation experiment in a laboratory using the three-axis rate table. Two different MEMS systems were tested during the experiment. Results showed that the proposed technique could significantly limit the long-term growth of the position errors. The experiments were performed for almost 2 h and demonstrated no significant divergence of the RISS algorithm.

Kick-Off Point (KOP) and End of Buildup (EOB) Data Analysis in Trajectory Design

Well X is a development well which is directionally drilled. Directional drilling is choosen because the coordinate target of Well X is above the buffer zone. The directional track plan needs accurate survey calculation in order to make the righ track for directional drilling. There are many survey calculation in directional drilling such as tangential, underbalance, average angle, radius of curvature, and mercury method. Minimum curvature method is used in this directional track plan calculation. This method is used because it gives less error than other method. Kick-Off Point (KOP) and End of Buildup (EOB) analysis is done at 200 ft, 400 ft, and 600 ft depth to determine the trajectory design and optimal inclination. The hole problem is also determined in this trajectory track design. Optimal trajectory design determined at 200 ft depth because the inclination below 35º and also already reach the target quite well at 1632.28 ft TVD and 408.16 AHD. The optimal inclination at 200 ft KOP depth because the maximum inclination is 18.87º which is below 35º. Hole problem will occur if the trajectory designed at 600 ft. The problems are stuck pipe and the casing or tubing will not able to bend.

Wellbore-Trajectory Control by Use of Minimum Well-Profile-Energy Criterion for Drilling Automation

Summary When the actual well path deviates from the planned path, it is imperative for a drilling system to take corrective actions. A new trajectory-control model has been developed on the basis of a minimum well-profile-energy criterion to achieve smooth well paths. In this model, the S-shaped returning path from a deviated position to the planned wellbore trajectory is divided into two sections, each of which has its length, inclination-change rate, and azimuth-change rate. Different trajectory-calculation algorithms are used to solve the deviation-correction parameters of the two sections. Results obtained from the simple balanced tangential method, the industry-standard minimum-curvature method, and the more-accurate natural-curve method are consistent with one another. The model was tested by use of wellbore-trajectory simulations of different 2D and 3D well paths. The simulation results show that the new trajectory-control model, in comparison with proportional-integral-derivative (PID) -control and fuzzy-control methods, yields much-smoother wellbore trajectories. Consequently, the new model is promising for the reduction of torque, drag, and friction of the drillstring. Unlike PID- and fuzzy-control methods, which usually require subjective entry of several controller parameters, the new trajectory-control model provides deterministic solutions on the basis of an objective minimum-energy criterion, which represents a significant advantage for the limited computation power of downhole tools. In addition, the settings of constant inclination- and azimuth-change rates in each correction section also provide benefits, such as requiring less-frequent steering, resulting in reduced electric-power consumption and reduced abrasion failure of downhole tools.

Drillstring Analysis With a Discrete Torque/Drag Model

Summary The only standard drillstring model in use today is the torque/drag model because of its simplicity and general availability. Field experience indicates that this model generally gives good results but sometimes performs poorly. For example, some friction loads predicted for casing running in horizontal wells have not been consistent with field data. In the standard torque/drag model, the drillstring shape is taken as the wellbore shape. However, given that the most-common method for determining the wellbore shape is the minimum-curvature method, this assumed wellbore shape forces the bending moment to be discontinuous at survey points. This defect is dealt with by neglecting the bending moment. A different approach assumes that the drillstring position corresponds with the minimum-curvature wellbore only at discrete points. The obvious choice for these discrete points is at the positions of the tool joints in the drillstring. Although these tool joints are fixed in position, they are allowed to rotate within the wellbore. These extra degrees of freedom allow solution of the bending-moment problem, because continuity of bending moment can now be ensured at each tool joint. This paper gives a complete description of the drillstring calculation. Typical torque/drag problems are studied to compare the two torque/drag formulations. These studies give comparisons in drag forces and torques for the two models, and for the new formulation, the magnitude of the bending moments.

Modelling the Velocity Field in a Regular Grid in the Area of Poland on the Basis of the Velocities of European Permanent Stations

The paper presents the results of testing the various methods of permanent stations’ velocity residua interpolation in a regular grid, which constitutes a continuous model of the velocity field in the territory of Poland. Three packages of software were used in the research from the point of view of interpolation: GMT (The Generic Mapping Tools), Surfer and ArcGIS. The following methods were tested in the softwares: the Nearest Neighbor, Triangulation (TIN), Spline Interpolation, Surface, Inverse Distance to a Power, Minimum Curvature and Kriging. The presented research used the absolute velocities’ values expressed in the ITRF2005 reference frame and the intraplate velocities related to the NUVEL model of over 300 permanent reference stations of the EPN and ASG-EUPOS networks covering the area of Europe. Interpolation for the area of Poland was done using data from the whole area of Europe to make the results at the borders of the interpolation area reliable. As a result of this research, an optimum method of such data interpolation was developed. All the mentioned methods were tested for being local or global, for the possibility to compute errors of the interpolated values, for explicitness and fidelity of the interpolation functions or the smoothing mode. In the authors’ opinion, the best data interpolation method is Kriging with the linear semivariogram model run in the Surfer programme because it allows for the computation of errors in the interpolated values and it is a global method (it distorts the results in the least way). Alternately, it is acceptable to use the Minimum Curvature method. Empirical analysis of the interpolation results obtained by means of the two methods showed that the results are identical. The tests were conducted using the intraplate velocities of the European sites. Statistics in the form of computing the minimum, maximum and mean values of the interpolated North and East components of the velocity residuum were prepared for all the tested methods, and each of the resulting continuous velocity fields was visualized by means of the GMT programme. The interpolated components of the velocities and their residua are presented in the form of tables and bar diagrams.

Moving Surface Spline Interpolation Based on Green’s Function

Some commonly used interpolation algorithms are analyzed briefly in this paper. Among all of the methods, biharmonic spline interpolation, which is based on Green’s function and proposed by Sandwell, has become the mainstream method for its high precision, simplicity and flexibility. However, the minimum curvature method has two flaws. First, it suffers from undesirable oscillations between data points, which is solved by interpolation with splines in tension. Second, the computation time is approximately proportional to the cube of the number of data constraints, making the method slow for situations with dense data coverage. Focusing on the second problem, this paper introduces the moving surface spline interpolation method based on Green’s function, and the interpolation error equations are deduced. Because the proposed method only chooses the nearest data points by using the merge sort algorithm for interpolating, the computation time is greatly decreased. The optimal number of the nearest points can be determined by using the interpolation error estimation equation. No matter how many data points there are, this method can be implemented without difficulty. Examples show that the proposed method can obtain high interpolation precision and high computation speed at the same time.

A Compendium of Directional Calculations Based on the Minimum-Curvature Method—Part 2: Extension to Steering and Landing Applications

Summary The point-to-target calculations contained in Part 1 of the compendium (Sawaryn and Thorogood 2005) were restricted to those cases in which the 3D target coordinates were stated explicitly. However, another class of problems exists where the target's structural position is determined indirectly from other constraints defining the arc's orientation. This new paper builds on the earlier work and contains complete details of twelve explicit algorithms, including the calculation of a target on the basis of the toolface at the start or end of an arc and for the landing of a well path parallel to a formation bedding plane. These cases find practical application in computing trajectories of motor runs and in whipstock operations. The curvature of the trajectory landing on a bedding plane varies with direction and has a distinct minimum and maximum. These values may be used either to minimize the distance to the target or to limit the dogleg severity (DLS) to avoid drillpipe fatigue, a concern in short-radius drilling applications. The algorithms add to the compendium and are useful extensions to the engineer's computational toolkit. The paper shows that the trajectories, computed using the minimum-curvature calculation, are contained within the geometric surfaces defined by a torus or cyclide. These geometries explain why the explicit solutions exist, opening up possibilities for obtaining solutions to the more-complex cases.

Improving LWD Image and Formation Evaluation by Using Dynamically Corrected Drilling-Derived LWD Depth and Continuous Inclination and Azimuth Measurements

Summary The paper illustrates the improvements in logging while drilling (LWD) images and subsequent formation evaluation by using a new methodology for depth and survey measurements corrections. LWD depth measurements are often considered inaccurate and, therefore, not as reliable for well-to-well correlations, correlations with data acquired with wireline measurements and formation layer thickness determinations. The reasons for these inaccuracies generally originate from the traditional practice that LWD depth is purposely made equal to the driller's depth, which is a static pipe length measurement made by tape at the surface. There is almost always a difference between the actual measured depth (MD) of the LWD sensor downhole and this static pipe measurement, because downhole the drillpipe is subject to an environment that is not representative of the derrick (e.g., varying drilling mechanical conditions and temperature changes). Here, we demonstrate the applications of the method, which allows dynamic driller's depth correction for the effects of drillstring weight, downhole friction, weight on bit, thermal expansion, residual rig heave, and tide. Another significant inaccuracy source is a standard practice of calculating borehole position from stationary survey points typically taken every 90 feet (ft) using the minimum curvature method. Neglecting the complex borehole shape between survey stations can lead to a systematic error in determining the borehole position. We consider using continuous inclination and azimuth measurements along with stationary surveys to correct these errors. We provide comparisons of LWD images before and after the depth and survey corrections to illustrate how the measurement errors affect formation dips interpreted from the images. We demonstrate how improved accuracy allows filtering out the artifacts and provides more decisive and accurate identification of geologic features. We show how using the corrected 3D position improves accuracy of the formation thicknesses calculations and therefore improves the reservoir summation results. As a result, we propose a borehole 3D position measurement that is accurate, consistent between wells (regardless of rig type or bottomhole assembly [BHA] configuration), and independent of the drilling mode. Using this new measurement significantly improves the quality of the formation evaluation.