High-precision well inclination and azimuth measurement method based on multi-axis sensors

Abstract

The present invention discloses a high-precision well inclination and azimuth measurement method based on a multi-axis sensor. The method includes: Step 1: Considering the influence of the earth curvature and the earth rotation, establish a local navigation coordinate system for the downhole environment to obtain a reconstructed signal; Step 2: Based on the sensor quality of the four-axis sensor, considering the influence of the Coriolis force caused by the earth rotation, calculate the Coriolis force compensation vector; Step 3: Calculate the projection of the geomagnetic field in the local navigation coordinate system to obtain the geomagnetic field projection vector; Step 4: According to the gravity compensation value, the Coriolis force compensation vector and the geomagnetic field projection vector, combined with the reconstructed signal, calculate the corrected well inclination angle and the corrected azimuth angle. The present invention significantly improves the accuracy of well inclination and azimuth measurement.

Description

Technical Field

[0001] The present invention relates to the field of measurement technology, and particularly to a high-precision well inclination and azimuth measurement method based on a multi-axis sensor. Background Art

[0002] The accurate measurement of well inclination and azimuth is a crucial technical link in oil and gas drilling, mineral extraction, and geological engineering. In the complex downhole environment, accurately obtaining the spatial attitude information of the wellbore (i.e., well inclination angle and azimuth angle) not only helps to ensure the stability and safety of the wellbore trajectory but also directly affects the efficiency and cost of resource extraction. Although the existing technology has made certain progress in the field of well inclination and azimuth measurement, there are still many technical bottlenecks and application difficulties in deep wells, highly deviated wells, and complex geological conditions, resulting in the accuracy and reliability of the measurement results being difficult to meet the high-standard engineering requirements.

[0003] Inertial sensors (such as accelerometers and gyroscopes) are one of the basic devices for well inclination and azimuth measurement. The accelerometer calculates the well inclination angle by measuring the components of the gravitational acceleration, while the gyroscope calculates the azimuth angle through the integration of the angular velocity. The technology based on inertial sensors has the advantages of strong real-time performance and no need for external references, especially in the downhole environment where radio signals cannot cover, it has become a common solution. However, inertial sensors have the following problems: the drift error of the gyroscope will accumulate over time, resulting in the measurement result deviating from the true value. Especially in deep well operations, this cumulative drift may reach an unacceptable level. The accelerometer is easily affected by dynamic interference under vibration, shock, or rapid movement conditions, resulting in measurement deviation of the gravitational direction, thus affecting the calculation accuracy of the well inclination angle. Under the conditions of deep wells or highly deviated wells, due to the influence of the earth's curvature and the change of the geomagnetic field, the measurement method relying solely on inertial sensors often fails to accurately reflect the true attitude of the wellbore.

[0004] The magnetometer calculates the azimuth angle of the wellbore by measuring the direction and intensity of the geomagnetic field. This method is relatively simple and has low requirements for power consumption and volume. However, the magnetometer is affected in the downhole environment as follows: due to the complexity of geological conditions (such as iron ore layers, metal pipelines, etc.), the geomagnetic field may show significant anomalies locally, resulting in the magnetometer measurement value deviating from the true value. Under the condition of rapid rotation or vibration of the sensor, the direction measurement of the magnetometer is easily affected by error interference, resulting in unstable calculation results of the azimuth angle. The intensity of the geomagnetic field changes with depth and latitude, and these factors have not been fully considered in the existing technology for their impact on the measurement accuracy. Summary of the Invention

[0005] The object of the present invention is to provide a high-precision well inclination and azimuth measurement method based on multi-axis sensors, which integrates the data of accelerometers, gyroscopes, magnetometers and velocimeters, and realizes high-precision attitude measurement in the complex downhole environment through technologies such as constructing a local navigation coordinate system, signal reconstruction, Coriolis force compensation, geomagnetic field projection correction and gravity anomaly compensation. The present invention significantly improves the accuracy of well inclination and azimuth measurement, effectively solves the error problems caused by the earth curvature, rotation effect, geomagnetic field anomaly and gravity field change in the traditional method, and provides a reliable guarantee for high-precision measurement in deep wells, highly deviated wells and complex geological conditions.

[0006] To solve the above technical problems, the present invention provides a high-precision well inclination and azimuth measurement method based on multi-axis sensors, and the method includes:

[0007] Step 1: Considering the influence of the earth curvature and the earth rotation, establish a local navigation coordinate system for the downhole environment; under the local navigation coordinate system, perform signal reconstruction on the measurement signals of the four-axis sensor to obtain the reconstructed signals;

[0008] Step 2: Based on the sensor mass of the four-axis sensor, the three-dimensional velocity components measured by the four-axis sensor and the geographical coordinate position of the four-axis sensor, considering the influence of the Coriolis force caused by the earth rotation, calculate the Coriolis force compensation vector;

[0009] Step 3: Calculate the projection of the geomagnetic field in the local navigation coordinate system to obtain the geomagnetic field projection vector; considering the influence of gravity, combine the geological density and the formation density in the downhole environment to calculate the gravity compensation value;

[0010] Step 4: According to the gravity compensation value, the Coriolis force compensation vector and the geomagnetic field projection vector, combine with the reconstructed signals to calculate the corrected well inclination angle and the corrected azimuth angle.

[0011] Furthermore, the four-axis sensor includes: a gyroscope, a magnetometer, a three-axis velocimeter and a three-axis accelerometer.

[0012] Furthermore, the local navigation coordinate system in Step 1 is represented by the following formula:

[0013] ;

[0014] wherein, is the average radius of the earth, with a value of 6371 km; is the height of the downhole measurement point where the four-axis sensor is located from the earth center; is the geographical latitude of the downhole measurement point where the four-axis sensor is located; is the geographical longitude of the downhole measurement point where the four-axis sensor is located; is the angular velocity of the earth rotation, with a value of , with the unit of rad / s; is the speed of light; is the eccentricity of the Earth, with a value of 0.0818191908426.

[0015] Furthermore, in step 1, the measurement signals of the four-axis sensor are signal-reconstructed in the local navigation coordinate system through the following formula to obtain the reconstructed signal :

[0016] ;

[0017] where is the X-axis acceleration component of the three-axis accelerometer; is the Y-axis acceleration component of the three-axis accelerometer; is the Z-axis acceleration component of the three-axis accelerometer; is the X-axis angular velocity component of the gyroscope; is the Y-axis angular velocity component of the gyroscope; is the initial well inclination angle,

[0018] ;

[0019] is the Earth's gravitational constant; is the geomagnetic field intensity of the magnetometer; is the initial direction angle,

[0020] ;

[0021] is the X-axis geomagnetic field intensity component of the magnetometer; is the Y-axis geomagnetic field intensity component of the magnetometer; represents the modulus operation of a vector; is the standard geomagnetic field intensity, with a value of 49.6, and the unit is microtesla; is the atmospheric scale height, with a value of 7.4 kilometers.

[0022] Furthermore, in step 2, the Coriolis force compensation vector is calculated through the following formula :

[0023] ;

[0024] where is the mass of the four-axis sensor; is the X-axis velocity component of the three-axis velocimeter; is the Y-axis velocity component of the three-axis velocimeter; is the Z-axis velocity component of the three-axis velocimeter.

[0025] Further, in step 3, the projection of the geomagnetic field in the local navigation coordinate system is calculated by the following formula :

[0026] ;

[0027] wherein is the geomagnetic dip angle; is the geomagnetic declination; is the geomagnetic field attenuation coefficient, with a value of 640; is the temperature coefficient, with a value of 0.0033; is the current temperature; is the standard temperature, with a value of 20 degrees Celsius.

[0028] Further, in step 3, the gravity compensation value is calculated by the following formula :

[0029] ;

[0030] wherein is the earth shape coefficient, with a value of 0.00108263; is the integer subscript index, with an upper limit of 4, to simplify the continuous density distribution of the earth's strata into a 4-layer stratified model, representing the crust, mantle, outer core, and inner core respectively; is the geological average density at the bottom of the th layer, which is a set value; is the standard formation density, with a value of 2.67, in the unit of .

[0031] Further, in step 3, the corrected well inclination angle is calculated by the following formula:

[0032] ;

[0033] wherein is the corrected well inclination angle.

[0034] Further, in step 3, the corrected azimuth angle is calculated by the following formula:

[0035] ;

[0036] wherein is the corrected azimuth angle.

[0037] The high-precision well inclination and azimuth measurement method based on a multi-axis sensor of the present invention has the following beneficial effects:

[0038] The present invention significantly improves the accuracy of well deviation and azimuth measurement. Traditional measurement methods usually rely on a single sensor, such as an accelerometer or a magnetometer. Although this method is simple, it is difficult to ensure sufficient accuracy in a complex downhole environment. Downhole operations are affected by multiple factors, including the earth's rotation, geomagnetic anomalies, and changes in the gravity field distribution. The existing technologies have not fully addressed these problems, resulting in the accumulation of measurement errors. The present invention fundamentally improves the measurement accuracy by adopting a multi-axis sensor fusion technology, including accelerometers, gyroscopes, magnetometers, and velocimeters, and combining signal reconstruction of multi-dimensional data, earth curvature correction, gravity anomaly compensation, and geomagnetic projection correction. For example, the data fusion of the gyroscope and the accelerometer can dynamically adjust the drift error in attitude measurement, and the data linkage of the magnetometer and the velocimeter makes the calculation of the azimuth angle more consistent with the true geomagnetic field direction. Through the dynamic correction of the data of each sensor and the optimization of the physical model, the present invention can provide more stable and reliable well deviation and azimuth data under complex working conditions such as deep wells and highly deviated wells.

[0039] Secondly, the present invention demonstrates excellent adaptability in various complex geological and dynamic environments. The downhole environment is complex and variable, and the interference of different latitudes, depths, and geological structures on measurement is significantly different. Traditional methods are difficult to adapt to this dynamic change in real time, and measurement errors accumulate, which may ultimately lead to inaccurate wellbore trajectory control. The present invention constructs a local navigation coordinate system to map the earth's curvature, rotation effect, and geomagnetic field distribution into the same reference system, thereby ensuring that the data collected by the sensors has a unified reference standard at any geographical location, well depth, or inclination angle.

[0040] In addition, the present invention introduces a dynamic compensation mechanism. By modeling and correcting the real-time changes in the gravity field and the geomagnetic field, it can quickly adjust the measurement results when the environmental parameters fluctuate. For example, in a geomagnetic anomaly area or a high-latitude area, the present invention can avoid the interference of magnetic anomalies on azimuth measurement by dynamically correcting the intensity and direction of the geomagnetic field. Another example is that under deep well conditions, due to the gravity anomaly caused by the change in crust density, the present invention significantly reduces the influence of gravity anomaly on the calculation of the well deviation angle through the application of a formation density stratification model. BRIEF DESCRIPTION OF THE DRAWINGS

[0041] In order to more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the drawings required for the description of the embodiments or the prior art. Obviously, the drawings in the following description are only the embodiments of the present invention. For those of ordinary skill in the art, other drawings can be obtained according to the provided drawings without creative efforts.

[0042] Figure 1 It is a schematic flow chart of a high-precision well deviation and azimuth measurement method based on multi-axis sensors provided by an embodiment of the present invention. Detailed implementation manners

[0043] To make the objectives, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are some, but not all, of the embodiments of the present invention. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.

[0044] Example 1. Refer to Figure 1 : A high-precision well deviation and azimuth measurement method based on a multi-axis sensor, the method comprising:

[0045] Step 1: Considering the influence of the earth curvature and the earth rotation, establish a local navigation coordinate system for the downhole environment; under the local navigation coordinate system, perform signal reconstruction on the measurement signals of the four-axis sensor to obtain reconstructed signals;

[0046] The core of Step 1 is to consider the influence of the Earth's curvature and rotation on measurement accuracy, construct a local navigation coordinate system suitable for the complex downhole environment, and reconstruct the measurement signals of the four-axis sensor in this coordinate system. The four-axis sensor includes a gyroscope, a magnetometer, a velocimeter, and a three-axis accelerometer. These sensors work together to comprehensively capture the dynamic changes and spatial characteristics of the downhole environment. To ensure high-precision well inclination and azimuth measurement, it is necessary to fully combine the physical characteristics of the Earth with sensor signal processing technology, establish a coordinate reference suitable for the downhole environment, and correct the errors in the sensor data. The construction of the local navigation coordinate system is the basis of this step. The ellipsoidal shape of the Earth, the centrifugal force caused by the Earth's rotation, and the geological distribution characteristics downhole make the sensors vulnerable to error interference when collecting data. To eliminate these interferences, the present invention first starts from the Earth's reference system and maps its position to the local navigation coordinate system according to the geographical location of the sensor (including longitude, latitude, and depth). The construction process of this coordinate system fully considers the geometric shape changes brought about by the Earth's curvature and the influence of the Earth's rotation on inertial forces, and corrects these factors through a mathematical model to ensure that the finally constructed coordinate system can truly reflect the physical state of the downhole environment. In this coordinate system, clear reference directions are set: the X-axis is eastward, the Y-axis is northward, and the Z-axis is vertically upward (the opposite direction of the gravity direction), ensuring that subsequent signal processing and measurement results have a unified reference standard. After the local navigation coordinate system is constructed, the present invention reconstructs the signals of the four-axis sensor. The gyroscope is responsible for measuring the angular velocity of the sensor in three-dimensional space, providing key data for the dynamic attitude change of the sensor; the magnetometer measures the direction and intensity of the geomagnetic field, which is an important basis for calculating the azimuth angle; the velocimeter captures the motion speed components of the sensor in three-dimensional space, providing basic information for describing dynamic motion; the three-axis accelerometer measures the gravitational acceleration and linear acceleration components, which are used to calculate the inclination angle and the gravity direction. However, the measurement data of a single sensor are often affected by environmental vibration, noise, and dynamic changes. Directly using the original signals may lead to significant errors. Therefore, the present invention fuses the data of the four-axis sensor through signal reconstruction to improve the reliability and accuracy of the signals. The key to signal reconstruction lies in unifying the measurement data of all sensors into the local navigation coordinate system and processing the mutual correlation between different data components through a mathematical model. First, the data of the three-axis accelerometer and the velocimeter are used to identify the dynamic motion state of the sensor, and combined with the angular velocity data of the gyroscope, the non-inertial components caused by acceleration are compensated to obtain accurate gravity direction information. At the same time, the data of the magnetometer are used to correct the attitude direction of the sensor to eliminate the influence of the changes in the geomagnetic field under different latitudes and geological conditions. Through these processing steps, the reconstructed signals can comprehensively reflect the physical state of the downhole environment, such as the true acceleration direction, gravity direction, and geomagnetic field direction.During the signal reconstruction process, the present invention also makes full use of the complementary characteristics of multi-sensor data. For example, a gyroscope can capture the dynamic rotational changes of a sensor, but its measured values are prone to drift over a long period of time. The geomagnetic field direction information provided by a magnetometer can correct this drift, thereby ensuring the accuracy of azimuth calculation. On the other hand, the gravity components measured by a triaxial accelerometer may be affected by vibrations or abnormal underground geological densities. At this time, the dynamic data of a velocimeter can provide additional correction basis. Through the mutual complementation and fusion of these multi-sensor data, the reconstructed signal not only eliminates the deficiencies of single-sensor measurements but also enhances the robustness and accuracy of the overall measurement.

[0047] Step 2: Based on the sensor mass of the four-axis sensor, the three-dimensional velocity components measured by the four-axis sensor, and the geographical coordinate position of the four-axis sensor, considering the influence of the Coriolis force caused by the Earth's rotation, calculate the Coriolis force compensation vector;

[0048] Due to the particularity of the underground environment, the measurement system is not only affected by the complex underground geological conditions but also needs to cope with the inertial force interference exerted by the Earth's rotation on moving objects. The Coriolis force is a pseudo force caused by the Earth's rotation, and its essence is an inertial effect generated by the interaction between the Earth's rotation and the relative motion of an object. The influence produced by this force on the Earth's surface varies with changes in geographical location and the speed of the object. Especially in underground operations, since the equipment and sensors are in a narrow and restricted space, the action of the Coriolis force may significantly change the speed and direction information measured by the sensors, resulting in deviations in well inclination and azimuth measurements. Therefore, effective compensation for the Coriolis force is the key to ensuring the accuracy of measurement results. The calculation of the Coriolis force requires combining multiple dynamic factors, including the mass of the four-axis sensor itself, its speed, and the underground geographical location. First, the mass of the sensor determines the magnitude of the Coriolis force because, according to physical principles, force is proportional to mass. In the present invention, the mass of the sensor is known, and by combining its real-time measured velocity components, the Coriolis force received by the sensor in the Earth's rotation inertial system can be deduced. The three-dimensional components of the velocity are measured by a velocimeter and include the horizontal component and the vertical component along the underground channel direction. These components not only describe the motion state of the sensor but also have a clear physical relationship with the Earth's angular velocity of rotation. The Earth's angular velocity of rotation is a known constant, but its contribution to the Coriolis force varies at different geographical latitudes because objects on the Earth's surface experience different linear velocities of rotation with changes in latitude. Especially in the underground environment, the increase in depth may also indirectly affect the distribution of velocity components, so it is necessary to further consider the specific underground location (i.e., longitude, latitude, and depth) to comprehensively consider the effect of the Coriolis force.

[0049] When calculating the Coriolis force compensation vector, the present invention converts the effect of the Earth's rotation into a vector form that can be directly analyzed and compensated by establishing a local navigation coordinate system. In this way, the direction and magnitude of the Coriolis force can be clearly described in the local coordinate system. Specifically, the direction of the Coriolis force is closely related to the velocity components of the object and the Earth's axis of rotation. In the local navigation coordinate system, the Earth's axis of rotation is usually decomposed into components parallel to the local horizontal plane and the vertical direction. Thus, through the velocity data provided by the velocimeter, the Coriolis force vector components in each direction under the influence of the Earth's rotation can be calculated. This calculation method ensures the adaptability of the compensation process in a dynamic environment. Regardless of whether the sensor is in an accelerating, decelerating, or steady motion state, the compensation vector can be adjusted in a timely manner. The introduction of the compensation vector is to solve the interference of the Coriolis force on the measurement results of the four-axis sensor. Without compensation, the Coriolis force may cause systematic errors in the velocity measurement of the sensor, thereby affecting the calculation of the well deviation angle and azimuth angle. For example, if a sensor moves at high speed along a downhole channel, the Coriolis force caused by the Earth's rotation will cause its measurement results to deviate, and this deviation cannot be corrected by simple static calibration. Through the introduction of the compensation vector, the present invention can not only eliminate this dynamic error but also ensure the reliability of the sensor in a complex environment. The Coriolis force compensation vector is a dynamically adjusted process, and its magnitude and direction are updated in real time as the motion state of the sensor changes. This dynamic adjustment depends on the real-time acquisition of sensor data and the accuracy of the local navigation coordinate system, ensuring the effectiveness and real-time nature of the compensation. In addition, the implementation of Coriolis force compensation also involves the isolation of other interference factors. For example, gravity anomalies caused by geological conditions may have additional effects on the velocity and direction measurements of the sensor, which requires combination with gravity compensation to ensure the independence and accuracy of Coriolis force compensation. At the same time, the directional and intensity changes of the geomagnetic field may also interfere with the compensation process. Therefore, the present invention further corrects the direction of the Coriolis force compensation vector through the data of the magnetometer to make it more consistent with the actual environment.

[0050] Step 3: Calculate the projection of the geomagnetic field in the local navigation coordinate system to obtain the geomagnetic field projection vector; considering the influence of gravity, combine the geological density and formation density in the downhole environment to calculate the gravity compensation value;

[0051] This process calculates the projection vector of the geomagnetic field in the local navigation coordinate system, and combines the geological density and formation density of the downhole environment to calculate the gravity compensation value, thereby providing a more accurate physical basis for the subsequent calculation of the well inclination angle and azimuth angle. The geomagnetic field and the gravity field are two key factors affecting the measurement accuracy of well inclination and azimuth. Their distributions are not only related to the natural characteristics of the Earth, but also significantly affected by the special downhole environment. Therefore, the projection and compensation of the geomagnetic field and the gravity field are necessary means to ensure high-precision measurement results. First, the distribution and projection of the geomagnetic field are a key point in this step. On the Earth's surface, the geomagnetic field can be regarded as a vector field, and its direction and intensity vary with different geographical locations. The geomagnetic field in the downhole environment is not only affected by the Earth's core magnetic field, but may also be disturbed by local geological structures. Therefore, in order to ensure the accuracy of the measurement, the present invention uses a magnetometer in a four-axis sensor to collect the component data of the geomagnetic field in real time. These component data include the three-direction projections of the geomagnetic field in space, and the vector direction of the geomagnetic field can be accurately determined through these data. In the local navigation coordinate system, the vector of the geomagnetic field is decomposed into horizontal and vertical components, and this decomposition method can more clearly describe the contribution of the geomagnetic field to azimuth measurement. For example, the horizontal component of the geomagnetic field is mainly used to determine the azimuth angle of the sensor, while the vertical component is related to the measurement of the well inclination angle.

[0052] The calculation of the geomagnetic field projection vector depends not only on the data from magnetometers but also requires the combination of reference directions in the local navigation coordinate system. In the present invention, by defining the standard direction of the geomagnetic field (i.e., the direction of the geomagnetic field under ideal conditions) in the navigation coordinate system and projecting the measured actual geomagnetic field vector onto this standard direction, a corrected geomagnetic field vector is obtained. This correction process takes into account the perturbation effects of the local geomagnetic field, such as geomagnetic field distortion caused by underground geological anomalies or interference from metal structures. By using the corrected geomagnetic field projection vector, the accuracy of azimuth angle calculation can be significantly improved. On the other hand, the compensation of the gravitational field is another core aspect of this step. The gravitational field in the underground environment is affected by various factors, including the characteristics of the Earth's gravitational distribution and changes in local geological density. The Earth's gravitational distribution is not completely uniform but is jointly influenced by the shape of the Earth, geological strata, and differences in crust density. In the present invention, the accelerometer and gravitometer in the four-axis sensor are used to measure the intensity and direction of the gravitational field in real time. However, these measurement results may deviate due to changes in underground geological density, so precise compensation of the gravitational field is required. To calculate the gravitational compensation value, the present invention combines the geological density and underlying density information of the underground environment. Geological density is a physical parameter that describes the density of materials in different geological strata, while underlying density is used to represent the density distribution characteristics at deeper levels underground. These density parameters are usually obtained through underground geological surveys or historical data and are used as the basis for gravitational compensation calculations. In the compensation calculation, the distribution of geological density is processed in layers, and the contribution of the density of each layer to the total gravitational field is calculated by weighted accumulation. This calculation method fully considers the density differences between different geological strata and their local effects on the gravitational field, thus accurately describing the actual distribution of the underground gravitational field. The calculation of the gravitational compensation value is ultimately used to correct the direction and intensity of the gravity measured by the sensor. Without compensation, gravitational anomalies may cause deviations in the measurement results of the well deviation angle, especially in areas with large differences in crust density, and this deviation may accumulate into significant measurement errors. By introducing the gravitational compensation value, the present invention can effectively eliminate this error and ensure that the measurement results are closer to the actual underground physical state.

[0053] Step 4: Calculate the corrected well deviation angle and corrected azimuth angle based on the gravitational compensation value, Coriolis force compensation vector, and geomagnetic field projection vector, in combination with the reconstructed signal.

[0054] Specifically, the calculation of the well deviation angle and azimuth angle relies on the data of multi-axis sensors. After being processed in the previous steps, most of the interferences caused by the earth's rotation, the earth's curvature, local geomagnetic anomalies, and gravity anomalies have been removed. However, even after compensation, the original signals of the sensors still contain certain non-linear errors. Especially in the case of dynamic motion, the data inconsistency between sensors will lead to unstable measurement results. Therefore, in step 4 of the present invention, a correction algorithm based on multi-axis fusion is introduced, taking the gravity compensation value, the Coriolis force compensation vector, and the geomagnetic field projection vector as key correction factors, and fusing them with the signal reconstruction result to ensure that the calculation process of the well deviation angle and azimuth angle can reflect the dynamic changes of the downhole environment in real time. First, the calculation of the well deviation angle is based on the direction of gravity. The well deviation angle is the angle between the sensor axis and the direction of gravity. Therefore, the data of the accelerometer and the gravimeter play a core role in this process. The sensor data after signal reconstruction provides a corrected three-dimensional acceleration vector, which has eliminated the influence of dynamic acceleration and environmental noise. On this basis, the gravity compensation value is used to further correct the interference of downhole gravity anomalies on the measurement result. By performing an inner product operation on the reconstructed acceleration vector and the corrected gravity direction vector, the cosine value of the well deviation angle can be accurately calculated, and then the well deviation angle can be deduced. It should be noted that due to the dynamics of the downhole environment, the calculation of the well deviation angle requires real-time adjustment of the sensor's attitude parameters to adapt to the external disturbances that change over time. Therefore, the Coriolis force compensation vector is introduced at this stage to correct the inertial interference caused by the earth's rotation. Although this interference is weak on the surface, it will be amplified in the case of a large downhole depth. Therefore, the compensation process is a necessary means to ensure the accuracy of the well deviation angle. The calculation of the azimuth angle is based on the geomagnetic field. The horizontal component of the geomagnetic field is the main reference direction for the azimuth angle. The geomagnetic field vector measured by the magnetometer is projected into a horizontal component and a vertical component in the local navigation coordinate system. After being compensated in the previous steps, the direction information of the geomagnetic field has been corrected. However, to achieve high-precision azimuth angle calculation, it is still necessary to fuse the geomagnetic field vector with other sensor data. In the present invention, the horizontal projection direction of the geomagnetic field is defined as the reference direction, and the angle between the actual geomagnetic field vector measured by the magnetometer and this reference direction is the azimuth angle. To further improve the accuracy, the Coriolis force compensation vector and the signal reconstruction data play a role again here. The Coriolis force compensation vector is used to correct the magnetic field direction offset caused by inertial changes during the dynamic motion of the sensor, and the signal reconstruction data provides a dynamically consistent reference frame to ensure the consistency of data fusion between the magnetometer and other sensors.

[0055] Embodiment 2: The four-axis sensor includes: a gyroscope, a magnetometer, a three-axis velocimeter, and a three-axis accelerometer.

[0056] Specifically, the gyroscope is one of the core components in the four-axis sensor system. It is responsible for measuring the angular velocity changes of the sensor in three-dimensional space. Since downhole equipment often rotates or shifts under complex geological conditions, the gyroscope can provide dynamic attitude information by capturing the angular velocity in real time. This data is crucial for the calculation of well inclination and azimuth because the angular velocity can reflect the rotation state of the sensor relative to the reference direction. In the present invention, the data of the gyroscope works in cooperation with the data of the magnetometer to correct the attitude drift problem in a dynamic environment. By fusing the angular velocity data of the gyroscope, the system can dynamically adjust the attitude calculation model, enabling the measurement results to remain highly accurate in the complex downhole environment. The magnetometer, as another important part of the four-axis sensor, is mainly used to measure the direction and intensity of the geomagnetic field. This data is the basis for azimuth calculation because the projection of the geomagnetic field on the horizontal plane directly indicates the direction of the sensor relative to the geomagnetic north. However, the geomagnetic field is not evenly distributed, especially in the downhole environment, where it may be disturbed by geological structures or metal materials, resulting in magnetic field anomalies. The present invention corrects these anomalies by collecting data with the magnetometer and combining signal reconstruction and compensation algorithms, making the measured value of the geomagnetic field closer to the true value. In addition, the data of the magnetometer is combined with the angular velocity data of the gyroscope to solve the direction error that may occur during the dynamic movement of the sensor, thus significantly improving the calculation accuracy of the azimuth.

[0057] The triaxial accelerometer is a component in the four-axis sensor responsible for measuring the linear velocity components. It can capture in real time the movement velocity of the sensor in the three-dimensional downhole space, including the horizontal and vertical components along the downhole passage. These velocity data are not only used to describe the movement state of the sensor but also play a crucial role in Coriolis force compensation. Due to the Earth's rotation imposing a Coriolis force on moving objects, the interaction between the velocity components and the Earth's angular velocity significantly affects the measurement accuracy. In the present invention, the real-time velocity data provided by the triaxial accelerometer are used to calculate the Coriolis force compensation vector, thereby eliminating the interference of the Earth's rotation on the calculation of the well inclination angle and azimuth angle. In addition, the data of the accelerometer combined with the data of the velocimeter can be used to detect the acceleration or deceleration state of the sensor, thus providing richer information for dynamic correction. The triaxial accelerometer is a component used to measure the linear acceleration and gravitational acceleration received by the sensor. In the downhole environment, the data of the accelerometer are the core input for well inclination angle calculation because the direction of the gravitational acceleration defines the direction of the reference gravitational field. By measuring the three-dimensional acceleration components, the accelerometer can determine the angle between the sensor and the direction of gravity, and then deduce the well inclination angle. However, the accelerometer may be interfered by linear acceleration and environmental vibration during dynamic movement, and these interferences may cause errors in the measurement of the direction of gravity. The present invention eliminates the influence of dynamic acceleration by introducing signal reconstruction and compensation algorithms to fuse the data of the accelerometer with the data of the gravimeter and velocimeter. In addition, the data of the accelerometer can also be used in combination with the data of the gyroscope and magnetometer to further correct the attitude drift problem of the sensor, making the calculation result of the well inclination angle more stable and reliable.

[0058] Example 3: The local navigation coordinate system in Step 1 It is represented by the following formula:

[0059] ;

[0060] Wherein, is the average radius of the Earth, with a value of 6371 km; is the height of the downhole measurement point where the four-axis sensor is located from the center of the Earth; is the geographical latitude of the downhole measurement point where the four-axis sensor is located; is the geographical longitude of the downhole measurement point where the four-axis sensor is located; is the angular velocity of the Earth's rotation, with a value of , in the unit of rad / s; is the speed of light; is the eccentricity of the Earth, with a value of 0.0818191908426.

[0061] Specifically, in practical applications, the downhole measurement points are often hundreds or even thousands of meters below the surface. This parameter usually appears as a negative value, but its physical meaning is still the outward (or inward) distance from the earth's center to the location of the sensor. Due to the average radius of the earth being 6371 km, if we ignore the few kilometers or a few hundred meters of depth from the surface to the underground, traditional methods often do not consider the tiny curvature deviation. However, for the high-precision well inclination and azimuth measurement pursued by the present invention, even a change of several kilometers may accumulate a non-negligible coordinate offset. When and are determined, the position vector formed by these three-dimensional components can not only reflect the true spatial coordinates of the sensor in the east-west, north-south, and vertical directions, but also correct the difference between the polar radius and the equatorial radius through the ellipsoid parameter , thus better conforming to the actual geometric shape of the earth. This means that when conducting underground measurements in high-latitude or low-latitude regions, the obtained coordinate deviation can be reduced to an extremely low level, significantly better than the traditional method of simply considering the earth as a regular sphere. As for the part at the end of the formula, it is mainly used to perform exponential correction on the inertial effect caused by the earth's rotation. The earth's angular velocity is not large in value, but the centrifugal force accumulated during long-term measurement activities will affect the positioning accuracy in all directions, especially in scenarios where the underground sensor needs to maintain high attitude stability or move long distances in the wellbore. This exponential correction can be understood as a "relativistic" level of fine-tuning: under strict accuracy requirements, using to reflect the latitude difference, so that the centrifugal force correction at different latitudes is no longer simply unified but varies with latitude; at the same time, introducing the factor of to characterize the effect of the light speed magnitude, so as to ensure that even a tiny drift can be identified and compensated in time. Compared with those systems that only consider relativistic factors in high-precision satellite navigation or astrometry, the present invention brings such corrections into the field of underground measurement earlier, greatly improving the adaptability of the coordinate system to the actual rotation environment, and thus reducing the additional correction steps required in subsequent well inclination and azimuth calculations.

[0062] On the other hand, the construction of this local navigation coordinate system also corresponds to the data fusion strategy of multi-axis sensors. Since the four-axis sensor includes a gyroscope, a magnetometer, a three-axis speedometer, and a three-axis accelerometer, the data collected by each sensor underground needs to be projected onto the same reference system for fusion and compensation. If such a coordinate framework that fully considers the geophysical characteristics of the earth is not established first, then subsequent Coriolis force compensation, geomagnetic field projection, and gravity field anomaly correction may lack a unified alignment benchmark. It is also because of , , , and Only by incorporating key earth parameters such as the position vector into the expression method, the present invention can compensate for the errors caused by these parameters in a hierarchical and phased manner in the subsequent steps. For example, the Coriolis force compensation will be more obvious in higher latitudes. If it is not considered in advance in the coordinate system Even if the compensation algorithm itself is sophisticated, it cannot fundamentally avoid the system deviation caused by improper selection of coordinate system. This part specifically reflects the degree of contraction of the earth in the pole direction, so that when the sensor is close to the pole or is more north (south) relative to the equator, the difference in longitudinal radius can be fully incorporated into the calculation formula of the position vector. For well inclination and azimuth measurement, longitudinal error often directly affects the assessment of well inclination angle or relative formation distribution. If the influence of the earth's eccentricity is ignored, it is particularly easy to cause inaccurate inclination azimuth estimation in deep well scenarios. The formula of the present invention is written in explicit form as and This combination is designed to take into account the Earth's ellipsoidal parameters in both horizontal and vertical directions, thereby providing relatively consistent measurement accuracy in various geographical environments between the poles and the equator.

[0063] Embodiment 4: In step 1, the measurement signal of the four-axis sensor is reconstructed in the local navigation coordinate system by the following formula to obtain the reconstructed signal :

[0064] ;

[0065] in, is the X-axis acceleration component of the three-axis accelerometer; is the Y-axis acceleration component of the three-axis accelerometer; is the Z-axis acceleration component of the three-axis accelerometer; is the X-axis angular velocity component of the gyroscope; is the Y-axis angular velocity component of the gyroscope; is the initial well inclination angle,

[0066] ;

[0067] is the Earth's gravitational constant; is the geomagnetic field strength of the magnetometer; is the initial direction angle,

[0068] ;

[0069] is the X-axis geomagnetic field intensity component of the magnetometer; is the Y-axis geomagnetic field intensity component of the magnetometer; Represents the operation of the vector modulus length; is the standard intensity of the geomagnetic field, with a value of 49.6 and the unit of microtesla; is the atmospheric scale height, with a value of 7.4 kilometers.

[0070] Specifically, in this formula, respectively represent the acceleration components of the triaxial accelerometer. These acceleration data contain both the linear acceleration of the sensor during dynamic motion and the information in the direction of gravity. However, due to the often complex geological and mechanical vibrations in the underground environment, if only relying on the accelerometer data itself to estimate the well inclination, significant errors will be faced. In the present invention, by multiplying by and multiplying by and other methods, the angular velocity components of the accelerometer and the gyroscope are coupled together, enabling the sensor to rely on the gyroscope data to correct the real-time changes of the accelerometer when the sensor rotates rapidly or the attitude changes suddenly. And when the sensor tends to be stable, it can also correct the cumulative drift of the gyroscope through the gravity information provided by the accelerometer. In particular, is defined as the initial well inclination angle, which is given by , meaning that when the sensor is first placed or recalibrated, the included angle with the vertical direction of the ground can be obtained through the static acceleration components, thus providing a reference value for subsequent dynamic compensation; similarly, the initial direction angle in the azimuth can be obtained by , which also benefits from the measurement of the projection component of the geomagnetic field on the horizontal plane by the magnetometer and the coordinate unification through the local navigation coordinate system constructed in the previous steps of the present invention, avoiding the problem of inconsistent coordinates during the three-dimensional space attitude transformation of the device.

[0071] Meanwhile, the appearing in the formula reflects the idea of combining the earth's gravitational constant with the radius of the current measurement point, which enables the slight changes in the gravity magnitude to be taken into account when the sensor is at different depths or latitudes and longitudes, and is of great significance for the well inclination angle measurement with extremely high precision requirements. If the term is not introduced, significant measurement deviations may occur during deep well operations or under extreme geological conditions. And further projects this coupling relationship between gravity and position onto the unit direction vector, enabling the gravity vector and the position vector to be understood and used on the same reference scale, and further leaving room for the scale adjustment and compensation factor behind this formula. It should be noted that the role of this ratio in the formula is to compare the measured local geomagnetic field intensity of the sensor with the geomagnetic standard intensity By comparison, regional anomalies of the geomagnetic field or magnetic field differences in different regions of the world can be normalized, ensuring relatively unified quantitative correction of sensor data in both weak and strong geomagnetic areas. Since the geomagnetic field may be disturbed by rock formations or metallic substances on the surface and underground, this normalization is of considerable value for azimuth correction. Without normalization, systematic deviations are often introduced in azimuth calculations. And this exponential decay factor, from the perspective of the atmospheric scale height simulates the field strength decay characteristics caused by changes in depth or height. When the sensor is far from the surface, various atmospheric or near-surface effects gradually weaken. For example, the effects of electromagnetic wave refraction and temperature gradient changes on the equipment also change accordingly. With the help of this decay factor, these interferences can be approximately processed at the mathematical level, making the reconstructed signal closer to the actual downhole conditions and reducing measurement fluctuations caused by changes in environmental parameters. It is precisely because this formula internally couples the accelerometer, gyroscope, and geomagnetic field data one by one and superimposes multiple corrections of the gravitational constant and environmental attenuation that the finally obtained becomes a comprehensive reconstructed signal, laying a key digital foundation for the high-precision well inclination and azimuth measurement of the present invention. In subsequent steps, when the system needs to calculate the well inclination angle and azimuth angle, it can directly use in combination with other compensation terms (such as Coriolis force compensation, geomagnetic field projection correction, or geological density correction), greatly simplifying the data processing flow and enabling each sensor channel to be synchronously incorporated into the same algorithm framework. In this way, any measurement errors generated by individual sensors will also be offset or weakened during the integration into , ultimately achieving higher measurement accuracy than traditional single sensors or simple data splicing. Especially in deep wells, deviated wells, or high-temperature and high-pressure wells, real-time acquisition of accurate well inclination and azimuth angles is of crucial significance for drilling trajectory control.

[0072] Example 5: In step 2, the Coriolis force compensation vector is calculated through the following formula :

[0073] ;

[0074] wherein is the mass of the four-axis sensor; is the X-axis velocity component of the three-axis accelerometer; is the Y-axis velocity component of the three-axis accelerometer; is the Z-axis velocity component of the three-axis accelerometer.

[0075] Specifically, due to the Earth's rotation, an inertial force, i.e., the Coriolis force, is exerted on moving objects. If not considered, it often causes systematic deviations in the calculation of velocity and attitude in the downhole environment. Therefore, the present invention obtains the velocity components of the sensor in the X, Y, and Z directions through a triaxial velocimeter, and combines the mass of the sensor , the angular velocity of the Earth's rotation , and the geographical location of the measurement point (including and ) to perform vector calculation and compensation of the Coriolis force according to a given formula. The most intuitive part of the formula is the coefficient in the front, which comes from the definition of the Coriolis force in classical mechanics, i.e., . However, simply cross-multiplying the angular velocity of the Earth's rotation and the velocity components is not enough, because in the downhole environment, the latitude and longitude will directly determine the projection direction and intensity of each component in the local coordinate system: near the equator, approaches 1, and the centrifugal force component increases accordingly. In high-latitude regions, the contribution of will be more prominently reflected.

[0076] In the present invention, by combining with and respectively in the formula, it is ensured that each direction component of the interaction between the three-dimensional velocity vector and the Earth's rotation is accurately characterized. At the same time, a correction coefficient is particularly introduced, which is not common in the traditional Coriolis force calculation formula. The reason for using this additional factor is mainly to compensate for the errors caused by the distribution of the Earth's gravitational potential energy and the fine-tuning of the relativistic effect in the deep well environment; when the sensor is at different depths, the value of will change, making this compensation factor vary slightly with depth, so as to more realistically reflect the inertial correction of the Earth's rotation system for different gravitational potential heights. Coupled with the fact that the present invention maps all vector components to the previously established local navigation coordinate system, the Coriolis force can not only be accurately described in vector form theoretically, but also be calculated and updated in real time numerically in engineering practice. When the sensor moves in the wellbore at a certain speed, the Coriolis force compensation vector can be obtained immediately according to this formula, and then directly applied to the measurement model during signal reconstruction and attitude calculation to eliminate the inertial interference caused by velocity changes. Especially in the scenarios of deep wells or high-speed penetration of formations, if the Coriolis force compensation is not performed, the velocity and acceleration data measured by the sensor will be mixed with some false components from the Earth's rotation, thus affecting the calculation accuracy of the subsequent well inclination angle and azimuth angle. The present invention distinguishes the velocity components With the angular velocity of the Earth's rotation and the longitude and latitude , the purpose is precisely to strip the proportion of the Coriolis force from the dynamic signals collected by the three-axis accelerometer and retain the information that truly reflects the actual movement of the sensor in the formation. It should be noted that although the angular velocity of the Earth's rotation is not large, as the moving speed of the downhole equipment increases, the influence of the Coriolis force will also be amplified; and in the high-latitude region or near the polar region, the item undergoes significant attenuation, and the contribution of the item to the formula is highlighted. The vector operation adopted in the present invention explicitly reflects these geographical factors, greatly improving the adaptability and reliability.

[0077] Example 6: In step 3, the projection of the geomagnetic field in the local navigation coordinate system is calculated through the following formula :

[0078] ;

[0079] wherein, is the magnetic dip angle; is the magnetic declination; is the geomagnetic field attenuation coefficient, with a value of 640; is the temperature coefficient, with a value of 0.0033; is the current temperature; is the standard temperature, with a value of 20 degrees Celsius.

[0080] Specifically, here and are respectively the magnetic dip angle and the magnetic declination, which determine the angular distribution of the magnetic field lines in space. Generally speaking, the magnetic dip angle represents the angle between the geomagnetic field and the horizontal plane, while the magnetic declination represents the deviation degree between the geomagnetic north and the geographic north. Through , and , the geomagnetic field can be decomposed in three-dimensional coordinates to obtain the magnetic field components under ideal conditions. This component is usually measured or deduced in the ground reference frame or the global geomagnetic model. If directly applied to the downhole environment, significant deviations will occur. Therefore, it is necessary to perform multiple corrections on it. Next, is used to describe the attenuation and change of the geomagnetic field in depth or height. The parameter can be regarded as a geomagnetic field attenuation coefficient, and its magnitude is related to the geomagnetic model. Since downhole operations are usually located hundreds or thousands of meters below the Earth's crust, if the influence of well depth on the magnetic field intensity is ignored, obvious errors may occur in azimuth measurement. This exponential factor can be based on (The height of the underground measurement point relative to the earth's center, usually negative) is used to dynamically adjust the magnetic field intensity, making the model closer to the real underground scenario. When constantly increases, it will have a certain degree of weakening or strengthening effect, providing the necessary field strength correction for deep well measurement.

[0081] The vector introduced later is the normalized form of the local navigation coordinate system vector established in the previous steps. In the method system of the present invention, it not only records the earth's curvature, underground longitude and latitude information, but also includes the earth's rotation correction factor. Multiplying it by the geomagnetic field aims to reproject the geomagnetic vector in the same reference coordinate frame, so that the measurement results of the magnetometer are consistent with other physical quantities (such as the gravitational field or the Coriolis force). In other words, this step can be regarded as "aligning" the magnetic field information with the underground coordinate system, avoiding errors caused by improper conversion of data between different coordinates. As for this term, it is a linear correction for the subtle influence of temperature on the geomagnetic field. Since the temperature of the geomagnetic probe or magnetometer is often much higher than the ground environment during underground operation, and the magnetic susceptibility of magnetic materials is closely related to temperature, the temperature change of the equipment and the surrounding environment will cause changes in the probe sensitivity and zero drift. If this is ignored, especially in the working conditions where the well temperature changes violently or the measurement point depth is relatively deep, the original magnetic measurement data may have systematic offsets. Here, is the temperature coefficient, which is given as 0.0033 in this embodiment, meaning that when the temperature deviates from the standard temperature , and are multiplied to correct the effective amplitude of the geomagnetic field. Although this correction based on a linear assumption simplifies the complex temperature-magnetic relationship, it can bring quite accurate compensation effects within the temperature range of most engineering applications, ensuring the effectiveness of the geomagnetic field projection vector.

[0082] Embodiment 7: In step 3, calculate the gravity compensation value through the following formula :

[0083] ;

[0084] where, is the earth shape coefficient, with a value of 0.00108263; is an integer subscript index, with an upper limit of 4, to simplify the continuous density distribution of the earth's strata into a 4-layer stratified model, representing the crust, mantle, outer core and inner core respectively; is the geological average density at the bottom of the th layer, which is a set value; is the standard formation density, with a value of 2.67 and the unit of .

[0085] Specifically, the first part of the formula is the classical Newtonian gravity formula, which describes the gravitational force of the Earth on an object, where is the gravitational constant, is the mass of the Earth, represents the radial distance from the center of the Earth to the measurement point. This term is the basis of the gravity distribution under the ideal spherical model of the Earth. However, due to the actual shape of the Earth being an oblate spheroid and the gravity values varying at different latitudes, further corrections need to be introduced on this basis. The second part is the Earth shape correction term, used to compensate for the oblate spheroid effect of the Earth being slightly bulged at the equator and slightly flattened at the poles due to its rotation. The Earth shape coefficient is a standardized value that quantifies the influence of the oblateness of the Earth on the gravity field distribution. In this correction term, is used to describe the influence of the latitude where the measurement point is located. The difference of the three terms reflects the geometric distribution characteristics of the gravity variation in different latitude regions of the Earth. For example, in the equatorial region, is close to 1, resulting in a reduction of the correction term, indicating a smaller gravity value; while near the poles, is close to 0, and the correction term increases, reflecting a larger gravity value at the poles. Through this correction, the formula can not only consider the shape effect of the Earth but also accurately reflect the gravity differences at different latitudes, making the measurement results closer to the actual situation.

[0086] The last part of the formula is the correction for the density of the geological stratification inside the Earth. Due to the huge differences in the density distributions of the crust, mantle, outer core, and inner core, the gravity value in downhole operations is not only related to the overall mass of the Earth but also affected by the local formation density. In the present invention, the interior of the Earth is simplified into a 4-layer stratification model, and the density of each layer corresponds to the average density of the crust, mantle, outer core, and inner core respectively. The advantage of this stratification modeling is that it can explicitly quantify the contributions of different depth regions to the gravity field without the need for complex integral calculations of continuous density distributions. The standard formation density is a commonly used geological reference value and serves as the normalization benchmark for relative density. In the stratification correction, the contribution of the density of each layer is added in the form of , where is a weighting factor used to describe the phenomenon that the cumulative effect of density in the depth direction gradually weakens. For example, the density change of the crust (the first layer) has a much greater impact on the gravity at the measurement point than the density change of the inner core (the fourth layer) because the inner core is farther from the measurement point and its contribution is relatively smaller. By combining the Earth shape correction and the geological density correction, the finally calculated gravity compensation value It can truly reflect the gravity distribution in the complex downhole environment. This result will be directly applied to the acceleration data processing of the sensor to eliminate the influence of gravity anomalies in dynamic measurements. For example, the calculation of the well deviation angle depends on the gravity direction measured by the accelerometer. Without considering gravity compensation, the sensor may mistake the gravity deviation caused by local geological anomalies for attitude changes, thus affecting the measurement accuracy. By introducing , the present invention can accurately correct these interferences, making the data of the accelerometer more reliable. In addition, the design of the geological density correction part fully reflects the consideration of the present invention for the formation complexity. Although the density distribution inside the earth is continuously changing, in actual engineering, it is often difficult to achieve fast operation with a continuous model. The present invention adopts a 4-layer stratified model, simplifies the complex geological characteristics into an operable calculation model, and at the same time maintains high sensitivity to the main density change regions. Especially in deep well operations, the long-distance influence of the outer core and the inner core is reflected through the correction of the third and fourth layers, while the short-distance influence of the crust and the mantle is fully described by the correction of the first and second layers. This method achieves a good balance between computational complexity and accuracy, enabling the formula to not only meet the requirements of downhole real-time calculation but also ensure the accuracy of the measurement results.

[0087] Example 8: In step 3, the corrected well deviation angle is calculated through the following formula:

[0088] ;

[0089] wherein, is the corrected well deviation angle.

[0090] Specifically, the core part of the formula is , which describes the relationship between the calculation of the well deviation angle and multiple physical quantities in the local navigation coordinate system. First, is the dot product of the reconstructed signal and the geomagnetic field projection vector, used to measure the consistency of their directions. The reconstructed signal is the fusion result of the sensor data, including the measurement values of the accelerometer, gyroscope, velocimeter, and magnetometer, and its direction can reflect the actual attitude of the sensor; while the geomagnetic field projection vector provides a stable reference direction. The result of the dot product indicates the angle between the actual attitude of the sensor and the geomagnetic field direction, and this information is the basis for calculating the well deviation angle. However, relying solely on is not sufficient to fully reflect the complex influence in the downhole environment, so is further introduced into the formula. is the Coriolis force compensation vector, is the gravity compensation value, and the dot product of the two represents the interference component of the earth's rotation and gravity anomalies on the measurement result. This part is subtracted from the dot product Subtracted from it, it plays a role in eliminating false signals. Especially in high-speed motion or deep well environments, the dynamic impact of the Coriolis force on sensor measurements is relatively significant, while the gravity compensation value takes into account the changes in the gravitational field caused by the shape of the Earth and geological stratification. Through the comprehensive correction of the two, the reliability of the measurement can be effectively improved.

[0091] The denominator part is used to normalize the dot product result to ensure that the output result of the formula is always within a reasonable value range (i.e., ). The magnitudes of the reconstructed signal and the geomagnetic projection vector respectively represent their intensities. Through the normalization operation, the errors caused by intensity changes during the measurement process can be eliminated, making the calculation of the well deviation angle only related to the direction and not affected by the signal amplitude. After the core calculation part is completed, the formula also introduces two additional correction factors, which are and . The first correction factor is the comprehensive correction of the Earth's gravitational field and relativistic effects, where is the description of relativistic gravitational redshift, reflecting the subtle deformation effects of the gravitational field on measurement time and space when the downhole depth continuously increases. Although this effect may be small under normal conditions, for deep well operations or scenarios requiring long-term high-precision measurements, its introduction can significantly improve the reliability of the results. The second correction factor is used to simulate the exponential decay effect of depth on measurement accuracy, where represents the atmospheric scale height. As the well depth increases, the sensor signal may be affected by changes in the external environment (such as temperature, pressure, magnetic field strength, etc.). Through this correction factor, the impact of these changes on the calculation result of the well deviation angle can be dynamically compensated.

[0092] Example 9: In step 3, the corrected azimuth angle is calculated through the following formula:

[0093] ;

[0094] where, is the corrected azimuth angle.

[0095] Specifically, the core part of the formula is . Here, represents the projection vector of the geomagnetic field in the local navigation coordinate system, is the reconstructed signal vector obtained through signal reconstruction in step 1, and is the Coriolis force compensation vector calculated in step 2. By performing cross product and dot product operations on these three vectors, the formula attempts to capture the spatial relationship and mutual influence between them, thereby obtaining a preliminary estimate of the azimuth angle. Specifically, represents the cross product between the geomagnetic field vector and the reconstructed signal vector, and this operation generates a new vector that is perpendicular to and the plane where they are located, reflecting the relative direction and intensity between the two. Subsequently, the dot product operation with the Coriolis force compensation vector further quantifies the manifestation of these spatial relationships under the inertial effects caused by the Earth's rotation. This composite operation can effectively take into account the complex interaction between the geomagnetic field and the dynamic movement of the sensor, ensuring that the azimuth calculation not only depends on static magnetic field information but also can dynamically adapt to the changes caused by rotation and movement in the downhole environment. The denominator part is the normalization process of the result of the numerator. By taking the product of the magnitudes of the three vectors, the denominator ensures that the dot product result is within a dimensionless range, thus enabling the input value of the function to be kept within a reasonable range (i.e., between ). This normalization operation not only eliminates the influence between data of different magnitudes but also ensures the stability and consistency of the calculation result, making the azimuth calculation not affected by the change in the measurement amplitude of the sensor.

[0096] In the formula the function is applied because the azimuth is essentially an angular quantity, and the arctangent function is needed to convert the proportional relationship into an angular value. In this way, the formula can convert the result of complex vector operations into an angular value that is easy to understand and apply, and directly used for the output of well deviation and azimuth measurement. Next, the correction factors and in the formula play a further role in correction and adjustment. represents the local geomagnetic field intensity, while is the standard intensity of the geomagnetic field, with a value of 49.6 microteslas. By taking the ratio , the formula realizes the normalization process of the change in the local geomagnetic field intensity. The introduction of this ratio aims to eliminate the influence of the difference in geomagnetic field intensity in different geographical locations or geological conditions on the azimuth calculation, ensuring that the calculation result can maintain consistent accuracy and reliability whether in a geomagnetically strong area or a weak area. The exponential term in the correction factor takes into account the small correction of the inertial effect caused by the Earth's rotation on the measurement result. The Earth's angular velocity is , and the speed of light is . The introduction of this exponential term is mainly to compensate for the small inertial effect brought about by the Earth's rotation. Especially in high-precision measurements, this small correction can significantly improve the accuracy of the measurement result. Although The value is extremely small. However, in the downhole measurement environment with high-precision requirements, this correction factor is effectively incorporated into the calculation in the form of an exponential function, ensuring more accurate and stable correction of the azimuth angle.

[0097] The present invention has been introduced in detail above. Specific examples are used herein to illustrate the principle and implementation manner of the present invention. The description of the above embodiments is only used to help understand the method and its core idea of the present invention. It should be noted that for those of ordinary skill in the art in this technical field, without departing from the principle of the present invention, several improvements and modifications can be made to the present invention, and these improvements and modifications also fall within the protection scope of the claims of the present invention.

Claims

1. A high-precision well inclination and azimuth measurement method based on a multi-axis sensor, characterized in that: The method comprises: Step 1: Considering the influence of the earth's curvature and rotation, a local navigation coordinate system of the underground environment is established; in the local navigation coordinate system, the measurement signal of the four-axis sensor is reconstructed to obtain a reconstructed signal; Step 2: Based on the sensor quality of the four-axis sensor, the three-dimensional velocity components measured by the four-axis sensor and the geographic coordinate position of the four-axis sensor, the Coriolis force compensation vector is calculated by considering the influence of the Coriolis force caused by the rotation of the earth; Step 3: Calculate the projection of the geomagnetic field in the local navigation coordinate system to obtain the geomagnetic field projection vector; consider the influence of gravity, combine the geological density and bottom density in the downhole environment, and calculate the gravity compensation value; Step 4: Calculate the corrected well inclination angle and corrected azimuth angle based on the gravity compensation value, the Coriolis force compensation vector and the geomagnetic field projection vector in combination with the reconstructed signal; The local navigation coordinate system in step 1 Use the following formula to express it: ； in, is the average radius of the earth, which is 6371 km; is the height from the earth's center to the downhole measuring point where the four-axis sensor is located; is the geographical latitude of the downhole measuring point where the four-axis sensor is located; is the geographical longitude of the downhole measuring point where the four-axis sensor is located; is the angular velocity of the Earth’s rotation, and its value is , the unit is rad / s; is the speed of light; is the eccentricity of the Earth, and its value is 0.0818191908426.

2. The high-precision well inclination and azimuth measurement method based on a multi-axis sensor as claimed in claim 1, characterized in that: The four-axis sensor includes a gyroscope, a magnetometer, a three-axis speedometer and a three-axis accelerometer.

3. The high-precision well inclination and azimuth measurement method based on a multi-axis sensor as claimed in claim 2, characterized in that: In step 1, the measurement signal of the four-axis sensor is reconstructed in the local navigation coordinate system by the following formula to obtain the reconstructed signal : ； in, is the X-axis acceleration component of the three-axis accelerometer; is the Y-axis acceleration component of the three-axis accelerometer; is the Z-axis acceleration component of the three-axis accelerometer; is the X-axis angular velocity component of the gyroscope; is the Y-axis angular velocity component of the gyroscope; is the initial well inclination angle, ； is the Earth's gravitational constant; is the geomagnetic field strength of the magnetometer; is the initial direction angle, ； is the X-axis geomagnetic field intensity component of the magnetometer; is the Y-axis geomagnetic field intensity component of the magnetometer; Represents the modulus operation of a vector; is the standard strength of the Earth's magnetic field, with a value of 49.6 and a unit of microtesla; is the atmospheric scale height, and its value is 7.4 km.

4. The high-precision well inclination and azimuth measurement method based on a multi-axis sensor as claimed in claim 3, characterized in that: In step 2, the Coriolis force compensation vector is calculated using the following formula: : ； in, is the mass of the four-axis sensor; is the X-axis velocity component of the three-axis speedometer; is the Y-axis velocity component of the three-axis speedometer; is the Z-axis velocity component of the three-axis velocimeter.

5. The high-precision well inclination and azimuth measurement method based on a multi-axis sensor as claimed in claim 4, characterized in that: In step 3, the projection of the geomagnetic field in the local navigation coordinate system is calculated by the following formula: : ； in, is the geomagnetic inclination; is the magnetic declination; is the geomagnetic field attenuation coefficient, which is 640; is the temperature coefficient, and its value is 0.0033; is the current temperature; The standard temperature is 20 degrees Celsius.

6. The high-precision well inclination and azimuth measurement method based on a multi-axis sensor as claimed in claim 5, characterized in that: In step 3, the gravity compensation value is calculated by the following formula: : ； in, is the earth shape factor, and its value is 0.00108263; is an integer subscript index with an upper limit of 4, which simplifies the continuous density distribution of the strata into a 4-layer model, representing the crust, mantle, outer core and inner core respectively; For the The geological average density of the bottom layer is the set value; is the standard formation density, with a value of 2.67 and a unit of .

7. The high-precision well inclination and azimuth measurement method based on a multi-axis sensor as claimed in claim 6, characterized in that: In step 3, the corrected well inclination angle is calculated using the following formula: ； in, To correct the well inclination.

8. The high-precision well inclination and azimuth measurement method based on a multi-axis sensor as claimed in claim 7, characterized in that: In step 3, the corrected azimuth is calculated using the following formula: ； in, To correct the azimuth.

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