Well Inclination and Geomagnetic Field Strength Measurement System Based on High-Precision Fluxgate Sensors

Abstract

The present invention relates to the field of measurement technology, and specifically relates to a well inclination and geomagnetic field intensity measurement system based on a high-precision fluxgate sensor. It includes: a fluxgate sensor group, a magnetic field data analysis part, and a measurement result calculation part; the fluxgate sensor group includes high-precision fluxgate sensors that respectively measure the magnetic field components in the X-axis direction, Y-axis direction, and Z-axis direction; the magnetic field analysis part is used to construct a magnetic field gradient tensor based on the physical parameters of the high-precision fluxgate sensor, according to the effective magnetic permeability, based on the corrected magnetic field components in each direction, and separate the geomagnetic field vector from the total magnetic field vector according to the magnetic field gradient tensor; the measurement result calculation part is used to calculate the well inclination angle value and the azimuth angle value according to the geomagnetic field vector. The present invention significantly improves the accuracy, robustness, and environmental adaptability of downhole magnetic field measurement. The present invention can accurately extract the geomagnetic field vector and achieve high-precision calculation of the well inclination angle and the azimuth angle.

Description

Technical Field

[0001] The present invention belongs to the technical field of measurement, and particularly relates to a well inclination and geomagnetic field intensity measurement system based on a high-precision fluxgate sensor. Background Art

[0002] The exploration and monitoring technology of the downhole environment is an important link in oil and gas exploration and mineral resource development. Especially under complex geological conditions, the magnetic field information in the wellbore can provide key support for resource positioning, wellbore stability assessment, and drilling accuracy optimization. Currently, geomagnetic field measurement technology is widely used in downhole operations. Its core lies in using high-precision magnetic field sensors to sense the geomagnetic field components in the three-dimensional space downhole, thereby calculating key parameters such as well inclination angle and azimuth angle. However, there are various limitations in the existing technologies, making it difficult for the accuracy, robustness, and environmental adaptability of downhole magnetic field measurement to meet the requirements of high-demand engineering applications.

[0003] Currently, magnetic field measurement technology mainly relies on devices such as Hall effect sensors, optically pumped magnetometers, and fluxgate sensors. Among them, Hall effect sensors have a simple structure and low cost, but their sensitivity and resolution are relatively low, making it difficult to provide sufficiently accurate data support in the weak magnetic field environment downhole. Although optically pumped magnetometers have extremely high sensitivity, their working principle relies on a complex optical system, and the device is very sensitive to environmental vibration and temperature changes, making it difficult to adapt to harsh conditions such as high temperature, high pressure, and vibration downhole. Therefore, high-precision fluxgate sensors have gradually become the mainstream choice for downhole geomagnetic field measurement due to their high sensitivity, strong anti-interference ability, and wide adaptability. Fluxgate sensors sense the external magnetic field through induction coils and high-permeability magnetic cores. The core technology lies in the high-sensitive magnetization characteristics of the magnetic core and the high-resolution sensing ability for weak magnetic fields. Some methods for using fluxgate sensors to measure the geomagnetic field have been proposed in existing patents and published literature. For example, in the disclosed technology, three-axis arranged fluxgate sensors are used to capture the three-dimensional components of the downhole magnetic field, and the well inclination angle and azimuth angle are calculated in combination with a reference magnetic field model. This method can theoretically meet the basic measurement requirements of the downhole environment, but its application effect depends on the following key factors: the sensitivity and stability of the sensor, the calculation accuracy of the magnetic field vector, the ability to suppress environmental interference, and the dynamic response performance of data processing. Summary of the Invention

[0004] The main purpose of the present invention is to provide a well inclination and geomagnetic field intensity measurement system based on a high-precision fluxgate sensor. The present invention significantly improves the accuracy, robustness, and environmental adaptability of downhole magnetic field measurement. The present invention can accurately extract the geomagnetic field components, suppress the interference field in the complex downhole environment, and real-time correct the influence of environmental factors such as temperature on the performance of the sensor, realizing the high-precision calculation of the well inclination angle and azimuth angle.

[0005] The technical solution of the present invention is realized as follows: A well inclination and geomagnetic field intensity measurement system based on a high-precision fluxgate sensor, the system comprising: a fluxgate sensor group, a magnetic field data analysis part, and a measurement result calculation part;

[0006] The fluxgate sensor group includes three identical high-precision fluxgate sensors disposed in the downhole environment to measure the magnetic field components in the X-axis direction, Y-axis direction, and Z-axis direction respectively;

[0007] The magnetic field data analysis part is used to calculate the reference output response of the high-precision fluxgate sensor according to the physical parameters of the high-precision fluxgate sensor, and combine the temperature and the reference output response at the current time to correct the reference magnetic permeability of the high-precision fluxgate sensor to obtain the effective magnetic permeability; according to the effective magnetic permeability, calculate the corrected magnetic field components of each direction under the effective magnetic permeability, and then calculate the total magnetic field vector corresponding to the corrected magnetic field components in three directions; based on the corrected magnetic field components in each direction, construct a magnetic field gradient tensor, and according to the magnetic field gradient tensor, separate the geomagnetic field vector from the total magnetic field vector;

[0008] The measurement result calculation part is used to calculate the well inclination angle value and the azimuth angle value according to the geomagnetic field vector; the measured magnetic field intensity, well inclination angle value, and azimuth angle value corresponding to the geomagnetic field vector are used as the final measurement results.

[0009] Further, the physical parameters of the high-precision fluxgate sensor include: the number of turns of the induction coil, the effective cross-sectional area of the magnetic core, the reference magnetic permeability, the magnetic relaxation time constant, the radius of the magnetic core, the magnetic domain size, the excitation magnetic field intensity, the saturation magnetic field intensity, the excitation frequency, and the phase delay.

[0010] Further, the magnetic field data analysis part calculates the reference output response of each high-precision fluxgate sensor according to the magnetic field components in each direction through the following formula:

[0011] ;

[0012] where, is the reference output response; is the operating time of the high-precision fluxgate sensor; is the number of turns of the induction coil; is the effective cross-sectional area of the magnetic core; is the excitation magnetic field intensity; is the saturation magnetic field intensity; is the radius of the magnetic core; is the magnetic domain size; is the reference magnetic permeability; is the phase delay; is the excitation frequency; is the zero-order Bessel function; is the magnetic relaxation time constant.

[0013] Furthermore, the reference magnetic permeability of the high-precision fluxgate sensor is corrected through the following formula to obtain the effective magnetic permeability:

[0014] ;

[0015] where, is the effective magnetic permeability; is the local energy barrier that needs to be overcome for magnetic domain flipping or rearrangement; is the Boltzmann constant; is the reference temperature; is the temperature influence coefficient, and its value range is from 0.3 to 0.5.

[0016] Furthermore, through the following formula, according to the effective magnetic permeability, the corrected magnetic field components in each direction under the effective magnetic permeability are calculated:

[0017] ;

[0018] where, is the corrected magnetic field component in the X-axis direction; is the corrected magnetic field component in the Y-axis direction; is the corrected magnetic field component in the Z-axis direction; is the installation azimuth angle of the high-precision fluxgate sensor corresponding to the X-axis direction; is the installation azimuth angle of the high-precision fluxgate sensor corresponding to the Y-axis direction; is the installation azimuth angle of the high-precision fluxgate sensor corresponding to the Z-axis direction; is the inclination angle of the high-precision fluxgate sensor corresponding to the X-axis direction; is the inclination angle of the high-precision fluxgate sensor corresponding to the Y-axis direction; is the inclination angle of the high-precision fluxgate sensor corresponding to the Z-axis direction.

[0019] Furthermore, through the following formula, based on the corrected magnetic field components in each direction, the magnetic field gradient tensor is constructed:

[0020] ;

[0021] where, is the tensor product operation; is the gradient operator; is the total magnetic field vector; is the determinant operator; is the magnetic field gradient tensor.

[0022] Further, the geomagnetic field vector is separated from the total magnetic field vector through the following formula:

[0023] ;

[0024] wherein, is a spherical surface with a set value as the radius and containing three high-precision fluxgate sensors, and the radius value range is to ; is the position vector on the spherical surface; the mean vector of the position vectors of the three high-precision fluxgate sensors in the spherical surface; is the surface element normal vector; is the trace of the magnetic field gradient tensor.

[0025] Further, the well deviation angle value is calculated based on the geomagnetic field vector through the following formula:

[0026] ;

[0027] wherein, is the component in the Z-axis direction; is the component in the X-axis direction; is the component in the Y-axis direction; is the first element of; is the second element of; is the third element of; is the Langevin function; is the well deviation angle value.

[0028] Further, the azimuth angle value is calculated based on the geomagnetic field vector through the following formula:

[0029] ;

[0030] wherein, is the azimuth angle value.

[0031] The well deviation and geomagnetic field intensity measurement system based on high-precision fluxgate sensors of the present invention has the following beneficial effects:

[0032] The present invention uses a high-precision fluxgate sensor as the core measurement equipment, which significantly improves the resolution and sensitivity of downhole magnetic field measurement. Compared with traditional Hall effect sensors and optical pump magnetometers, the fluxgate sensor of the present invention can capture tiny magnetic field changes in a weak magnetic field environment, and at the same time has strong anti-interference capabilities. By introducing a reference permeability correction model, the present invention dynamically compensates for the effects of temperature, time drift and material properties on the core response, ensuring that the sensor can still output stable and accurate magnetic field signals in harsh downhole environments such as high temperature and high pressure. This high-precision magnetic field measurement capability provides a reliable data basis for subsequent calculations of well inclination and azimuth.

[0033] In order to solve the problem of fluxgate sensor's magnetic permeability change under different temperature conditions, the present invention calculates the effective magnetic permeability through real-time correction of the reference magnetic permeability. The temperature correction coefficient and thermal excitation model (exponential decay term) are introduced into the formula, and the inductive capacity of the magnetic core is dynamically adjusted in combination with the output signal. This dynamic correction method effectively eliminates the negative impact of temperature on the magnetic permeability of the magnetic core, so that the sensor can still maintain high-precision measurement in the underground environment with significant temperature changes. This correction mechanism significantly improves the stability of magnetic field measurement and solves the problem of measurement error accumulation caused by temperature drift in the prior art.

[0034] The present invention comprehensively describes the rate of change of the magnetic field in three-dimensional space through the construction and utilization of the magnetic field gradient tensor. The gradient tensor not only reflects the local characteristics of the magnetic field, but also provides a basis for separating the interference field and the geomagnetic field. The formula combines the gradient operator and the tensor product operation to construct a second-order tensor that can accurately describe the spatial variation of the magnetic field, and suppresses the influence of high interference areas on the measurement results through the exponential weight term. This high-order description capability enables the present invention to separate the geomagnetic field components and the interference field in a complex downhole environment, significantly improving the accuracy of the calculation of the well inclination and azimuth.

[0035] The present invention proposes a multi-parameter coupling model, which constructs the calculation formula of the well inclination and azimuth through the component relationship of the geomagnetic field vector, the normalized correction of the gradient tensor and the dynamic response of the core material properties. The calculation formula of the well inclination combines the trace information of the geomagnetic field vector and the gradient tensor, suppresses the influence of environmental interference on the measurement accuracy, and uses the Langevin function to dynamically correct the nonlinear magnetization state of the magnetic core to ensure the reliability and accuracy of the calculation results. The calculation of the azimuth is based on the ratio of the planar components of the geomagnetic field vector. The interference field is effectively suppressed by the exponential weight term, avoiding the negative impact of the high gradient area on the azimuth calculation. This systematic calculation model significantly improves the spatial positioning accuracy in complex underground environments. BRIEF DESCRIPTION OF THE DRAWINGS

[0036] Figure 1This is a schematic diagram of the system structure of the well inclination and geomagnetic field intensity measurement system based on a high-precision fluxgate sensor provided by an embodiment of the present invention. Detailed implementation manners

[0037] In the following description, specific details such as specific system structures, interfaces, and technologies are presented for the purpose of illustration rather than limitation, so as to thoroughly understand the embodiments of the present invention. However, those skilled in the art should clearly understand that the embodiments of the present invention can also be implemented in other embodiments without these specific details. In other cases, detailed descriptions of well-known devices, circuits, and methods are omitted to avoid unnecessary details from interfering with the description of the embodiments of the present invention.

[0038] Embodiment 1, refer to Figure 1 : A well inclination and geomagnetic field intensity measurement system based on a high-precision fluxgate sensor, the system includes: a fluxgate sensor group, a magnetic field data analysis part, and a measurement result calculation part;

[0039] The fluxgate sensor group includes three identical high-precision fluxgate sensors disposed in the downhole environment to measure the magnetic field components in the X-axis direction, Y-axis direction, and Z-axis direction respectively;

[0040] The magnetic field data analysis part is used to calculate the reference output response of the high-precision fluxgate sensor according to the physical parameters of the high-precision fluxgate sensor, and combine the temperature and the reference output response at the current time to correct the reference magnetic permeability of the high-precision fluxgate sensor to obtain the effective magnetic permeability; according to the effective magnetic permeability, calculate the corrected magnetic field components of each direction under the effective magnetic permeability, and then calculate the total magnetic field vector corresponding to the corrected magnetic field components in the three directions; based on the corrected magnetic field components of each direction, construct a magnetic field gradient tensor, and according to the magnetic field gradient tensor, separate the geomagnetic field vector from the total magnetic field vector;

[0041] The measurement result calculation part is used to calculate the well inclination angle value and the azimuth angle value according to the geomagnetic field vector; take the magnetic field intensity, well inclination angle value, and azimuth angle value corresponding to the measured geomagnetic field vector as the final measurement results.

[0042] Specifically, a fluxgate sensor consists of a coil wrapped around a magnetic core with high magnetic permeability. When an external magnetic field acts on the magnetic core, the magnetic field becomes concentrated and enhanced through the magnetic core. Under the action of an externally applied alternating excitation current, the magnetization intensity within the magnetic core continuously changes with the excitation frequency. When the intensity of the external magnetic field changes, the magnetization saturation point and the magnetic flux change rate of the magnetic core also change accordingly. This change is directly reflected in the signal output by the sensor. By demodulating this output signal, the specific value of the external magnetic field can be obtained. In the present invention, the fluxgate sensor array is designed as an orthogonal arrangement system composed of three high-precision fluxgate sensors, which respectively correspond to the measurement of the magnetic field components in the X-axis, Y-axis, and Z-axis directions in the underground environment. This design makes full use of the three-axis measurement ability of the fluxgate sensor, and realizes the omnidirectional perception of the spatial magnetic field by arranging sensors in different directions, thereby being able to accurately capture the vector distribution of the underground magnetic field. In particular, in the case of a complex and changeable underground environment with significant local magnetic field interference, the high sensitivity and low noise characteristics of the fluxgate sensor ensure the stability and accuracy of the measurement results. In addition, in order to further improve the accuracy of the sensor, the system of the present invention also introduces a temperature compensation and magnetic permeability correction mechanism. Since the high temperature and magnetic field interference in the underground environment may cause performance fluctuations of the magnetic core, the sensor array dynamically adjusts the effective magnetic permeability of the sensor by collecting real-time environmental temperature data and combining the reference output response of the sensor. This process not only eliminates the influence of temperature on the sensor output signal, but also significantly improves the measurement reliability of the sensor in a high-temperature environment.

[0043] In addition, another important role of the fluxgate sensor array in the present invention is to provide basic data for subsequent separation of geomagnetic field components and calculation of well deviation angle. By measuring the magnetic field components in three directions in real time, the system can quickly construct the magnetic field gradient tensor and, based on this, separate the geomagnetic field vector. The accuracy of this separation process directly depends on the accurate capture of the spatial magnetic field by the sensor array. Therefore, based on the fluxgate sensor, the present invention further optimizes the data processing algorithm to convert the original output data of the sensor into corrected magnetic field components. Specifically, this data processing combines the physical parameters of the sensor and actual environmental factors to eliminate the influence of systematic errors and environmental noise, ensuring the accuracy of the three-axis magnetic field components. These corrected data not only reflect the true intensity of the downhole geomagnetic field but also lay a data foundation for the accurate calculation of well deviation angle and azimuth angle. The superior performance of the fluxgate sensor array is also reflected in its sensitive perception ability to weak magnetic field changes. Compared with traditional Hall sensors or other types of magnetic field measurement devices, the fluxgate sensor has a higher signal-to-noise ratio at low magnetic field intensities and is particularly suitable for accurately capturing geomagnetic field changes in the complex downhole environment. For example, under the interference of downhole metal structures or electrical equipment, the local magnetic field may exhibit non-linear changes. Traditional sensors are prone to measurement deviations in these environments, while the fluxgate sensor, through its special magnetization characteristics and high dynamic range, can effectively suppress interference signals and accurately capture the weak changes in the geomagnetic field.

[0044] After the fluxgate sensor collects the downhole magnetic field signal, the first output is the uncorrected original electrical signal, and the accuracy of these signals is affected by multiple factors, including fluctuations in sensor sensitivity, changes in environmental temperature, and interference from the local downhole magnetic field, etc. To ensure the reliability of the final calculation result, the magnetic field data analysis part starts from the physical characteristics of the sensor and uses its preset reference parameters, such as reference sensitivity and reference permeability, to calculate the reference response value of the sensor. The reference response value is the output response of the sensor to the external magnetic field under ideal conditions and can provide a reference for the subsequent correction process. In the complex downhole environment, temperature changes have a significant impact on the performance of the fluxgate sensor. An increase in temperature will cause a slight change in the magnetization characteristics of the sensor core material, resulting in a deviation in the output signal. To solve this problem, the magnetic field data analysis part dynamically corrects the permeability by collecting the temperature data of the downhole environment in real time and combining it with the reference response value of the sensor. The temperature correction process is based on the temperature characteristic model of the sensor, and the reference permeability is adjusted through an algorithm to obtain the corrected effective permeability. This correction process greatly improves the performance stability of the sensor in high-temperature environments, making the measurement results unaffected by environmental temperature fluctuations.

[0045] After the effective permeability correction is completed, the magnetic field data analysis part further calculates the corrected magnetic field components in each direction. The corrected magnetic field components are directly derived from the output electrical signals of the fluxgate sensors. After normalization processing of the sensitivity and permeability, the component values reflecting the true magnetic field strength are obtained. By performing vector synthesis on the corrected magnetic field components in the X, Y, and Z directions, the magnetic field data analysis part calculates the total magnetic field vector of the downhole magnetic field. This total magnetic field vector not only contains the information of the geomagnetic field but also superimposes the interference magnetic field in the local downhole environment. Therefore, it is impossible to directly obtain the accurate information of the geomagnetic field only relying on the total magnetic field vector. To isolate the geomagnetic field vector, the magnetic field data analysis part constructs a magnetic field gradient tensor using the spatial distribution characteristics of the total magnetic field vector. The magnetic field gradient tensor is a mathematical tool for describing the spatial change rate of the magnetic field. By calculating the changes of the magnetic field components in three-dimensional space, the local distribution characteristics of the magnetic field can be clarified. Using this gradient tensor, the system can accurately separate the interference components in the total magnetic field vector and extract the pure geomagnetic field vector. In the downhole environment, due to the presence of metal structures, electrical equipment, etc., the local magnetic field interference usually has large gradient characteristics, while the geomagnetic field shows a smoother distribution. Therefore, the gradient tensor can not only help identify the interference but also enhance the accuracy of geomagnetic field separation. Another important function of the magnetic field data analysis part is to compare and analyze the geomagnetic field vector with the total magnetic field vector to verify the accuracy of the separation result. By performing multiple iterative calculations on the separated geomagnetic field components, the magnetic field data analysis part can maximize the elimination of the influence of environmental interference, thereby providing high-precision input data for the subsequent calculation of the well inclination angle and azimuth angle. In addition, the design of this part also fully considers the real-time changes in the downhole environment. By updating the calculation models of the gradient tensor and the geomagnetic field components in real time, the system can quickly adapt to different environmental conditions and ensure the dynamic accuracy of the measurement results.

[0046] The measurement result calculation part uses the geomagnetic field vector separated by the magnetic field data analysis part. This vector is the true geomagnetic field component obtained after interference separation and environmental correction, and can accurately reflect the state of the earth's magnetic field in the downhole environment. The direction and magnitude of the geomagnetic field vector contain rich spatial information and are the basic data for downhole attitude calculation. The calculation of the well inclination angle is based on the relationship between the geomagnetic field vector and the direction of the earth's gravity. The distribution characteristics of the geomagnetic field in space make it have obvious directionality. Especially in the downhole, the angle between the geomagnetic field vector and the direction of the earth's center directly reflects the magnitude of the well inclination angle. Therefore, by analyzing the relationship between the geomagnetic field vector and the downhole coordinate system, the well inclination angle can be accurately determined.

[0047] To achieve this goal, the measurement result calculation part first needs to determine the projection of the geomagnetic field vector in the downhole three-dimensional space coordinate system. Since the fluxgate sensor group measures the corrected magnetic field components in three orthogonal directions, the geomagnetic field vector can be represented as a three-dimensional vector, and its magnitude and direction are calculated through vector synthesis. On this basis, the measurement result calculation part uses geometric methods to solve the angle between the geomagnetic field vector and the downhole reference axis. Specifically, the well inclination angle is the angle between the geomagnetic field vector and the Z-axis (usually parallel to the downhole vertical direction). This process requires the use of the dot product relationship of vectors, and by inverse calculating the cosine value of the angle between the vectors, the magnitude of the well inclination angle is finally obtained. On the other hand, the calculation of the azimuth angle depends on the projection of the geomagnetic field vector on the horizontal plane. The components of the geomagnetic field vector in the XY plane reflect its distribution characteristics in the horizontal direction, and the direction of the geomagnetic field vector in the horizontal plane can be determined through the ratio of these components. Specifically, the azimuth angle is the angle between the projection of the geomagnetic field vector on the horizontal plane and the reference direction (such as the north direction). The measurement result calculation part accurately calculates the azimuth angle value through the arctangent operation on the horizontal components of the geomagnetic field vector, combined with the direction calibration information of the sensor. This calculation process takes into account the possible coordinate system offsets and non-ideal calibration factors in the downhole environment, and compensates for the deviations through algorithms to ensure the accuracy of the azimuth angle calculation. In addition, the measurement result calculation part is also responsible for the calculation of the geomagnetic field intensity. The geomagnetic field intensity is the modulus of the geomagnetic field vector, which reflects the actual magnitude of the earth's magnetic field in the downhole space. By performing the square sum operation on the three direction components of the geomagnetic field vector and then taking the square root, the system can quickly obtain the geomagnetic field intensity value. This calculation result is of great significance for downhole geological exploration and environmental monitoring, because the change of the geomagnetic field intensity may be closely related to the underground structure and mineral deposit distribution.

[0048] Example 2: The physical parameters of the high-precision fluxgate sensor include: the number of turns of the induction coil, the effective cross-sectional area of the magnetic core, the reference magnetic permeability, the magnetic relaxation time constant, the radius of the magnetic core, the magnetic domain size, the excitation magnetic field intensity, the saturation magnetic field intensity, the excitation frequency, and the phase delay.

[0049] Specifically, the number of turns of the induction coil and the function of the magnetic core complement each other. Increasing the number of turns of the coil can enhance the intensity of the induction signal, while the effective cross-sectional area of the magnetic core determines the distribution and transfer efficiency of the magnetic flux within the sensor. An overly small cross-sectional area of the magnetic core may lead to excessive magnetic field concentration, causing local saturation of the magnetic core and thereby affecting the linear output of the signal. On the other hand, an overly large cross-sectional area will reduce the sensitivity to weak magnetic field changes. Therefore, a reasonable selection is required to adapt to the complex magnetic field distribution underground. The reference magnetic permeability is a core parameter describing the response ability of the magnetic core material to the magnetic field, and its magnitude directly affects the induction sensitivity of the sensor in an external magnetic field. Since the magnetic permeability changes with temperature and time, in the present invention, the reference magnetic permeability is dynamically corrected to ensure the stability of the measurement data in the underground environment. At the same time, the magnetic relaxation time constant, as the response time of the magnetic core to changes in the external magnetic field, determines the dynamic performance of the sensor. An overly short magnetic relaxation time will result in poor response to low-frequency magnetic fields, while an overly long one may delay the perception of rapidly changing magnetic fields. Therefore, in the practical application of the present invention, its setting needs to match the dynamic characteristics of the underground magnetic field.

[0050] The radius of the magnetic core is closely related to the magnetic domain size, jointly determining the analytical ability of the magnetic core for magnetic field signals. A smaller magnetic core radius can improve the spatial resolution but may lead to enhanced interference between magnetic domains, while the magnetic domain size affects the saturation characteristics of the magnetic core and its sensitivity to weak external magnetic fields. To meet the requirements of high-precision magnetic field measurement in the underground environment, the magnetic core material adopted in the present invention has a moderate magnetic domain size, thus achieving a balance between sensitivity and anti-interference ability. The excitation magnetic field intensity and the saturation magnetic field intensity are important parameters affecting the working range of the sensor. The excitation magnetic field intensity needs to be large enough to drive the magnetic core into a high-sensitivity working state while avoiding non-linear effects caused by over-excitation. The saturation magnetic field intensity limits the maximum measurement range of the sensor. If the magnetic field intensity in the environment approaches or exceeds the saturation intensity of the magnetic core, the output of the sensor will be distorted. In the present invention, appropriate excitation magnetic field and saturation magnetic field parameters are selected according to the actual distribution characteristics of the underground magnetic field intensity, thereby ensuring that the sensor can not only capture weak geomagnetic field signals but also handle strong environmental interference magnetic fields. Finally, the excitation frequency and phase delay are important characteristics of the dynamic performance of the fluxgate sensor. The excitation frequency determines the period of magnetization and demagnetization of the magnetic core, and its selection needs to consider both the shielding effect on low-frequency noise and the response speed to the target magnetic field signal. The phase delay reflects the lag characteristic of signal processing, and an overly large phase delay will reduce the synchronization between the measurement result and the real magnetic field change. In the present invention, the setting of these parameters is directly related to whether the sensor can efficiently capture the complex magnetic field changes in the underground environment, providing a reliable basis for subsequent data processing and calculation.

[0051] Embodiment 3: The magnetic field data analysis part calculates the reference output response of each high-precision fluxgate sensor according to the magnetic field components in each direction through the following formula:

[0052] ;

[0053] where, is the reference output response; is the operating time of the high-precision fluxgate sensor; is the number of turns of the induction coil; is the effective cross-sectional area of the magnetic core; is the excitation magnetic field strength; is the saturation magnetic field strength; is the radius of the magnetic core; is the magnetic domain size; is the reference permeability; is the phase delay; is the excitation frequency; is the zero-order Bessel function; is the magnetic relaxation time constant.

[0054] Specifically, in the formula, the output response is directly proportional to the number of turns of the induction coil and the effective cross-sectional area of the magnetic core . These two together determine the amount of magnetic flux change that the magnetic core can sense per unit time. The more turns of the induction coil, the stronger the induced electromotive force caused by the magnetic flux change; while the effective cross-sectional area of the magnetic core affects the uniformity of the magnetic field distribution and the conduction efficiency of the magnetic flux. In the complex magnetic field environment underground, this proportional relationship ensures that the sensor can capture sufficient magnetic field signal strength, especially crucial for the accurate measurement of weak geomagnetic field components. The formula further reflects the response ability of the magnetic core material to the magnetic field through the reference permeability . The higher the permeability, the more sensitive the magnetic core is to the external magnetic field, thus improving the induction ability of the sensor. However, the permeability is not a constant value but dynamically adjusts with changes in temperature and magnetic field strength. Therefore, in actual calculations, it needs to be corrected through the reference output and temperature parameters. In the present invention, special emphasis is placed on the real-time correction of this parameter to adapt to the influence of underground temperature changes on the sensor output, thereby ensuring the stability of the output signal.

[0055] The part in the formula describes the driving effect of the excitation magnetic field on the magnetic core. This non-linear function characterizes the magnetic core when approaching the saturation magnetic field strength Response characteristics at that time. When the excitation magnetic field approaches the saturation magnetic field, the magnetization state of the magnetic core tends to be stable, and the output signal gradually saturates. This non-linear characteristic is very important in practical applications because it avoids the infinite amplification of the output signal and enables the sensor to respond precisely to weak magnetic field changes. The time decay term reflects the dynamic characteristics of the magnetic core, where is the magnetic relaxation time constant. This term describes the process of the magnetic core recovering from the excited magnetization state to the equilibrium state and determines the response speed of the sensor to dynamic magnetic field changes. In the downhole environment, the magnetic field may change rapidly over time, and the introduction of the time decay term enables the sensor to effectively distinguish rapidly changing magnetic field signals from static magnetic field components, providing more realistic input data for subsequent magnetic field component correction and total magnetic field vector calculation. The zero-order Bessel function introduces the spatial distribution characteristics of the magnetic core, where is the radius of the magnetic core, is the magnetic domain size. This part reflects the distribution pattern of the magnetic field inside the magnetic core and is a mathematical modeling of the internal microstructure of the magnetic core. The size of the magnetic core radius affects the response ability of the sensor to spatial resolution, while the magnetic domain size determines the sensitivity of the sensor to magnetic fields of different frequencies. By introducing the Bessel function, the formula fully considers the non-uniformity inside the magnetic core, making the measurement of the magnetic field in three-dimensional space by the sensor more accurate. Finally, the sine term characterizes the periodic characteristics of the excitation signal. Among them, is the excitation frequency, is the phase delay. The periodic change of the excitation signal can effectively drive the magnetic core to complete the magnetization and demagnetization processes, while the phase delay describes the time lag characteristic in signal processing. This part ensures that the sensor can synchronously sense dynamic magnetic field signals and provides support for the real-time measurement of downhole magnetic field changes.

[0056] Example 4: The reference magnetic permeability of the high-precision fluxgate sensor is corrected through the following formula to obtain the effective magnetic permeability:

[0057] ;

[0058] where is the effective magnetic permeability; is the local energy barrier that needs to be overcome for the magnetic domain to flip or rearrange; is the Boltzmann constant; is the reference temperature; is the temperature influence coefficient, and its value range is from 0.3 to 0.5.

[0059] Specifically, the core of the formula is the reference magnetic permeability Correction. Permeability is a key physical parameter of the magnetic core material, which describes the material's ability to respond to a magnetic field. However, in practical applications, permeability is affected by multiple factors such as temperature, the microscopic characteristics within the magnetic core material, and changes in the external magnetic field. Therefore, a single reference permeability cannot accurately reflect the performance of a fluxgate sensor in a dynamic environment. This formula quantifies and incorporates these effects into the calculation by introducing multiple correction terms to obtain a more realistic effective permeability. First, the temperature correction term in the formula describes the linear adjustment relationship of permeability with temperature change. Among them, is the temperature influence coefficient, and its value range is from 0.3 to 0.5, which reflects the sensitivity of different magnetic core materials to temperature. When the ambient temperature deviates from the reference temperature , the permeability will change according to the linear relationship of this term. Generally, an increase in temperature will lead to a decrease in permeability because the magnetic domain arrangement within the magnetic core material is disrupted by thermal motion, thereby reducing the material's ability to respond to the external magnetic field. This formula quantifies this change through the temperature correction term to ensure that the sensor can still maintain high-precision measurement performance in the downhole environment with temperature fluctuations.

[0060] Secondly, the exponential correction term considers the local energy barrier that needs to be overcome when magnetic domains flip or rearrange. This energy barrier is determined by the internal structure of the magnetic core material and the interaction of magnetic domains, which affects the dynamic response ability of the magnetic core under the action of an external magnetic field. The formula describes the thermal excitation mechanism of this process through the Boltzmann factor. When the ambient temperature rises, the thermal motion within the magnetic core increases, and the probability of magnetic domain flipping and rearrangement increases, thus affecting the magnitude of permeability. This correction term accurately captures the dynamic influence of temperature on the microscopic magnetic structure of the magnetic core material through the mathematical description of the thermal excitation mechanism. Finally, the output response introduced in the formula is the actual output signal of a high-precision fluxgate sensor. By taking Incorporated into the calculation of the effective permeability, the formula directly correlates the sensor response under the action of an external magnetic field with the permeability correction process. This design combines static characteristics with dynamic response, ensuring that the corrected permeability can more accurately reflect the actual performance of the sensor in a complex magnetic field. Overall, through the combined action of the reference permeability, temperature correction term, exponential correction term, and output response, this formula comprehensively describes the dynamic change process of the effective permeability. Compared with traditional methods, this formula not only considers the influence of temperature and energy distribution, but also incorporates the actual output signal of the sensor into the correction model, making the calculation results closer to the real situation in the complex downhole environment. This correction mechanism is of great significance in the present invention because the downhole environment has significant temperature changes and complex magnetic field distributions. By accurately calculating the effective permeability, the accuracy of subsequent magnetic field component measurement and well inclination angle calculation can be significantly improved.

[0061] Example 5: According to the following formula, based on the effective permeability, calculate the corrected magnetic field components of the magnetic field components in each direction under the effective permeability:

[0062] ;

[0063] Where, is the corrected magnetic field component in the X-axis direction; is the corrected magnetic field component in the Y-axis direction; is the corrected magnetic field component in the Z-axis direction; is the installation azimuth angle of the high-precision fluxgate sensor corresponding to the X-axis direction; is the installation azimuth angle of the high-precision fluxgate sensor corresponding to the Y-axis direction; is the installation azimuth angle of the high-precision fluxgate sensor corresponding to the Z-axis direction; is the inclination angle of the high-precision fluxgate sensor corresponding to the X-axis direction; is the inclination angle of the high-precision fluxgate sensor corresponding to the Y-axis direction; is the inclination angle of the high-precision fluxgate sensor corresponding to the Z-axis direction.

[0064] Specifically, the core idea of the formula is to project the original magnetic field component onto the standard rectangular coordinate system according to the installation angle of the sensor, and dynamically adjust it in combination with the effective permeability, so as to calculate the corrected magnetic field component . First, the effective permeability It plays a role in unified calibration. Since the magnetic permeability is affected by factors such as temperature and magnetic domain structure, which directly affect the sensitivity and measurement accuracy of the sensor, it must be corrected by the aforementioned formula before being introduced into the calculation of the magnetic field components. Through this processing step, the formula effectively reduces the interference of environmental variables on magnetic field measurement, making the final corrected magnetic field components more in line with the actual situation underground. The azimuth angle in the matrix and the dip angle directly affect the directional calibration of the magnetic field components. The actual installation of the fluxgate sensor is not strictly aligned with the rectangular coordinate system. Instead, due to the requirements of the complex underground environment, there may be a certain angular deviation. The azimuth angle and dip angle describe the angular relationship between the installation direction of the sensor and the spatial coordinate axes. Through matrix multiplication, the projections of the original magnetic field components in different directions are remapped to the standard rectangular coordinate system.

[0065] For the three columns in the matrix, they respectively represent the spatial distribution patterns of the magnetic field components in three directions. The first column is mainly dominant, mainly describing the direct influence of the sensor on the magnetic field strength; the second and third columns combine and respectively to describe the component changes of the magnetic field in the plane. Through the combination of these trigonometric functions, the formula can completely capture the distribution characteristics of the magnetic field in three-dimensional space, ensuring that the corrected magnetic field components not only have accuracy but also retain the integrity of the magnetic field in space. The corrected magnetic field components are important input data finally used for calculating the total magnetic field vector. By eliminating the influence of factors such as the sensor installation angle and magnetic permeability change, the corrected magnetic field components truly reflect the actual intensity and direction of the external magnetic field. This processing is crucial for the accurate calculation of the well deviation angle and the geomagnetic field vector. Especially in the underground environment, the magnetic field is not only directly affected by the geomagnetic field but may also be superimposed with interference signals caused by surrounding well walls, equipment, etc. Through this correction formula, the influence of these interferences can be significantly reduced, minimizing the error of the sensor measurement results.

[0066] Example 6: Through the following formula, based on the corrected magnetic field components in each direction, a magnetic field gradient tensor is constructed:

[0067] ;

[0068] where is the tensor product operation; is the gradient operator; is the total magnetic field vector; is the determinant operator; is the magnetic field gradient tensor.

[0069] Specifically, the core of the formula lies in constructing the magnetic field gradient tensor by applying the gradient operator to the corrected magnetic field components. The gradient operator describes the rate of change of a field in space. When it acts on the vector field , a second-order tensor is generated, which reflects the change of each magnetic field component with respect to the spatial coordinate axes. Specifically, this change is described by the components of the gradient tensor. For example, the component represents the rate of change of the magnetic field component in the direction with respect to the coordinate, while the component represents the gradient of the magnetic field component in the direction. This description method is of great physical significance because it can reveal the local change trend of the magnetic field in three-dimensional space, thus providing accurate data support for subsequent separation of geomagnetic field components and localization of interference sources. The tensor product is a key operation in the construction of the gradient tensor. It expands the interaction between the gradient operator and the magnetic field vector into the form of a two-dimensional matrix. This process not only captures the independent change characteristics of each magnetic field component but also reflects their mutual correlation. For example, when there is an obvious change in a magnetic field component in a certain direction, this change may induce additional effects in another direction, and the tensor product is used to characterize this correlation. Therefore, the magnetic field gradient tensor not only provides local information about the magnetic field change but also reflects the overall characteristics of the magnetic field distribution through the tensor structure. This high-order description ability is particularly important for magnetic field measurements in complex downhole environments because in downhole environments, the magnetic field is usually affected by multiple factors, including the geomagnetic field, equipment interference, and geological structure, and simple scalar or vector descriptions can no longer meet the accuracy requirements.

[0070] The exponential correction term in the formula is a dynamic adjustment to the calculation result of the magnetic field gradient tensor. It improves the reliability of the gradient tensor by eliminating the influence of non-physical divergence. According to Maxwell's equations, in the case of a magnetic field without external sources, the divergence of the magnetic field should be zero, that is However, due to the complexity of the downhole environment, the sensor may be interfered by various factors, including temperature fluctuations, equipment noise, and measurement errors of magnetic field components. These factors can cause the divergence value to deviate from the ideal state, thereby affecting the accuracy of the magnetic field gradient tensor. The introduction of the exponential correction term suppresses the interference of the interference signal on the tensor calculation result by weakening the influence of the high-divergence region. For example, when the divergence value is small, the value of the exponential term is close to 1 and has little impact on the tensor; while when the divergence value is large, the exponential term decays rapidly, thus significantly reducing the weight of the interference signal in the gradient tensor. This dynamic adjustment mechanism enhances the anti-interference ability of the system, making the measured magnetic field gradient tensor closer to the true distribution in a complex environment. The practical application of the magnetic field gradient tensor lies not only in its description of the magnetic field distribution but also in its important role in the separation of geomagnetic field components. In the measurement system of the present invention, the extraction of the geomagnetic field is one of the key steps, and the gradient tensor provides the necessary basic data. By performing eigenvalue decomposition on the gradient tensor, the main trend of the magnetic field distribution can be analyzed, and the influence of environmental interference can be eliminated. For example, when the gradient characteristics in a certain direction deviate significantly from other directions, this may indicate that this direction is significantly affected by the interference source, and this interference characteristic can be clearly identified and quantified through the higher-order characteristics of the gradient tensor. In addition, by analyzing the symmetry of the gradient tensor and the change patterns of each component, the distribution law of the geomagnetic field in space can be further understood, and the pure geomagnetic field vector can be extracted accordingly. The construction and correction of the gradient tensor also provide important support for the high-precision calculation of the well deviation angle and azimuth angle. The calculation of the well deviation angle requires accurate acquisition of the spatial distribution characteristics of the magnetic field, which is closely related to the magnetic field gradient. By analyzing the gradient tensor, the change direction and intensity distribution of the magnetic field in space can be accurately determined, thereby improving the accuracy of the well deviation angle calculation. Similarly, the calculation of the azimuth angle also depends on the directional information of the magnetic field distribution. The gradient tensor provides the necessary vector basis, making the calculation result more stable and reliable. In addition, in downhole geological exploration, the gradient tensor can also be used to analyze the magnetic field characteristics of geological structures. By finely describing the magnetic field distribution, potential mineral resources or geological anomaly points can be identified, which provides more possibilities for the practical application of the present invention.

[0071] Embodiment 7: The geomagnetic field vector is separated from the total magnetic field vector through the following formula:

[0072] ;

[0073] where is a spherical surface with a set value as the radius and containing three high-precision fluxgate sensors, and the radius value range is to ; is the position vector on the spherical surface; The mean vector of the position vectors of three high-precision fluxgate sensors in a spherical surface; is the normal vector of the surface element; is the trace of the magnetic field gradient tensor.

[0074] Specifically, the first part of the formula is the core of the extraction of the geomagnetic field vector. Here, represents the total magnetic field vector, which contains the superposition of the geomagnetic field and the downhole environmental interference field. In order to separate the geomagnetic field from it, the formula adopts a method based on spherical surface integration, and focuses on analyzing the local variation characteristics of the total magnetic field in space. The surface is a spherical surface centered on the sensor, and its radius range is taken as to , where is the radius of the sensor core. Such a spherical surface selection can effectively cover the spatial range around the sensor, ensuring that all possible interference sources are considered in the integration process. At each surface element on the spherical surface, the magnetic field gradient tensor characterizes the changing trend of the magnetic field in this direction through its dot product with the normal vector . The dot product provides a scalar measure that describes the component of the gradient field in the direction of the normal vector. This measure, combined with the reciprocal of the spatial position vector difference , further emphasizes the importance of spatial position for the contribution of the interference field. In other words, the points farther away from the sensor position have less influence on the integration result, thus mathematically realizing a distance-weighted interference suppression mechanism.

[0075] The exponential correction term of the formula then further introduces a dynamic adjustment to the trace of the magnetic field gradient tensor. This term suppresses the influence of non-physical changes in the gradient field through the exponential decay of the square of the trace. The trace of the magnetic field gradient tensor is essentially the sum of the main diagonal elements of the gradient tensor, reflecting the overall change intensity of the magnetic field in all directions. According to Maxwell's equations, in the absence of an external magnetic field, the ideal magnetic field should satisfy the conditions of zero divergence and zero curl, that is . However, in the actual downhole environment, local interference magnetic fields and measurement errors may cause the trace value to deviate from zero, and this deviation will significantly affect the extraction accuracy of the geomagnetic field. Through the exponential correction term, the formula effectively suppresses the adverse effects of high-trace value regions on the integration result, thus ensuring that the finally separated geomagnetic field vector is closer to the true value. The integration operation in the formula not only captures the local changes of the magnetic field, but also realizes the spatial screening of interference sources through the geometric characteristics of the spherical surface. The normal vector of the surface element The introduction of [[]] provides directionality for the integration process, enabling the integration result to reflect the distribution characteristics of the magnetic field in different directions. This characteristic is crucial for eliminating local interference fields from the total magnetic field. For example, if the gradient field changes significantly in a certain direction, it may indicate the presence of significant local interference in that direction, and the integration result can suppress the contribution of this direction through weight adjustment, thereby improving the accuracy of geomagnetic field extraction. In addition, the position vector in the formula represents the mean position of the sensor within the spherical surface. The introduction of this mean further balances the non-uniformity of spatial positions, ensuring that the overall result will not deviate due to abnormal values at individual positions during the integration process. Combining with the distance factor , the integration result can more accurately reflect the global characteristics of the magnetic field distribution on the spherical surface.

[0076] Example 8: Through the following formula, calculate the well deviation angle value based on the geomagnetic field vector:

[0077] ;

[0078] where, is the component in the Z-axis direction; is the component in the X-axis direction; is the component in the Y-axis direction; is the first element of is the second element of is the third element of is the Langevin function; is the well deviation angle value.

[0079] Specifically, the main variables in the formula are the components of the geomagnetic field vector in different directions: , and . These components respectively represent the distribution intensities of the geomagnetic field in the , and directions, constituting the basic information of the geomagnetic field vector. The well deviation angle is calculated based on the spatial relationships of these components. The inverse cosine function represents the angle between the geomagnetic field vector and the axis. Specifically, the square root operation in the denominator part calculates the magnitude of the geomagnetic field vector, while the numerator part takes the component of the geomagnetic field vector in the direction. The ratio of the two reflects the geomagnetic field in the The proportion of the component in the [direction] is converted into an angle value directly related to the well inclination angle through the inverse cosine function. To further correct the errors caused by environmental interference and magnetic field gradient, the formula introduces an exponential weight term . The magnetic field gradient tensor The magnitude of describes the overall change intensity of the magnetic field in space, while , and are the main components of the gradient tensor respectively, representing the gradient characteristics of the magnetic field in different directions. Through this normalization process, the exponential weight term can effectively weaken the influence of abnormal gradients on the calculation of the well inclination angle. For example, when the gradient in a certain direction is significantly higher than that in other directions, this may reflect the existence of local interference sources, and the weight term can dynamically reduce the weight of this direction in the calculation of the well inclination angle, thereby improving the robustness of the result.

[0080] The formula also introduces the influence of the nonlinear characteristics of the magnetic core material on the calculation of the well inclination angle through the Langevin function . The Langevin function is a classical function that describes the magnetization state of the magnetic core under the action of an external magnetic field. Its input parameter combines the effective magnetic permeability , the saturation magnetic field intensity , the Boltzmann constant and the environmental temperature . This parameter reflects the magnetization degree of the magnetic core under the current temperature and magnetic field conditions. Since the magnetization state of the magnetic core directly affects the sensitivity of the fluxgate sensor to the geomagnetic field, the introduction of the Langevin function can theoretically quantify and correct the characteristics of the magnetic core. Specifically, as the temperature increases, the magnetization degree of the magnetic core will weaken, resulting in a decrease in the sensor sensitivity. The Langevin function incorporates this influence into the calculation process of the well inclination angle through a nonlinear response, ensuring accurate measurement results can still be obtained in the downhole environment with significant temperature changes. The structure of the formula reflects the characteristics of multi-level correction and multi-parameter fusion. From the basic relationship of the geomagnetic field vector components to the normalization weight of the gradient tensor, and then to the nonlinear description of the magnetic core material characteristics, each part has carried out mathematical modeling and quantitative correction for different environmental variables and physical phenomena. This design is of great significance in the complex downhole environment. Since the downhole magnetic field distribution is affected by various factors, including the component changes of the geomagnetic field, the superposition of local interference fields, and the influence of temperature on the sensor characteristics, simple geometric relationships cannot meet the requirements of high-precision well inclination angle calculation. Through this formula, the system can comprehensively consider the action mechanisms of various variables and calculate the well inclination angle with higher accuracy and robustness. The well inclination angle value The final calculation result is not only directly used to describe the inclination state of the wellbore, but also provides a key reference for the geomagnetic field strength measurement and azimuth calculation of the entire measurement system. Accurate well inclination angle measurement is particularly important for practical applications such as oil and gas exploration and mine surveying, because in these scenarios, the well inclination angle directly affects the positioning and calibration of measurement equipment. In addition, the introduction of the exponential weight term and the Langevin function in the formula also reflects the technological innovation of the present invention. By combining mathematical and physical models, it successfully copes with various interferences in the complex downhole environment, providing a solid theoretical and practical basis for the wide application of the system of the present invention.

[0081] Example 9: According to the following formula, calculate the azimuth value based on the geomagnetic field vector:

[0082] ;

[0083] where is the azimuth value.

[0084] Specifically, the core part of the formula expresses the directional relationship of the geomagnetic field vector in the horizontal plane. Here, is the ratio of the components of the geomagnetic field in the direction and the direction, describing the projection direction of the geomagnetic field vector on the horizontal plane. Through the arctangent function , this ratio is converted into the angle between the geomagnetic field vector and the axis, thus determining the basic value of the azimuth . This part is the geometric basis for azimuth calculation and can directly reflect the planar distribution characteristics of the geomagnetic field. However, the measurement results of the geomagnetic field vector in the downhole environment are often affected by local interference fields and equipment errors. Simply relying on geometric ratio calculation may not meet the high-precision requirements. Therefore, the formula further introduces the exponential weight term to dynamically correct the interference effect of the gradient tensor. The components of the gradient tensor , and describe the rate of change of the magnetic field in different directions. The normalized component ratio characterizes the proportion of the horizontal gradient in the total gradient. When the horizontal gradient ( and ) is significantly higher than the vertical gradient ( ), it may mean that the influence of the interference field in the horizontal plane is larger. The exponential term reduces the influence of the interference field on the azimuth calculation result by reducing the weight in this case, thereby improving the robustness of the calculation.

[0085] The formula also uses the Langevin function The non - linear characteristics of the magnetic core material are introduced for the correction of azimuth calculation. The Langevin function is a classical model describing the magnetization state of the magnetic core, and its input parameters combine the effective magnetic permeability , saturation magnetic field strength , ambient temperature , and Boltzmann constant . This parameter reflects the magnetization degree of the magnetic core under the current temperature and magnetic field conditions. Since the magnetization state of the magnetic core directly affects the sensing sensitivity of the fluxgate sensor to the geomagnetic field components, the introduction of the Langevin function can quantitatively correct the temperature change and magnetic core characteristics, thereby ensuring more accurate azimuth calculation results. In the practical application of the present invention, the accuracy of the azimuth value is crucial for the overall performance of the system. The geomagnetic field in the downhole environment is not only affected by geological structures and geomagnetic field distributions, but may also be disturbed by various complex factors such as equipment operation and electromagnetic interference. Therefore, simple geometric ratio calculations may fail due to these interferences, while the formula in Embodiment 9 significantly enhances the anti - interference ability of the system through multiple correction means. For example, when the ambient temperature rises and the magnetization performance of the magnetic core decreases, the Langevin function dynamically adjusts the sensitivity of azimuth calculation; when a local interference field causes an abnormal horizontal gradient, the exponential weight term significantly weakens its impact on the result. Through these multi - level corrections, the formula can still maintain high - precision measurement of the azimuth in a complex environment. In addition, the design of this formula also fully considers the synergistic effect between azimuth calculation and well - inclination angle measurement. In actual measurement, the azimuth and well - inclination angle jointly determine the precise positioning of the wellbore in space. The gradient tensor and magnetic core characteristic correction terms introduced in the formula not only improve the calculation accuracy of the azimuth, but also share some physical models and parameters with the well - inclination angle formula in Embodiment 8, such as the normalization processing of the effective magnetic permeability and magnetic field gradient tensor. This synergistic effect is of great significance in the overall implementation of the system, which can effectively reduce the error transmission between different measurement modules and improve the overall accuracy of the measurement system. Embodiment 10: In this embodiment, the system uses a high - precision fluxgate sensor group arranged in a three - axis orthogonal manner, and the main parameter values are as follows: the number of turns of the induction coil : 1200 turns; the effective cross - sectional area of the magnetic core : 0.015 m²; the reference magnetic permeability : 2500 H / m; the magnetic relaxation time constant : 0.002 s; the radius of the magnetic core : 0.005 m; the magnetic domain size : 0.0002 m; the excitation magnetic field strength : 50 A / m; the saturation magnetic field strength : 500 A / m; the excitation frequency : 1000 Hz (the angular frequency is about rad / s); Phase delay : 10° (about 0.1745 radians); The downhole environmental temperature is monitored in real time, and the reference temperature is set to K, Temperature influence coefficient Take 0.4, Activation energy for magnetic domain rearrangement Take 0.1 eV, Boltzmann constant eV / K.

[0086] In addition, for the convenience of accurately calibrating the downhole magnetic field, specific installation angle parameters are introduced during the installation of the sensor in this embodiment, as follows: Azimuth angle when installing the X-axis sensor : 30° (0.5236 radians), Dip angle : 5° (0.0873 radians); Azimuth angle when installing the Y-axis sensor : 120° (2.0944 radians), Dip angle : 8° (0.1396 radians); Azimuth angle when installing the Z-axis sensor : 0° (0 radians), Dip angle : 0° (perfect vertical installation); The overall system architecture is as Figure 1 shown. Each module is interconnected through a high-speed data acquisition system, and the original output signal of the sensor is transmitted to the magnetic field data analysis part for real-time data processing.

[0087] Specific calculation of the reference output response of the fluxgate sensor: Based on the foregoing parameters, the magnetic field data analysis part first calculates the reference output response of the fluxgate sensor in each direction according to the following formula : ; Where: , , H / m; Exciting magnetic field intensity A / m and saturation magnetic field intensity A / m, so there is ; Magnetic relaxation time constant s, Sensor running time Generally take t = 0.001 s for preliminary calibration in the initial stage; Core radius , Magnetic domain size m, then the Bessel function part The value obtained by numerical calculation tends to a small oscillating value, and this is corrected through a pre-established look-up table in actual data processing; Excitation frequency rad / s, and phase delay Radians. In actual calculations, the system performs digital signal processing on the time derivative and periodic sine terms of the above function, and uses a real-time filtering algorithm to smooth the output, ensuring that each sensor can provide stable reference response data in a dynamic environment.

[0088] Dynamic correction of the reference permeability: Considering the influence of downhole high temperature and environmental disturbances on the characteristics of the magnetic core material, the magnetic field data analysis part uses the following formula to correct the reference permeability to obtain the effective permeability : ; where the temperature is the real-time acquired data. Suppose the downhole temperature is 310K during a certain measurement, then: the temperature correction term is (Note: The calculated value of the temperature compensation factor is relatively large here. In actual applications, it can be corrected according to the characteristics of the magnetic core. This is only an example for illustration); the exponential correction term is ; Combining the sensor output through numerical integration or filtering to obtain a stable output value. For example, take V (the actual value depends on the calibration result). Therefore, after this correction, we get:

[0089] , This correction result enables the system to still adjust the sensitivity of the magnetic core in real time in a high-temperature environment, thus ensuring the accuracy of the measurement data.

[0090] Correction calculation of the three-axis magnetic field components: After obtaining the original magnetic field component data of the sensor group, project it into the standard rectangular coordinate system through the following formula, and combine the effective permeability to perform correction and calculate the corrected magnetic field components : ; Taking the actual sensor data as an example, suppose the original magnetic field components obtained in a single acquisition are respectively: mV, mV, mV. After amplification, filtering and normalization processing, convert them into corresponding digital quantities. Using the aforementioned installation angle parameters: ; ; ; ; ; ; ; ; ; ; For the Z-axis sensor, the inclination angle is 0°, so , ; After matrix calculation, the corrected magnetic field components in each direction can be determined. Combining the aforementioned corrected H / m, numerical calculations can be performed to ensure that the magnetic field values in each direction accurately reflect the actual downhole magnetic field conditions.

[0091] Construction and correction of the magnetic field gradient tensor: Using the corrected three-axis magnetic field components, in this embodiment, a gradient operator is used to construct the magnetic field gradient tensor : ; where: represents the partial differential operation on the spatial coordinates. For ease of implementation, a high-precision spatial sampling unit is built into this system, and its sampling interval is set to 0.1 m; takes the same value as the excitation magnetic field strength, i.e., 50 A / m; the exponential correction term is used to weaken the influence of non-zero divergence caused by local interference. For example, after obtaining the components of the gradient tensor through numerical calculations, assume that there are the following values (all units are in the standard international unit system) in a certain sampling area: T / m, T / m, T / m; T / m, T / m, T / m; T / m, T / m, T / m; after performing the determinant or divergence operation on the gradient tensor and processing it with the exponential correction term, it is ensured that the gradient tensor data can be used for subsequent geomagnetic field separation. The specific numerical calculation process has been automated in the digital signal processing module.

[0092] Geomagnetic field vector separation algorithm: In order to remove the downhole local interference magnetic field from the total magnetic field vector, the geomagnetic field vector is separated from the total magnetic field vector . The surface is a spherical surface centered on the sensor group, and its radius is taken in the range from to ; here, the radius is taken as m; is the position vector of each point on the spherical surface, is the mean vector of the sensor positions; is the normal vector of the surface element; is the trace of the gradient tensor, obtained by summing the main diagonal elements of the tensor. By integrating all the surface elements within the spherical surface, the system can effectively filter out the local interference magnetic field. For example, in a measurement, after integral calculation, it is determined that the interference component is about 0.0003 T. After exponential correction, the finally separated geomagnetic field vector has a value closer to the true geomagnetic field value. This process is completed using a numerical integration algorithm inside the system and runs in real time on the digital signal processor.

[0093] Well deviation angle calculation: Using the separated geomagnetic field vector , the measurement result calculation part calculates the well deviation angle according to the following formula :

[0094] ; where: , , are the components of the geomagnetic field vector in the X, Y, and Z directions respectively; , , are the numerical values of the main components in the gradient tensor respectively; is the Langevin function. Taking the data of this example, take H / m, A / m, eV / K, K, then there is: The corresponding Langevin function A stable value can be obtained through numerical calculation (the specific value is determined by the pre-calibration function). Let the numerical values of the separated geomagnetic field vector be: T, T, T, after calculation its modulus is about T, then the well deviation angle calculation is: ; where, assuming that the exponential term value after gradient tensor normalization is 0.95, and the result of the Langevin function is about 0.98, then the finally calculated well deviation angle is about: ; This angle value can accurately reflect the actual inclination state of the wellbore.

[0095] Azimuth calculation: Similarly, based on the separated geomagnetic field vector, this embodiment uses the following formula to calculate the wellbore azimuth : ; Let the horizontal component of the geomagnetic field vector be T, T, then the preliminary calculation gives: ; Combining the aforementioned exponential correction term (assuming the normalization result is 0.97) and the Langevin function (0.98), then the finally calculated azimuth is: . This angle value reflects the true orientation of the wellbore on the horizontal plane.

[0096] To ensure the accurate calculation of the parameters of each of the above modules, the system is built-in with a high-precision data acquisition card, whose sampling frequency is set to 10 kHz to ensure that the periodic changes of the excitation signal can be accurately captured when the excitation frequency is 1000 Hz. After all signals pass through the analog front-end amplification circuit and the low-pass filter (the cut-off frequency is set to 1.2 kHz), they enter the analog-to-digital conversion module. The digital signal processor (DSP) is responsible for processing the collected raw data through the following steps: Time-domain filtering: The Kalman filtering and moving average filtering algorithms are used to smooth the raw data to eliminate high-frequency noise and environmental interference. Temperature compensation: The downhole temperature data is collected in real time (the error is controlled within ±0.5 K), and the permeability is corrected through the aforementioned temperature correction formula. Multi-channel data fusion: The data of the three-direction sensors are fused into the standard rectangular coordinate system by using matrix transformation, and the spatial vector reconstruction is realized in combination with the calibration parameters. Gradient tensor calculation and integration: The magnetic field gradient tensor of each sampling point in space is calculated by using the difference algorithm, and numerical integration is implemented within the spherical region to separate the local interference field. Angle calculation: Based on the separated geomagnetic field vector, the well inclination angle and the azimuth angle are obtained through the arccosine and arctangent operations respectively, and further correction is carried out by using the exponential correction and the Langevin function. The data acquisition and processing are all realized through the real-time software module, and the calculation results of each step can be monitored through the host computer software. The user interface provided by the system can display the magnetic field components, gradient tensor parameters, geomagnetic field vector before and after correction, and the finally calculated well inclination angle and azimuth angle in real time, which is convenient for engineering personnel to adjust the correction parameters according to the actual situation.

[0097] To verify the specific parameters and data processing flow in Embodiment 10, this embodiment conducts experiments in the actual downhole environment. The test well depth is about 1000 m, and there are interferences from metal pipes and electrical equipment in the wellbore. After preliminary calibration, the system optimizes and adjusts the parameters of each sensor, and the specific results are as follows: After temperature compensation and permeability correction, the stability of the sensor output signal is increased by about 35%, and the noise level is reduced to 60% of the original; After data fusion and gradient tensor separation, the error between the separated geomagnetic field vector and the data in the national geomagnetic field database is less than 5%; The measured values of the well inclination angle and the azimuth angle are 36.2° and 33.8° respectively. Compared with the measurement data of the traditional gyroscope, the deviation is controlled within ±2°. The test results show that the specific parameters and data processing methods adopted in this embodiment can effectively cope with the magnetic field interference in the complex downhole environment and ensure that the measurement results have high accuracy and stability.

[0098] The above is only the specific implementation manner of the present invention, but the protection scope of the present invention is not limited thereto. Any person skilled in the art can easily think of changes or substitutions within the technical scope disclosed by the present invention, and all of them should be covered by the protection scope of the present invention. Therefore, the protection scope of the present invention should be subject to the protection scope of the claims.

Claims

1. The well inclination and geomagnetic field strength measurement system based on high-precision fluxgate sensor is characterized by: The system comprises: a fluxgate sensor group, a magnetic field data analysis part and a measurement result calculation part; The fluxgate sensor group includes three high-precision fluxgate sensors which are arranged in an underground environment and respectively measure the magnetic field components in the X-axis direction, the Y-axis direction and the Z-axis direction; The magnetic field data analysis part is used to calculate the reference output response of the high-precision fluxgate sensor according to the physical parameters of the high-precision fluxgate sensor, and correct the reference magnetic permeability of the high-precision fluxgate sensor in combination with the temperature and the reference output response at the current time to obtain the effective magnetic permeability; according to the effective magnetic permeability, calculate the corrected magnetic field component of the magnetic field component in each direction under the effective magnetic permeability, and then calculate the total magnetic field vector corresponding to the corrected magnetic field components in the three directions; construct a magnetic field gradient tensor based on the corrected magnetic field component in each direction, and separate the geomagnetic field vector from the total magnetic field vector according to the magnetic field gradient tensor; The measurement result calculation part is used to calculate the well inclination value and the azimuth value according to the geomagnetic field vector; the magnetic field intensity, well inclination value and azimuth value corresponding to the measured geomagnetic field vector are used as the final measurement result; The reference magnetic permeability of the high-precision fluxgate sensor is corrected by the following formula to obtain the effective magnetic permeability: ； in, is the effective magnetic permeability; The local energy barrier that needs to be overcome for magnetic domains to flip or rearrange; is the Boltzmann constant; is the reference temperature; is the temperature influence coefficient, ranging from 0.3 to 0.5; is the benchmark output response; is the reference magnetic permeability; is the ambient temperature.

2. The well inclination and geomagnetic field strength measurement system based on high-precision fluxgate sensor according to claim 1, characterized in that: The physical parameters of the high-precision fluxgate sensor include: number of turns of the induction coil, effective cross-sectional area of ​​the magnetic core, reference magnetic permeability, magnetic relaxation time constant, magnetic core radius, magnetic domain size, excitation magnetic field strength, saturation magnetic field strength, excitation frequency and phase delay.

3. The well inclination and geomagnetic field intensity measurement system based on high-precision fluxgate sensor according to claim 2, characterized in that: The magnetic field data analysis part calculates the reference output response of each high-precision fluxgate sensor according to the magnetic field component in each direction through the following formula: ； in, is the operating time of the high-precision fluxgate sensor; is the number of turns of the induction coil; is the effective cross-sectional area of ​​the core; is the excitation magnetic field strength; is the saturation magnetic field strength; is the core radius; is the magnetic domain size; is the phase delay; is the excitation frequency; is the zero-order Bessel function; is the magnetic relaxation time constant.

4. The well inclination and geomagnetic field intensity measurement system based on high-precision fluxgate sensor according to claim 3, characterized in that: The corrected magnetic field component of the magnetic field component in each direction under the effective magnetic permeability is calculated by the following formula according to the effective magnetic permeability: ； in, is the corrected magnetic field component in the X-axis direction; is the corrected magnetic field component in the Y-axis direction; is the corrected magnetic field component in the Z-axis direction; is the installation azimuth angle of the high-precision fluxgate sensor corresponding to the X-axis direction; The installation azimuth angle of the high-precision fluxgate sensor corresponding to the Y-axis direction; The installation azimuth angle of the high-precision fluxgate sensor corresponding to the Z-axis direction; is the inclination angle of the high-precision fluxgate sensor corresponding to the X-axis direction; is the inclination angle of the high-precision fluxgate sensor corresponding to the Y-axis direction; is the inclination angle of the high-precision fluxgate sensor corresponding to the Z-axis direction.

5. The well inclination and geomagnetic field intensity measurement system based on high-precision fluxgate sensor according to claim 4, characterized in that: The magnetic field gradient tensor is constructed based on the corrected magnetic field component in each direction using the following formula: ； in, is the tensor product operation; is the gradient operator; is the total magnetic field vector; is the determinant operator; is the magnetic field gradient tensor.

6. The well inclination and geomagnetic field intensity measurement system based on high-precision fluxgate sensor according to claim 5, characterized in that: The geomagnetic field vector is separated from the total magnetic field vector by the following formula: ； in, The spherical surface with a set value as the radius contains three high-precision fluxgate sensors. The radius range is arrive ; is the position vector on the spherical surface; The mean vector of the position vectors of three high-precision fluxgate sensors on the spherical surface; is the surface element normal vector; is the trace of the magnetic field gradient tensor.

7. The well inclination and geomagnetic field intensity measurement system based on high-precision fluxgate sensor according to claim 6, characterized in that: The well inclination angle is calculated according to the geomagnetic field vector using the following formula: ； in, for The component in the Z-axis direction; for The component in the X-axis direction; for The component in the Y-axis direction; for The first element of for The second element of for The third element of It is Lang's ten thousand functions; is the well inclination angle value.

8. The well inclination and geomagnetic field intensity measurement system based on high-precision fluxgate sensor according to claim 7, characterized in that: The azimuth value is calculated according to the geomagnetic field vector using the following formula: ； in, is the azimuth value.

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