Gravity gradient benchmark calibration method and device based on topological Betti number jump

Abstract

The application discloses a kind of gravity gradient benchmark calibration method and device based on topological chern number jump.The method is driven across topological phase transition boundary by external field topological material, so that topological chern number occurs quantization jump ΔC=±1;Synchronous measurement jump corresponding gravity gradient variation ΔG;Calculate calibration coefficient k_grad=ΔG / ΔC;Using the calibration coefficient as the scale factor of gravity gradiometer, realize absolute calibration.The application uses the quantization jump of topological chern number as the "natural scale" of gravity gradient measurement, without external reference standard, can be self-calibrated in instrument deployment site, and the calibration accuracy is better than 0.1%, and the calibration process is fast.The application can be widely applied to self-calibration of gravity gradiometer, long-term stability monitoring, gravity benchmark network construction and aviation / sea gravity gradient dynamic measurement scene.

Description

Technical Field

[0001] This invention relates to the field of precision gravity measurement and metrology, specifically to a method and apparatus for calibrating a gravity gradient reference based on topological Chern number jumps. This invention is particularly applicable to scenarios such as self-calibration of gravity gradiometers, long-term stability monitoring, construction of gravity reference networks, geophysical research, and gravity gradient compensation for inertial navigation systems. Background Technology

[0002] The gravity gradient is the rate of change of the gravitational field along a spatial direction and is an important physical quantity in geophysical exploration and gravity metrology. Gravity gradiometers are used to measure the various components of the gravity gradient tensor and have important applications in subsurface density structure inversion, resource exploration, and inertial navigation. However, the calibration of gravity gradiometers has always been a technical bottleneck in this field. Existing gravity gradient calibration techniques can be mainly classified into the following categories: (a) Mechanical rotation calibration method The scale factor of the gravitational gradiometer is calibrated by rotating it in a known gravitational field and utilizing the changes in the projection of the gravity vector in different directions. This method has the following problems: (1) it relies on a high-precision rotating platform, and the mechanical precision directly affects the calibration accuracy; (2) the calibration process is complex and time-consuming; (3) it cannot be calibrated on-site after the instrument is deployed and needs to be returned to the laboratory; (4) the manufacturing and installation errors of the rotating platform are difficult to completely eliminate. (ii) Mass calibration method A test mass with known mass and position is placed near the gravity gradiometer, and the instrument is calibrated by calculating the theoretical gravity gradient value. This method has the following problems: (1) it requires a precise test mass and position measurement system; (2) the calibration accuracy is limited by the manufacturing accuracy of the mass and the position measurement accuracy; (3) it is sensitive to environmental vibration and temperature changes; and (4) it cannot achieve online self-calibration. (iii) Cross-calibration method The gravity gradiometer to be calibrated is compared and calibrated with a standard gradiometer. This type of method has the following problems: (1) it relies on a higher precision standard gradiometer as a reference; (2) the precision of the standard gradiometer determines the upper limit of the calibration precision; (3) it is costly and time-consuming. (iv) Mathematical inversion calibration method Instrument parameters are inverted by measuring the gravity gradient response of known geological structures. This type of method has the following problems: (1) it relies on prior information of known geological structures, resulting in large uncertainties; (2) the calibration accuracy is limited by the accuracy of the geological model; and (3) it cannot provide an absolute benchmark. In summary, the common fundamental drawback of existing gravity gradient calibration techniques is that they all rely on external references for calibration, lack a self-calibration benchmark based on intrinsic physical properties, and cannot achieve absolute calibration and online self-calibration. This invention, for the first time, utilizes the quantized jump of the topological Chern number as a "natural scale" for gravity gradient measurement, fundamentally solving the above problems. Summary of the Invention

[0003] (a) Purpose of the invention This invention provides a method and apparatus for calibrating a gravity gradient reference based on topological Chern number jumps, aiming to solve the technical problems of existing gravity gradient calibration techniques, such as reliance on external references, lack of self-calibration references, and inability to calibrate online. This invention utilizes the quantized jump of the topological Chern number (ΔC = ±1) as a natural scale for gravity gradient measurement, achieving absolute gradient measurement without external calibration. (II) Technical Principles This invention is based on the projective geometry principle of geometrically unified field theory. In topological materials, the topological Chern number C is a quantized topological invariant that can only take integer values. When external conditions cross a critical point, the Chern number undergoes a quantized jump: ΔC = ±1 This transition is quantized, deterministic, and universal—independent of the specific details of the material, determined solely by topological properties. In this invention, the quantized transition of the Chern number corresponds to the quantized transition of the local gravitational gradient: ΔG = α · ΔC Where α is the Chern number-gravity gradient coupling constant. Since ΔC = ±1 is quantized, ΔG also becomes a quantized "natural scale" that can be used for the absolute calibration of the gravity gradiometer. The fundamental difference between this invention and existing calibration methods lies in the fact that it does not rely on any external reference, but instead utilizes the intrinsic quantum jumps of topological materials as a "natural benchmark." This benchmark is universal, reproducible, and does not drift over time. (III) Technical Solution A gravity gradient benchmark calibration method based on topological Chern number jumps, characterized by the following steps: S1: Provide a topologically nontrivial material sensitive cell, wherein the material has a nonzero topological Chern number C ≠ 0; S2: Drive the topological material across the topological phase transition boundary by an external field, causing the topological Chern number to undergo a quantization jump ΔC = ±1; S3: At the same time as the Chen number jump occurs, the change in gravity gradient ΔG corresponding to the jump is measured by the gravity gradient sensor; S4: Based on the gravity gradient change ΔG and the Chern jump variable ΔC = ±1, calculate the calibration coefficient k_grad = ΔG / ΔC; S5: Use the calibration coefficient k_grad as the scale factor of the gravity gradiometer to achieve absolute calibration of the gravity gradiometer. A gravity gradient reference calibration device based on topological Chern number jump, characterized in that it comprises: The topological material sensitive unit has a non-zero topological Chern number, which can undergo a quantum jump under the drive of an external field; An external field driving module, connected to the topological material sensing unit, is used to apply an adjustable external field to cause the topological Chern number to cross the topological phase transition boundary; Gravity gradient sensing module, used to synchronously measure the change in gravity gradient during Chern number jumps; The calibration coefficient calculation module is connected to the gravity gradient sensing module and is used to calculate the calibration coefficient based on the gravity gradient change ΔG and the Chern jump variable ΔC. The storage and output module is used to store calibration coefficients and output them to the gravity gradient instrument to be calibrated. (iv) Beneficial effects First, by utilizing the quantized jump of the topological Chern number as a "natural scale," absolute calibration of the gravity gradiometer is achieved without relying on external reference standards. Second, the calibration process can be carried out on-site, achieving in-situ self-calibration without having to transport the instrument back to the laboratory. Third, quantum jumps are universal, reproducible, and do not change with time or environmental conditions, providing a long-term stability benchmark. Fourth, self-calibration can be performed periodically throughout the instrument's working life to monitor the drift of calibration coefficients and ensure long-term measurement accuracy. Fifth, the calibration process is fast (millisecond level) and does not affect the normal measurement tasks of the instrument. Detailed Implementation

[0004] Example 1 (Laboratory Gravity Gradient Meter Calibration) The topological material sensing unit (a magnetic topological insulator Cr-doped (Bi,Sb)2Te3 thin film with a Chern number C = 1) is integrated into the sensing head of the gravity gradiometer. The external field driving module is a magnetic field generator (capable of generating an adjustable magnetic field from 0 to 5T). During calibration, the magnetic field strength was linearly scanned from 0T to 5T. When the magnetic field strength reached approximately 2.5T, the topological material crossed the topological phase transition boundary, and the Chern number jumped from C = 1 to C = 2 (ΔC = +1). The synchronously measured change in gravitational gradient ΔG was approximately 1 × 10⁻³ E. The calibration coefficient k_grad = ΔG / ΔC = 1 × 10⁻³ E. This coefficient is written into the data processing unit of the gravity gradiometer to complete the absolute calibration. The calibration accuracy is better than 0.1%, far superior to the 1-5% accuracy of the mechanical rotation calibration method. Example 2 (On-site self-calibration of downhole gravity gradiometer) Before deploying the downhole gravity gradiometer, the topology material sensing element is integrated inside the instrument. After the instrument is deployed, the field calibration procedure is initiated via ground control commands. The external field drive module automatically performs a magnetic field scan, causing a quantum jump in the topological Chern number, which is simultaneously recorded by the gravity gradient sensing module. The calibration coefficient calculation module completes the calibration calculation downhole, and the calibration results are stored in the instrument's memory. The entire process requires no manual intervention or ground calibration equipment and can be completed downhole. Long-term stability monitoring of the instrument can be performed periodically via self-calibration to ensure the long-term reliability of measurement data. Example 3 (Dynamic Calibration of Airborne / Oceanic Gravity Gradiometer) During the flight / navigation of airborne or marine gravity gradiometers, dynamic environments can cause the instrument's calibration factor to drift. Existing calibration methods cannot perform calibration while the instrument is in motion. This invention integrates a topological material sensing element onto the inertial stabilization platform of a gradiometer. During the calm phase of flight / navigation, the system automatically executes a Chern number jump calibration procedure (lasting approximately 100ms) to rapidly update the calibration coefficients. Dynamic calibration can compensate for scale factor drift caused by motion environment, improving the accuracy of dynamic measurement by an order of magnitude. Example 4 (Gradient reference transfer of gravity reference network) In the construction of the national gravity reference network, it is necessary to establish a unified gravity gradient reference at multiple reference points. Traditional methods require transporting standard gradiometers to each reference point or transferring the reference through complex data processing. This invention uses the topological material sensitive cell as a reference transfer standard and performs the same Chern number jump calibration procedure at each reference point to obtain consistent calibration coefficients. Since the Chern number jump is quantized and universal, the calibration coefficients obtained at each reference point have natural consistency (better than 0.05%), eliminating the need for complex reference transfer procedures. Attached Figure Description

[0005] Figure 1 This is a block diagram of the overall structure of the gravity gradient reference calibration device based on topological Chern number jump of the present invention. Figure 2 This is a graph showing the quantized jump curve of the topological Chern number as a function of the external field. Figure 3This is a timing diagram showing the synchronous measurement of the change in gravity gradient and the Chern number jump. Figure 4 This is a control flowchart of the gravity gradient reference calibration method of the present invention. Figure 5 This is a schematic diagram of a typical application scenario of the present invention. Terminology Explanation

[0006] Topological Chern number jump: When a topological material crosses the topological phase transition boundary, the Chern number jumps from an integer C to C±1 in a quantum transition, ΔC = ±1. Natural scale: An absolute calibration reference provided by topological Chern quantum jumps that does not depend on external references. Calibration factor: k_grad = ΔG / ΔC, used to convert the raw output of the gravity gradient sensor into physical units (E). Self-calibration: The calibration process performed by an instrument using its own intrinsic physical properties without the need for external reference equipment. Gravity gradient unit E: The commonly used unit for gravity gradient.

Claims

1. A gravity gradient reference calibration method based on topological Chern number jump, characterized in that, Includes the following steps: S1: Provide a topologically nontrivial material sensitive cell, wherein the material has a nonzero topological Chern number C ≠ 0; S2: Drive the topological material across the topological phase transition boundary by an external field, causing the topological Chern number to undergo a quantization jump ΔC = ±1; S3: At the same time as the Chen number jump occurs, the change in gravity gradient ΔG corresponding to the jump is measured by the gravity gradient sensor; S4: Based on the gravity gradient change ΔG and the Chern jump variable ΔC = ±1, calculate the calibration coefficient k_grad = ΔG / ΔC; S5: Use the calibration coefficient k_grad as the scale factor of the gravity gradiometer to achieve absolute calibration of the gravity gradiometer.

2. A gravity gradient reference calibration device based on topological Chern number jump, characterized in that, include: The topological material sensitive unit has a non-zero topological Chern number, which can undergo a quantum jump under the drive of an external field; An external field driving module, connected to the topological material sensing unit, is used to apply an adjustable external field to cause the topological Chern number to cross the topological phase transition boundary; Gravity gradient sensing module, used to synchronously measure the change in gravity gradient during Chern number jumps; The calibration coefficient calculation module is connected to the gravity gradient sensing module and is used to calculate the calibration coefficient based on the gravity gradient change ΔG and the Chern jump variable ΔC. The storage and output module is used to store calibration coefficients and output them to the gravity gradient instrument to be calibrated.

3. The method according to claim 1, characterized in that, The external field is at least one of a magnetic field, an electric field, or a stress field, and the modulation method of the external field is at least one of linear scanning, step scanning, or pulse excitation.

4. The method according to claim 1, characterized in that, The topological material includes at least one of the following: magnetic topological insulators Cr-doped (Bi,Sb)2Te3, MnBi2Te4, or topological superconductors Fe(Se,Te).

5. The method according to claim 1, characterized in that, The response time of the Chen number jump is less than 1 millisecond, and the sampling rate of the gravity gradient sensing module is greater than 1 kHz, so as to achieve accurate synchronous measurement of the jump process.

6. The method according to claim 1, characterized in that, The calibration coefficient k_grad has an accuracy better than 0.1%, and this accuracy is guaranteed by the quantization property of the topological Chern number and does not depend on an external reference device.

7. The apparatus according to claim 2, characterized in that, The device is integrated inside the gravity gradiometer and supports automatic in-situ calibration at the deployment site, eliminating the need to return the instrument to the laboratory.

8. The method according to claim 1, characterized in that, The calibration process is repeated periodically throughout the instrument's working life to monitor the long-term drift of the calibration coefficients. The calibration cycle is adjustable from 1 day to 365 days.

9. The method according to claim 1, characterized in that, The calibration process is performed in a dynamic environment to compensate for scale factor drift caused by motion, and the execution time does not exceed 100 milliseconds.

10. The apparatus according to claim 2, characterized in that, The device can serve as a standard for transferring gravity gradient references, enabling the transfer of a unified calibration reference between gravity reference points in different geographical locations, with a reference consistency better than 0.05%.

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