A Gravity Gradient Measurement Method Based on Elastic Beams

Abstract

This invention discloses a method for measuring gravity gradient based on an elastic beam. The steps include: constructing two identical measurement units, each unit comprising an angle measuring instrument, an elastic beam, and a mass block. The mass block is positioned at the tail end of the elastic beam, and the fiber optic loop of the angle measuring instrument is positioned on the mass block. The mass of the elastic beam is much smaller than the mass of the mass block. When measuring the diagonal component Γ in the i-direction of the gravity gradient... ii During measurement, the first ends of the two elastic beams are fixedly connected to a base, and the elastic beams in the two measuring units are placed parallel and symmetrically along the i-direction; the distance between the two mass blocks and the axis of symmetry is h; then the diagonal component Γ is calculated using the formula. ii When performing the off-diagonal component Γ in the gravity gradient ji During measurement, the elastic beams in the two measurement units are placed end to end along the j direction.

Description

Technical Field

[0001] This invention relates to a gravity gradient measurement method based on an elastic beam, which can be used for observing the Earth's gravity gradient field. This device has important value for basic physics research, geological structure research, earthquake early warning, and inertial navigation. Background Technology

[0002] The Earth's gravitational potential W consists of two parts: the gravitational potential V caused by the Earth's mass and the centrifugal potential Q generated by the Earth's rotation. The gravitational acceleration g is the spatial first derivative of the gravitational potential W. The gravitational gradient Γ is the second tensor of the Earth's gravitational potential, representing the spatial rate of change of gravitational acceleration. The conceptual relationships among these three are shown in expressions (1) to (3):

[0003]

[0004] g(r)=grad W(r) (2)

[0005]

[0006] The diagonal components of the Γ matrix and Γ xx +Γ yy +Γ zz =4πGρ+2w 2 Since the second-order partial derivatives of the gravitational potential can be calculated in interchangeable orders, the elements of the Γ matrix are symmetric about the main diagonal, i.e., Γ xy =Γ yx ,Γ xz =Γ zx ,Γ yz =Γ zy Based on the above constraints, a single Γ matrix contains only 5 independent components.

[0007] Compared to gravitational acceleration g, the gravity gradient Γ contains more high-frequency information about geological space, making it an important source of information for geological structure inversion, geophysical research, and earthquake prediction. Therefore, the development of a high-precision gravity gradiometer is of great significance.

[0008] Current gravity gradiometer measurement schemes mainly include cold atom interferometry (CAIF) gravity gradiometers and differential accelerometer gravity gradiometers. CAIF gravity gradiometers utilize a single vertical laser beam to simultaneously measure the vertical acceleration experienced by a pair of laser-driven cold atoms falling freely from different heights, thereby obtaining the gravity gradient. However, CAIF gravity gradiometers require complex cryogenic maintenance and magnetic shielding devices, limiting their engineering practicality. Differential accelerometer gravity gradiometers use four accelerometers integrated on a rotating disk, paired and differentially matched, to solve for the gravity gradient. However, this scheme requires external drive and has extremely high requirements for the consistency between the sensors. Summary of the Invention

[0009] To address the technical problems existing in the prior art, the present invention aims to provide a gravity gradient measurement method based on an elastic beam. The instrument of this invention utilizes an elastic beam structure to induce rotational motion of a mass block under the influence of a gravity gradient. A dual-ring Sagnac interferometer structure based on a shared light source is mounted on the paired mass blocks, and the angular motion of both mass blocks is sensed in real time. The gravity gradient is calculated based on the difference in angular motion between the two mass blocks. The dual-ring Sagnac interferometer with a shared light source can suppress relative intensity noise of the light source and environmental common-mode noise, improve the measurement accuracy of the instrument, and reduce the instrument's requirements for equipment and environment.

[0010] This invention utilizes two mass blocks A and B of equal mass connected to a fixed base by parallel, equally long elastic beams. The principle of measuring the diagonal component of the gravitational gradient is illustrated below. Figure 1 The principle of off-diagonal component gravity gradient measurement is shown in the figure below. Figure 2 The midpoint of the two masses is O, and the distance between the two masses and O is h. The gravitational acceleration in the y-direction at position O is expressed as g. y0 .

[0011] First, let's take the measurement of the diagonal component of the gravitational gradient as an example. According to the definition of the gravitational gradient, the gravitational accelerations at points A and B are respectively... and in Due to the existence of a gravitational gradient, the difference in gravity experienced by the two masses leads to differences in their angular motion characteristics. The rotational torques experienced by masses A and B are respectively...

[0012]

[0013]

[0014] In the formula, m represents the mass of A and B. The vector is parallel to the elastic beam and has a modulus equal to the length of the elastic beam. The rotational motion of the two mass blocks is described by the equations of motion:

[0015]

[0016]

[0017] When the mass of the elastic beam is much smaller than that of the mass block, the moment of inertia is I = mL. 2 θ A θ B Let A and B represent the rotation angles of mass blocks A and B relative to their initial positions, respectively, where γ is the system damping coefficient and k is the elastic modulus of the elastic beam. From this, we can derive the equation describing the difference in angular motion between the two masses:

[0018]

[0019] Where Δθ=θ A -θ B Substituting equations (4) and (5) into equation (8) yields the gravitational gradient Γ. yy Relationship with angular motion difference:

[0020]

[0021] In the formula, h represents the distance between the two mass blocks and the center O. A fiber optic Sagnac interferometer is installed on mass blocks A and B respectively to measure θ. A With θ B Based on the measured θ A θ B Solve for the diagonal component of the spatial gravity gradient Γ using formula (9). yy .

[0022] Change the orientation of the elastic beam and the relative positions of the two mass blocks, such as... Figure 2 As shown, the gravity gradient Γ at this time xy Relationship with angular motion difference:

[0023]

[0024] Based on the measured θ A θ B The off-diagonal component of the spatial gravity gradient Γ is solved using formula (10). xy .

[0025] The angular motion sensor used in this invention is a Sagnac interferometer. Because it is necessary to measure the motion difference between the two mass blocks, this invention constructs a RIN-suppressed Sagnac interferometer structure based on a shared light source. The schematic diagram of the device is shown below. Figure 3 Since relative intensity noise is a common-mode component in both gyroscopes, this system can eliminate relative intensity noise while calculating the difference in angular acceleration, thus improving measurement accuracy. Simultaneously, environmental noise can also be suppressed through this differential method, reducing the environmental requirements of the gravity gradient measurement scheme.

[0026] The technical solution of this invention is as follows:

[0027] A method for measuring gravity gradient based on an elastic beam, comprising the following steps:

[0028] 1) Construct two identical measurement units. Each measurement unit includes an angle measuring instrument, an elastic beam, and a mass block. The mass block is located at the tail end of the elastic beam, and the fiber optic loop of the angle measuring instrument is located on the mass block.

[0029] The mass of the elastic beam is much smaller than the mass of the mass block. The length of the elastic beam is L, and the mass of the mass block is m. The mass block of the first measuring unit is denoted as mass block A, and the mass block of the second measuring unit is denoted as mass block B.

[0030] 2) When calculating the diagonal component Γ in the i-direction of the gravitational gradient ii During measurement, the first ends of the two elastic beams are fixedly connected to a base, and the elastic beams in the two measuring units are placed parallel and symmetrically along the i-direction; the distances of mass block A and mass block B from the axis of symmetry are both h; then the rotation angle of the mass block relative to its initial position is measured using the angle measuring instrument, and then the formula is used. The diagonal component Γ was calculated. ii ;

[0031] Where i is x, y, or z; θ A Let θ represent the rotation angle of mass block A relative to its initial position. B This represents the rotation angle of mass block B relative to its initial position; Δθ = θ A -θ B Moment of inertia I = mL 2 γ is the damping coefficient, and k is the elastic coefficient of the elastic beam;

[0032] 3) When performing the off-diagonal component Γ in the gravity gradient ji During measurement, the elastic beams in the two measurement units are placed end to end along the j direction, and the first ends of the two elastic beams are fixedly connected to a base respectively; the midpoint between the mass block A and the mass block B is recorded as O, and the distance from the midpoint O to both the mass block A and the mass block B is h;

[0033] Then, the rotation angle of the mass block relative to its initial position is measured using the angle measuring instrument, and then the formula is used.

[0034] The off-diagonal component Γ was calculated. ji ; i is x, y, or z, j is x, y, or z, and i is not equal to j; θ A Let θ represent the rotation angle of mass block A relative to its initial position. B This represents the rotation angle of mass block B relative to its initial position; Δθ = θ A -θ B Moment of inertia I = mL 2 γ is the damping coefficient, and k is the elastic coefficient of the elastic beam.

[0035] Furthermore, the angle measuring instrument is a Sagnac interferometer.

[0036] Furthermore, the angle measuring instrument is an angular accelerometer, an angle sensor, or an angular motion sensor.

[0037] Furthermore, the angle measuring instruments of both measurement units share the same light source.

[0038] A gravity gradient measuring device based on an elastic beam is characterized by comprising a data processing unit and two identical measuring units. Each measuring unit includes an angle measuring instrument, an elastic beam, and a mass block. The mass block is disposed at the tail end of the elastic beam, and the fiber optic loop of the angle measuring instrument is disposed on the mass block. The mass of the elastic beam is much smaller than the mass of the mass block. The length of the elastic beam is L, and the mass of the mass block is m. The mass block of the first measuring unit is denoted as mass block A, and the mass block of the second measuring unit is denoted as mass block B.

[0039] When considering the diagonal component Γ in the i-direction of the gravitational gradient... ii During measurement, the first ends of the two elastic beams are fixedly connected to a base, and the elastic beams in the two measurement units are placed parallel and symmetrically along the i direction; the distances of mass block A and mass block B from the axis of symmetry are both h; where i is x, y or z;

[0040] When considering the off-diagonal component Γ of the gravity gradient ji During measurement, the elastic beams in the two measurement units are placed end to end along the j direction, and the first ends of the two elastic beams are fixedly connected to a base respectively; the midpoint between the mass block A and the mass block B is marked as O, and the distance from the midpoint O to the mass block A and the mass block B is h; i is x, y or z, j is x, y or z, and i is not equal to j;

[0041] The angle measuring instrument is used to measure the rotation angle of the mass block relative to its initial position and send it to the data processing unit;

[0042] The data processing unit is used to utilize the formula The diagonal component Γ was calculated. ii ; and using formulas The off-diagonal component Γ was calculated. ji ; where θ A Let θ represent the rotation angle of mass block A relative to its initial position. B This represents the rotation angle of mass block B relative to its initial position; Δθ = θ A -θ B Moment of inertia I = mL 2 γ is the damping coefficient, and k is the elastic coefficient of the elastic beam.

[0043] Compared with the prior art, the positive effects of the present invention are as follows:

[0044] The entire device consists only of a fiber optic Sagnac interferometer and an elastic beam structure, making its components simple. Compared with existing gravity gradient measurement techniques, it eliminates the need for complex cryogenic control equipment. This invention offers high scalability; the measurement accuracy can be flexibly adjusted by changing the size of the fiber optic Sagnac interferometer. The use of differential-mode detection effectively eliminates the influence of common-mode noise, including environmental vibration noise and relative intensity noise from the light source, thus reducing the environmental requirements of the gravity gradient measurement scheme. Attached Figure Description

[0045] Figure 1 A schematic diagram of the diagonal component gravity gradient measurement based on the Sagnac interferometer with an elastic beam.

[0046] Figure 2 Schematic diagram of off-diagonal component gravity gradient measurement based on the Sagnac interferometer with an elastic beam.

[0047] Figure 3 Schematic diagram of RIN suppression optical path structure based on shared light source. Detailed Implementation

[0048] The present invention will now be described in further detail with reference to the accompanying drawings.

[0049] The angle measurement principle of this invention is as follows: Figure 3 As shown, measuring the gravitational gradient component requires at least one pair of elastic beam Sagnac interferometer structures. One elastic beam structure, one mass block, and one Sagnac interferometer are defined as a measurement element. Measuring one gradient requires two measurement units: the first measurement unit consists of one elastic beam structure, one mass block A, and Sagnac interferometer A; the second measurement unit consists of one elastic beam structure, one mass block B, and Sagnac interferometer B. Both measurement units are fixed to the same base.

[0050] Natural ground vibrations can affect the angle detection of a single measuring element. However, in practice, the interference experienced by two paired measuring elements is highly correlated. The differential mode detection expressed by formulas (9) and (10) can eliminate some of the influence of ground vibration interference.

[0051] The relative intensity noise of the light source refers to the random fluctuations in the output optical power of the broadband light source. Since the present invention adopts the differential mode detection structure of the shared light source, the relative intensity noise of the light source belongs to the common mode noise in the differential pairing Sagnac interferometer, and can be suppressed by the differential mode detection expressed by formula (9) and formula (10).

[0052] Other gravity gradient components can be obtained by adjusting the orientation and relative position distribution of the elastic beams of the device.

[0053] The Sagnac interferometer used to measure angular motion differences in the above implementation examples can be replaced with other angle measuring instruments.

[0054] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for measuring gravity gradient based on an elastic beam, comprising the following steps: 1) Construct two identical measurement units. Each measurement unit includes an angle measuring instrument, an elastic beam, and a mass block. The mass block is located at the tail end of the elastic beam, and the fiber optic loop of the angle measuring instrument is located on the mass block. The mass of the elastic beam is much smaller than the mass of the mass block. The length of the elastic beam is L, and the mass of the mass block is m. The mass block of the first measurement unit is denoted as mass block A, and the mass block of the second measurement unit is denoted as mass block B. 2) When calculating the diagonal component Γ in the i-direction of the gravitational gradient ii During measurement, the first ends of the two elastic beams are fixedly connected to a base, and the elastic beams in the two measuring units are placed parallel and symmetrically along the i-direction; the distances of mass block A and mass block B from the axis of symmetry are both h; then the rotation angle of the mass block relative to its initial position is measured using the angle measuring instrument, and then the formula is used. The diagonal component Γ was calculated. ii Where i is x, y, or z; θ A Let θ represent the rotation angle of mass block A relative to its initial position. B This represents the rotation angle of mass block B relative to its initial position; Δθ = θ A -θ B Moment of inertia I = mL 2 γ is the damping coefficient, and k is the elastic coefficient of the elastic beam; 3) When performing the off-diagonal component Γ in the gravity gradient ji During measurement, the elastic beams in the two measuring units are placed end-to-end along the j-direction, with the first ends of each beam fixedly connected to a base. The midpoint between mass block A and mass block B is denoted as O, and the distances from both mass block A and mass block B to the midpoint O are both h. Then, the rotation angle of the mass block relative to its initial position is measured using the angle measuring instrument, and then the formula is applied. The off-diagonal component Γ was calculated. ji ; i is x, y, or z, j is x, y, or z, and i is not equal to j; θ A Let θ represent the rotation angle of mass block A relative to its initial position. B This represents the rotation angle of mass block B relative to its initial position; Δθ = θ A -θ B Moment of inertia I = mL 2 γ is the damping coefficient, and k is the elastic coefficient of the elastic beam.

2. The method according to claim 1, characterized in that, The angle measuring instrument is a Sagnac interferometer.

3. The method according to claim 1, characterized in that, The angle measuring instrument is an angular accelerometer, an angle sensor, or an angular motion sensor.

4. The method according to claim 1, 2, or 3, characterized in that, The angle measuring instruments of the two measuring units share the same light source.

5. A gravity gradient measuring device based on an elastic beam, characterized in that, The device includes a data processing unit and two identical measurement units. Each measurement unit includes an angle measuring instrument, an elastic beam, and a mass block. The mass block is located at the tail end of the elastic beam, and the fiber optic loop of the angle measuring instrument is located on the mass block. The mass of the elastic beam is much smaller than the mass of the mass block. The length of the elastic beam is L, and the mass of the mass block is m. The mass block of the first measurement unit is denoted as mass block A, and the mass block of the second measurement unit is denoted as mass block B. When considering the diagonal component Γ in the i-direction of the gravitational gradient... ii During measurement, the first ends of the two elastic beams are fixedly connected to a base, and the elastic beams in the two measurement units are placed parallel and symmetrically along the i direction; the distances of mass block A and mass block B from the axis of symmetry are both h; where i is x, y or z; When considering the off-diagonal component Γ of the gravity gradient ji During measurement, the elastic beams in the two measurement units are placed end to end along the j direction, and the first ends of the two elastic beams are fixedly connected to a base respectively; the midpoint between the mass block A and the mass block B is marked as O, and the distance from the midpoint O to the mass block A and the mass block B is h; i is x, y or z, j is x, y or z, and i is not equal to j; The angle measuring instrument is used to measure the rotation angle of the mass block relative to its initial position and send it to the data processing unit; The data processing unit is used to utilize the formula The diagonal component Γ was calculated. ii ; and using formulas The off-diagonal component Γ was calculated. ji ; where θ A Let θ represent the rotation angle of mass block A relative to its initial position. B This represents the rotation angle of mass block B relative to its initial position; Δθ=θ A -θ B Moment of inertia I = mL 2 γ is the damping coefficient, and k is the elastic coefficient of the elastic beam.

6. The gravity gradient measuring device according to claim 5, characterized in that, The angle measuring instrument is a Sagnac interferometer.

7. The gravity gradient measuring device according to claim 5, characterized in that, The angle measuring instrument is an angular accelerometer, an angle sensor, or an angular motion sensor.

8. The gravity gradient measuring device according to claim 5, 6, or 7, characterized in that, The angle measuring instruments of the two measuring units share the same light source.

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