CN105717553A - Calibration method for gravity gradient instrument of rotary accelerometer - Google Patents

Abstract

The invention discloses a calibration method for a gravity gradient instrument of a rotary accelerometer. Mass bodies are arranged at four different positions of an outside space of the gravity gradient instrument successively, the mass of the mass bodies is changed to change a gravity field at the center of the gravity gradient instrument, and the gravity gradient instrument is sensitive to the changed gravity field. Filtering and gravity demodulation are carried out on output signals of the gravity gradient instrument, and a gravity gradient measuring result of the gravity gradient instrument is obtained. The measuring result is calculated and then compared with a theoretical gravity gradient value which is obtained by calculating mass change of the mass bodies, and zero positions and scale coefficients of two gravity gradient components of the gravity gradient instrument are obtained. The calibration method of the invention can be used to calibrate the gradient of the gravity gradient instrument of the rotary accelerometer.

Description

Calibration method for gravity gradiometer of rotating accelerometer

Technical Field

The invention relates to a gravity gradient calibration method for a gravity gradiometer of a rotary accelerometer, in particular to a method for realizing gravity gradient calibration of the gravity gradiometer of the rotary accelerometer by changing the mass of a mass body, belonging to the technical field of precision measurement.

Background

The high-precision gravity gradient measurement has very important application value and application prospect in the aspects of energy exploration, space science, earth science, geological science, inertial navigation and the like. The gravity gradient measurement has obvious advantages compared with the gravity measurement, can provide higher resolution for the information of the shape, the size, the buried depth and the like of the geological structure, and is particularly suitable for detecting and researching the local geological structure and the details thereof. At present, the gravity gradiometers which are researched abroad and have application prospects mainly comprise a rotary accelerometer gravity gradiometer, a superconducting gravity gradiometer, a cold atom gravity gradiometer, a satellite gravity gradiometer and the like, wherein the rotary accelerometer gravity gradiometer has the most mature technology, is the gravity gradiometer which is firstly commercially used and has already performed a great deal of exploration work; the application prospect of the gravity gradiometer is noticed at the end of the last century in China, a plurality of scientific research units cooperate to carry out related research, and the research directions of the gravity gradiometer with a plurality of different measurement principles are branched, wherein the gravity gradiometer comprises a rotary accelerometer type gravity gradiometer, a superconducting gravity gradiometer, a cold atom gravity gradiometer, a gravity gradiometer based on a micro-mechanical system (MEMS) structure, a satellite gravity gradiometer and the like, the theoretical research of the rotary accelerometer gravity gradiometer is basically mature, a gravity gradiometer model machine has been developed by national scientific research institutes, and the resolution of the gravity gradiometer is still lower due to the reasons of sensor performance, rotary structure stability, temperature.

The gravity gradiometer is a high-precision measuring instrument, and is very difficult to manufacture a gravity gradiometer with excellent performance, even an enterprise capable of manufacturing the gravity gradiometer cannot carry out batch production, and one of important reasons is that measuring elements are difficult to produce in batches, and only a small amount of qualified sensitive devices can be screened out from a large amount of samples. In order to measure more accurate gravity gradient, the gravity gradiometer needs to be calibrated before use. At present, no relevant patent or literature publication or publication exists about the calibration method of the gravity gradiometer of the rotating accelerometer.

Disclosure of Invention

The technical problem is as follows: the invention provides a calibration method of a gravity gradiometer of a rotary accelerometer, which is simple, efficient, convenient to realize and has important practical value.

The technical scheme is as follows: the invention discloses a calibration method of a gravity gradiometer of a rotary accelerometer, which comprises the following steps:

1) the operation before gravity gradient calibration is carried out on the rotating accelerometer gravity gradiometer comprises the following specific contents:

establishing a gravity gradiometer coordinate system as a northeast geographic coordinate system, and recording the coordinate system as OXYZ, wherein an origin O is the center of a rotating disk of the gravity gradiometer; at the initial moment, an accelerometer A on the disc is set₁The center of mass of (2) is located in the positive direction of the X axis;

setting 4 mass body placing positions which are equidistant to a coordinate origin on an XY plane of a gravity gradiometer coordinate system, wherein the position 1 is in the positive direction of X and an axis, the position 2 is in the positive direction of Y axis, the position 3 is in the linear equation Y which is equal to X, and the position 4 is in the linear equation Y which is equal to X;

2) placing a mass body at a placing position, and performing gravity gradient demodulation on the output signal of the gravity gradiometer to obtain a gravity gradient component (_yy-_xx)_1,1(ii) a Then on the basis of the number of the mass bodies placed at the last time, the mass of the mass bodies at the placing positions is changed gradually, and the gravity gradient demodulation is carried out on the output signal of the gravity gradiometer, wherein the mass of the mass body placed at each time is twice of that of the mass body placed at the last time; for each placement position, according to the above operation, the following results are obtained:

gravity gradient component of position 1: (_yy-_xx)_1,1、(_yy-_xx)_1,2、(_yy-_xx)_1,4、……、(_yy-_xx)_1,2 ^n--1

Gravity gradient component of position 2: (_yy-_xx)_2,1、(_yy-_xx)_2,2、(_yy-_xx)_2,4、……、(_yy-_xx)_2,2 ^n-1；

Gravity gradient component of position 3: (_xy)_3,1、(_xy)_3,2、(_xy)_3,4、……、(_xy)_3,2 ^n-1；

Gravity gradient component of position 4: (_xy)_4,1、(_xy)_4,2、(_xy)_4,4、……、(_xy)_4,2 ^n-1；

Wherein n is the ordinal number of gravity gradient demodulation, n is 1 when the mass body is placed for the first time, and the ordinal number n is increased by 1 when the mass body is changed every time;

3) calculating the gravity gradient component of the gravity gradiometer according to the formula (_yy-_xx) Zero position of (2):

${\mathrm{\Γ}}_{yy-xx}^{c0}=\frac{1}{n}\underset{i=1}{\overset{n}{\Σ}}\frac{{({\mathrm{\Γ}}_{yy}-{\mathrm{\Γ}}_{xx})}_{1,2^{i-1}}+{({\mathrm{\Γ}}_{yy}-{\mathrm{\Γ}}_{xx})}_{2,2^{i-1}}}{2}$

calculating the gravity gradient component of the gravity gradiometer according to the formula (_xy) Zero position of (2):

${\mathrm{\Γ}}_{xy}^{c0}=\frac{1}{n}\underset{i=1}{\overset{n}{\Σ}}\frac{{\left({\mathrm{\Γ}}_{xy}\right)}_{3,2^{i-1}}+{\left({\mathrm{\Γ}}_{xy}\right)}_{4,2^{i-1}}}{2}$

calculating the gravity gradient component theoretical value generated by the mass body to the center of the gravity gradiometer according to the following formula:

$\left\{\begin{array}{c}{({\mathrm{\Γ}}_{yy}-{\mathrm{\Γ}}_{xx})}_{2^{i-1}}^t=3G\mathrm{\ρ}{\∫}_{W_i-w/2}^{W_i+w/2}dx{\∫}_{D_i-d/2}^{D_i+d/2}dy{\∫}_{H_i-h/2}^{H_i+h/2}\frac{(y^2-x^2)}{{(x^2+y^2+x^2)}^{5/2}}dz\\ {\left({\mathrm{\Γ}}_{xy}\right)}_{2^{i-1}}^t=3G\mathrm{\ρ}{\∫}_{W_i-w/2}^{W_i+w/2}dx{\∫}_{D_i-d/2}^{D_i+d/2}dy{\∫}_{H_i-h/2}^{H_i+h/2}\frac{xy}{{(x^2+y^2+z^2)}^{5/2}}dz\end{array}\right.$

wherein, (x, y, z) is the position coordinate of any point in the mass body, (W)_i,D_i,H_i) The mass center coordinate of the mass body is placed for the ith time, G is a Newton universal gravitation constant, rho is the density of the mass body, w, d and h are respectively the length, width and height of the mass body,_xxis the spatial derivative of the gravitational acceleration component on the X-axis in the direction of the X-axis,_yyis the spatial derivative of the gravitational acceleration component on the Y-axis in the Y-direction,_xyis the spatial derivative of the acceleration of gravity in the X (Y) axis in the direction of the Y (X) axis;

4) the gravity gradient component measured by the gravity gradiometer when the mass of different masses at the position 1 is obtained by calculation according to the following formula is:

${({\mathrm{\Γ}}_{yy}-{\mathrm{\Γ}}_{xx})}_{2^{i-1}}^c=\frac{{({\mathrm{\Γ}}_{yy}-{\mathrm{\Γ}}_{xx})}_{1,2^{i-1}}-{({\mathrm{\Γ}}_{yy}-{\mathrm{\Γ}}_{xx})}_{2,2^{i-1}}}{2}$

performing linear fitting on the above formula to obtain a linear relation formula of the mass body and the gravity gradient value, and then calculating according to the following formula to obtain the gravity gradient component (_yy-_xx) Scale factor of (c):

$K_{yy-xx}=\frac{K_{yy-n}^t}{K_{yy-n}^c}$

whereinAs theoretical values of gravity gradient componentsThe slope of the linear relation obtained by linear fitting,measuring gravity gradient components for a gravity gradiometer of position 1Linearly fitting to obtain the slope of a linear relation;

the gravity gradient component measured by the gravity gradiometer when the number of different masses at the position 3 is calculated according to the following formula is: ${\left({\mathrm{\Γ}}_{xy}\right)}_{2^{i-1}}^c=\frac{{\left({\mathrm{\Γ}}_{xy}\right)}_{1,2^{i-1}}-{\left({\mathrm{\Γ}}_{xy}\right)}_{2,2^{i-1}}}{2}$

to the above formula go onLinear fitting to obtain a linear relation between the mass of the mass body and the gravity gradient value, and calculating to obtain the gravity gradient component according to the following formula_xy) Scale factor of (c):

$K_{xy}=\frac{K_{xy}^t}{K_{xy}^c}$

whereinAs theoretical values of gravity gradient componentsLinearly fitting the slope of the resulting linear relationship, wherein,measuring the gravity gradient component for a gravity gradiometer of position 3And linearly fitting the slope of the obtained linear relation.

Furthermore, in the method, the mass body is a cube, and the density distribution is uniform.

Further, in the method of the present invention, in the step 2), the mass of the mass body at the placement position is increased by preparing a plurality of mass bodies having the same density and volume and increasing the number of the mass bodies to be placed.

In the invention, a certain mass body is sequentially arranged at four different positions of the outer space of the gravity gradiometer, the gravitational field at the center of the gravity gradiometer is changed by changing the mass body, the changed gravitational field is sensed by the gravity gradiometer, then the gravity gradiometer output signal is filtered and subjected to gradient demodulation to obtain the gravity gradient measurement result of the gravity gradiometer, and the measurement result is compared with the gravity gradient theoretical value to obtain the zero position and the scale coefficient of two gravity gradient components of the gravity gradiometer.

Has the advantages that: compared with the prior art, the invention has the following advantages:

the invention provides a calibration method of a gravity gradiometer of a rotary accelerometer for the first time. Generally, the gravity gradiometer calibration method is to fix the mass of a mass body and realize the calibration by changing the distance from the mass center of the mass body to the center of the gravity gradiometer, but the method has serious gravity gradient distortion caused by a small distance, the distance from the mass center of the mass body to the center of the gravity gradiometer and a gravity gradient component are not in a linear relation, and the gravity gradient calibration error is large; the method of the invention adopts the distance from the center of the fixed mass body to the center of the gravity gradiometer and realizes gravity gradient calibration by changing the mass of the mass body, and the method can obviously reduce the gravity gradient distortion caused by the mass body at a short distance, and ensure that the mass of the mass body and the gravity gradient component form a linear relation in a certain range, thereby improving the calibration precision of the gravity gradient.

Drawings

FIG. 1 is a schematic diagram of a mass placement of a rotational accelerometer gravity gradiometer.

FIG. 2 shows the gravity gradient component measured by the gravity gradiometer (_yy-_xx) And the number of the mass bodies.

FIG. 3 shows the gravity gradient component measured by the gravity gradiometer (_xy) And the number of the mass bodies.

Detailed Description

The invention is further described with reference to the following examples and the accompanying drawings.

1) The operation before gravity gradient calibration is carried out on the rotating accelerometer gravity gradiometer comprises the following specific contents:

establishing a gravity gradiometer coordinate system as a northeast geographic coordinate system, and recording the coordinate system as OXYZ, wherein an origin O is the center of a rotating disk of the gravity gradiometer; at the initial moment, an accelerometer A on the disc is set₁The center of mass of (2) is located in the positive direction of the X axis;

setting 4 mass body placing positions which are equidistant to a coordinate origin on an XY plane of a gravity gradiometer coordinate system, wherein the position 1 is in the positive direction of X and an axis, the position 2 is in the positive direction of Y axis, the position 3 is in the linear equation Y which is equal to X, and the position 4 is in the linear equation Y which is equal to X;

2) placing a mass body at a placing position, and performing gravity gradient demodulation on the output signal of the gravity gradiometer to obtain a gravity gradient component (_yy-_xx)_1,1(ii) a Then on the basis of the number of the mass bodies placed at the last time, the mass of the mass bodies at the placing positions is changed gradually, and the gravity gradient demodulation is carried out on the output signal of the gravity gradiometer, wherein the mass of the mass body placed at each time is twice of that of the mass body placed at the last time; for each placement position, according to the above operation, the following results are obtained:

gravity gradient component of position 1: (_yy-_xx)_1,1、(_yy-_xx)_1,2、(_yy-_xx)_1,4、……、(_yy-_xx)_1,2 ^n--1

Gravity gradient component of position 2: (_yy-_xx)_2,1、(_yy-_xx)_2,2、(_yy-_xx)_2,4、……、(_yy-_xx)_2,2 ^n-1；

Gravity gradient component of position 3: (_xy)_3,1、(_xy)_3,2、(_xy)_3,4、……、(_xy)_3,2 ^n-1；

Gravity gradient component of position 4: (_xy)_4,1、(_xy)_4,2、(_xy)_4,4、……、(_xy)_4,2 ^n-1；

Wherein n is the ordinal number of gravity gradient demodulation, n is 1 when the mass body is placed for the first time, and the ordinal number n is increased by 1 when the mass body is changed every time;

3) calculating the gravity gradient component of the gravity gradiometer according to the formula (_yy-_xx) Zero position of (2):

${\mathrm{\Γ}}_{yy-xx}^{c0}=\frac{1}{n}\underset{i=1}{\overset{n}{\Σ}}\frac{{({\mathrm{\Γ}}_{yy}-{\mathrm{\Γ}}_{xx})}_{1,2^{i-1}}+{({\mathrm{\Γ}}_{yy}-{\mathrm{\Γ}}_{xx})}_{2,2^{i-1}}}{2}---\left(1\right)$

calculating the gravity gradient component of the gravity gradiometer according to the formula (_xy) Zero position of (2):

${\mathrm{\Γ}}_{xy}^{c0}=\frac{1}{n}\underset{i=1}{\overset{n}{\Σ}}\frac{{\left({\mathrm{\Γ}}_{xy}\right)}_{3,2^{i-1}}+{\left({\mathrm{\Γ}}_{xy}\right)}_{4,2^{i-1}}}{2}---\left(2\right)$

calculating the gravity gradient component theoretical value generated by the mass body to the center of the gravity gradiometer according to the following formula:

$\left\{\begin{array}{c}{({\mathrm{\Γ}}_{yy}-{\mathrm{\Γ}}_{xx})}_{2^{i-1}}^t=3G\mathrm{\ρ}{\∫}_{W_i-w/2}^{W_i+w/2}dx{\∫}_{D_i-d/2}^{D_i+d/2}dy{\∫}_{H_i-h/2}^{H_i+h/2}\frac{(y^2-x^2)}{{(x^2+y^2+x^2)}^{5/2}}dz\\ {\left({\mathrm{\Γ}}_{xy}\right)}_{2^{i-1}}^t=3G\mathrm{\ρ}{\∫}_{W_i-w/2}^{W_i+w/2}dx{\∫}_{D_i-d/2}^{D_i+d/2}dy{\∫}_{H_i-h/2}^{H_i+h/2}\frac{xy}{{(x^2+y^2+z^2)}^{5/2}}dz\end{array}\right.---\left(3\right)$

wherein, (x, y, z) is the position coordinate of any point in the mass body, (W)_i,D_i,H_i) The mass center coordinate of the mass body is placed for the ith time, G is a Newton universal gravitation constant, rho is the density of the mass body, w, d and h are respectively the length, width and height of the mass body,_xxis the spatial derivative of the gravitational acceleration component on the X-axis in the direction of the X-axis,_yyis the spatial derivative of the gravitational acceleration component on the Y-axis in the Y-direction,_xyis the spatial derivative of the acceleration of gravity in the X (Y) axis in the direction of the Y (X) axis;

4) the gravity gradient component of position 1: (_yy-_xx)_1,2 ^n-1Component of gravity gradient with position 2: (_yy-_xx)_2,2 ^n-1Subtracting the difference in one-to-one correspondence and then dividing by 2 to obtain the gravity gradient component measured by the gravity gradiometer when the number of different masses at the position 1 is obtained, namely:

${({\mathrm{\Γ}}_{yy}-{\mathrm{\Γ}}_{xx})}_{2^{i-1}}^c=\frac{{({\mathrm{\Γ}}_{yy}-{\mathrm{\Γ}}_{xx})}_{1,2^{i-1}}-{({\mathrm{\Γ}}_{yy}-{\mathrm{\Γ}}_{xx})}_{2,2^{i-1}}}{2}---\left(4\right)$

i gravity gradient components measured by gradiometer: (_yy-_xx)_1,2 ^i-1Linear fitting is carried out, and the gravity gradient component (a) obtained by calculation is set_yy-_xx) The linear relationship is:

${\mathrm{\Γ}}_{yy-xx}^c=K_{yy-xx}^{c}N+B_{yy-n}^c---\left(5\right)$

wherein,respectively the gravity gradient component (_yy-_xx) The slope and intercept of the linear relationship are measured,n is the number of mass bodies.

Calculating a theoretical gravity gradient component generated by the mass body at the same position to the center of the gravity gradiometer by using a gravity gradient component theoretical calculation formula (3) ((_yy-_xx) And performing linear fitting on the calculated gravity gradient theoretical value, and setting the linear fitting relation obtained by calculation as follows:

${\mathrm{\Γ}}_{yy-xx}^t=K_{yy-xx}^{t}N+B_{yy-xx}^t---\left(6\right)$

wherein,respectively the gravity gradient component (_yy-_xx) The slope and intercept of the theoretical linear relation, and N is the number of the mass bodies.

Calculating the gravity gradient component according to the formula (_yy-_xx) Scale factor of (c):

$K_{yy-xx}=\frac{K_{yy-xx}^t}{K_{yy-xx}^c}---\left(7\right)$

the gravity gradient component of position 3: (_xy)_3,2 ^n-1Component of the gravity gradient with position 4: (_xy)_4,2 ^n-1Subtracting the difference in a one-to-one correspondence manner and then dividing the difference by 2 to obtain the gravity gradient components measured by the gravity gradiometer when the number of different masses at the position 3 is obtained as follows:

${\left({\mathrm{\Γ}}_{xy}\right)}_{2^{i-1}}^c=\frac{{\left({\mathrm{\Γ}}_{xy}\right)}_{1,2^{i-1}}-{\left({\mathrm{\Γ}}_{xy}\right)}_{2,2^{i-1}}}{2}---\left(8\right)$

i gravity gradient components measured by gradiometer: (_xy)_3,2 ^i-1Linear fitting is carried out, and the gravity gradient component (a) obtained by calculation is set_xy) The linear relationship is:

${\mathrm{\Γ}}_{xy}^c=K_{xy}^{c}N+B_{xy}^c---\left(9\right)$

wherein,respectively the gravity gradient component (_xy) The slope and intercept of the linear relationship are measured.

Calculating the mass-to-weight at the same position by using the gravity gradient component theory calculation formula (3)Theoretical gravitational gradient component generated at the center of the force gradiometer: (_xy) And performing linear fitting on the calculated gravity gradient theoretical value, and setting the linear fitting relation obtained by calculation as follows:

${\mathrm{\Γ}}_{xy}^t=K_{xy}^{t}N+B_{xy}^t---\left(10\right)$

wherein,respectively the gravity gradient component (_xy) Slope and intercept of the theoretical linear relationship.

Calculating the gravity gradient component according to the formula (_xy) Scale factor of (c):

$K_{xy}=\frac{K_{xy}^t}{K_{xy}^c}---\left(11\right)$

it should be understood that the above examples are only for illustrating the preferred embodiments of the technical solution of the present invention, and are not intended to limit the scope of the present invention. Various equivalent modifications and alterations of this invention will occur to those skilled in the art after reading this disclosure, and it is intended to cover such alternatives and modifications as fall within the scope of the invention as defined by the appended claims.

Claims (3)

1. A calibration method for a gravity gradiometer of a rotary accelerometer is characterized by comprising the following steps:

1) the operation before gravity gradient calibration is carried out on the rotating accelerometer gravity gradiometer comprises the following specific contents:

establishing a gravity gradiometer coordinate system as a northeast geographic coordinate system, and recording the coordinate system as OXYZ, wherein an origin O is the center of a rotating disk of the gravity gradiometer; at the initial moment, an accelerometer A on the disc is set₁The center of mass of (2) is located in the positive direction of the X axis;

setting 4 mass body placing positions which are equidistant to a coordinate origin on an XY plane of a gravity gradiometer coordinate system, wherein the position 1 is in the positive direction of X and an axis, the position 2 is in the positive direction of Y axis, the position 3 is in the linear equation Y which is equal to X, and the position 4 is in the linear equation Y which is equal to X;

2) placing a mass body at a placing position, and performing gravity gradient demodulation on the output signal of the gravity gradiometer to obtain a gravity gradient component (_yy-_xx)_1,1(ii) a Then on the basis of the number of the mass bodies placed at the last time, the mass of the mass bodies at the placing positions is changed gradually, and the gravity gradient demodulation is carried out on the output signal of the gravity gradiometer, wherein the mass of the mass body placed at each time is twice of that of the mass body placed at the last time; for each placement position, according to the above operation, the following results are obtained:

gravity gradient component of position 1: (_yy-_xx)_1,1、(_yy-_xx)_1,2、(_yy-_xx)_1,4、……、(_yy-_xx)_1,2 ^n--1

Gravity gradient component of position 2: (_yy-_xx)_2,1、(_yy-_xx)_2,2、(_yy-_xx)_2,4、……、(_yy-_xx)_2,2 ^n-1；

Gravity gradient component of position 3: (_xy)_3,1、(_xy)_3,2、(_xy)_3,4、……、(_xy)_3,2 ^n-1；

Gravity gradient component of position 4: (_xy)_4,1、(_xy)_4,2、(_xy)_4,4、……、(_xy)_4,2 ^n-1；

Wherein n is the ordinal number of gravity gradient demodulation, n is 1 when the mass body is placed for the first time, and the ordinal number n is increased by 1 when the mass body is changed every time;

3) calculating the gravity gradient component of the gravity gradiometer according to the formula (_yy-_xx) Zero position of (2):

${\mathrm{\Γ}}_{yy-xx}^{c0}=\frac{1}{n}\underset{i=1}{\overset{n}{\mathrm{\Σ}}}\frac{{({\mathrm{\Γ}}_{yy}-{\mathrm{\Γ}}_{xx})}_{1,2^{i-1}}+{({\mathrm{\Γ}}_{yy}-{\mathrm{\Γ}}_{xx})}_{2,2^{i-1}}}{2}$

calculating the gravity gradient component of the gravity gradiometer according to the formula (_xy) Zero position of (2):

${\mathrm{\Γ}}_{xy}^{c0}=\frac{1}{n}\underset{i=1}{\overset{n}{\mathrm{\Σ}}}\frac{{\left({\mathrm{\Γ}}_{xy}\right)}_{3,2^{i-1}}+{\left({\mathrm{\Γ}}_{xy}\right)}_{4,2^{i-1}}}{2}$

calculating the gravity gradient component theoretical value generated by the mass body to the center of the gravity gradiometer according to the following formula:

$\left\{\begin{array}{c}{\left({\mathrm{\Γ}}_{yy}-{\mathrm{\Γ}}_{xx}\right)}_{2^{i-1}}^t=3G\mathrm{\ρ}{\∫}_{W_i-w/2}^{W_i+w/2}dx{\∫}_{D_i-d/2}^{D_i+d/2}dy{\∫}_{H_i-h/2}^{H_i+h/2}\frac{\left(y^2-x^2\right)}{{\left(x^2+y^2+z^2\right)}^{5/2}}dz\\ {\left({\mathrm{\Γ}}_{xy}\right)}_{2^{i-1}}^t=3G\mathrm{\ρ}{\∫}_{W_i-w/2}^{W_i+w/2}dx{\∫}_{D_i-d/2}^{D_i+d/2}dy{\∫}_{H_i-h/2}^{H_i+h/2}\frac{xy}{{\left(x^2+y^2+z^2\right)}^{5/2}}dz\end{array}\right.$

wherein, (x, y, z) is the position coordinate of any point in the mass body, (W)_i,D_i,H_i) The mass center coordinate of the mass body is placed for the ith time, G is a Newton universal gravitation constant, rho is the density of the mass body, w, d and h are respectively the length, width and height of the mass body,_xxis the gravity acceleration component on the X axis in the X axis directionThe spatial derivative of (a) is determined,_yyis the spatial derivative of the gravitational acceleration component on the Y-axis in the Y-direction,_xyis the spatial derivative of the acceleration of gravity in the X (Y) axis in the direction of the Y (X) axis;

4) the gravity gradient component measured by the gravity gradiometer when the mass of different masses at the position 1 is obtained by calculation according to the following formula is:

${({\mathrm{\Γ}}_{yy}-{\mathrm{\Γ}}_{xx})}_{2^{i-1}}^c=\frac{{({\mathrm{\Γ}}_{yy}-{\mathrm{\Γ}}_{xx})}_{1,2^{i-1}}-{({\mathrm{\Γ}}_{yy}-{\mathrm{\Γ}}_{xx})}_{2,2^{i-1}}}{2}$

performing linear fitting on the above formula to obtain a linear relation formula of the mass body and the gravity gradient value, and then calculating according to the following formula to obtain the gravity gradient component (_yy-_xx) Scale factor of (c):

$K_{yy-xx}=\frac{K_{yy-xx}^t}{K_{yy-xx}^c}$

whereinAs theoretical values of gravity gradient componentsThe slope of the linear relation obtained by linear fitting,measuring gravity gradient components for a gravity gradiometer of position 1Linearly fitting to obtain the slope of a linear relation;

the gravity gradient component measured by the gravity gradiometer when the number of different masses at the position 3 is calculated according to the following formula is:

${\left({\mathrm{\Γ}}_{xy}\right)}_{2^{i-1}}^c=\frac{{\left({\mathrm{\Γ}}_{xy}\right)}_{1,2^{i-1}}-{\left({\mathrm{\Γ}}_{xy}\right)}_{2,2^{i-1}}}{2}$

performing linear fitting on the above formula to obtain a linear relation formula of the mass body and the gravity gradient value, and then calculating according to the following formula to obtain the gravity gradient component (_xy) Scale factor of (c):

$K_{xy}=\frac{K_{xy}^t}{K_{xy}^c}$

whereinAs theoretical values of gravity gradient componentsLinearly fitting the slope of the resulting linear relationship, wherein,measuring the gradient component for a gravity gradiometer at position 3And linearly fitting the slope of the obtained linear relation.

2. The method for calibrating a gravity gradiometer of a rotary accelerometer according to claim 1 wherein the mass is a cube and the density distribution is uniform.

3. The calibration method for the gravity gradiometer of the rotary accelerometer according to claim 1 or 2, wherein in the step 2), the mass of the mass body at the placement position is increased by preparing a plurality of mass bodies with the same density and volume and increasing the number of the placed mass bodies.