CN103499845B - A kind of method utilizing gravity gradiometer to measure the Gradient of Gravitation - Google Patents

Abstract

The invention discloses a kind of method utilizing gravity gradiometer to measure the Gradient of Gravitation.The Gradient of Gravitation that the present invention acts on gravity gradiometer by gravitation generation device exports expression formula, determine the most significant track of theoretical the Gradient of Gravitation change in a space, then the optimum optimization track that gravitation generation device is derived in theory moves, measure the Gradient of Gravitation that gravitation generation device each aspect on track causes, through signal storage and process, the Gradient of Gravitation of measurement is compared work with theoretical the Gradient of Gravitation value judge, obtain measuring accuracy and the resolution of gravity gradiometer.The present invention can carry out accuracy test, the parameter calibration of gravity gradiometer and calibrate for error, and has filled up the blank of domestic gradiometry.

Description

A kind of method utilizing gravity gradiometer to measure the Gradient of Gravitation

Technical field

The present invention relates to a kind of method measuring the Gradient of Gravitation, particularly relate to a kind of method utilizing gravity gradiometer to measure the Gradient of Gravitation, belong to field of measuring technique.

Background technology

Along with the development of science and technology, high precision navigation, earth physical prospecting, submarine accurately to move under water etc. and all have higher requirement to acquisition gravity field information.Gravity gradiometer is a kind of important gravity field information measuring technique and method.Compare gravity meter, gravity gradiometer has following advantage: gravity gradiometer overcomes the impact of the linear acceleration of gradiometry system motion carrier; The Precision Potential of gravity gradiometer is huge; Gravity gradiometer can carry out gravity tensor measurement.At present, external gravity gradiometer correlation technique is ripe, and the eighties in last century, gravity gradiometer dropped into civilian.And domestic relevant gravity gradiometer development is also in the development of theoretical analysis, engineering prototype, relevant measuring technique, method are also in the more original stage.

Summary of the invention

Technology of the present invention is dealt with problems and is: overcome the deficiencies in the prior art, provide a kind of method utilizing gravity gradiometer to measure the Gradient of Gravitation, carried out the test of the Gradient of Gravitation by the movement of gravitation generation device on optimum optimization track, this measuring method is simple, and measuring accuracy is high.

Technical solution of the present invention is: a kind of gravity gradient instrument measurement method, and step is as follows:

(1) four accelerometers are distributed on the circular rotating members of single shaft gravity gradiometer, the sensitive axes of adjacent two accelerometers is mutually vertical, the sensitive axes direction of relative two accelerometers is contrary, the sensitive axes direction tangent circular rotating members of four accelerometers;

Wherein the coordinate of single shaft gravity gradiometer is sky, northeast geographic coordinate system, be designated as OXYZ, the center of circle of circular rotating members is the initial point O of coordinate system, and the rotational axis vertical of single shaft gravity gradiometer is in geoid surface, the radius of circular rotating members is r, and angular velocity of rotation is ω;

(2) gravitation generation device is arranged on apart from the space of circular rotating members center of circle 2m;

(3) theory calculate gravitation generation device acts on the Gradient of Gravitation of circular rotating members circle centre position, and computing formula is: ${\mathrm{\Γ}}_{\mathrm{xx}}-{\mathrm{\Γ}}_{\mathrm{yy}}=\frac{4\mathrm{G\π\ρ}{R}^3}{l^5}(x^2-y^2),{\mathrm{\Γ}}_{\mathrm{xy}}=\frac{4\mathrm{G\π\ρ}{R}^3}{l^5}\mathrm{xy};$

Wherein, Γ _xx, Γ _xy, Γ _yythe gravity gradient tensor component of circular rotating members circle centre position, Γ _xxfor the local derviation of gravitational acceleration component in X-axis of X-axis, Γ _xythe local derviation of gravitational acceleration component in Y-axis of X-axis, Γ _yybe the local derviation of gravitational acceleration component in Y-axis of Y-axis, G is Newton constant, and π is circular constant, and R is the radius of gravitation generation device, and ρ is the density of gravitation generation device, x, y, z are respectively the coordinate of gravitation generation device barycenter northeastward under sky geographic coordinate system:

(4) track of the Gradient of Gravitation to gravitation generation device calculated according to step (3) emulates the best mobile alignment obtaining gravitation generation device;

(5) single shaft gravity gradiometer is started, make gravitation generation device emulate along step (4) the best mobile alignment obtained to move, utilize the measurement of the Gradient of Gravitation measuring system obtain gravitation generation device act on circular rotating members circle centre position the Gradient of Gravitation change;

(6) the Gradient of Gravitation step (5) recorded and the Gradient of Gravitation of theory calculate compare, and calibrate the measuring accuracy of single shaft gravity gradiometer;

(7) after utilizing demarcation, single shaft gravity gradiometer carries out the Gradient of Gravitation measurement.

Described gravitation generation device is spheroid, and material is plumbous, and even density distributes.

When described step (4) emulates, the radius R of gravitation generation device gets 0.1m.

Angular range between described single shaft gravity gradiometer circular rotating members and the earth surface level is [-0.3 °, 0.3 °].

Described the Gradient of Gravitation measuring system is by four accelerating velocity meters, four I/V change-over circuits, two one-level amplifying circuits, second amplifying circuit, trap circuit, bandwidth-limited circuit, phase-sensitive detection circuit and low-pass filter circuit composition, four road current signals of four accelerometer generations convert four road voltage signals to respectively through four I/V change-over circuits, the two-way voltage signal often organizing accelerometer conversion carries out amplification respectively through an one-level amplifying circuit and processes for the anti-multiple-frequency modulation signal of offset voltage signal Semi-polarity, and two multiple-frequency modulation signals of same polarity are carried out addition amplification, second amplifying circuit carries out addition to the voltage signal that two one-level amplifying circuits export and amplifies, trap circuit carries out a frequency-doubled signal suppression to the voltage signal after second amplifying circuit amplification and again deducts a residual multiple-frequency modulation signal, bandwidth-limited circuit carries out bandpass filtering to the voltage signal that trap circuit exports, voltage signal after bandpass filtering eventually passes low-pass filter circuit filtering after carrying out phase sensitive detection by phase-sensitive detection circuit and obtains gradient tensor voltage signal.

Described I/V change-over circuit is by anti-phase scaling circuit, integrating circuit, voltage follower circuit and resistance R _fcomposition, wherein the first operational amplifier A ₁with resistance R _f, electric capacity C _oform anti-phase scaling circuit and realize the conversion of current signal to voltage signal, resistance R _f, electric capacity C _othe first operational amplifier A is connected on after parallel connection ₁reverse input and output side between, the second operational amplifier A ₂, resistance R ₁form integrating circuit with electric capacity C, electric capacity C is connected on the second operational amplifier A ₂reverse input end and output terminal between, resistance R ₁be connected on the first operational amplifier A ₁output terminal and the second operational amplifier A ₂reverse input end between, the 3rd operational amplifier A ₃, resistance R ₂with resistance R ₃composition voltage follower, resistance R ₂be connected on the second operational amplifier A ₂output terminal and the 3rd operational amplifier A ₃reverse input end between, resistance R ₃be connected on the 3rd operational amplifier A ₃reverse input end and output terminal between, the 3rd operational amplifier A ₃output terminal and the indirect resistance R of input current _f, the first operational amplifier A ₁, the second operational amplifier A ₂with the 3rd operational amplifier A ₃positive input ground connection.

Described bandwidth-limited circuit is by four operational amplifier A ₄, A ₅, A ₆, A ₇, 8 resistance R ₄, R ₅, R ₆, R ₇, R ₈, R ₉, R ₁₀, R ₁₁with two electric capacity C ₁, C ₂composition, resistance R ₄the output of a termination trap circuit, another termination four-operational amplifier A ₄reverse input end, resistance R ₅be connected on four-operational amplifier A ₄output terminal and reverse input end between, four-operational amplifier A ₄output terminal connecting resistance R successively ₆, R ₇form the output of band-pass circuit, the 6th operational amplifier A ₆positive input be connected on resistance R ₆, R ₇between, resistance R ₉be connected on the 6th operational amplifier A ₆reverse input end and output terminal between, resistance R ₈be connected on the 5th operational amplifier A ₅reverse input end and the 6th operational amplifier A ₆output terminal between, resistance R ₁₀be connected on the 6th operational amplifier A ₆reverse input end and the 7th operational amplifier A ₇output terminal between, electric capacity C ₂be connected on the 5th operational amplifier A ₅reverse input end and output terminal between, the 5th operational amplifier A ₅output terminal connecting resistance R ₇output terminal, electric capacity C ₁be connected on the 7th operational amplifier A ₇reverse input end and output terminal between, resistance R ₁₁be connected on the 7th operational amplifier A ₇reverse input end and the 5th operational amplifier A ₅output terminal between, operational amplifier A ₄, A ₅, A ₇positive input ground connection.

Described trap circuit is made up of operational amplification circuit A8, resistance R12, R13, R14 and bandwidth-limited circuit according to claim 3, between the output terminal that resistance R14 is connected on operational amplification circuit A8 and reverse input end, resistance R13 and bandwidth-limited circuit series connection are between the output terminal and reverse input end of operational amplification circuit A8, the output of the one termination second amplifying circuit of resistance R12, the reverse input end of another termination operational amplification circuit A8, the output of operational amplification circuit A8 is as the output of trap circuit.

The invention has the beneficial effects as follows: the Gradient of Gravitation that the present invention acts on gravity gradiometer by gravitation generation device exports expression formula, determine the most significant track of theoretical the Gradient of Gravitation change in a space, then the optimum optimization track that gravitation generation device is derived in theory moves, measure the Gradient of Gravitation that gravitation generation device each aspect on track causes, through signal storage and process, the Gradient of Gravitation of measurement is compared work with theoretical the Gradient of Gravitation value judge, obtain measuring accuracy and the resolution of gravity gradiometer.The present invention can carry out accuracy test, the parameter calibration of gravity gradiometer and calibrate for error, and has filled up the blank of domestic gradiometry.

Accompanying drawing explanation

Fig. 1 is measurement procedure figure of the present invention;

Fig. 2 is the position view of gravitation generation device in geographic coordinate system OXYZ;

Fig. 3 is gravity gradiometer measuring principle figure of the present invention;

Fig. 4 is the Gradient of Gravitation measuring system theory of constitution figure;

Fig. 5 is the theory of constitution figure of I/V conversion circuit;

Fig. 6 is the theory of constitution figure of bandwidth-limited circuit;

Fig. 7 is the theory of constitution figure of trap circuit.

Embodiment

As shown in Figure 1, performing step of the present invention is as follows:

(1) four accelerometers are distributed on the circular rotating members of single shaft gravity gradiometer, every two accelerometers form one group, often organize accelerometer symmetry to install, the sensitive axes of adjacent two accelerometers is mutually vertical, the sensitive axes direction of relative two accelerometers is contrary, the sensitive axes direction tangent circular rotating members of four accelerometers;

Wherein the coordinate of single shaft gravity gradiometer is sky, northeast geographic coordinate system, be designated as OXYZ, the center of circle of circular rotating members is the initial point O of coordinate system, and the rotational axis vertical of single shaft gravity gradiometer is in geoid surface, the radius of circular rotating members is r, and angular velocity of rotation is ω;

(2) gravitation generation device is arranged on apart from the space of circular rotating members center of circle 2m;

(3) theory calculate gravitation generation device acts on the Gradient of Gravitation of circular rotating members circle centre position, and computing formula is: ${\mathrm{\Γ}}_{\mathrm{xx}}-{\mathrm{\Γ}}_{\mathrm{yy}}=\frac{4\mathrm{G\π\ρ}{R}^3}{l^5}(x^2-y^2),{\mathrm{\Γ}}_{\mathrm{xy}}=\frac{4\mathrm{G\π\ρ}{R}^3}{l^5}\mathrm{xy};$

Wherein, Γ _xx, Γ _xy, Γ _yythe gravity gradient tensor component of circular rotating members circle centre position, Γ _xxfor the local derviation of gravitational acceleration component in X-axis of X-axis, Γ _xythe local derviation of gravitational acceleration component in Y-axis of X-axis, Γ _yybe the local derviation of gravitational acceleration component in Y-axis of Y-axis, G is Newton constant, and π is circular constant, and R is the radius of gravitation generation device, and ρ is the density of gravitation generation device, x, y, z are respectively the coordinate of gravitation generation device barycenter northeastward under sky geographic coordinate system, as shown in Figure 2;

(4) track of the Gradient of Gravitation to gravitation generation device calculated according to step (3) emulates the best mobile alignment obtaining gravitation generation device;

(5) single shaft gravity gradiometer is started, make gravitation generation device emulate along step (4) the best mobile alignment obtained to move, utilize the measurement of the Gradient of Gravitation measuring system obtain gravitation generation device act on circular rotating members circle centre position the Gradient of Gravitation change; During the barycenter relative coordinate initial point O place of gravitation generation device far point position n far away, the Gradient of Gravitation that gravitation generation device acts in gradiometry system is about 0, gravitation generation device barycenter in position 1,2,3 ..., n-1 time the Gradient of Gravitation measuring system the Gradient of Gravitation generation device that to export with the difference that exports of the Gradient of Gravitation measuring system during the n of position be this point act on the Gradient of Gravitation at initial point O place.

(6) the Gradient of Gravitation step (5) recorded and the Gradient of Gravitation of theory calculate compare, and calibrate the measuring accuracy of single shaft gravity gradiometer;

(7) after utilizing demarcation, single shaft gravity gradiometer carries out the Gradient of Gravitation measurement.

Embodiment:

As shown in Figure 3, its embodiment is as follows:

It is gravity gradiometer that the Gradient of Gravitation measures facility, and its model simplification is cylindrical, gets the radius r of gravity gradiometer, and it is gravitation generation device that the Gradient of Gravitation produces facility, and gravitation generation device is spherical, radius R, even material ρ.

Set up gravity gradiometer northeast sky geographic coordinate system OXYZ, turning axle OZ axle is perpendicular to geoid surface, and rotational speed is ω, and the plane of four accelerometer formations and the intersection point of turning axle are the initial point O of coordinate system; The coordinate signal of gravitation generation device in coordinate system OXYZ as shown in Figure 2.

From gravitational field concept, derivation gravitation generation device is on the impact of gradiometry system, and gravitation generation device barycenter acts on the gravitation at true origin O place when (x, y, z) puts:

$\stackrel{\→}{g}=\left(\frac{\mathrm{G\ρ}}{l}\underset{\mathrm{\Ω}}{\∫\∫\∫}\frac{1}{x^{\′2}+y^{\′2}+z^{\′2}}{\mathrm{dx}}^{\′}{\mathrm{dy}}^{\′}{\mathrm{dz}}^{\′}\right)\·\stackrel{\→}{l}---\left(1\right)$

Do not add the expression formula provided after Integration Solving of derivation, gravitational acceleration distribution in each coordinate axis of gravity gradiometer coordinate system OXYZ:

$g\left(x\right)=\frac{4\mathrm{\π\ρG}{R}^3}{{3l}^3}x\stackrel{\→}{i},g\left(y\right)=\frac{4\mathrm{\π\ρG}{R}^3}{{3l}^3}y\stackrel{\→}{j},g\left(z\right)=\frac{4\mathrm{\π\ρG}{R}^3}{{3l}^3}z\stackrel{\→}{k}---\left(2\right)$

Gravity gradient tensor is the gradient of gravitational acceleration, is expressed as Γ:

$\mathrm{\Γ}=\left[\begin{array}{ccc}{\mathrm{\Γ}}_{\mathrm{xx}}& {\mathrm{\Γ}}_{\mathrm{xy}}& {\mathrm{\Γ}}_{\mathrm{xz}}\\ {\mathrm{\Γ}}_{\mathrm{yx}}& {\mathrm{\Γ}}_{\mathrm{yy}}& {\mathrm{\Γ}}_{\mathrm{yz}}\\ {\mathrm{\Γ}}_{\mathrm{zx}}& {\mathrm{\Γ}}_{\mathrm{zy}}& {\mathrm{\Γ}}_{\mathrm{zz}}\end{array}\right]=\▿g(x,y,z)---\left(3\right)$

Gravitation generation device is at the gravity gradient tensor component of coordinate system OXYZ initial point:

$\left\{\begin{array}{c}{\mathrm{\Γ}}_{\mathrm{xx}}=\frac{4\mathrm{G\π\ρ}{R}^3}{{3l}^5}({3x}^2-l^2)\\ {\mathrm{\Γ}}_{\mathrm{yy}}=\frac{4\mathrm{G\π\ρ}{R}^3}{{3l}^5}({3y}^2-l^2)\\ {\mathrm{\Γ}}_{\mathrm{zz}}=\frac{4\mathrm{G\π\ρ}{R}^3}{3l^5}\left({3z^2-l}^2\right)\end{array}\right.\left\{\begin{array}{c}{\mathrm{\Γ}}_{\mathrm{xy}}={\mathrm{\Γ}}_{\mathrm{yx}}=\frac{4\mathrm{G\π\ρ}{R}^3}{l^5}\mathrm{xy}\\ {\mathrm{\Γ}}_{\mathrm{xz}}={\mathrm{\Γ}}_{\mathrm{zx}}=\frac{4\mathrm{G\π\ρ}{R}^3}{l^5}\mathrm{xz}\\ {\mathrm{\Γ}}_{\mathrm{yz}}={\mathrm{\Γ}}_{\mathrm{zy}}=\frac{4\mathrm{G\π\ρ}{R}^3}{{3l}^5}\mathrm{yz}\end{array}\right.---\left(4\right)$

Single shaft gravity gradiometer can only measure the gradient component Γ in circular rotating members plane _xx-Γ _yy, Γ _xy, three axle gravity gradiometers could measure whole gradient component, and what discuss herein is single shaft gravity gradient instrument.By Newton second law, the Detection job of accelerometer 1 detects gravitational acceleration vector in space :

${\stackrel{\→}{a}}_1=({\stackrel{\→}{a}}_o-{\stackrel{\→}{g}}_o)+\stackrel{\·}{\mathrm{\ω}\×\stackrel{\→}{r}}+2{\stackrel{\→}{\mathrm{\ω}}}_e\×(\stackrel{\→}{\mathrm{\ω}}\×\stackrel{\→}{r})+\stackrel{\→}{\mathrm{\ω}}\×(\stackrel{\→}{\mathrm{\ω}}\×\stackrel{\→}{r})+{\stackrel{\→}{\mathrm{\ω}}}_e\×({\stackrel{\→}{\mathrm{\ω}}}_e\×\stackrel{\→}{r})-\mathrm{\Γ}\·\stackrel{\→}{r}---\left(5\right)$

Wherein, the acceleration that to be circular rotating members circle centre position O point produce by the impact of the celestial body such as the earth, the sun; it is the terrestrial gravitation acceleration of circular rotating members circle centre position O point; it is the rotating angular acceleration of rotary part; the acceleration of Detection job relative to terrestrial coordinate system of accelerometer; it is the spin velocity of the earth.

According to gravity gradiometer measuring principle, the measurement equation of gravity gradiometer is by the combination of four accelerometer sense acceleration output shaft components, its expression formula:

$\frac{({\stackrel{\→}{a}}_1\·{\stackrel{\→}{\mathrm{\τ}}}_1+{\stackrel{\→}{a}}_3\·{\stackrel{\→}{\mathrm{\τ}}}_3)-({\stackrel{\→}{a}}_2\·{\stackrel{\→}{\mathrm{\τ}}}_2+{\stackrel{\→}{a}}_4\·{\stackrel{\→}{\mathrm{\τ}}}_4)}{2r}=({\mathrm{\Γ}}_{\mathrm{xx}}-{\mathrm{\Γ}}_{\mathrm{yy}})\sin 2\left(\mathrm{\ωt}\right)-2{\mathrm{\Γ}}_{\mathrm{xy}}\cos 2\left(\mathrm{\ωt}\right)---\left(6\right)$

Wherein, it is the output shaft direction of accelerometer i.

By formula (4), formula (6), obtain:

$\frac{({\stackrel{\→}{a}}_1\·{\stackrel{\→}{\mathrm{\τ}}}_1+{\stackrel{\→}{a}}_3\·{\stackrel{\→}{\mathrm{\τ}}}_3)-({\stackrel{\→}{a}}_2\·{\stackrel{\→}{\mathrm{\τ}}}_2+{\stackrel{\→}{a}}_4\·{\stackrel{\→}{\mathrm{\τ}}}_4)}{2r}=\frac{4\mathrm{G\π\ρ}{R}^3}{l^5}[(x^2-y^2)\sin 2\left(\mathrm{\ωt}\right)-2\mathrm{xy}\cos 2\left(\mathrm{\ωt}\right)]---\left(7\right)$

According to concrete size, if gravitation generation device is circular, material is plumbous, and the radius R of gravitation generation device gets 0.1m, carries out theory calculate, determines the track that a Gradient of Gravitation is changed significantly, for the movement of gravitation generation device.

As shown in Figure 3, start gradiometry system, between the near point position (1), far point position (n) of optimum optimization track, get (2), (3) ... Deng n-2 location point, when gravitation generation device barycenter is in these, carry out the measurement of the Gradient of Gravitation.It should be noted that: approximate says, the gradient signal that the Gradient of Gravitation generation device of far point position causes is 0, and the major part in gravity gradiometer measuring-signal is steady state noise.So, gravitation generation device barycenter position (1), (2) ..., (n-1) time the Gradient of Gravitation that produces at initial point O place of the Gradient of Gravitation measuring system the Gradient of Gravitation generation device that to export with the difference that exports of the Gradient of Gravitation measuring system during position (n) be this position.

Simulating signal low-pass filtering is carried out in the output of the Gradient of Gravitation measuring system, suggestion filter cutoff frequency scope [0, ω/10 π]; Note E _s, E _cfor gravitation generation device k, a k ∈ (1,2 ... the n) sinusoidal component of the theoretical gradient value at place and cosine component, E _ps, E _pcfor gravitation generation device is at the sinusoidal component of the actual gradient value at a k place and cosine component.

$E_s=\frac{4\mathrm{G\π\ρ}{R}^3}{l_k^5}(x_k^2-y_k^2),E_c=\frac{4\mathrm{G\π\ρ}{R}^3}{l_k^5}(-2x_k{y}_k)$

E _ps, E _pcbe calculated as:

E _ps=(E _Sin) _k-(E _Sin) _n；E _pc=(E _Cos) _k-(E _Cos) _n

Wherein, x _k, y _k, l _kthe position of gravitation generation device in the sky geographic coordinate system OXYZ of gravity gradiometer northeast; (E _sin) _k, (E _sin) _ngravitation generation device respectively k, a k ∈ (1,2 ... the gravity gradiometer measuring system sinusoidal component that n) place, n place cause exports, (E _cos) _k, (E _cos) _ngravitation generation device respectively k, a k ∈ (1,2 ... the gravity gradiometer measuring system cosine component that n) place, n place cause exports.

Setting gravitation generation device is positioned at a n place, the actual gradient of gradiometry system: $E_{\mathrm{ps}}^1={\left(E_{\mathrm{Sin}}\right)}_{\mathrm{ni}}-{\left(E_{\mathrm{Sin}}\right)}_{\mathrm{nj}};E_{\mathrm{pc}}^1={\left(E_{\mathrm{Cos}}\right)}_{\mathrm{ni}}-{\left(E_{\mathrm{Cos}}\right)}_{\mathrm{nj}}.$ Wherein (E _sin) _ni, (E _cos) _nirepresent (E _sin) _k, (E _cos) _ni-th time measure, (E _sin) _nj, (E _cos) _njrepresent (E _sin) _k, (E _cos) _njth time measure. the Γ of the Gradient of Gravitation component _xx-Γ _yy,-2 Γ _xymeasuring accuracy.To be positioned in real process k, a k ∈ (1,2 ... n) the Gradient of Gravitation component E that causes of the gravitation generation device at place _ps, E _pcwith theoretical the Gradient of Gravitation component E _s, E _ccompare, if then get E _ps, E _pcthat the Gradient of Gravitation of gravity gradiometer in self precision is measured.

As shown in Figure 4, the Gradient of Gravitation measuring system is by four accelerating velocity meters, four I/V change-over circuits, two one-level amplifying circuits, second amplifying circuit, trap circuit, bandwidth-limited circuit, phase-sensitive detection circuit and low-pass filter circuit composition, four road current signals of four accelerometer generations convert four road voltage signals to respectively through four I/V change-over circuits, the two-way voltage signal often organizing accelerometer conversion carries out amplification respectively through an one-level amplifying circuit and processes for the anti-multiple-frequency modulation signal of offset voltage signal Semi-polarity, and two multiple-frequency modulation signals of same polarity are carried out addition amplification, second amplifying circuit carries out addition to the voltage signal that two one-level amplifying circuits export and amplifies, trap circuit carries out a frequency-doubled signal suppression to the voltage signal after second amplifying circuit amplification and again deducts a residual multiple-frequency modulation signal, bandwidth-limited circuit carries out bandpass filtering to the voltage signal that trap circuit exports, voltage signal after bandpass filtering eventually passes low-pass filter circuit filtering after carrying out phase sensitive detection by phase-sensitive detection circuit and obtains gradient tensor voltage signal.

Concrete principle is as follows: the I of circuit of the present invention _a, I _b, I _c, I _dfour road electric currents are input as gravity gradiometer four acceierometer sensor output signals, and signal comprises a multiple-frequency modulation signal, two multiple-frequency modulation signals, DC bias signal and noise, and in the signal of every road, the amplitude of each component is identical, phase place is different.Four current input signals are become voltage signal by four I/V change-over circuit after-current signals and are amplified 50000 times, and direct current biasing component is deducted simultaneously; In A, B road voltage signal input first order inverting amplifier, a multiple-frequency modulation signal polarity wherein in A, B road is contrary, by a multiple-frequency modulation signal subtraction after first order amplifier, two multiple-frequency modulation signal polarities are identical, amplify 10 times by phase adduction after first order amplifier.Same A, B road, C, D road; Signal polarity after the amplification of two-way one-level is identical, passes in secondary see-saw circuit and sues for peace and amplify 2 times; Signal after secondary amplifies passes in a trap circuit, and object is a multiple-frequency modulation signal remaining in filtered signal and amplifies useful two multiple-frequency modulation signal 10 times; Signal after trap passes in bandwidth-limited circuit, and object makes two multiple-frequency modulation signals pass through and amplify 10 times, other frequency signals and noise filtering; Signal after band is logical passes in phase-sensitive detection circuit, and the signal after phase sensitive detection passes in low-pass filter circuit, and final output signal is just gravity gradient tensor signal.Because gravity gradient tensor is only contained in two frequency multiplication sinewave modulation signal, therefore this main circuit will eliminate DC component, frequency multiplication component sine waves, other higher hamonic waves and random noise, from two extremely faint frequency-doubled signals, detect gradient tensor signal.This circuit suppresses a multiple-frequency modulation signal greatly, amplifies two multiple-frequency modulation signals, effectively detects buried two frequency-doubled signal components in DC component, a frequency-doubled signal component.

As shown in Figure 5, I/V change-over circuit is by anti-phase scaling circuit, integrating circuit, voltage follower circuit and resistance R _fcomposition, wherein the first operational amplifier A ₁with resistance R _f, electric capacity C _oform anti-phase scaling circuit and realize the conversion of current signal to voltage signal, resistance R _f, electric capacity C _othe first operational amplifier A is connected on after parallel connection ₁reverse input and output side between, the second operational amplifier A ₂, resistance R ₁form integrating circuit with electric capacity C, electric capacity C is connected on the second operational amplifier A ₂reverse input end and output terminal between, resistance R ₁be connected on the first operational amplifier A ₁output terminal and the second operational amplifier A ₂reverse input end between, the 3rd operational amplifier A ₃, resistance R ₂with resistance R ₃composition voltage follower, resistance R ₂be connected on the second operational amplifier A ₂output terminal and the 3rd operational amplifier A ₃reverse input end between, resistance R ₃be connected on the 3rd operational amplifier A ₃reverse input end and output terminal between, the 3rd operational amplifier A ₃output terminal and the indirect resistance R of input current _f, the first operational amplifier A ₁, the second operational amplifier A ₂with the 3rd operational amplifier A ₃positive input ground connection.

As shown in Figure 6, bandwidth-limited circuit is by four operational amplifier A ₄, A ₅, A ₆, A ₇, 8 resistance R ₄, R ₅, R ₆, R ₇, R ₈, R ₉, R ₁₀, R ₁₁with two electric capacity C ₁, C ₂composition, resistance R ₄the output of a termination trap circuit, another termination four-operational amplifier A ₄reverse input end, resistance R ₅be connected on four-operational amplifier A ₄output terminal and reverse input end between, four-operational amplifier A ₄output terminal connecting resistance R successively ₆, R ₇form the output of band-pass circuit, the 6th operational amplifier A ₆positive input be connected on resistance R ₆, R ₇between, resistance R ₉be connected on the 6th operational amplifier A ₆reverse input end and output terminal between, resistance R ₈be connected on the 5th operational amplifier A ₅reverse input end and the 6th operational amplifier A ₆output terminal between, resistance R ₁₀be connected on the 6th operational amplifier A ₆reverse input end and the 7th operational amplifier A ₇output terminal between, electric capacity C ₂be connected on the 5th operational amplifier A ₅reverse input end and output terminal between, the 5th operational amplifier A ₅output terminal connecting resistance R ₇output terminal, electric capacity C ₁be connected on the 7th operational amplifier A ₇reverse input end and output terminal between, resistance R ₁₁be connected on the 7th operational amplifier A ₇reverse input end and the 5th operational amplifier A ₅output terminal between, operational amplifier A ₄, A ₅, A ₇positive input ground connection.

As shown in Figure 7, trap circuit is made up of operational amplification circuit A8, resistance R12, R13, R14 and band-pass circuit, between the output terminal that resistance R14 is connected on operational amplification circuit A8 and reverse input end, resistance R13 and band-pass circuit series connection are between the output terminal and reverse input end of operational amplification circuit A8, the output of the one termination second amplifying circuit of resistance R12, the reverse input end of another termination operational amplification circuit A8, the output of operational amplification circuit A8 is as the output of trap circuit.

The non-detailed description of the present invention is known to the skilled person technology.

Claims (6)

1. utilize gravity gradiometer to measure a method for the Gradient of Gravitation, it is characterized in that step is as follows:

(1) four accelerometers are distributed on the circular rotating members of single shaft gravity gradiometer, every two accelerometers form one group, often organize accelerometer symmetry to install, the sensitive axes of adjacent two accelerometers is mutually vertical, the sensitive axes direction of relative two accelerometers is contrary, the sensitive axes direction tangent circular rotating members of four accelerometers;

Wherein the coordinate of single shaft gravity gradiometer is sky, northeast geographic coordinate system, be designated as OXYZ, the center of circle of circular rotating members is the initial point O of coordinate system, and the rotational axis vertical of single shaft gravity gradiometer is in geoid surface, the radius of circular rotating members is r, and angular velocity of rotation is ω;

(2) gravitation generation device is arranged on apart from the space of circular rotating members center of circle 2m;

(3) theory calculate gravitation generation device acts on the Gradient of Gravitation of circular rotating members circle centre position, and computing formula is: ${\mathrm{\Γ}}_{xx}-{\mathrm{\Γ}}_{yy}=\frac{4{\mathrm{G\π\ρR}}^3}{l^5}(x^2-y^2),{\mathrm{\Γ}}_{xy}=\frac{4{\mathrm{G\π\ρR}}^3}{l^5}xy;$

Wherein, Γ _xx, Γ _xy, Γ _yythe gravity gradient tensor component of circular rotating members circle centre position, Γ _xxfor the local derviation of gravitational acceleration component in X-axis of X-axis, Γ _xythe local derviation of gravitational acceleration component in Y-axis of X-axis, Γ _yybe the local derviation of gravitational acceleration component in Y-axis of Y-axis, G is Newton constant, and π is circular constant, and R is the radius of gravitation generation device, and ρ is the density of gravitation generation device, x, y, z are respectively the coordinate of gravitation generation device barycenter northeastward under sky geographic coordinate system:

(4) track of the Gradient of Gravitation to gravitation generation device calculated according to step (3) emulates the best mobile alignment obtaining gravitation generation device;

(5) single shaft gravity gradiometer is started, make gravitation generation device emulate along step (4) the best mobile alignment obtained to move, utilize the measurement of the Gradient of Gravitation measuring system obtain gravitation generation device act on circular rotating members circle centre position the Gradient of Gravitation change;

(6) the Gradient of Gravitation step (5) recorded and the Gradient of Gravitation of theory calculate compare, and calibrate the measuring accuracy of single shaft gravity gradiometer;

(7) after utilizing demarcation, single shaft gravity gradiometer carries out the Gradient of Gravitation measurement;

Described the Gradient of Gravitation measuring system is by four accelerometers, four I/V change-over circuits, two one-level amplifying circuits, second amplifying circuit, trap circuit, bandwidth-limited circuit, phase-sensitive detection circuit and low-pass filter circuit composition, four road current signals of four accelerometer generations convert four road voltage signals to respectively through four I/V change-over circuits, the two-way voltage signal often organizing accelerometer conversion carries out amplification respectively through an one-level amplifying circuit and processes for the anti-multiple-frequency modulation signal of offset voltage signal Semi-polarity, and two multiple-frequency modulation signals of same polarity are carried out addition amplification, second amplifying circuit carries out addition to the voltage signal that two one-level amplifying circuits export and amplifies, trap circuit carries out a multiple-frequency modulation signal suppressing to the voltage signal after second amplifying circuit amplification and again deducts a residual multiple-frequency modulation signal, bandwidth-limited circuit carries out bandpass filtering to the voltage signal that trap circuit exports, voltage signal after bandpass filtering eventually passes low-pass filter circuit filtering after carrying out phase sensitive detection by phase-sensitive detection circuit and obtains gradient tensor voltage signal,

Described I/V change-over circuit is by anti-phase scaling circuit, integrating circuit, voltage follower circuit and resistance R _fcomposition, wherein the first operational amplifier A ₁with resistance R _f, electric capacity C _oform anti-phase scaling circuit and realize the conversion of current signal to voltage signal, resistance R _f, electric capacity C _othe first operational amplifier A is connected on after parallel connection ₁reverse input end and output terminal between, the second operational amplifier A ₂, resistance R ₁form integrating circuit with electric capacity C, electric capacity C is connected on the second operational amplifier A ₂reverse input end and output terminal between, resistance R ₁be connected on the first operational amplifier A ₁output terminal and the second operational amplifier A ₂reverse input end between, the 3rd operational amplifier A ₃, resistance R ₂with resistance R ₃composition voltage follower circuit, resistance R ₂be connected on the second operational amplifier A ₂output terminal and the 3rd operational amplifier A ₃reverse input end between, resistance R ₃be connected on the 3rd operational amplifier A ₃reverse input end and output terminal between, the 3rd operational amplifier A ₃output terminal and the indirect resistance R of input current _f, the first operational amplifier A ₁, the second operational amplifier A ₂with the 3rd operational amplifier A ₃positive input ground connection.

2. a kind of method utilizing gravity gradiometer to measure the Gradient of Gravitation according to claim 1, is characterized in that: described bandwidth-limited circuit is by four operational amplifier A ₄, A ₅, A ₆, A ₇, eight resistance R ₄, R ₅, R ₆, R ₇, R ₈, R ₉, R ₁₀, R ₁₁with two electric capacity C ₁, C ₂composition, resistance R ₄the output terminal of a termination trap circuit, another termination four-operational amplifier A ₄reverse input end, resistance R ₅be connected on four-operational amplifier A ₄output terminal and reverse input end between, four-operational amplifier A ₄output terminal connecting resistance R successively ₆, R ₇form the output of bandwidth-limited circuit, the 6th operational amplifier A ₆positive input be connected on resistance R ₆, R ₇between, resistance R ₉be connected on the 6th operational amplifier A ₆reverse input end and output terminal between, resistance R ₈be connected on the 5th operational amplifier A ₅reverse input end and the 6th operational amplifier A ₆output terminal between, resistance R ₁₀be connected on the 6th operational amplifier A ₆reverse input end and the 7th operational amplifier A ₇output terminal between, electric capacity C ₂be connected on the 5th operational amplifier A ₅reverse input end and output terminal between, the 5th operational amplifier A ₅output terminal connecting resistance R ₇output terminal, electric capacity C ₁be connected on the 7th operational amplifier A ₇reverse input end and output terminal between, resistance R ₁₁be connected on the 7th operational amplifier A ₇reverse input end and the 5th operational amplifier A ₅output terminal between, operational amplifier A ₄, A ₅, A ₇positive input ground connection.

3. a kind of method utilizing gravity gradiometer to measure the Gradient of Gravitation according to claim 2, is characterized in that: described trap circuit is by operational amplification circuit A ₈, resistance R ₁₂, R ₁₃, R ₁₄form with bandwidth-limited circuit according to claim 2, resistance R ₁₄be connected on operational amplification circuit A ₈output terminal and reverse input end between, resistance R ₁₃with bandwidth-limited circuit series connection at operational amplification circuit A ₈output terminal and reverse input end between, resistance R ₁₂the output terminal of a termination second amplifying circuit, another termination operational amplification circuit A ₈reverse input end, operational amplification circuit A ₈output as the output of trap circuit.

4. a kind of method utilizing gravity gradiometer to measure the Gradient of Gravitation according to claim 1, it is characterized in that: described gravitation generation device is spheroid, material is plumbous, and even density distributes.

5. a kind of method utilizing gravity gradiometer to measure the Gradient of Gravitation according to claim 1, is characterized in that: when described step (4) emulates, the radius R of gravitation generation device gets 0.1m.

6. a kind of method utilizing gravity gradiometer to measure the Gradient of Gravitation according to claim 1, is characterized in that: the angular range between described single shaft gravity gradiometer circular rotating members and the earth surface level is [-0.3 °, 0.3 °].