CN103499845A - Method utilizing gravity gradiometer to measure gravity gradients - Google Patents

Abstract

The invention discloses a method utilizing a gravity gradiometer to measure gravitation gradients. According to the method, an expression is output according to the gravitation gradients acted on the gravity gradiometer by a gravitation generating device, a track having the most obvious changes of the theoretical gravitation gradients in space is determined, then the gravitation generating device moves on the most optimized track derived in theory, the gravitation gradients caused by the gravitation generating device on various points of the track are measured, and stored and processed through signals, the measured gravitation gradients and the theoretical gravitation gradients are compared for judgment, and measuring accuracy and the resolution ratio of the gravity gradiometer are obtained. The method can be used for conducting accuracy measurement, parameter standardization and error correction of the gravity gradiometer, and fill the measuring blank of the gravitation gradients inland.

Description

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

Technical field

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

Background technology

Along with scientific and technical development, high precision navigation, earth physical prospecting, submarine accurately move under water etc. and all to have higher requirement to obtaining gravity field information.Gravity gradiometer is a kind of important gravity field information measuring technique and method.The gravity meter of comparing, gravity gradiometer has following advantage: gravity gradiometer has overcome the impact of the linear acceleration of gradiometry system motion carrier; The Precision Potential of gravity gradiometer is huge; Gravity gradiometer can carry out the gravity tensor measurement.At present, external gravity gradiometer correlation technique is ripe, and the eighties in last century, gravity gradiometer dropped into civilian.And the also development in theoretical analysis, engineering prototype of domestic relevant gravity gradiometer development, 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, a kind of method of utilizing gravity gradiometer to measure the Gradient of Gravitation is provided, the test of the Gradient of Gravitation is carried out in movement by the gravitation generation device on the optimum optimization track, and 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 parts of single shaft gravity gradiometer, the sensitive axes of adjacent two accelerometers is mutually vertical, the sensitive axes opposite direction of relative two accelerometers, the sensitive axes direction tangent circular rotating parts of four accelerometers;

Wherein the coordinate of single shaft gravity gradiometer is the geographical coordinate system in sky, northeast, be designated as OXYZ, the initial point O that the center of circle of circular rotating parts is coordinate system, the turning axle of single shaft gravity gradiometer is perpendicular to geoid surface, the radius of circular rotating parts is r, and angular velocity of rotation is ω;

(2) the gravitation generation device is arranged in 2m space, the circular rotating parts center of circle;

(3) theoretical calculating gravitation generation device acts on the Gradient of Gravitation of circular rotating parts 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 parts circle centre position, Γ _xxfor the local derviation of gravitational acceleration component on X-axis of X-axis, Γ _xythe local derviation of gravitational acceleration component on Y-axis of X-axis, Γ _yybe the local derviation of gravitational acceleration component on Y-axis of Y-axis, G is newton's universal gravitational constant, and π is circular constant, the radius that R is the gravitation generation device, and the density that ρ is the gravitation generation device,

x, y, z is respectively the gravitation generation device barycenter coordinate under day geographical coordinate system northeastward:

(4) the Gradient of Gravitation calculated according to step (3) carries out to the track of gravitation generation device the best mobile alignment that emulation obtains the gravitation generation device;

(5) start the single shaft gravity gradiometer, the best mobile alignment that the gravitation generation device is obtained along step (4) emulation is moved, and utilizes the Gradient of Gravitation measuring system to measure the Gradient of Gravitation variation that the gravitation generation device acts on circular rotating parts circle centre position;

(6) the Gradient of Gravitation step (5) recorded compares with the theoretical the Gradient of Gravitation calculated, and calibrates the measuring accuracy of single shaft gravity gradiometer;

(7) utilize the rear single shaft gravity gradiometer of demarcation to carry out the Gradient of Gravitation measurement.

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

When described step (4) is carried out emulation, the radius R of gravitation generation device is got 0.1m.

Angular range between described single shaft gravity gradiometer circular rotating parts 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 form, four road current signals of four accelerometer generations convert four road voltage signals to through four I/V change-over circuits respectively, the two-way voltage signal of every group of accelerometer conversion amplifies and processes a multiple-frequency modulation signal anti-for the offset voltage signal Semi-polarity through an one-level amplifying circuit respectively, and two multiple-frequency modulation signals of same polarity are carried out to the addition amplification, second amplifying circuit carries out the addition amplification to the voltage signal of two one-level amplifying circuit outputs, voltage signal after trap circuit amplifies second amplifying circuit carries out a frequency-doubled signal inhibition and again deducts a residual multiple-frequency modulation signal, bandwidth-limited circuit carries out bandpass filtering to the voltage signal of trap circuit output, voltage signal after bandpass filtering is undertaken obtaining the gradient tensor voltage signal finally by crossing the low-pass filtering circuit filtering after phase sensitive detection by phase-sensitive detection circuit.

Described I/V change-over circuit is by anti-phase ratio amplifying circuit, integrating circuit, voltage follower circuit and resistance R _fform, wherein the first operational amplifier A ₁with resistance R _f, capacitor C _oform anti-phase ratio amplifying circuit and realize the conversion of current signal to voltage signal, resistance R _f, capacitor C _obe connected on the first operational amplifier A after parallel connection ₁reverse input and output side between, the second operational amplifier A ₂, resistance R ₁form integrating circuit with capacitor C, capacitor 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 ₂and resistance R ₃form 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 input current between connecting resistance R _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 capacitor C ₁, C ₂form 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, capacitor 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, capacitor 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 comprised of operational amplification circuit A8, resistance R 12, R13, R14 and bandwidth-limited circuit claimed in claim 3, resistance R 14 is connected between the output terminal and reverse input end of operational amplification circuit A8, resistance R 13 and bandwidth-limited circuit series connection are between the output terminal and reverse input end of operational amplification circuit A8, the output of one termination second amplifying circuit of resistance R 12, 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 present invention acts on the Gradient of Gravitation output expression formula of gravity gradiometer by the gravitation generation device, determined that in a space, theoretical the Gradient of Gravitation changes the most significant track, then on the optimum optimization track that the gravitation generation device is derived in theory, move, measure the Gradient of Gravitation caused on gravitation generation device each aspect on track, through signal storage and processing, the Gradient of Gravitation of measurement and theoretical the Gradient of Gravitation value are relatively judged, 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.

The 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;

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

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

The theory of constitution figure that Fig. 7 is 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 parts of single shaft gravity gradiometer, every two accelerometers form one group, every group of symmetrical installation of accelerometer, the sensitive axes of adjacent two accelerometers is mutually vertical, the sensitive axes opposite direction of relative two accelerometers, the sensitive axes direction tangent circular rotating parts of four accelerometers;

Wherein the coordinate of single shaft gravity gradiometer is the geographical coordinate system in sky, northeast, be designated as OXYZ, the initial point O that the center of circle of circular rotating parts is coordinate system, the turning axle of single shaft gravity gradiometer is perpendicular to geoid surface, the radius of circular rotating parts is r, and angular velocity of rotation is ω;

(2) the gravitation generation device is arranged in 2m space, the circular rotating parts center of circle;

(3) theoretical calculating gravitation generation device acts on the Gradient of Gravitation of circular rotating parts 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 parts circle centre position, Γ _xxfor the local derviation of gravitational acceleration component on X-axis of X-axis, Γ _xythe local derviation of gravitational acceleration component on Y-axis of X-axis, Γ _yybe the local derviation of gravitational acceleration component on Y-axis of Y-axis, G is newton's universal gravitational constant, and π is circular constant, the radius that R is the gravitation generation device, and the density that ρ is the gravitation generation device,

x, y, z is respectively the gravitation generation device barycenter coordinate under day geographical coordinate system northeastward, as shown in Figure 2;

(4) the Gradient of Gravitation calculated according to step (3) carries out to the track of gravitation generation device the best mobile alignment that emulation obtains the gravitation generation device;

(5) start the single shaft gravity gradiometer, the best mobile alignment that the gravitation generation device is obtained along step (4) emulation is moved, and utilizes the Gradient of Gravitation measuring system to measure the Gradient of Gravitation variation that the gravitation generation device acts on circular rotating parts circle centre position; During the far point position n far away of the barycenter relative coordinate initial point O place of gravitation generation device, the Gradient of Gravitation that the gravitation generation device acts on the gradiometry system is about 0, gravitation generation device barycenter in position 1,2,3 ..., the Gradient of Gravitation measuring system output of the output of the Gradient of Gravitation measuring system during n-1 during with position n the difference the Gradient of Gravitation generation device that is this point act on the Gradient of Gravitation at initial point O place.

(6) the Gradient of Gravitation step (5) recorded compares with the theoretical the Gradient of Gravitation calculated, and calibrates the measuring accuracy of single shaft gravity gradiometer;

(7) utilize the rear single shaft gravity gradiometer of demarcation to carry 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 is measured facility, and its model simplification is cylindrical, the radius r of getting gravity gradiometer, and it is the gravitation generation device that the Gradient of Gravitation produces facility, the gravitation generation device is spherical, radius R, evenly material ρ.

Set up the geographical coordinate system OXYZ in sky, gravity gradiometer northeast, 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 the gravitational field concept, the impact of derivation gravitation generation device on the gradiometry system, gravitation generation device barycenter acts on the gravitation at true origin O place when (x, y, z) point:

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

What do not add derivation provides the expression formula after Integration Solving, gravitational acceleration

distribution on each coordinate axis of gravity gradiometer coordinate system OXYZ:

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

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

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

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

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

The single shaft gravity gradiometer can only measure the gradient component Γ in circular rotating parts plane _xx-Γ _yy, Γ _xy, three axle gravity gradiometers could be measured whole gradient components, this paper discussion be single shaft gravity gradient instrument.By Newton second law, the detection quality of accelerometer 1 detects the 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,

it is the acceleration that circular rotating parts circle centre position O point is produced by the impact of the celestial bodies such as the earth, the sun;

it is the terrestrial gravitation acceleration that circular rotating parts circle centre position O is ordered; it is the rotating angular acceleration of rotary part; the acceleration of the detection quality of accelerometer with respect to terrestrial coordinate system;

it is the spin velocity of the earth.

According to the gravity gradiometer measuring principle, the measurement equation of gravity gradiometer is the combination by 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:

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

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

As shown in Figure 3, start the gradiometry system, between the near point position (1) of optimum optimization track, far point position (n), get (2), (3) ... Deng n-2 location point, gravitation generation device barycenter carries out the measurement of the Gradient of Gravitation while being in these.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 the gravity gradiometer measuring-signal is steady state noise.So, gravitation generation device barycenter in position (1), (2) ..., the Gradient of Gravitation measuring system output of the output of the Gradient of Gravitation measuring system when (n-1) during with position (n) the difference the Gradient of Gravitation generation device that be this position at the Gradient of Gravitation of initial point O place generation.

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

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

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 geographical coordinate system OXYZ in sky, gravity gradiometer northeast; (E _sin) _k, (E _sin) _nbe respectively the gravitation generation device at a k, k ∈ (1,2 ... the output of the gravity gradiometer measuring system sinusoidal component that n) locate, the n place causes, (E _cos) _k, (E _cos) _nbe respectively the gravitation generation device at a k, k ∈ (1,2 ... the output of the gravity gradiometer measuring system cosine component that n) locate, the n place causes.

Set the gravitation generation device and be positioned at a n place, the actual gradient of gradiometry system: $E_{\mathrm{ps}}^1={\left(E_{\mathrm{Sin}}\right)}_{\mathrm{ni}}-{\left(E_{\mathrm{Sin}}\right)}_{\mathrm{nj}};$ $E_{\mathrm{pc}}^1={\left(E_{\mathrm{Cos}}\right)}_{\mathrm{ni}}-{\left(E_{\mathrm{Cos}}\right)}_{\mathrm{nj}}.$ (E wherein _sin) _ni, (E _cos) _nimean (E _sin) _k, (E _cos) _nmeasure for the i time, (E _sin) _nj, (E _cos) _njmean (E _sin) _k, (E _cos) _nmeasure for the j time.

the Γ of the Gradient of Gravitation component _xx-Γ _yy,-2 Γ _xymeasuring accuracy.To being positioned at a k in real process, and k ∈ (1,2 ... the Gradient of Gravitation component E that the gravitation generation device of n) locating causes _ps, E _pcwith theoretical the Gradient of Gravitation component E _s, E _ccompare, if

get E _ps, E _pcthe Gradient of Gravitation that is gravity gradiometer on 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 form, four road current signals of four accelerometer generations convert four road voltage signals to through four I/V change-over circuits respectively, the two-way voltage signal of every group of accelerometer conversion amplifies and processes a multiple-frequency modulation signal anti-for the offset voltage signal Semi-polarity through an one-level amplifying circuit respectively, and two multiple-frequency modulation signals of same polarity are carried out to the addition amplification, second amplifying circuit carries out the addition amplification to the voltage signal of two one-level amplifying circuit outputs, voltage signal after trap circuit amplifies second amplifying circuit carries out a frequency-doubled signal inhibition and again deducts a residual multiple-frequency modulation signal, bandwidth-limited circuit carries out bandpass filtering to the voltage signal of trap circuit output, voltage signal after bandpass filtering is undertaken obtaining the gradient tensor voltage signal finally by crossing the low-pass filtering circuit filtering after phase sensitive detection by phase-sensitive detection circuit.

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 four acceierometer sensor output signals of gravity gradiometer, and signal comprises that the amplitude of each component in a multiple-frequency modulation signal, two multiple-frequency modulation signals, direct current biasing signal and noise ，Mei road signal is identical, phase place is different.Four current input signals become voltage signal and amplify 50000 times by four I/V change-over circuit after-current signals, and the direct current biasing component is deducted simultaneously; In A, B road voltage signal input first order inverting amplifier, wherein the multiple-frequency modulation signal polarity 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, by phase adduction after first order amplifier, amplify 10 times.C, the same A in D road, B road; Signal polarity after the two-way one-level is amplified is identical, passes in the secondary see-saw circuit and sues for peace and amplify 2 times; Signal after secondary amplifies passes in a trap circuit, and purpose is a multiple-frequency modulation signal remaining in filtered signal and amplifies 10 times of two useful multiple-frequency modulation signals; Signal after trap passes in bandwidth-limited circuit, purpose be make two multiple-frequency modulation signals by 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 the gravity gradient tensor signal.Because gravity gradient tensor only is contained in two frequency multiplication sinewave modulation signal, therefore this main circuit will be eliminated DC component, frequency multiplication component sine waves, other higher hamonic waves and random noise, from two extremely faint frequency-doubled signals, detects the 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, the I/V change-over circuit is by anti-phase ratio amplifying circuit, integrating circuit, voltage follower circuit and resistance R _fform, wherein the first operational amplifier A ₁with resistance R _f, capacitor C _oform anti-phase ratio amplifying circuit and realize the conversion of current signal to voltage signal, resistance R _f, capacitor C _obe connected on the first operational amplifier A after parallel connection ₁reverse input and output side between, the second operational amplifier A ₂, resistance R ₁form integrating circuit with capacitor C, capacitor 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 ₂and resistance R ₃form 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 input current between connecting resistance R _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 capacitor C ₁, C ₂form 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, capacitor 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, capacitor 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 comprised of operational amplification circuit A8, resistance R 12, R13, R14 and band-pass circuit, resistance R 14 is connected between the output terminal and reverse input end of operational amplification circuit A8, resistance R 13 and band-pass circuit series connection are between the output terminal and reverse input end of operational amplification circuit A8, the output of one termination second amplifying circuit of resistance R 12, 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 present invention not detailed description is known to the skilled person technology.

Claims (8)

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

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

Wherein the coordinate of single shaft gravity gradiometer is the geographical coordinate system in sky, northeast, be designated as OXYZ, the initial point O that the center of circle of circular rotating parts is coordinate system, the turning axle of single shaft gravity gradiometer is perpendicular to geoid surface, the radius of circular rotating parts is r, and angular velocity of rotation is ω;

(2) the gravitation generation device is arranged in 2m space, the circular rotating parts center of circle;

(3) theoretical calculating gravitation generation device acts on the Gradient of Gravitation of circular rotating parts 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 parts circle centre position, Γ _xxfor the local derviation of gravitational acceleration component on X-axis of X-axis, Γ _xythe local derviation of gravitational acceleration component on Y-axis of X-axis, Γ _yybe the local derviation of gravitational acceleration component on Y-axis of Y-axis, G is newton's universal gravitational constant, and π is circular constant, the radius that R is the gravitation generation device, and the density that ρ is the gravitation generation device,

x, y, z is respectively the gravitation generation device barycenter coordinate under day geographical coordinate system northeastward:

(4) the Gradient of Gravitation calculated according to step (3) carries out to the track of gravitation generation device the best mobile alignment that emulation obtains the gravitation generation device;

(5) start the single shaft gravity gradiometer, the best mobile alignment that the gravitation generation device is obtained along step (4) emulation is moved, and utilizes the Gradient of Gravitation measuring system to measure the Gradient of Gravitation variation that the gravitation generation device acts on circular rotating parts circle centre position;

(6) the Gradient of Gravitation step (5) recorded compares with the theoretical the Gradient of Gravitation calculated, and calibrates the measuring accuracy of single shaft gravity gradiometer;

(7) utilize the rear single shaft gravity gradiometer of demarcation to carry out the Gradient of Gravitation measurement.

2. a kind of method of 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 be plumbous, the even density distribution.

3. a kind of method of utilizing gravity gradiometer to measure the Gradient of Gravitation according to claim 1, it is characterized in that: when described step (4) is carried out emulation, the radius R of gravitation generation device is got 0.1m.

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

5. a kind of method of utilizing gravity gradiometer to measure the Gradient of Gravitation according to claim 1, it is characterized in that: 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 form, four road current signals of four accelerometer generations convert four road voltage signals to through four I/V change-over circuits respectively, the two-way voltage signal of every group of accelerometer conversion amplifies and processes a multiple-frequency modulation signal anti-for the offset voltage signal Semi-polarity through an one-level amplifying circuit respectively, and two multiple-frequency modulation signals of same polarity are carried out to the addition amplification, second amplifying circuit carries out the addition amplification to the voltage signal of two one-level amplifying circuit outputs, voltage signal after trap circuit amplifies second amplifying circuit carries out a frequency-doubled signal inhibition and again deducts a residual multiple-frequency modulation signal, bandwidth-limited circuit carries out bandpass filtering to the voltage signal of trap circuit output, voltage signal after bandpass filtering is undertaken obtaining the gradient tensor voltage signal finally by crossing the low-pass filtering circuit filtering after phase sensitive detection by phase-sensitive detection circuit.

6. a kind of method of utilizing gravity gradiometer to measure the Gradient of Gravitation according to claim 1, it is characterized in that: described I/V change-over circuit is by anti-phase ratio amplifying circuit, integrating circuit, voltage follower circuit and resistance R _fform, wherein the first operational amplifier A ₁with resistance R _f, capacitor C _oform anti-phase ratio amplifying circuit and realize the conversion of current signal to voltage signal, resistance R _f, capacitor C _obe connected on the first operational amplifier A after parallel connection ₁reverse input and output side between, the second operational amplifier A ₂, resistance R ₁form integrating circuit with capacitor C, capacitor 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 ₂and resistance R ₃form 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 input current between connecting resistance R _f, the first operational amplifier A ₁, the second operational amplifier A ₂with the 3rd operational amplifier A ₃positive input ground connection.

7. a kind of method of utilizing gravity gradiometer to measure the Gradient of Gravitation according to claim 1, it is characterized in that: 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 capacitor C ₁, C ₂form 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, capacitor 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, capacitor 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.

8. a kind of method of utilizing gravity gradiometer to measure the Gradient of Gravitation according to claim 1, it is characterized in that: described trap circuit is by operational amplification circuit A8, resistance R 12, R13, R14 and bandwidth-limited circuit claimed in claim 3 form, resistance R 14 is connected between the output terminal and reverse input end of operational amplification circuit A8, resistance R 13 and bandwidth-limited circuit series connection are between the output terminal and reverse input end of operational amplification circuit A8, the output of one termination second amplifying circuit of resistance R 12, 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.

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