CN107272084A - A kind of method for creating the even value gravity gradient tensor excitation of Local approximation - Google Patents
A kind of method for creating the even value gravity gradient tensor excitation of Local approximation Download PDFInfo
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- CN107272084A CN107272084A CN201710317828.3A CN201710317828A CN107272084A CN 107272084 A CN107272084 A CN 107272084A CN 201710317828 A CN201710317828 A CN 201710317828A CN 107272084 A CN107272084 A CN 107272084A
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Abstract
The present invention relates to a kind of method for creating the even value gravity gradient tensor excitation of Local approximation, its technical characterstic is to comprise the following steps：Build the even value gravity gradient tensor exciting bank of high tensor Local approximation；According to required gradient excitation amplitude, range, excitation step-length and the measurement scale scope of the approximate even value gravity gradient tensor excitation of high tensor are set, the spatial gradient tensor under the Gradient of Gravitation excitation model is calculated, range is controllable, the even value of Local approximation high tensor the Gradient of Gravitation excitation so as to be formed.The present invention is by reasonable in design, instrument output is demarcated using the excitation of even value gravity gradient tensor in the range of gravity gradient sensor measurement scale, the high tensor the Gradient of Gravitation excitation of the characteristics such as controllable, the even value of Local approximation of range is formed, the problem of existing gravity gradient sensor calibration method does not possess the even value gradient field characteristic showed in horizontal gravity gradient measuring principle is solved.
Description
Technical field
The invention belongs to gravity gradiometer technical field, especially a kind of even value gravity gradient tensor of Local approximation that creates swashs
The method encouraged.
Background technology
Gravity gradiometer is the special equipment of sensitive VARIATION OF GRAVITY FIELD trend, in order to realize to VARIATION OF GRAVITY FIELD quantitative measurment
Accuracy, effectively accurate demarcation must be just carried out to the output result of gravity gradiometer.And realize that Accurate Calibration is most effective
Method be exactly build even value, controllable gravity gradient field excitation, but be limited to existing rotary accelerometer formula gravity gradiometer
Element level and principle scheme restriction, want to realize effective demarcation (theoretical resolution to horizontal local tensors gravity gradiometer
The E of rate tens), it is necessary to create the mass attraction ladder for possessing high tensor excitation and approximate even value characteristic being presented in certain space yardstick
Field is spent, to solve the demarcation demand for equipment.
Quantitatively calibrating method mainly uses two frequency multiplication resolution ratio equivalent mass gravity gradient tensor advocate approach, i.e. root at this stage
According to the law of universal gravitation, the excitation mass attraction with the corresponding each sampled point of gravity gradient sensor rotation modulation frequency is calculated
Active constituent of the acceleration along each heavy terraced accelerometer sensitive axle, then rotates to the volume of data that theoretical calculation is obtained
Data at the frequency multiplication of modulating frequency two are extracted, and are revolved while measuring true excitation obtained each sampled point output electric signal down
Turn the demodulation at the frequency multiplication of modulating frequency two and filtering process, the theory for finally obtaining the output signal after processing and calculating is effectively
Acceleration information carries out scale operation, so that obtaining the terraced accelerometer of weight is adjusting the effective resolution at two frequencys multiplication, it is indirectly real
Show to encourage with the equivalent even value the Gradient of Gravitation of the resolution capability and demarcated.But above-mentioned scaling method does not have real build and met
Even value gradient field excitation described in horizontal tensor gradiometry principle, is only embodied used in integrated gravity gradient sensor
The terraced accelerometer of weight possess the measurement resolution capability that sensitive equivalent even value gravity gradient is encouraged.
The content of the invention
The even value the Gradient of Gravitation of Local approximation is created it is an object of the invention to overcome the deficiencies of the prior art and provide one kind
The method for measuring excitation, the existing gravity gradient sensor calibration method of solution does not possess to be showed in horizontal gravity gradient measuring principle
Even value gradient field characteristic the problem of.
The present invention solves existing technical problem and takes following technical scheme to realize：
A kind of method for creating the even value gravity gradient tensor excitation of Local approximation, comprises the following steps：
The even value gravity gradient tensor exciting bank of step 1, the high tensor Local approximation of structure；
Step 2, range, excitation step-length and the measurement scale model that the approximate even value gravity gradient tensor excitation of high tensor is set
Enclose, calculate the spatial gradient tensor under the Gradient of Gravitation excitation model, range is controllable, the even value of Local approximation high tensor so as to be formed
The Gradient of Gravitation is encouraged.
The even value gravity gradient tensor exciting bank of high tensor Local approximation includes linear motion slide rail, encouraged by quality
Line style gravitational mass body and gravity gradient sensor that unit is constituted, gravity gradient sensor are arranged on two line style gravitational masses
The center of body and two line style gravitational mass bodies are arranged on linear motion slide rail, the quality of two line style gravitational mass bodies
Central plane is overlapped with the pivot plane of gravity gradient sensor.
The line style gravitational mass body is made up of tungsten copper alloy.
The measurement scale scope is the square region around gravity gradient sensing device.
The gravity gradient forward modeling recurrence formula of the step 2 is：
In formula, G is universal gravitational constant；ρ is gravitational mass body
Mass density；ξiAnd ξi' be respectively 8 summits of both sides symmetric Gravitational mass body x-axis coordinate value；ηiAnd ηi' it is respectively both sides pair
Cite approvingly the y-axis coordinate value on 8 summits of mechanical mass body；γiAnd γi' be respectively 8 summits of both sides symmetric Gravitational mass body z-axis sit
Scale value；X, y, z are the coordinate of any observation station in rectangular coordinate system；For both sides any summit of symmetric Gravitational mass body and arbitrarily
Distance between observation station；For direction coefficient.
Advantages and positive effects of the present invention are：
The present invention is by the mechanism of production of the approximate even value gravitational gradient field of analysis, distribution character and for gravity gradiometer
The practical function of demarcation, builds the even value gravity gradient tensor exciting bank of high tensor Local approximation, is surveyed in gravity gradient sensor
Instrument output is demarcated using the excitation of even value gravity gradient tensor in the range of gage degree, formation range is controllable, Local approximation
The high tensor the Gradient of Gravitation excitation of the characteristics such as even value, solves existing gravity gradient sensor calibration method and does not possess horizontal gravity
The problem of even value gradient field characteristic showed in gradiometry principle.
Brief description of the drawings
Fig. 1 is point source Mass Distribution schematic diagram；
Fig. 2 is setting observation scope schematic diagram in Fig. 1；
Fig. 3 is Txx、TyyAnd Txx-TyySchematic diagram of calculation result；
The even value gravity gradient tensor exciting bank structure chart of high tensor Local approximation that Fig. 4 builds for the present invention；
Fig. 5 is Fig. 4 top view；
Fig. 6 is that line style Symmetric Mass is distributed the lower gradient fields distribution schematic diagram produced when 50E is encouraged；
Fig. 7 is that line style Symmetric Mass is distributed the lower gradient fields distribution schematic diagram produced when 100E is encouraged；
Fig. 8 is that line style Symmetric Mass is distributed the lower gradient fields distribution schematic diagram produced when 150E is encouraged；
Wherein, 1 in Fig. 4 and Fig. 5 is linear motion slide rail, 2 is gravitational mass body (being made up of quality exciting unit), 3
It is measurement scale scope for gravity gradient sensing device, 4.
Embodiment
The embodiment of the present invention is further described below in conjunction with accompanying drawing：
It is a kind of create the method that the even value gravity gradient tensor of Local approximation is encouraged design principle be：
According to the symmetrical basis for producing local even value line gravitational gradient field of point source quality, it is considered herein that line style quality
Plane is symmetrical can equally produce the even value the Gradient of Gravitation characteristic of similar part plan.Mass Distribution is as shown in figure 1, two
Line style quality can be expressed as follows in the gravity gradient tensor that-ξ ＜ x ＜ ξ regions are produced：
ξ is the x-axis coordinate value of arbitrfary point on line style mass body in formula；η, η ' it is respectively that the symmetrical line style mass body in both sides is taken up an official post
The y-axis coordinate value of meaning point；X is the x-axis coordinate value of the symmetrical any observation station in line style mass body intermediate region in both sides；Y is both sides pair
Claim the y-axis coordinate value of any observation station in line style mass body intermediate region；
Knowable to each tensor is calculated in formula, when line mass source takes (- ∞ ,+∞) in y-coordinate axle interval, TxyAnd Tyx
Item is zero, and the other three tensor for measuring (demarcation) care is：
For easy analysis, finite interval integral and calculating is carried out to above formula using numerical integrating, and choose certain sight
Survey scope to be observed using diagrammatic representation, to study the Gradient of Gravitation Field distribution characteristic under symmetrical line style Mass Distribution.Assuming that
Line density ρ takes 1, ξ to take 2, η to take (- 10,10) interval, and observation scope takes the square region of the length of side 0.2 centered on the origin of coordinates
Domain, as shown in Figure 2.Txx、TyyAnd Txx-TyyResult of calculation as shown in Figure 3 and Table 1.
Each gravity gradient tensor excitation under the line of symmetry Mass Distribution of table 1. in definite measured yardstick plane
From result of calculation as can be seen that when Mass Sources are symmetrical into line style on observation coordinate system y-axis, to observe seat
The T in certain observation area plane centered on mark system originxx-TyyTensor is approximately equal to TxxTensor and approximate even value is presented
Characteristic, and TyyTensor is approximately 0.Therefore, by the gravitational gradient field quantitative analysis symmetrical to line style Mass Sources, exist really
Symmetrical centre regional area, which can be produced, both has certain tensor value, the gravitational gradient field with approximate even value characteristic, so be
The follow-up approximate even value gravitational gradient field how quantitatively created needed for being demarcated available for Gravity Gradient Sensor is laid a good foundation.
The present invention is specifically described with reference to Fig. 4 and Fig. 5 instantiation provided.
The even value gravity gradient tensor exciting bank of high tensor Local approximation is built first, as shown in Figures 4 and 5.Line style is drawn
Mass centre's plane of mechanical mass body 2 is overlapped with the pivot plane (X/Y plane in figure) of gravity gradient sensor 3, is passed through
Symmetrical mobile line style gravitational mass body 2, along the increase of line style direction, reduces gravitational mass body 2 on the symmetrical sliding track mechanism 1 of linear pattern
Or integrally increase, reduce the columns of line style gravitational mass body 2 along symmetrical displacement direction, to produce with high tensor and weigh
The gravity gradient tensor excitation of approximate even value characteristic is presented in the measurement scale scope 4 of power gradient sensing device 3.
Then obtained gravitational mass body 2 is calculated according to gravity gradient forward modeling recurrence formula according to required gradient excitation amplitude
Line style distribution length, along the distribution columns of the symmetrical moving direction of sliding track mechanism 1 of linear pattern, and with gravity gradient sensor
Horizontal distribution spacing, the corresponding required quality driver element of configuration, while controlling symmetrical line sliding track mechanism 1 corresponding according to what is obtained
Moving direction is symmetrically moved, and running fix precision is better than 1mm.Specific method is：
The spatial gradient tensor distribution formula calculated under the Gradient of Gravitation excitation model is as follows：
In formula,
And
According to the demarcation demand of gravity gradient sensor 3, the approximate even value gravity gradient tensor of high tensor for drafting establishment swashs
Encourage as range 150E, excitation step-length is 50E, the measurement scale scope 4 for delimiting gravity gradient sensor 3 is 340 × 340 (units：
Mm square region), while limiting the approximate even value the Gradient of Gravitation excitation error created is not more than excitation tensor numerical value
10% is boundary condition, it is assumed that using 100mm × 100mm × 100mm tungsten copper alloy, (its density is 18 × 103kg/m3) be
The component units of gravitational mass body 2, the gravitational mass body 2 of establishment condition is met using forward modeling recurrence calculation method search
Symmetrical distance, Mass Distribution length and gradient Field distribution characteristic (as shown in Fig. 6 to 8 and table 2,3).
T in the line style Symmetric Mass of the table 2. distribution effective measurement scale of Gradient instrumentxx、Tyy、Txx-yyGravity gradient tensor swashs
Encourage
Txy gravity gradient tensors excitation in the line style Symmetric Mass of the table 3. distribution effective measurement scale of Gradient instrument
Finally, it is the even value gradient tensor characteristic of Local approximation under checking symmetric Gravitational quality excitation, that is, verifies gravity ladder
The sensing value of degree sensor 3 is to the horizontal level distance of the relative gravity gradient sensing device 3 of gravitational mass body 2 near symmetrical centre
The insensitive characteristic of change, can be when realizing the excitation of symmetric Gravitational quality, along the symmetrical sliding track mechanism 1 of linear pattern, small model in the same direction
Parallel mobile gravitational mass body 2 is enclosed, to observe the fluctuating change of gravity gradient sensor sensing value, is realized to local even value characteristic
Checking.
It is emphasized that embodiment of the present invention is illustrative, rather than it is limited, therefore present invention bag
Include and be not limited to embodiment described in embodiment, it is every by those skilled in the art's technique according to the invention scheme
The other embodiment drawn, also belongs to the scope of protection of the invention.
Claims (5)
1. a kind of method for creating the even value gravity gradient tensor excitation of Local approximation, it is characterised in that comprise the following steps：
The even value gravity gradient tensor exciting bank of step 1, the high tensor Local approximation of structure；
Step 2, range, excitation step-length and the measurement scale scope that the approximate even value gravity gradient tensor excitation of high tensor is set, meter
The spatial gradient tensor under the Gradient of Gravitation excitation model is calculated, range is controllable, the even value of Local approximation high tensor gravitation so as to be formed
Gradient is encouraged.
2. a kind of method for creating the even value gravity gradient tensor excitation of Local approximation according to claim 1, its feature exists
In：The even value gravity gradient tensor exciting bank of high tensor Local approximation includes linear motion slide rail, by quality exciting unit
The line style gravitational mass body and gravity gradient sensor of composition, gravity gradient sensor are arranged on two line style gravitational mass bodies
Center and two line style gravitational mass bodies are arranged on linear motion slide rail, the mass centre of two line style gravitational mass bodies
Plane is overlapped with the pivot plane of gravity gradient sensor.
3. a kind of method for creating the even value gravity gradient tensor excitation of Local approximation according to claim 2, its feature exists
In：The line style gravitational mass body is made up of tungsten copper alloy.
4. a kind of method for creating the even value gravity gradient tensor excitation of Local approximation according to claim 1, its feature exists
In：The measurement scale scope is the square region around gravity gradient sensing device.
5. a kind of method for creating the even value gravity gradient tensor excitation of Local approximation according to claim 1, its feature exists
In：The formula that the step 2 calculates the spatial gradient tensor under the Gradient of Gravitation excitation model is：
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In formula, N=1,2；G is universal gravitational constant；ρ is gravitational mass constitution
Metric density；ξiAnd ξi' be respectively 8 summits of both sides symmetric Gravitational mass body x-axis coordinate value；ηiAnd ηi' it is respectively that both sides are symmetrical
The y-axis coordinate value on 8 summits of gravitational mass body；γiAnd γi' be respectively 8 summits of both sides symmetric Gravitational mass body z-axis coordinate
Value；X, y, z are the coordinate of any observation station in rectangular coordinate system；For both sides any summit of symmetric Gravitational mass body and any sight
Distance between measuring point；For direction coefficient.
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