CN110110347A - A kind of airborne gravity vector downward continuation method and system based on point mass method - Google Patents
A kind of airborne gravity vector downward continuation method and system based on point mass method Download PDFInfo
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Abstract
The present invention discloses a kind of airborne gravity vector downward continuation method and system based on point mass method.This method comprises: obtaining aerial gravitational vectors measurement data；Grid processing is carried out to the aerial gravitational vectors measurement data, obtains the aerial gravitational vectors measurement data of grid；According to the relationship of the aerial gravitational vectors measurement data of the grid and virtual Point-mass Model midpoint quality, the virtual Point-mass Model under burial ground is constructed；The corresponding ground perturbation gravitation three component seismic data of the point mass is determined according to the virtual Point-mass Model, obtains continuation face gravitational vectors data.The present invention provides a kind of effective way for the downward continuation of airborne gravity vector measurement data, and Method And Principle is simple, easy to use, lower to the performance requirement of computer.And in the specific implementation, continuation result precision of the present invention is higher, will not introduce systematic error.
Description
Technical field
The present invention relates to airborne gravity measurement field, more particularly to it is a kind of based on the airborne gravity vector of point mass method to
Lower continuation method and system.
Background technique
Airborne gravity vector measurement is to disturb gravitation to the earth using airborne gravity vector measurement system using aircraft as carrier
The mode that three-component measures.Airborne gravity vector has apparent advantage, in the identical activity duration compared with scalar
Interior, the earth gravitational field information that it is obtained is three times of scalar measurement, two horizontal components (east orientation and north component) therein,
High-precision deviation of plumb line information can be obtained through conversion.In addition, the three-component information that vector method is measured carries out reasonable combination,
The determination precision of partial geoid ' can be significantly improved, this is for the ambits such as geodesic survey, geophysics and state
Anti- science is of great significance to.
Airborne gravity measurement data is in use, generally require in continuation to earth surface or geoid, main use
In the fusion of different type gravity survey data, the building in the whole world or region earth gravity field model, the whole world or region the earth water
Gravity datum map generalization etc. in the refining of quasi- face, subaqueous gravity matching assisting navigation.Currently used downward continuation method is equal
It is to be directed to airborne gravity scalar measurement data, and downward continuation then cannot achieve for airborne gravity vector measurement data.
Summary of the invention
The airborne gravity vector downward continuation method and system based on point mass method that the object of the present invention is to provide a kind of are
The downward continuation of airborne gravity vector measurement data provides a kind of effective way.
To achieve the above object, the present invention provides following schemes:
A kind of airborne gravity vector downward continuation method based on point mass method, comprising:
Obtain aerial gravitational vectors measurement data；
Grid processing is carried out to the aerial gravitational vectors measurement data, obtains the aerial gravitational vectors measurement of grid
Data；
According to the relationship of the aerial gravitational vectors measurement data of the grid and virtual Point-mass Model midpoint quality, structure
Build the virtual Point-mass Model under burial ground；
The corresponding ground perturbation gravitation three component seismic data of the point mass is determined according to the virtual Point-mass Model, is obtained
Continuation face gravitational vectors data.
Optionally, described to obtain aerial gravitational vectors measurement data, it specifically includes:
The gravitational vectors data on aerial survey line are obtained using airborne gravity vector measurement system, obtain aerial gravitational vectors
Measurement data.
Optionally, described that grid processing is carried out to the aerial gravitational vectors measurement data, obtain the aerial of grid
Gravitational vectors measurement data, specifically includes:
Equivalent conversion, error compensation, Data Format Transform, inertial navigation are carried out to the aerial gravitational vectors measurement data
Resolve, GNSS resolve and inertia/GNSS integrated navigation resolving, uniform data sample rate, survey line Gravity Disturbance Vector resolve and it is low
After pass filter processing, the aerial gravitational vectors measurement data of grid is obtained.
Optionally, the aerial gravitational vectors measurement data according to the grid and virtual Point-mass Model midpoint matter
The relationship of amount constructs the virtual Point-mass Model under burial ground, specifically includes:
According toDetermine disturbing potential T of the aerial point p in virtual Point-mass Modelp, wherein G is the earth
Gravitational constant, m are the number of point mass, MjFor j-th of point mass in virtual Point-mass Model, ρpjFor j-th of point mass and sky
The distance between midpoint p,rpIndicate the earth's core of aerial point p to diameter, rp=Re+
hp, ReIndicate average the earth's core to continuation region to diameter, hpIndicate the flying height when measurement of aerial gravitational vectors,N indicates the number of continuation face ground point, and R indicates the mean radius of the earth；RjIndicate at j-th point
The earth's core of quality is to diameter, Rj=Re-Dj, DjIndicate the buried depth of j-th of point mass；ψpjFor point p in the air and j-th of point mass
Between centre of sphere angle away from, Indicate aerial point p's
Reduced latitude, λpIndicate the geocentric longitude of aerial point p,Indicate the reduced latitude of j-th of point mass, λjIndicate j-th matter
The geocentric longitude of amount；
According to aerial disturbing potential of the point p in virtual Point-mass Model, the disturbance gravitation three-component δ of aerial point p is determinedp、And δλ:
Wherein,To disturb component of gravity δpJ-th of direction point mass,To disturb component of gravityDirection jth
A point mass,To disturb component of gravity δλJ-th of direction point mass；
Formula (1), (2) (3) are solved according to the aerial gravitational vectors measurement data of grid, determine virtual point mass mould
Point mass in type constructs the virtual Point-mass Model under burial ground.
Optionally, the aerial gravitational vectors measurement data according to grid solves formula (1), (2) (3), determines
Point mass in virtual Point-mass Model, constructs the virtual Point-mass Model under burial ground, specifically includes:
Formula (1), (2) (3) are solved according to the aerial gravitational vectors measurement data of grid using Matrix Solving mode,
Process is as follows:
Matrix form is converted by formula (1), (2) (3) correspondence, is obtained:
Lρ=AρMρ (4)
Lλ=AλMλ (6)
Wherein, Lρ、And LλRespectively indicate the disturbance gravitation three-component δ put in the airρ、And δλThe vector of composition, Mρ、And MλRespectively indicate the vector of the corresponding point mass composition of disturbance gravitation three-component, Aρ、And AλRespectively indicate corresponding system
Matrix number；
Using the aerial gravitational vectors measurement data of the grid as the disturbance gravitation three component seismic data put in the air in the air,
Substitute into formula (4), (5), (6)；
When the aerial gravitational vectors measurement data number of grid is identical as point mass number, the formula (4), (5),
(6) unique solution is obtained:
When the aerial gravitational vectors measurement data number of grid is greater than point mass number, formula (4), (5), (6) are obtained
To least square solution:
Wherein, Pρ、PλRespectively indicate the power battle array of the aerial gravitational vectors measurement data of grid.
Optionally, described to determine that the corresponding ground perturbation gravitation three of the point mass divides according to the virtual Point-mass Model
Data are measured, continuation face gravitational vectors data is obtained, specifically includes:
Utilize formula
Measure corresponding ground perturbation gravitation three component seismic data δ 'p、With δ 'λ, obtain continuation face gravitational vectors data；Wherein, riIt indicates
The earth's core of ground point i to diameter,Indicate the reduced latitude of ground point i, λiIndicate the geocentric longitude of ground point i, ρijIt indicates j-th
The distance between point mass and ground point i, ψpjCentre of sphere angle between ground point i and j-th of point mass away from.
The airborne gravity vector downward continuation system based on point mass method that the present invention also provides a kind of, comprising:
Aerial gravitational vectors measurement data obtains module, for obtaining aerial gravitational vectors measurement data；
Grid processing module obtains grid for carrying out grid processing to the aerial gravitational vectors measurement data
The aerial gravitational vectors measurement data changed；
Virtual Point-mass Model constructs module, for according to the aerial gravitational vectors measurement data of the grid and virtual
The relationship of point mass in Point-mass Model constructs the virtual Point-mass Model under burial ground；
Continuation face gravitational vectors data acquisition module, for determining the point mass pair according to the virtual Point-mass Model
The ground perturbation gravitation three component seismic data answered, obtains continuation face gravitational vectors data.
Optionally, the grid module is used to carry out equivalent conversion, error to the aerial gravitational vectors measurement data
Compensation, Data Format Transform, inertial navigation resolves, GNSS is resolved and inertia/GNSS integrated navigation resolving, uniform data sampling
After rate, the resolving of survey line Gravity Disturbance Vector and low-pass filtering treatment, the aerial gravitational vectors measurement data of grid is obtained.
Optionally, the virtual Point-mass Model building module specifically includes:
Disturbing potential determination unit is used for basisDetermine aerial point p disturbing in virtual Point-mass Model
Dynamic position Tp, wherein G is Gravitational coefficient of the Earth, and m is the number of point mass, MjFor j-th of point mass in virtual Point-mass Model,
ρpjFor the distance between j-th point mass and aerial point p,rpIndicate aerial point
The earth's core of p is to diameter, rp=Re+hp, ReIndicate average the earth's core to continuation region to diameter, hpIt indicates when aerial gravitational vectors measures
Flying height,N indicates the number of continuation face ground point, and R indicates the mean radius of the earth；RjIt indicates
The earth's core of j-th of point mass is to diameter, Rj=Re-Dj, DjIndicate the buried depth of j-th of point mass；ψpjFor point p in the air and j-th
Centre of sphere angle between point mass away from, Indicate empty
The reduced latitude of midpoint p, λpIndicate the geocentric longitude of aerial point p,Indicate the reduced latitude of j-th of point mass, λjIndicate jth
The geocentric longitude of a point mass；
Gravitation three-component determination unit is disturbed, for determining according to aerial disturbing potential of the point p in virtual Point-mass Model
The disturbance gravitation three-component δ of aerial point pp、And δλ:
Wherein,To disturb component of gravity δpJ-th of direction point mass,To disturb component of gravityDirection jth
A point mass,To disturb component of gravity δλJ-th of direction point mass；
Unit is solved, for solving according to the aerial gravitational vectors measurement data of grid to formula (1), (2) (3), really
Point mass in fixed virtual Point-mass Model, constructs the virtual Point-mass Model under burial ground.
Optionally, the continuation face gravitational vectors data acquisition module is used to utilize formulaDetermine that the corresponding ground of point mass is disturbed
Dynamic gravitation three component seismic data δ 'p、With δ 'λ, obtain continuation face gravitational vectors data；Wherein, riIndicate ground point i the earth's core to
Diameter,Indicate the reduced latitude of ground point i, λiIndicate the geocentric longitude of ground point i, ρijIndicate j-th of point mass and ground point i
The distance between, ψpjCentre of sphere angle between ground point i and j-th of point mass away from.
The specific embodiment provided according to the present invention, the invention discloses following technical effects:
The present invention provides a kind of effective way, Method And Principle letter for the downward continuation of airborne gravity vector measurement data
It is single, it is easy to use, it is lower to the performance requirement of computer.And in the specific implementation, continuation result precision of the present invention is higher, will not
Introduce systematic error.
Detailed description of the invention
It in order to more clearly explain the embodiment of the invention or the technical proposal in the existing technology, below will be to institute in embodiment
Attached drawing to be used is needed to be briefly described, it should be apparent that, the accompanying drawings in the following description is only some implementations of the invention
Example, for those of ordinary skill in the art, without any creative labor, can also be according to these attached drawings
Obtain other attached drawings.
Fig. 1 is that the present invention is based on the flow diagrams of the airborne gravity vector downward continuation method of point mass method；
Fig. 2 is that the present invention is based on the structural schematic diagrams of the airborne gravity vector downward continuation system of point mass method；
Fig. 3 is the flow diagram of present invention specific implementation case.
Specific embodiment
Following will be combined with the drawings in the embodiments of the present invention, and technical solution in the embodiment of the present invention carries out clear, complete
Site preparation description, it is clear that described embodiments are only a part of the embodiments of the present invention, instead of all the embodiments.It is based on
Embodiment in the present invention, it is obtained by those of ordinary skill in the art without making creative efforts every other
Embodiment shall fall within the protection scope of the present invention.
In order to make the foregoing objectives, features and advantages of the present invention clearer and more comprehensible, with reference to the accompanying drawing and specific real
Applying mode, the present invention is described in further detail.
Fig. 1 is the flow diagram of the airborne gravity vector downward continuation method based on point mass method.As shown in Figure 1, institute
State method the following steps are included:
Step 100: obtaining aerial gravitational vectors measurement data.Aerial survey line is obtained using airborne gravity vector measurement system
On gravitational vectors data, available aerial gravitational vectors measurement data.Airborne gravity vector measurement system is by gravity sensitive
The compositions such as device subsystem, GNSS positioning subsystem, posture subsystem, laser-measured height subsystem, data acquisition subsystem.
Step 200: grid processing being carried out to aerial gravitational vectors measurement data, obtains the aerial gravitational vectors of grid
Measurement data.Gridization processing mainly includes equivalent conversion, error compensation, Data Format Transform, inertial navigation resolves, GNSS is solved
Calculation and inertia/GNSS integrated navigation resolving, data sampling rate is unified, survey line Gravity Disturbance Vector resolves and the processing such as low-pass filtering
Process.
Step 300: according to the pass of the aerial gravitational vectors measurement data of grid and virtual Point-mass Model midpoint quality
System constructs the virtual Point-mass Model under burial ground.Detailed process is as follows:
According toDetermine disturbing potential T of the aerial point p in virtual Point-mass Modelp, wherein G is the earth
Gravitational constant, m are the number of point mass, MjFor j-th of point mass in virtual Point-mass Model, ρpjFor j-th of point mass and sky
The distance between midpoint p,rpIndicate the earth's core of aerial point p to diameter, rp=Re+
hp, ReIndicate average the earth's core to continuation region to diameter, hpIndicate the flying height when measurement of aerial gravitational vectors,N indicates the number of continuation face ground point, and R indicates the mean radius of the earth；RjIndicate j-th matter
The earth's core of amount is to diameter, Rj=Re-Dj, DjIndicate the buried depth of j-th of point mass；ψpjFor point p in the air and j-th point mass it
Between centre of sphere angle away from, Indicate the ground of aerial point p
Heart latitude, λpIndicate the geocentric longitude of aerial point p,Indicate the reduced latitude of j-th of point mass, λjIndicate j-th of point mass
Geocentric longitude；
According to aerial disturbing potential of the point p in virtual Point-mass Model, the disturbance gravitation three-component δ of aerial point p is determinedp、And δλ:
Wherein,To disturb component of gravity δpJ-th of direction point mass,To disturb component of gravityDirection jth
A point mass,To disturb component of gravity δλJ-th of direction point mass；
Formula (1), (2) (3) are solved according to the aerial gravitational vectors measurement data of grid, determine virtual point mass mould
Point mass in type constructs the virtual Point-mass Model under burial ground.The disturbance gravitation three-component δ of aerial point pp、And δλWith
Aerial gravitational vectors measurement data is consistent, therefore, brings aerial gravitational vectors measurement data into above formula, can solve to obtain virtual
Point mass in Point-mass Model, the virtual Point-mass Model under the burial ground just constructed.Specific solution procedure is according to reality
Border demand selects suitable mode to solve, for example, Matrix Solving mode can be used, process is as follows:
It is write formula (1), (2) (3) correspondence as matrix form, is obtained:
Lρ=AρMρ
Lλ=AλMλ
Wherein, Lρ、And LλRespectively indicate the vector of airborne gravity vector three component seismic data composition, Mρ、And MλRespectively
Indicate the vector of the corresponding point mass composition of airborne gravity vector three-component, Aρ、And AλCoefficient matrix is respectively indicated, according to public affairs
Coefficient matrix can be obtained in formula (1), (2) (3) correspondence.When airborne gravity vector observation data amount check is identical as point mass number
When, above-mentioned matrix has unique solution:
When airborne gravity vector observation data amount check is greater than point mass number, matrix has least square solution:
Wherein, Pρ、PλRespectively indicate the power battle array of airborne gravity vector observation data.
Step 400: the corresponding ground perturbation gravitation three component seismic data of point mass being determined according to virtual Point-mass Model, is obtained
Continuation face gravitational vectors data.After the completion of virtual Point-mass Model building, i.e., it can utilize its disturbance that earth surface is calculated
Gravitation three component seismic data δ 'p、With δ 'λ, obtain continuation face gravitational vectors data；Formula are as follows:
Wherein, riIndicate the earth's core of ground point i to diameter,Indicate the reduced latitude of ground point i, λiIndicate the ground of ground point i
Longitude centroid, ρijIndicate that the distance between j-th of point mass and ground point i, calculation formula areψpjCentre of sphere angle between ground point i and j-th of point mass away from,It is so just that airborne gravity vector measurement data are downward
In continuation to earth surface.
The airborne gravity vector downward continuation system based on point mass method that the present invention also provides a kind of, Fig. 2 are base of the present invention
In the structural schematic diagram of the airborne gravity vector downward continuation system of point mass method.As shown in Fig. 2, the system comprises:
Aerial gravitational vectors measurement data obtains module 201, for obtaining aerial gravitational vectors measurement data；
Grid processing module 202 obtains lattice for carrying out grid processing to the aerial gravitational vectors measurement data
The aerial gravitational vectors measurement data of networking；
Virtual Point-mass Model constructs module 203, for according to the aerial gravitational vectors measurement data of the grid with
The relationship of virtual Point-mass Model midpoint quality, constructs the virtual Point-mass Model under burial ground；
Continuation face gravitational vectors data acquisition module 204, for determining described matter according to the virtual Point-mass Model
Corresponding ground perturbation gravitation three component seismic data is measured, continuation face gravitational vectors data are obtained.
It is obtained specifically, the aerial gravitational vectors measurement data obtains module 201 using airborne gravity vector measurement system
The gravitational vectors data on aerial survey line are taken, aerial gravitational vectors measurement data is obtained.
The grid module 202 be used to carry out the aerial gravitational vectors measurement data equivalent conversion, error compensation,
Data Format Transform, inertial navigation resolve, GNSS is resolved and inertia/GNSS integrated navigation resolving, uniform data sample rate, survey line
Gravity Disturbance Vector is resolved with after low-pass filtering treatment, obtains the aerial gravitational vectors measurement data of grid.
The virtual Point-mass Model building module 203 specifically includes:
Disturbing potential determination unit is used for basisDetermine aerial point p disturbing in virtual Point-mass Model
Dynamic position Tp, wherein G is Gravitational coefficient of the Earth, and m is the number of point mass, MjFor j-th of point mass in virtual Point-mass Model,
ρpjFor the distance between j-th point mass and aerial point p,rpIndicate aerial point
The earth's core of p is to diameter, rp=Re+hp, ReIndicate average the earth's core to continuation region to diameter, hpIt indicates when aerial gravitational vectors measures
Flying height,N indicates the number of continuation face ground point, and R indicates the mean radius of the earth；RjIt indicates
The earth's core of j-th of point mass is to diameter, Rj=Re-Dj, DjIndicate the buried depth of j-th of point mass；ψpjFor point p in the air and j-th
Centre of sphere angle between point mass away from, Indicate empty
The reduced latitude of midpoint p, λpIndicate the geocentric longitude of aerial point p,Indicate the reduced latitude of j-th of point mass, λjIndicate jth
The geocentric longitude of a point mass；
Gravitation three-component determination unit is disturbed, for determining according to aerial disturbing potential of the point p in virtual Point-mass Model
The disturbance gravitation three-component δ of aerial point pp、And δλ:
Wherein,To disturb component of gravity δpJ-th of direction point mass,To disturb component of gravityDirection jth
A point mass,To disturb component of gravity δλJ-th of direction point mass；
Unit is solved, for solving according to the aerial gravitational vectors measurement data of grid to formula (1), (2) (3), really
Point mass in fixed virtual Point-mass Model, constructs the virtual Point-mass Model under burial ground.
The continuation face gravitational vectors data acquisition module 204 is used to utilize formulaDetermine that the corresponding ground of point mass is disturbed
Dynamic gravitation three component seismic data δ 'p、With δ 'λ, obtain continuation face gravitational vectors data；Wherein, riIndicate ground point i the earth's core to
Diameter,Indicate the reduced latitude of ground point i, λiIndicate the geocentric longitude of ground point i, ρijIndicate j-th of point mass and ground point i
The distance between, ψpjCentre of sphere angle between ground point i and j-th of point mass away from.
The present invention utilizes aerial gravitational vectors three-component measurement data, constructs the virtual point mass of certain buried depth first
Model so that these virtual disturbing point masses systems can equally replace the practical gravitation field source of the earth, and makes these disturbances
The empty disturbance gravitation generated can approach airborne gravity vector measurement to particle on earth with permissible accuracy；Followed by virtual
Point-mass Model calculates the gravitational vectors three-component measurement data on earth surface, so just realizes the survey of airborne gravity vector
Measure the downward continuation of data.The present invention can get the gravitational vectors continuation on earth surface or geoid as a result, precision compared with
Height, to be the fusion of different type gravity survey data, the building in the whole world or region earth gravity field model, the whole world or region
The application such as gravity datum map generalization provides reliable basic number in the refining of geoid, subaqueous gravity matching assisting navigation
According to support.
The solution of the present invention is further illustrated below with reference to a specific implementation case, as shown in figure 3, Fig. 3 is the present invention
The flow diagram of case is embodied.
Firstly, obtaining the gravitational vectors data on aerial survey line using airborne gravity vector measurement system, process is a series of
Aerial grid point data is formed after processing.
Then, using point mass method, by aerial grid points gravitational vectors data downward continuation to earth surface or the earth water
On quasi- face, and the data are made to the application of next step.
According to imperial lattice theorem, outside of the earth disturbing potential can be with including that harmonic function outside one spherical surface of earth interior is forced
Closely, which is commonly referred to as Bjerhammar ball.So-called virtual Point-mass Model, exactly to be distributed in multiple Bjerhammar spherical surfaces
On virtual disturbing point masses system come equally replace the practical gravitation field source of the earth, it is desirable that these disturbing point masses generate at the earth's surface
Disturbing potential and its derived quantity field member observed quantity approached with permissible accuracy.
It is with the formula that disturbing point masses characterize outside of the earth disturbing potentialWherein, TpExist for point p in the air
Disturbing potential in virtual Point-mass Model, G are Gravitational coefficient of the Earth, and m is the number of point mass, MjFor in virtual Point-mass Model
J-th of point mass, ρpjFor the distance between j-th of point mass and aerial point p, calculation formula are as follows:Wherein, rpIndicate the earth's core of aerial point p to diameter, rp=Re+hp, ReIt indicates wait prolong
The average the earth's core in region is opened up to diameter, hpIndicate the flying height when measurement of aerial gravitational vectors,N table
Show the number of continuation face ground point, R indicates the mean radius of the earth；RjIndicate the earth's core of j-th of point mass to diameter, Rj=Re-
Dj, DjIndicate the buried depth of j-th of point mass；ψpjFor the centre of sphere angle in the air between point p and j-th of point mass away from, Indicate the reduced latitude of aerial point p, λpIt indicates
The geocentric longitude of aerial point p,Indicate the reduced latitude of j-th of point mass, λjIndicate the geocentric longitude of j-th of point mass.
According to the relationship between disturbing potential and disturbance gravitation three-component, then can obtain
Wherein,To disturb component of gravity δpJ-th of direction point mass,To disturb component of gravityDirection jth
A point mass,To disturb component of gravity δλJ-th of direction point mass.
Using above formula, the Point-mass Model under burial ground can be constructed according to airborne gravity vector three component seismic data.Experience
Show generally proper using the buried depth roughly equal with particle spacing.Therefore, the buried depth of 1 ° × 1 ° point mass
100km or so can be taken, the buried depth of 20 ' × 20 ' point masses generally takes 40km or so, the buried depth of 5 ' × 5 ' point masses
10km or so can be taken, the buried depth of 1 ' × 1 ' point mass can take 2km or so.
Above formula is written respectively as matrix form, is then calculated using matrix and above formula is solved, obtain virtual Point-mass Model
In point mass.After the completion of point mass structure, i.e., it can utilize its disturbance gravitation three component seismic data that earth surface is calculated.
Each embodiment in this specification is described in a progressive manner, the highlights of each of the examples are with other
The difference of embodiment, the same or similar parts in each embodiment may refer to each other.For system disclosed in embodiment
For, since it is corresponded to the methods disclosed in the examples, so being described relatively simple, related place is said referring to method part
It is bright.
Used herein a specific example illustrates the principle and implementation of the invention, and above embodiments are said
It is bright to be merely used to help understand method and its core concept of the invention；At the same time, for those skilled in the art, foundation
Thought of the invention, there will be changes in the specific implementation manner and application range.In conclusion the content of the present specification is not
It is interpreted as limitation of the present invention.
Claims (10)
1. a kind of airborne gravity vector downward continuation method based on point mass method characterized by comprising
Obtain aerial gravitational vectors measurement data；
Grid processing is carried out to the aerial gravitational vectors measurement data, obtains the aerial gravitational vectors measurement number of grid
According to；
According to the relationship of the aerial gravitational vectors measurement data of the grid and virtual Point-mass Model midpoint quality, building is buried
Hide the virtual Point-mass Model of underground；
The corresponding ground perturbation gravitation three component seismic data of the point mass is determined according to the virtual Point-mass Model, obtains continuation
Face gravitational vectors data.
2. the airborne gravity vector downward continuation method according to claim 1 based on point mass method, which is characterized in that institute
It states and obtains aerial gravitational vectors measurement data, specifically include:
The gravitational vectors data on aerial survey line are obtained using airborne gravity vector measurement system, obtain aerial gravitational vectors measurement
Data.
3. the airborne gravity vector downward continuation method according to claim 1 based on point mass method, which is characterized in that institute
It states and grid processing is carried out to the aerial gravitational vectors measurement data, obtain the aerial gravitational vectors measurement data of grid,
It specifically includes:
Equivalent conversion, error compensation, Data Format Transform, inertial navigation solution are carried out to the aerial gravitational vectors measurement data
It calculates, GNSS is resolved and inertia/GNSS integrated navigation resolving, uniform data sample rate, the resolving of survey line Gravity Disturbance Vector and low pass
After filtering processing, the aerial gravitational vectors measurement data of grid is obtained.
4. the airborne gravity vector downward continuation method according to claim 1 based on point mass method, which is characterized in that institute
The relationship of the aerial gravitational vectors measurement data and virtual Point-mass Model midpoint quality according to the grid is stated, building is buried
The virtual Point-mass Model of underground, specifically includes:
According toDetermine disturbing potential T of the aerial point p in virtual Point-mass Modelp, wherein G is terrestrial gravitation
Constant, m are the number of point mass, MjFor j-th of point mass in virtual Point-mass Model, ρpjFor j-th of point mass and aerial point p
The distance between,rpIndicate the earth's core of aerial point p to diameter, rp=Re+hp, ReTable
Show average the earth's core to continuation region to diameter, hpIndicate the flying height when measurement of aerial gravitational vectors,N indicates the number of continuation face ground point, and R indicates the mean radius of the earth；RjIndicate j-th matter
The earth's core of amount is to diameter, Rj=Re-Dj, DjIndicate the buried depth of j-th of point mass；ψpjFor point p in the air and j-th point mass it
Between centre of sphere angle away from, Indicate the ground of aerial point p
Heart latitude, λpIndicate the geocentric longitude of aerial point p,Indicate the reduced latitude of j-th of point mass, λjIndicate j-th of point mass
Geocentric longitude；
According to aerial disturbing potential of the point p in virtual Point-mass Model, the disturbance gravitation three-component δ of aerial point p is determinedρ、With
δλ:
Wherein,To disturb component of gravity δpJ-th of direction point mass,To disturb component of gravityJ-th, direction matter
Amount,To disturb component of gravity δλJ-th of direction point mass；
Formula (1), (2) (3) are solved according to the aerial gravitational vectors measurement data of grid, are determined in virtual Point-mass Model
Point mass, construct burial ground under virtual Point-mass Model.
5. the airborne gravity vector downward continuation method according to claim 4 based on point mass method, which is characterized in that institute
It states and formula (1), (2) (3) is solved according to the aerial gravitational vectors measurement data of grid, determine in virtual Point-mass Model
Point mass constructs the virtual Point-mass Model under burial ground, specifically includes:
Formula (1), (2) (3) are solved according to the aerial gravitational vectors measurement data of grid using Matrix Solving mode, process
It is as follows:
Matrix form is converted by formula (1), (2) (3) correspondence, is obtained:
Lρ=AρMρ (4)
Lλ=AλMλ (6)
Wherein, Lρ、And LλRespectively indicate the disturbance gravitation three-component δ put in the airρ、And δλThe vector of composition, Mρ、And Mλ
Respectively indicate the vector of the corresponding point mass composition of disturbance gravitation three-component, Aρ、And AλRespectively indicate corresponding coefficient matrix；
Using the aerial gravitational vectors measurement data of the grid as the disturbance gravitation three component seismic data put in the air in the air, substitute into
Formula (4), (5), (6)；
When the aerial gravitational vectors measurement data number of grid is identical as point mass number, the formula (4), (5), (6)
Obtain unique solution:
When the aerial gravitational vectors measurement data number of grid is greater than point mass number, formula (4), (5), (6) are obtained most
Small two multiply solution:
Wherein, Pρ、PλRespectively indicate the power battle array of the aerial gravitational vectors measurement data of grid.
6. the airborne gravity vector downward continuation method according to claim 4 based on point mass method, which is characterized in that institute
It states and the corresponding ground perturbation gravitation three component seismic data of the point mass is determined according to the virtual Point-mass Model, obtain continuation face
Gravitational vectors data, specifically include:
Utilize formulaDetermine point mass pair
The ground perturbation gravitation three component seismic data δ ' answeredρ、With δ 'λ, obtain continuation face gravitational vectors data；Wherein, riIndicate ground
The earth's core of point i to diameter,Indicate the reduced latitude of ground point i, λiIndicate the geocentric longitude of ground point i, ρijIndicate j-th matter
The distance between amount and ground point i, ψpjCentre of sphere angle between ground point i and j-th of point mass away from.
7. a kind of airborne gravity vector downward continuation system based on point mass method characterized by comprising
Aerial gravitational vectors measurement data obtains module, for obtaining aerial gravitational vectors measurement data；
Grid processing module obtains grid for carrying out grid processing to the aerial gravitational vectors measurement data
Aerial gravitational vectors measurement data；
Virtual Point-mass Model constructs module, for the aerial gravitational vectors measurement data and virtual point matter according to the grid
The relationship of point mass in model is measured, the virtual Point-mass Model under burial ground is constructed；
Continuation face gravitational vectors data acquisition module, for determining that the point mass is corresponding according to the virtual Point-mass Model
Ground perturbation gravitation three component seismic data obtains continuation face gravitational vectors data.
8. the airborne gravity vector downward continuation system according to claim 6 based on point mass method, which is characterized in that institute
State grid module for the aerial gravitational vectors measurement data carry out equivalent conversion, error compensation, Data Format Transform,
Inertial navigation resolves, GNSS is resolved and inertia/GNSS integrated navigation resolving, uniform data sample rate, survey line Gravity Disturbance Vector
It resolves with after low-pass filtering treatment, obtains the aerial gravitational vectors measurement data of grid.
9. the airborne gravity vector downward continuation system according to claim 6 based on point mass method, which is characterized in that institute
Virtual Point-mass Model building module is stated to specifically include:
Disturbing potential determination unit is used for basisDetermine aerial disturbing potential of the point p in virtual Point-mass Model
Tp, wherein G is Gravitational coefficient of the Earth, and m is the number of point mass, MjFor j-th of point mass in virtual Point-mass Model, ρpjFor
The distance between j-th of point mass and aerial point p,rpIndicate aerial point p's
The earth's core is to diameter, rp=Re+hp, ReIndicate average the earth's core to continuation region to diameter, hpIt indicates to fly when the measurement of aerial gravitational vectors
Row height,N indicates the number of continuation face ground point, and R indicates the mean radius of the earth；RjIndicate the
The earth's core of j point mass is to diameter, Rj=Re-Dj, DjIndicate the buried depth of j-th of point mass；ψpjFor point p in the air and j-th point
Centre of sphere angle between quality away from, Indicate aerial
The reduced latitude of point p, λpIndicate the geocentric longitude of aerial point p,Indicate the reduced latitude of j-th of point mass, λjIt indicates j-th
The geocentric longitude of point mass；
Gravitation three-component determination unit is disturbed, for determining aerial according to aerial disturbing potential of the point p in virtual Point-mass Model
The disturbance gravitation three-component δ of point pρ、And δλ:
Wherein,To disturb component of gravity δρJ-th of direction point mass,To disturb component of gravityJ-th, direction matter
Amount,To disturb component of gravity δλJ-th of direction point mass；
Unit is solved, for being solved according to the aerial gravitational vectors measurement data of grid to formula (1), (2) (3), is determined empty
Point mass in quasi- Point-mass Model, constructs the virtual Point-mass Model under burial ground.
10. the airborne gravity vector downward continuation system according to claim 9 based on point mass method, which is characterized in that
The continuation face gravitational vectors data acquisition module is used to utilize formulaDetermine that the corresponding ground of point mass is disturbed
Dynamic gravitation three component seismic data δ 'p、With δ 'λ, obtain continuation face gravitational vectors data；Wherein, riIndicate ground point i the earth's core to
Diameter,Indicate the reduced latitude of ground point i, λiIndicate the geocentric longitude of ground point i, ρijIndicate j-th of point mass and ground point i
The distance between, ψpjCentre of sphere angle between ground point i and j-th of point mass away from.
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| WO2015042754A1 (en) * | 2013-09-29 | 2015-04-02 | 清华大学 | Method for parsing and calculating performance of satellite gravity field measurement by low-to-low satellite-to-satellite tracking |
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