CN109856691B - Aviation gravity vector downward continuation method and system based on gradient method - Google Patents
Aviation gravity vector downward continuation method and system based on gradient method Download PDFInfo
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Abstract
The invention discloses an aviation gravity vector downward continuation method and system based on a gradient method. The method comprises the following steps: calculating the correction number of three components of the gravity vector in the radial direction by using a high-precision ultra-high-order earth gravity field model; obtaining continuation height; calculating the correction value of the three components of the gravity vector in the radial direction according to the continuation height to obtain the correction value of the three components of the gravity vector in the radial direction; acquiring aviation gravity vector measurement data; correcting the aviation gravity vector measurement data according to the correction value of the gravity vector in the radial direction to obtain gravity vector three-component data on an extension surface; and carrying out precision evaluation on the gravity vector three-component data on the extension surface to obtain a precision evaluation result. The method can realize effective continuation of airborne gravity vector three-component measurement data at any point in the air, and the continuation result has higher precision.
Description
Technical Field
The invention relates to the field of aviation gravity measurement, in particular to an aviation gravity vector downward continuation method and system based on a gradient method.
Background
The aviation gravity vector measurement is an activity of measuring three components of earth disturbance gravity by using an aircraft as a carrier and using an aviation gravity vector measurement system. The aviation gravity vector has obvious advantages compared with a scalar, and the obtained earth gravity field information is three times of that of the scalar measurement in the same working time, wherein two horizontal components (east and north components) can be converted to obtain high-precision vertical deviation information. In addition, the three-component information measured by the vector method is reasonably combined, so that the determination precision of the local geohorizon can be obviously improved, and the method has very important practical significance for the subject fields of geodetic surveying, geophysical and the like and national defense science.
When the aerial gravity vector measurement data is applied, the aerial gravity vector measurement data generally needs to be extended to the earth surface or the ground level, and the aerial gravity vector measurement data is mainly used for fusion of different types of gravity measurement data, construction of a global or regional earth gravity field model, refinement of a global or regional (similar) ground level, generation of a gravity reference diagram in underwater gravity matching assisted navigation and the like.
At present, all the commonly used downward continuation methods are researched aiming at aviation gravity scalar quantity measurement data, and a downward continuation method suitable for aviation gravity vector measurement data is not provided.
Disclosure of Invention
The invention aims to provide a method and a system for continuation of an aerial gravity vector downwards based on a gradient method, which can realize effective continuation of three-component measurement data of the aerial gravity vector at any point in the air, and the continuation result has high precision.
In order to achieve the purpose, the invention provides the following scheme:
an aviation gravity vector downward continuation method based on a gradient method comprises the following steps:
calculating the correction number of three components of the gravity vector in the radial direction by using a high-precision ultra-high-order earth gravity field model;
obtaining continuation height;
calculating the correction value of the three components of the gravity vector in the radial direction according to the continuation height to obtain the correction value of the three components of the gravity vector in the radial direction;
acquiring aviation gravity vector measurement data;
correcting the aviation gravity vector measurement data according to the correction value of the gravity vector in the radial direction to obtain gravity vector three-component data on an extension surface;
and carrying out precision evaluation on the gravity vector three-component data on the extension surface to obtain a precision evaluation result.
Optionally, the calculating, by using the high-precision ultrahigh-order earth gravitational field model, the correction number of the three components of the gravity vector in the radial direction specifically includes:
utilizing high-precision ultra-high-order earth gravity field model and adopting formula
Calculating three components of the gravity vector in the radial direction; the three components include an east component, a north component, and a vertical component;
wherein the content of the first and second substances,rrepresenting the radial disturbance gravity vector and,
representing a latitudinal direction disturbance gravity vector,λrepresenting a longitude disturbance gravity vector, and fM represents the product of a universal gravity constant f and the total mass M of the earth; r is the mean radius of the earth; r is R + h, R represents the earth center radial of any point on the disturbance gravity vector measurement plane, and h represents the flying height; theta and lambda respectively represent the residual latitude and longitude of the geocentric;
representing the complete normalization of the earth disturbance gravitational potential coefficient; n and m respectively represent the order and the order of the spherical harmonic coefficient;
indicating a complete normalization of the associated legendre function,
indicating Legendre letterA first derivative is counted;
using a formula
Respectively calculating a first derivative and a second derivative of the three components in the radial direction to obtain a correction number of the three components of the gravity vector in the radial direction;
wherein the content of the first and second substances,
respectively representing a gradient value of three components of the air disturbance gravity vector in the radial direction;
respectively represents the second-order gradient value of three components of the air disturbance gravity vector in the radial direction.
Optionally, the calculating, according to the continuation height, a correction value of the three components of the gravity vector in the radial direction to obtain a correction value of the three components of the gravity vector in the radial direction includes:
using a formula according to said continuation height
Calculating the correction values of the three components of the gravity vector in the radial direction to obtain the correction values of the three components of the gravity vector in the radial direction;
wherein, Deltar(r, theta, lambda) represents radial disturbance gravity vector correction data,
representing the amount of modification, Δ, of the gravity vector for the latitudinal disturbanceλ(R, θ, λ) represents a longitudinal disturbance gravity vector correction amount, Δ R ═ R '-R, Δ R represents the extension height, and R' represents the earth-center-diameter of the corresponding point on the extension plane.
Optionally, the correcting the aerial gravity vector measurement data according to the correction value in the radial direction of the gravity vector to obtain gravity vector three-component data on an extension plane, specifically including:
and according to a gradient method for downward continuation of the aerial gravity vector measurement data, correcting the aerial gravity vector measurement data by adopting a correction value in the radial direction of the gravity vector to obtain gravity vector three-component data on a continuation surface.
Optionally, the correcting the aviation gravity vector measurement data according to the gradient method of downward continuation of the aviation gravity vector measurement data by using the correction value in the radial direction of the gravity vector to obtain gravity vector three-component data on a continuation surface specifically includes:
according to the gradient method of downward continuation of aviation gravity vector measurement data, the correction value of the radial direction of the gravity vector is adopted according to a formula
Correcting the aerial gravity vector measurement data to obtain gravity vector three-component data on an extension surface;
wherein the content of the first and second substances,
respectively representing three components of the ground disturbance gravity;
respectively, representing airborne gravity vector measurement data.
An aviation gravity vector downward continuation system based on a gradient method comprises the following steps:
the correction number calculation module is used for calculating the correction number of the three components of the gravity vector in the radial direction by utilizing a high-precision ultra-high-order earth gravity field model;
the first obtaining module is used for obtaining the continuation height;
the correction value calculation module is used for calculating the correction value of the three components of the gravity vector in the radial direction according to the extension height to obtain the correction value of the three components of the gravity vector in the radial direction;
the second acquisition module is used for acquiring aviation gravity vector measurement data;
the correction module is used for correcting the aviation gravity vector measurement data according to the correction value of the gravity vector in the radial direction to obtain gravity vector three-component data on an extension surface;
and the evaluation module is used for carrying out precision evaluation on the gravity vector three-component data on the extension surface to obtain a precision evaluation result.
Optionally, the correction number calculating module specifically includes:
a three-component calculation unit for using the high-precision ultra-high-order earth gravity field model and adopting the formula
Calculating three components of the gravity vector in the radial direction; the three components include an east component, a north component, and a vertical component;
wherein the content of the first and second substances,rrepresenting the radial disturbance gravity vector and,
representing a latitudinal direction disturbance gravity vector,λrepresenting a longitude disturbance gravity vector, and fM represents the product of a universal gravity constant f and the total mass M of the earth; r is the mean radius of the earth; r is R + h, R represents the earth center radial of any point on the disturbance gravity vector measurement plane, and h represents the flying height; theta and lambda respectively represent the residual latitude and longitude of the geocentric;
representing the complete normalization of the earth disturbance gravitational potential coefficient; n and m respectively represent the order and the order of the spherical harmonic coefficient;
indicating a complete normalization of the associated legendre function,
representing the first derivative of the Legendre function;
a three-component derivative calculation unit for employing the formula
Respectively calculating a first derivative and a second derivative of the three components in the radial direction to obtain a correction number of the three components of the gravity vector in the radial direction;
wherein the content of the first and second substances,
respectively representing a gradient value of three components of the air disturbance gravity vector in the radial direction;
respectively represents the second-order gradient value of three components of the air disturbance gravity vector in the radial direction.
Optionally, the correction value calculating module specifically includes:
a correction value calculating unit for adopting a formula according to the continuation height
Calculating the correction values of the three components of the gravity vector in the radial direction to obtain the correction values of the three components of the gravity vector in the radial direction;
wherein, Deltar(r, theta, lambda) represents radial disturbance gravity vector correction data,
representing the amount of modification, Δ, of the gravity vector for the latitudinal disturbanceλ(R, θ, λ) represents a longitudinal disturbance gravity vector correction amount, Δ R ═ R '-R, Δ R represents the extension height, and R' represents the earth-center-diameter of the corresponding point on the extension plane.
Optionally, the correction module specifically includes:
and the correction unit is used for correcting the aerial gravity vector measurement data by adopting the correction value in the radial direction of the gravity vector according to the downward continuation gradient method of the aerial gravity vector measurement data to obtain gravity vector three-component data on a continuation surface.
Optionally, the correction unit specifically includes:
a correction subunit, for adopting the correction value of the radial direction of the gravity vector according to a formula by a gradient method of downward continuation according to the aviation gravity vector measurement data
Correcting the aerial gravity vector measurement data to obtain gravity vector three-component data on an extension surface;
wherein the content of the first and second substances,
respectively representing three components of the ground disturbance gravity;
respectively, representing airborne gravity vector measurement data.
According to the specific embodiment provided by the invention, the invention discloses the following technical effects: the invention provides an aviation gravity vector downward continuation method based on a gradient method, which is characterized in that gradient values of three components of a gravity vector in a radial direction are calculated by utilizing a global high-precision ultra-high-order earth gravity field model, a correction value of the three components of the gravity vector in the radial direction is obtained by considering the continuation height, the correction value of the three components of the gravity vector in the radial direction is deducted from aviation gravity vector measurement data, gravity vector three-component data on a continuation surface can be obtained, and downward continuation of the aviation gravity vector measurement data can be realized. The method of the invention extends the aerial gravity vector measurement data to the ground by utilizing the gradient method, can obtain the gravity vector extension result on the earth surface or the ground level, has higher precision, and thus provides reliable basic data support for the fusion of different types of gravity measurement data, the construction of global or regional earth gravity field models, the refinement of global or regional (similar) ground level, the generation of gravity reference diagrams in underwater gravity matching assisted navigation and other applications.
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings needed to be used in the embodiments will be briefly described below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and it is obvious for those skilled in the art to obtain other drawings without inventive exercise.
FIG. 1 is a flow chart of the method for continuation of an aviation gravity vector downward based on a gradient method;
FIG. 2 is a diagram of the structure of the airborne gravity vector downward continuation system based on the gradient method.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
The invention aims to provide a method for continuation of an aerial gravity vector downwards based on a gradient method, which can realize effective continuation of three-component measurement data of the aerial gravity vector at any point in the air and has higher continuation result precision.
In order to make the aforementioned objects, features and advantages of the present invention comprehensible, embodiments accompanied with figures are described in further detail below.
The gradient method for extending the aerial gravity vector measurement data downwards is characterized in that an extension surface is used as a boundary surface S, the aerial gravity vector measurement data at an aerial point is projected onto the boundary surface S along a radial direction r, and then the gravity vector data on the extension surface can be obtained, wherein the gravity vector data on the extension surface refers to an east component, a north component and a vertical component of aerial disturbance gravity measured by a gravity vector instrument. Assuming that atmospheric density variations within the continuation altitude have negligible effect on the airborne gravity vector measurement data and that the airborne gravity vector measurement function is sufficiently smooth, downward continuation only needs to take account of its radial correction.
FIG. 1 is a flow chart of the aviation gravity vector downward continuation method based on the gradient method. As shown in fig. 1, a method for continuation of an aviation gravity vector downward based on a gradient method includes:
step 101: calculating the correction number of three components of the gravity vector in the radial direction by using a high-precision ultra-high-order earth gravity field model;
the method specifically comprises the following steps:
utilizing high-precision ultra-high-order earth gravity field model and adopting formula
Calculating three components of the gravity vector in the radial direction; the three components include an east component, a north component, and a vertical component;
wherein the content of the first and second substances,rrepresenting the radial disturbance gravity vector and,
representing a latitudinal direction disturbance gravity vector,λrepresenting a longitude disturbance gravity vector, and fM represents the product of a universal gravity constant f and the total mass M of the earth; r is the mean radius of the earth; r is R + h, R represents the earth center radial of any point on the disturbance gravity vector measurement plane, and h represents the flying height; theta and lambda respectively represent the residual latitude and longitude of the geocentric;
representing the complete normalization of the earth disturbance gravitational potential coefficient; n and m respectively represent the order and the order of the spherical harmonic coefficient;
indicating a complete normalization of the associated legendre function,
representing the first derivative of the Legendre function;
using a formula
Respectively calculating a first derivative and a second derivative of the three components in the radial direction to obtain a correction number of the three components of the gravity vector in the radial direction;
wherein the content of the first and second substances,
respectively representing a gradient value of three components of the air disturbance gravity vector in the radial direction;
respectively represents the second-order gradient value of three components of the air disturbance gravity vector in the radial direction.
Step 102: obtaining continuation height;
step 103: calculating the correction value of the three components of the gravity vector in the radial direction according to the continuation height to obtain the correction value of the three components of the gravity vector in the radial direction;
the method specifically comprises the following steps:
using a formula according to said continuation height
Calculating the correction values of the three components of the gravity vector in the radial direction to obtain the correction values of the three components of the gravity vector in the radial direction;
wherein, Deltar(r, theta, lambda) represents radial disturbance gravity vector correction data,
representing the amount of modification, Δ, of the gravity vector for the latitudinal disturbanceλ(R, θ, λ) represents a longitudinal disturbance gravity vector correction amount, Δ R ═ R '-R, Δ R represents the extension height, and R' represents the earth-center-diameter of the corresponding point on the extension plane.
Step 104: acquiring aviation gravity vector measurement data;
step 105: correcting the aviation gravity vector measurement data according to the correction value of the gravity vector in the radial direction to obtain gravity vector three-component data on an extension surface;
the method specifically comprises the following steps:
and according to a gradient method for downward continuation of the aerial gravity vector measurement data, correcting the aerial gravity vector measurement data by adopting a correction value in the radial direction of the gravity vector to obtain gravity vector three-component data on a continuation surface.
According to the gradient method of downward continuation of aviation gravity vector measurement data, the correction value of the radial direction of the gravity vector is adopted according to a formula
Correcting the aerial gravity vector measurement data to obtain gravity vector three-component data on an extension surface;
wherein the content of the first and second substances,
respectively representing three components of the ground disturbance gravity;
respectively, representing airborne gravity vector measurement data.
Step 106: and carrying out precision evaluation on the gravity vector three-component data on the extension surface to obtain a precision evaluation result.
Compared with the prior art, the invention has the following advantages:
1) the aviation gravity vector downward continuation method based on the gradient method provided by the invention utilizes the gradient method, and provides an effective way for downward continuation of aviation gravity vector measurement data;
2) the method has simple principle and convenient use, does not need to carry out grid processing on the aviation gravity vector measurement data, and has lower performance requirement on a computer;
3) the method has high continuation result precision and can not introduce system errors.
FIG. 2 is a diagram of the structure of the airborne gravity vector downward continuation system based on the gradient method. As shown in fig. 2, an aviation gravity vector downward continuation system based on a gradient method includes:
the correction number calculation module 201 is configured to calculate a correction number of three components of a gravity vector in a radial direction by using a high-precision ultra-high-order earth gravity field model;
a first obtaining module 202, configured to obtain an extension height;
the correction value calculation module 203 is configured to calculate a correction value of the three components of the gravity vector in the radial direction according to the extended height, so as to obtain a correction value of the three components of the gravity vector in the radial direction;
a second obtaining module 204, configured to obtain aviation gravity vector measurement data;
a correction module 205, configured to correct the aerial gravity vector measurement data according to a correction value in the radial direction of the gravity vector, so as to obtain gravity vector three-component data on an extension plane;
and the evaluation module 206 is configured to perform precision evaluation on the gravity vector three-component data on the extension plane to obtain a precision evaluation result.
The correction number calculating module 201 specifically includes:
a three-component calculation unit for using the high-precision ultra-high-order earth gravity field model and adopting the formula
Calculating three components of the gravity vector in the radial direction; the three components include an east component, a north component, and a vertical component;
wherein the content of the first and second substances,rrepresenting the radial disturbance gravity vector and,
representing a latitudinal direction disturbance gravity vector,λrepresenting a longitude disturbance gravity vector, and fM represents the product of a universal gravity constant f and the total mass M of the earth; r is the mean radius of the earth; r is R + h, R represents the earth center radial of any point on the disturbance gravity vector measurement plane, and h represents the flying height; theta and lambda are respectivelyRepresenting the geocentric latitude and geocentric longitude;
representing the complete normalization of the earth disturbance gravitational potential coefficient; n and m respectively represent the order and the order of the spherical harmonic coefficient;
indicating a complete normalization of the associated legendre function,
representing the first derivative of the Legendre function;
a three-component derivative calculation unit for employing the formula
Respectively calculating a first derivative and a second derivative of the three components in the radial direction to obtain a correction number of the three components of the gravity vector in the radial direction;
wherein the content of the first and second substances,
individual watchShowing a gradient value of three components of the air disturbance gravity vector in the radial direction;
respectively represents the second-order gradient value of three components of the air disturbance gravity vector in the radial direction.
The correction value calculating module 203 specifically includes:
a correction value calculating unit for adopting a formula according to the continuation height
Calculating the correction values of the three components of the gravity vector in the radial direction to obtain the correction values of the three components of the gravity vector in the radial direction;
wherein, Deltar(r, theta, lambda) represents radial disturbance gravity vector correction data,
representing the amount of modification, Δ, of the gravity vector for the latitudinal disturbanceλ(R, θ, λ) represents a longitudinal disturbance gravity vector correction amount, Δ R ═ R '-R, Δ R represents the extension height, and R' represents the earth-center-diameter of the corresponding point on the extension plane.
The correction module 205 specifically includes:
and the correction unit is used for correcting the aerial gravity vector measurement data by adopting the correction value in the radial direction of the gravity vector according to the downward continuation gradient method of the aerial gravity vector measurement data to obtain gravity vector three-component data on a continuation surface.
The correction unit specifically comprises:
a correction subunit, for adopting the correction value of the radial direction of the gravity vector according to a formula by a gradient method of downward continuation according to the aviation gravity vector measurement data
Correcting the aerial gravity vector measurement data to obtain gravity vector three-component data on an extension surface;
wherein the content of the first and second substances,
respectively representing three components of the ground disturbance gravity;
respectively, representing airborne gravity vector measurement data.
The embodiments in the present description are described in a progressive manner, each embodiment focuses on differences from other embodiments, and the same and similar parts among the embodiments are referred to each other. For the system disclosed by the embodiment, the description is relatively simple because the system corresponds to the method disclosed by the embodiment, and the relevant points can be referred to the method part for description.
The principles and embodiments of the present invention have been described herein using specific examples, which are provided only to help understand the method and the core concept of the present invention; meanwhile, for a person skilled in the art, according to the idea of the present invention, the specific embodiments and the application range may be changed. In view of the above, the present disclosure should not be construed as limiting the invention.
Claims (10)
1. An aviation gravity vector downward continuation method based on a gradient method is characterized by comprising the following steps:
calculating the correction number of three components of the gravity vector in the radial direction by using a high-precision ultra-high-order earth gravity field model;
obtaining continuation height;
calculating the correction value of the three components of the gravity vector in the radial direction according to the continuation height to obtain the correction value of the three components of the gravity vector in the radial direction;
acquiring aviation gravity vector measurement data;
correcting the aviation gravity vector measurement data according to the correction value of the gravity vector in the radial direction to obtain gravity vector three-component data on an extension surface;
and carrying out precision evaluation on the gravity vector three-component data on the extension surface to obtain a precision evaluation result.
2. The method for continuation of an aviation gravity vector downward based on a gradient method according to claim 1, wherein the calculation of the correction number of the three components of the gravity vector in the radial direction by using the high-precision ultra-high-order earth gravity field model specifically comprises:
utilizing high-precision ultra-high-order earth gravity field model and adopting formula
Calculating three components of the gravity vector in the radial direction; the three components include an east component, a north component, and a vertical component;
wherein the content of the first and second substances,rrepresenting the radial disturbance gravity vector and,
representing a latitudinal direction disturbance gravity vector,λrepresenting a longitude disturbance gravity vector, and fM represents the product of a universal gravity constant f and the total mass M of the earth; r is the mean radius of the earth; r is R + h, R represents the earth center radial of any point on the disturbance gravity vector measurement plane, and h represents the flying height; theta and lambda respectively represent the residual latitude and longitude of the geocentric;
representing the complete normalization of the earth disturbance gravitational potential coefficient; n and m respectively represent the order and the order of the spherical harmonic coefficient;
indicating a complete normalization of the associated legendre function,
representing the first derivative of the Legendre function;
using a formula
Respectively calculating a first derivative and a second derivative of the three components in the radial direction to obtain a correction number of the three components of the gravity vector in the radial direction;
wherein the content of the first and second substances,
respectively representing a gradient value of three components of the air disturbance gravity vector in the radial direction;
respectively represents the second-order gradient value of three components of the air disturbance gravity vector in the radial direction.
3. The method for continuation of an aviation gravity vector downward based on a gradient method according to claim 2, wherein the step of calculating the correction value of the three components of the gravity vector in the radial direction according to the continuation height to obtain the correction value of the three components of the gravity vector in the radial direction specifically comprises the steps of:
using a formula according to said continuation height
Calculating the correction values of the three components of the gravity vector in the radial direction to obtain the correction values of the three components of the gravity vector in the radial direction;
wherein, Deltar(r, theta, lambda) represents radial disturbance gravity vector correction data,
representing the amount of modification, Δ, of the gravity vector for the latitudinal disturbanceλ(R, θ, λ) represents a longitudinal disturbance gravity vector correction amount, Δ R ═ R '-R, Δ R represents the extension height, and R' represents the earth-center-diameter of the corresponding point on the extension plane.
4. The gradient-method-based aviation gravity vector downward continuation method according to claim 3, wherein the aviation gravity vector measurement data is corrected according to the correction value of the gravity vector in the radial direction to obtain gravity vector three-component data on a continuation plane, and the method specifically comprises the following steps:
and according to a gradient method for downward continuation of the aerial gravity vector measurement data, correcting the aerial gravity vector measurement data by adopting a correction value in the radial direction of the gravity vector to obtain gravity vector three-component data on a continuation surface.
5. The gradient method based on downward continuation of aviation gravity vector of claim 4, wherein the step of correcting the aviation gravity vector measurement data by using the correction value in the radial direction of the gravity vector according to the downward continuation gradient method of aviation gravity vector measurement data to obtain the gravity vector three-component data on the continuation surface specifically comprises the following steps:
according to the gradient method of downward continuation of aviation gravity vector measurement data, the correction value of the radial direction of the gravity vector is adopted according to a formula
Correcting the aerial gravity vector measurement data to obtain gravity vector three-component data on an extension surface;
wherein the content of the first and second substances,
respectively representing three components of the ground disturbance gravity;
respectively, representing airborne gravity vector measurement data.
6. An aviation gravity vector downward continuation system based on a gradient method is characterized by comprising the following steps:
the correction number calculation module is used for calculating the correction number of the three components of the gravity vector in the radial direction by utilizing a high-precision ultra-high-order earth gravity field model;
the first obtaining module is used for obtaining the continuation height;
the correction value calculation module is used for calculating the correction value of the three components of the gravity vector in the radial direction according to the extension height to obtain the correction value of the three components of the gravity vector in the radial direction;
the second acquisition module is used for acquiring aviation gravity vector measurement data;
the correction module is used for correcting the aviation gravity vector measurement data according to the correction value of the gravity vector in the radial direction to obtain gravity vector three-component data on an extension surface;
and the evaluation module is used for carrying out precision evaluation on the gravity vector three-component data on the extension surface to obtain a precision evaluation result.
7. The gradient method-based aviation gravity vector downward continuation system as claimed in claim 6, wherein the correction number calculation module specifically comprises:
a three-component calculation unit for using the high-precision ultra-high-order earth gravity field model and adopting the formula
Calculating three components of the gravity vector in the radial direction; the three components include an east component, a north component, and a vertical component;
wherein the content of the first and second substances,rrepresenting the radial disturbance gravity vector and,
representing a latitudinal direction disturbance gravity vector,λrepresenting a longitude disturbance gravity vector, and fM represents the product of a universal gravity constant f and the total mass M of the earth; r is the mean radius of the earth; r is R + h, R represents the earth center radial of any point on the disturbance gravity vector measurement plane, and h represents the flying height; theta and lambda respectively represent the residual latitude and longitude of the geocentric;
representing the complete normalization of the earth disturbance gravitational potential coefficient; n and m respectively represent the order and the order of the spherical harmonic coefficient;
indicating a complete normalization of the associated legendre function,
representing the first derivative of the Legendre function;
a three-component derivative calculation unit for employing the formula
Respectively calculating a first derivative and a second derivative of the three components in the radial direction to obtain a correction number of the three components of the gravity vector in the radial direction;
wherein the content of the first and second substances,
respectively representing a gradient value of three components of the air disturbance gravity vector in the radial direction;
respectively represents the second-order gradient value of three components of the air disturbance gravity vector in the radial direction.
8. The gradient-method-based aviation gravity vector downward continuation system as claimed in claim 7, wherein the correction value calculation module specifically comprises:
a correction value calculating unit for adopting a formula according to the continuation height
Calculating the correction values of the three components of the gravity vector in the radial direction to obtain the correction values of the three components of the gravity vector in the radial direction;
wherein, Deltar(r, theta, lambda) represents radial disturbance gravity vector correction data,
representing the amount of modification, Δ, of the gravity vector for the latitudinal disturbanceλ(R, θ, λ) represents a longitudinal disturbance gravity vector correction amount, Δ R ═ R '-R, Δ R represents the extension height, and R' represents the earth-center-diameter of the corresponding point on the extension plane.
9. The gradient-method-based airborne gravity vector downward continuation system according to claim 8, wherein the correction module specifically comprises:
and the correction unit is used for correcting the aerial gravity vector measurement data by adopting the correction value in the radial direction of the gravity vector according to the downward continuation gradient method of the aerial gravity vector measurement data to obtain gravity vector three-component data on a continuation surface.
10. The gradient-method-based airborne gravity vector downward continuation system according to claim 9, wherein the correction unit specifically comprises:
a correction subunit, for adopting the correction value of the radial direction of the gravity vector according to a formula by a gradient method of downward continuation according to the aviation gravity vector measurement data
Correcting the aerial gravity vector measurement data to obtain gravity vector three-component data on an extension surface;
wherein the content of the first and second substances,
respectively representing three components of the ground disturbance gravity;
respectively, representing airborne gravity vector measurement data.
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| CN111650659A (en) * | 2020-06-17 | 2020-09-11 | 宁夏大学 | Vertical line deviation estimation method and system based on aerial gravity anomaly |
| CN112965127B (en) * | 2021-02-08 | 2022-05-31 | 中国人民解放军92859部队 | Method for calculating external disturbance gravity radial component based on gravity anomaly |
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