CN110440753A - Consider the high accuracy DEM airborne gravity far field topographic correction method of earth curvature - Google Patents

Consider the high accuracy DEM airborne gravity far field topographic correction method of earth curvature Download PDF

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CN110440753A
CN110440753A CN201910746283.7A CN201910746283A CN110440753A CN 110440753 A CN110440753 A CN 110440753A CN 201910746283 A CN201910746283 A CN 201910746283A CN 110440753 A CN110440753 A CN 110440753A
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measuring point
dem
space
elevation
coordinate
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CN110440753B (en
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冯治汉
郭培虹
熊盛青
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XI'AN CENTER OF GEOLOGICAL SURVEY CGS
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01C—MEASURING DISTANCES, LEVELS OR BEARINGS; SURVEYING; NAVIGATION; GYROSCOPIC INSTRUMENTS; PHOTOGRAMMETRY OR VIDEOGRAMMETRY
    • G01C5/00—Measuring height; Measuring distances transverse to line of sight; Levelling between separated points; Surveyors' levels
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01V—GEOPHYSICS; GRAVITATIONAL MEASUREMENTS; DETECTING MASSES OR OBJECTS; TAGS
    • G01V9/00—Prospecting or detecting by methods not provided for in groups G01V1/00 - G01V8/00
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F16/00—Information retrieval; Database structures therefor; File system structures therefor
    • G06F16/20—Information retrieval; Database structures therefor; File system structures therefor of structured data, e.g. relational data
    • G06F16/29—Geographical information databases

Abstract

A kind of high accuracy DEM airborne gravity far field topographic correction method considering earth curvature, comprising: S1, the location information for obtaining measuring point Q.S2, according to measuring point Q location information, from the ground constructed in advance change in elevation database extract through coordinate conversion, rotation be located at the earth arctic to measuring point Q when, change to measuring point Q the elevation average value of all DEM units in rangeS3, the elevation average value for changing all DEM units in range according to measuring point QIn conjunction with preset measuring point Q topographic correction value calculation formula, the topographic correction value of measuring point Q is obtained.S4, the topographic correction value according to measuring point Q, accurately correct the gravity measurement of measuring point Q.Gravity far field topographic correction precision is greatly improved, while calculation amount is small, calculating speed is fast；The ground that the sliceable different times of long-term work are completed changes elevation database, to update and safeguard the elevation database.

Description

Consider the high accuracy DEM airborne gravity far field topographic correction method of earth curvature
Technical field
The present invention relates to technical field of geophysical exploration more particularly to a kind of high accuracy DEM boats for considering earth curvature Bare weight power far field topographic correction method.
Background technique
Topographic correction in gravity survey refers to and corrects geoid to the quality physical relief, divides close Middle area and far field carry out respectively.It (within radius 2km) by the earth is approximately unlimited flat that landform improvement in the area Jin Zhong, which is near measuring point, Plate eliminates the influence for being higher or lower than substance surplus or the loss of measuring point plane, is calculated with the upright square body formula of plane；Far field Landform improvement is to be carried out apart from the measuring point region (other than radius 2km within 166.7km) farther out by regional gravity database, Before gravimetric database is built up, constituent parts can be corrected voluntarily.
China's high mountain blazons, is rich in minerals, needs largely to carry out fast and efficiently airborne gravity measurement, but topography variation Influence to gravity value is very big, needs the method for high-precision airborne gravity far field topographic correction.And China's " regional gravity tune Look into specification " unification of (DZ/T0082-2006) regulation topographic correction range is to 166.7km, in order to compare and combine with ground gravity It explains, the topographic correction range of airborne gravity should also be unified for 166.7km.This computer capacity is not considering earth curvature influence When the gravity anomaly precision that calculates be unable to satisfy gravity interpretation requirement and ground observation gravity value difference it is larger.Therefore it needs A kind of high accuracy DEM airborne gravity far field topographic correction method considering earth curvature.
Topographic correction value in far field is calculated using RGIS in country's gravity measurement at present, uses the node elevation meter of 1km × 1km Calculate 5 ' × 5 ' sectorial block dispersed elevations, topographic correction precision about ± 0.2 × 10-5m/s2.But there are two defects for RGIS software: First is that high accuracy DEM data cannot be used, it is difficult to meet the requirement of current High-Precision Gravimeter Survey；Second is that measuring point is required to be located at ground Face is unable to satisfy the requirement of airborne gravity measurement.Test and preliminary popularization stage are only existed in for domestic air mail gravity measurement.Mesh Preceding foreign countries' airborne gravity measurement is mainly implemented in region of no relief, although using high accuracy DEM data calculates revaluate for gravity, ground Shape corrects that range is little, and when calculating does not consider the influence of earth curvature yet.
And what it is due to airborne gravity measurement acquisition is mass data, and currently used calculation method calculating speed is slower, difficult Needs are produced to meet.Therefore, it needs a kind of based on high accuracy DEM data, the influence of consideration earth curvature, calculating rapidly and efficiently The method of airborne gravity far field topographic correction value.
Summary of the invention
(1) technical problems to be solved
In order to solve the above problem of the prior art, the present invention provides a kind of high accuracy DEM boats for considering earth curvature Bare weight power far field topographic correction method.Gravity far field topographic correction precision is greatly improved, while calculation amount is small, calculating speed is fast； The ground that the sliceable different times of long-term work are completed changes elevation database, to update and safeguard the elevation database.
(2) technical solution
In order to achieve the above object, the main technical schemes that the present invention uses include:
A kind of high accuracy DEM airborne gravity far field topographic correction method considering earth curvature, comprising the following steps:
Step S1, the location information of measuring point Q is obtained.
Step S2, according to the location information of measuring point Q, change in elevation database from the ground constructed in advance and extract through coordinate turn It changes, rotate when being located at the earth arctic to measuring point Q, change to measuring point Q the elevation average value of all DEM units in range
Step S3, change the elevation average value of all DEM units in range according to measuring point QIn conjunction with preset measuring point Q topographic correction value calculation formula obtains the topographic correction value of measuring point Q.
Step S4, according to the topographic correction value of measuring point Q, the gravity measurement of measuring point Q is accurately corrected.
As a kind of improvement of the method for the present invention, preset measuring point Q topographic correction value calculation formula, including
Wherein, σ is that ground changes density；Rq=R+Z, R are earth mean radius, and Z is the elevation of measuring point Q；E (θ, r)=(2-r2- r cosθ-3cos2θ)+3sin2θ cos θ ln (r-cos θ+l),R is the distance away from the earth's core, θ is latitude；θ1、θ2Change the latitude scope of range with representing measuring point Q.
As a kind of improvement of the method for the present invention, after step S1, before step S2, further includes:
S11, digital complex demodulation is obtained.
S12, coordinate conversion and coordinate rotation are carried out, measuring point Q is made to be located at the earth arctic, obtain DEM unit top surface midpoint P's New geodetic coordinates in space.
S13, according to the new geodetic coordinates in space of DEM unit top surface midpoint P, it is mono- to change all DEM in range with calculating measuring point Q The elevation average value of member
S14, measuring point Q location information and the elevation average value are establishedChange elevation database associatedly.
As a kind of improvement of the method for the present invention, step S12 includes:
S121, the measuring point Q and DEM unit top surface midpoint P that projected coordinate system describes is converted to geodetic coordinates in space system and retouched The coordinate stated.
S122, the measuring point Q and DEM unit top surface midpoint P that geodetic coordinates in space system describes is converted into rectangular space coordinate It is the coordinate of description.
S123, rectangular coordinate system in space is rotated to measuring point Q it is located at the earth arctic, obtains new rectangular coordinate system in space, and Calculate the rotation angle of rectangular coordinate system in space.
S124, the foundation rectangular space coordinate of DEM unit top surface midpoint P and the rotation angle of rectangular coordinate system in space, calculate The new rectangular space coordinate of DEM unit top surface midpoint P.
S125, the new rectangular space coordinate according to DEM unit top surface midpoint P, calculate the new sky of DEM unit top surface midpoint P Between geodetic coordinates.
As a kind of improvement of the method for the present invention, the coordinate origin of rectangular coordinate system in space is the earth's core, and Z axis crosses earth north Pole.
As a kind of improvement of the method for the present invention, in step S13, change the height of all DEM units in range with calculating measuring point Q Journey average valueIt include: that calculate measuring point Q longitude range be 0-2 π, latitude scope is model apart from arctic arc length 20-166.7km Enclose the elevation average value of interior all DEM units
(3) beneficial effect
The beneficial effects of the present invention are:
1, it is based on high accuracy DEM, while considering to consider influence of the earth curvature to calculated result, with making ground gravity far field Shape correction precision is greatly improved.
2, change altitude data and only correspond to measuring point coordinate, it is unrelated with measuring point elevation, it is suitble to measuring point to be located at the weight of different elevations Power measures work.
3, get around directly calculate huge amount of calculation caused by revaluate, using being initially formed or change range using ground Ground changes elevation database, by reading the dispersed elevation in the database, calculates gravity far field ground revaluate using spherical shell sectorial block, Achieve the purpose that quickly to calculate.
4, the ground that the sliceable different times of long-term work are completed changes elevation database, to update and safeguard the altitude data Library.
Detailed description of the invention
The present invention is described by means of the following drawings:
Fig. 1 is the schematic diagram that the earth is approximately sphere in the specific embodiment of the invention；
Fig. 2 is that ellipsoid integrates schematic diagram after spheroidal coordinate conversion in the specific embodiment of the invention；
Fig. 3 is the high accuracy DEM airborne gravity far field topographic correction that earth curvature is considered in the specific embodiment of the invention The flow chart of method.
Specific embodiment
In order to preferably explain the present invention, in order to understand, with reference to the accompanying drawing, by specific embodiment, to this hair It is bright to be described in detail.
As shown in Figure 1, being approximately sphere by the earth, the earth's core is the centre of sphere.As shown in Fig. 2, to consider earth curvature and being based on High accuracy DEM data, calculate airborne gravity far field topographic correction value, and applicant passes through coordinate conversion and ellipsoid integral calculationPoint fan-shaped cylinder is to airborne gravity measuring pointGravity influence value.
Enabling the centre of sphere is coordinate origin, and Z axis is crossed sphere top (arctic), and airborne gravity measuring point Q is on Z axis.From the earth water The region of 20~166.7km around quasi- face to earth Free Surface, airborne gravity measuring point, along meridian direction with θ=θ0,θ1, θ2,…,θn, weft circle withIt is divided into m × n earth's crust sectorial block.Top surface midpoint is the fan of P Latitude, longitude and the elevation range of shape block (i, j) beAirborne gravity The influence of topography value of measuring point Q are as follows:
Wherein, R is earth mean radius, takes 6371.025km；Z is the elevation of airborne gravity measuring point Q；h1And h2Respectively The bottom surface elevation and elevation of top surface of sectorial block (i, j)；G is gravitational constant 6.67 × 10-8cm3/(g·s2)；σijFor sectorial block (i, J) averag density, generally takes 2.67g/cm3；R is the distance away from the earth's core.
The integral result of formula (1) are as follows:
Wherein, E (θ, r)=(2-r2-r cosθ-3cos2θ)+3sin2θ cos θ ln (r-cos θ+l),
From formula (2) if in as can be seen that airborne gravity measuring pointPositioned at the earth arctic, as long as finding out each Longitude and latitude and elevation of the DEM in new coordinate system can calculate it to the gravity influence value at measuring point.
The direct calculation method of high accuracy DEM airborne gravity far field topographic correction value based on above-mentioned consideration earth curvature, The gravity influence value of airborne gravity measuring point Q in real work is calculated.Specifically includes the following steps:
Step S1, the location information and digital complex demodulation of measuring point Q are obtained, coordinate conversion and coordinate rotation is carried out, makes Measuring point Q is located at the earth arctic, obtains the new geodetic coordinates in space of DEM unit top surface midpoint P.
Above-mentioned steps S1 includes:
Step S11, plane projection coordinate system is converted to geodetic coordinates in space system: by projected coordinate system description measuring point Q and DEM unit top surface midpoint P is converted to geodetic coordinates in space systemThe coordinate of description.So that the coordinate of Q and P all uses longitudeLatitude θ and absolute elevation h is indicated.
This is because in actual operation, measuring point Q coordinate generally uses plane projection coordinate, such as 6 ° of band projection coordinates of Gauss Coordinate data some Deng, high accuracy DEM unit is described using plane projection coordinate system, and some use space earth coordinates are retouched It states.When carrying out gravity far field topographic correction value and calculating, first have to carry out coordinate conversion, coordinate system is unified, it then could be into Row gravity terrain Correction calculates.6 ° of band projection coordinates of Gauss are uniformly converted to geodetic coordinates in space system by the present invention.Gauss projection Inversion formula are as follows:
Wherein, L0For central meridian longitude；Mf=a (1-e2)(1-e2sin2Bf)-3/2； tf=tanBf；BfLatitude corresponding to Meridian arc length for latitude of pedal, that is, as x=X Degree is iterated to calculate by Meridian arc length formula:
Step S12, geodetic coordinates in space system is converted to rectangular coordinate system in space: will be with longitudeLatitude θ, absolute elevation h The top surface the measuring point Q and DEM midpoint P of expression is converted to rectangular coordinate system in space coordinate (x, y, z).So that the coordinate of Q and P all use x, Y and z is indicated.Preferably, the coordinate origin of the rectangular coordinate system in space is the earth's core, and Z axis crosses the earth arctic.
Due to earth coordinates carry out three-dimensional coordinate rotation difficulty it is larger, it is straight that geodetic coordinates in space system is converted into space Angular coordinate system prepares for coordinate rotation.
Step S13, rectangular coordinate system in space is rotated to measuring point Q and is located at the earth arctic, obtain new rectangular coordinate system in space, And calculate the rotation angle of rectangular coordinate system in space.Simplify Gravity calculation.Include:
By rectangular coordinate system in space X, Y, Z axis distinguishes rotation alpha, obtains new rectangular coordinate system in space X ', Y ' after β, γ, Z ', coordinate of the former measuring point Q (x, y, z) in new coordinate system become Q (x ', y ', z ').When carrying out coordinate system rotation, first around z After axis rotates γ, the coordinate of Q (x, y, z) is (x1,y1, z):
Then after coordinate system rotates around x axis α, the coordinate of Q point is (x1,y′,z2):
For last coordinate system after y-axis rotation β, the coordinate of Q point is (x ', y ', z '):
X '=y '=0 is enabled,Above-mentioned equation group (7), (8), (9) are solved, rotation angle α is obtained, β, γ are respectively as follows:
S14, the foundation rectangular space coordinate of DEM unit top surface midpoint P and the rotation angle of rectangular coordinate system in space, calculate The new rectangular space coordinate of DEM unit top surface midpoint P.
The rectangular space coordinate P (x, y, z) at the top surface DEM midpoint new rectangular coordinate system in space coordinate be P (x ', y ', Z '):
S15, the new rectangular space coordinate according to DEM unit top surface midpoint P, calculate the new space of DEM unit top surface midpoint P Geodetic coordinates.
Wherein,For longitude of the DEM unit top surface midpoint P in new geodetic coordinates in space system, θ ' is latitude, and r ' is away from ground The distance of the heart.
Step S2, the new geodetic coordinates in space for changing all DEM units top surface midpoint P in range according to measuring point Q, in conjunction with public affairs Formula (2) calculates the gravity influence value of measuring point Q.
The above-mentioned calculating for gravity influence value at measuring point although being based on high accuracy DEM data, and considers earth song The influence of rate, but the ground revaluate of measuring point is directly calculated, cause huge amount of calculation, calculating speed is slow, it is difficult to meet Production requirement.
For this purpose, applicant is to the direct of the high accuracy DEM airborne gravity far field topographic correction value of above-mentioned consideration earth curvature Step S2 in calculation method is optimized, and the step S2 after optimization includes:
Step S21, according to the new geodetic coordinates in space of DEM unit top surface midpoint P, change in range with calculating measuring point Q and own The elevation average value of DEM unit
Elevation average valueIt is that the gravity value calculated by each sectorial block adds up, obtains the far field topographic correction value of measuring point ∑Δgi,j.Then change inverse ground revaluate ∑ Δ g in range on ground with formula (1)i,jCorresponding elevation h2(generally take h1=0). Here h2Be exactly measuring point change dispersed elevation in range.Due to elevation average valueIt is not the altimeter for directly using sectorial block Calculate, but the ground revaluate solution nonlinear equation by calculating obtains, error be mainly derived from coordinate convert, integral calculation and Nonlinear equation is solved, calculating speed is fast, and error is controllable, and precision is high.
Step S22, change the elevation average value of all DEM units top surface midpoint P in range according to measuring point QConvolution (2) deformation type (13) calculates the gravity influence value of measuring point Q.
Wherein, σ is that ground changes density, generally takes 2.67g/cm3；Rq=R+Z；θ1、θ2Change the latitude of range with representing measuring point Q Range.
It is above-mentioned according to elevation average valueThe gravity influence value of measuring point Q is calculated, amount of calculation is relatively small, calculates speed Degree is very fast.
Applicant to the method for the high accuracy DEM airborne gravity far field topographic correction value of above-mentioned consideration earth curvature carry out into One-step optimization, the airborne gravity far field topographic correction method of proposition, as shown in Figure 3, comprising:
Step S1, building ground changes elevation database.The following steps are included:
Step S11, the location information and digital complex demodulation of measuring point Q are obtained, coordinate conversion and coordinate rotation are carried out, So that measuring point Q is located at the earth arctic, obtains the new geodetic coordinates in space of DEM unit top surface midpoint P.
Step S12, according to the new geodetic coordinates in space of DEM unit top surface midpoint P, change in range with calculating measuring point Q and own The elevation average value of DEM unit
Step S13, measuring point Q location information and elevation average value are establishedChange elevation database associatedly.
Step S2, according to the location information of measuring point Q, change from the ground of building and extracted in elevation database through coordinate conversion, rotation When going to measuring point Q and being located at the earth arctic, change to measuring point Q the elevation average value of all DEM units in range
Step S3, change the elevation average value of all DEM units in range according to measuring point QConvolution (13) is calculated and is surveyed The gravity influence value of point Q.
Step S4, according to the gravity influence value of measuring point Q, the gravity measurement of measuring point Q is accurately corrected.
Preferably, change while measuring point Q is calculated in step S12 the elevation average value of all DEM units in rangeIncluding calculating Measuring point Q longitude range is 0-2 π, latitude scope is the elevation of all DEM units in the range of the arc length 20-166.7km of the arctic Average value
Method after above-mentioned optimization is based on high accuracy DEM, while considering influence of the earth curvature to calculated result；Ground changes Altitude data only corresponds to measuring point coordinate, unrelated with measuring point elevation, and measuring point is suitble to be located at the gravity measurement work of different elevations；It gets around Huge amount of calculation caused by ground revaluate is directly calculated, using being initially formed or change altitude data using the ground that ground changes range Library, by reading the dispersed elevation in the database, using spherical shell sectorial block calculating gravity far field revaluate, reaches quick calculating Purpose；The ground that the sliceable different times of long-term work are completed changes elevation database, to update and safeguard the elevation database.
To sum up, method provided by the invention has filled up the blank for considering the airborne gravity far field topographic correction of earth curvature； The drawbacks of RGIS cannot use high accuracy DEM is improved, ground gravity far field topographic correction precision is made to be greatly improved；Pass through Change database with precalculating, the speed of topographic correction calculating is greatly improved under the premise of guaranteeing computational accuracy.
The application above method is realized by computer program, and operation main body is substantially a controlling terminal.
It is to be appreciated that describing the skill simply to illustrate that of the invention to what specific embodiments of the present invention carried out above Art route and feature, its object is to allow those skilled in the art to can understand the content of the present invention and implement it accordingly, but The present invention is not limited to above-mentioned particular implementations.All various changes made within the scope of the claims are repaired Decorations, should be covered by the scope of protection of the present invention.

Claims (6)

1. a kind of high accuracy DEM airborne gravity far field topographic correction method for considering earth curvature, which is characterized in that including following Step:
Step S1, the location information of measuring point Q is obtained；
Step S2, according to the location information of measuring point Q, change from the ground constructed in advance and extracted in elevation database through coordinate conversion, rotation When going to measuring point Q and being located at the earth arctic, change to measuring point Q the elevation average value of all DEM units in range
Step S3, change the elevation average value of all DEM units in range according to the measuring point QIn conjunction with preset measuring point Q topographic correction value calculation formula obtains the topographic correction value of measuring point Q；
Step S4, according to the topographic correction value of measuring point Q, the gravity measurement of measuring point Q is accurately corrected.
2. the method according to claim 1, wherein the preset measuring point Q topographic correction value calculates public affairs Formula, comprising:
Wherein, σ is that ground changes density；Rq=R+Z, R are earth mean radius, and Z is the elevation of measuring point Q；E (θ, r)=(2-r2-rcos θ-3cos2θ)+3sin2θ cos θ ln (r-cos θ+l),R is the distance away from the earth's core, and θ is latitude Degree；θ1、θ2Change the latitude scope of range with representing measuring point Q.
3. the method according to claim 1, wherein after step S1, before step S2, further includes:
S11, digital complex demodulation is obtained；
S12, coordinate conversion and coordinate rotation are carried out, measuring point Q is made to be located at the earth arctic, obtain the new sky of DEM unit top surface midpoint P Between geodetic coordinates；
S13, according to the new geodetic coordinates in space of DEM unit top surface midpoint P, change all DEM units in range with calculating measuring point Q Elevation average value
S14, measuring point Q location information and the elevation average value are establishedChange elevation database associatedly.
4. according to the method described in claim 3, it is characterized in that, the step S12 includes:
S121, the measuring point Q and DEM unit top surface midpoint P that projected coordinate system describes is converted to the description of geodetic coordinates in space system Coordinate；
S122, the measuring point Q and DEM unit top surface midpoint P that the geodetic coordinates in space system describes is converted into rectangular space coordinate It is the coordinate of description；
S123, the rectangular coordinate system in space is rotated to measuring point Q it is located at the earth arctic, obtains new rectangular coordinate system in space, and Calculate the rotation angle of rectangular coordinate system in space；
S124, the foundation rectangular space coordinate of DEM unit top surface midpoint P and the rotation angle of the rectangular coordinate system in space, calculate The new rectangular space coordinate of DEM unit top surface midpoint P；
S125, according to the new rectangular space coordinate of DEM unit top surface midpoint P, calculate the new sky of DEM unit top surface midpoint P Between geodetic coordinates.
5. according to the method described in claim 4, it is characterized in that, the coordinate origin of the rectangular coordinate system in space is the earth's core, Z Axis crosses the earth arctic.
6. according to the method described in claim 3, it is characterized in that, changing all DEM in range with calculating measuring point Q in step S13 The elevation average value of unitIncluding
Calculating measuring point Q longitude range is 0-2 π, latitude scope is that all DEM are mono- in the range of the arc length 20-166.7km of the arctic The elevation average value of member
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