CN101713649B - Disturbing gravity-based quasi-geoid land-sea seamless splicing method - Google Patents

Abstract

The invention discloses a geoid-like seamless splicing method of land and sea based on disturbed gravity. This method makes full use of the physical characteristics of disturbance gravity that is not limited by the local elevation datum, uses the unified earth reference ellipsoid as the coordinate reference frame, and uses the global navigation and positioning system (GNSS) with the unified land and sea datum and gravity data to calculate the unified disturbance of land and sea Gravity, which introduces the uniform disturbance gravity of land and sea into the more rigorous algorithm proposed by the present invention, so as to realize the seamless splicing of land and sea similar to the geoid. Different from the existing fitting algorithm that uses gravity anomaly and Stokes formula to calculate land-sea elevation anomaly, this method is rigorous in theory and can effectively eliminate the result error caused by the singularity of kernel function.

Description

A kind of quasi-geoid land-sea seamless splicing method based on disturbing gravity

Technical field

The present invention is a kind of quasi-geoid land-sea seamless splicing method based on disturbing gravity, belongs to " PHYSICAL GEODESY " technical field in " geodetic surveying and measurement engineering " subject.

Background technology

The quasigeoid splicing of land sea is focus and the difficult point in the present physical geodesy section field.The main method of sea, land quasigeoid splicing at present has least square Least Squares Spectral Combination, iteration FFT method, least squares collocation etc.Domesticly in recent years developed a kind of " development method ", its ultimate principle is to calculate near land, the shore line respectively and the quasigeoid of ocean by gravity anomaly, utilize near the quasigeoid inverse fitting parameter that overlaps with land the shore line then, utilize the fitting parameter of being asked to carry out the ocean quasigeoid at last and proofread and correct, thus the quasigeoid of formation land-sea seamless splicing.

In fact, sea, existing land quasigeoid seamless joint method all is based on " gravity anomaly " this physical quantity.The while gravity anomaly generally is based on local height datum to be determined, so just forms based on " gravity anomaly " under the multiple local height datum, and benchmark disunity problem will certainly appear in the extra large quasigeoid in the land that utilizes this " gravity anomaly " to calculate.Only utilize these disunity problems of mathematical match simple process obviously not have the physical theory support.This is not subjected to the physical quantity of local height datum restriction to realize that also nobody sets foot in quasi-geoid land-sea seamless splicing so far and directly utilize " disturbing gravity ".

Summary of the invention

At the problem in the technical background, the present invention proposes to utilize disturbing gravity to realize the land-sea seamless splicing method of quasigeoid, and has proposed to utilize disturbing gravity to calculate the singular point disposal route of quasigeoid.

Purpose of the present invention can be achieved through the following technical solutions: a kind of quasi-geoid land-sea seamless splicing method based on disturbing gravity is characterized in that this method may further comprise the steps:

(1) with the gravimetric data pre-service of sea, land is sea, land disturbing gravity data;

(2) the unified disturbing gravity data graticule mesh processing in sea, land;

(3) the unified gravity quasigeoid in sea, land calculates;

(4) utilize near the GPS level data extract land in land and shore line sea gravity quasigeoid system poor;

(5) carry out system difference match and correct, realize a kind of land-sea seamless splicing of the quasigeoid based on disturbing gravity.

In the described step (1), be primarily characterized in that, comprise following content:

A. the marine gravity field data is treated to the ocean disturbing gravity data consistent, utilizes boat measurement disturbing gravity data validation ocean disturbing gravity data whether to have system poor,, then carry out system's difference match and correct if having with the land benchmark;

B. based on existing high precision earth gravity field model to the land disturbing gravity with carry out system's difference analysis through the corrected ocean of a step disturbing gravity data, and land and ocean disturbing gravity are carried out system's difference correction;

C. coastal zone disturbing gravity data being corrected aftertreatment through same gravity field model system difference is and the consistent coastal zone disturbing gravity of land benchmark data.

In the described step (2), be primarily characterized in that, carry out the unified Bouguer disturbing gravity graticule mesh processing in sea, land, and judge whether graticule mesh Bouguer disturbing gravity data have the saltus step phenomenon at the edge fit place, if sea, land benchmark unanimity should not have the saltus step phenomenon through the unified disturbing gravity data in the sea, land of graticule mesh processing at the edge fit place so; If any the saltus step phenomenon, should be standard detection system difference size then, and carry out corresponding system difference and correct according to land disturbing gravity data.

In the described step (3), be primarily characterized in that, proposed a kind of disposal route of Hotine integration singular point, singular point is handled formula and is

$\mathrm{\δN}=\frac{R\·\stackrel{\‾}{\mathrm{\δg}}}{2\mathrm{\γ}}\left\{\begin{array}{c}\cos \left({\mathrm{\ψ}}_0\right)+\frac{3{\cos }^2\left({\mathrm{\ψ}}_0\right)}{4}+\cos \left({\mathrm{\ψ}}_0\right)\ln [1+\csc \left(\frac{{\mathrm{\ψ}}_0}{2}\right)]\\ +2\ln [\cos \left(\frac{{\mathrm{\ψ}}_0}{4}\right)+\sin \left(\frac{{\mathrm{\ψ}}_0}{4}\right)]+\ln \left[\sin \left(\frac{{\mathrm{\ψ}}_0}{2}\right)\right]+2\sin \left(\frac{{\mathrm{\ψ}}_0}{2}\right)-\frac{7}{4}\end{array}\right\}$

In the following formula, δ N is the height anomaly influence of singular regions, and R is an earth mean radius, Be the disturbing gravity mean value of singular regions, γ is a normal gravity, ψ ₀Be bead hat spherical angle distance.By little spherical crown with through meridional difference graticule mesh (Δ λ is the longitude mesh spacing,

Be latitude,

Be the latitude mesh spacing) homalographic relation

Can obtain ψ ₀Computing formula, promptly

Compare with existing method, the present invention is based on the disturbing gravity data and finish the land-sea seamless splicing of quasigeoid, do not have the existing skimble-scamble problem of height datum of utilizing the gravity anomaly data in theory, the singular point disposal route that the present invention simultaneously proposes has tighter result than original method.

Description of drawings

Fig. 1 is a kind of quasi-geoid land-sea seamless splicing embodiment flow process based on disturbing gravity.

Embodiment

One, sea, land gravimetric data pre-service

Sea, land as referred to herein gravimetric data mainly comprises land gravimetric data, shore line gravimetric data, marine gravity data.Theoretically, if these three kinds of data all are based on united frame (gravity datum framework, triaxial ellipsoid reference frame etc.), these three kinds of data do not exist system poor so, promptly can realize seamless spliced fully.In fact, because gravity datum deviation and the not equal multiple factor of reference ellipsoid can cause three kinds of different pieces of informations to exist splicing poor, even in a kind of categorical data, also there is system deviation, for example just there are the system deviation of up tens milligals in the early stage gravimetric data of China and China's 2000 gravity datums, in the gravimetric data of pelagic division since the different system deviations that caused in source also be very different.Therefore different gravimetric datas need be treated to unified benchmark.

At first need land gravimetric data, coastal zone gravimetric data, marine gravity The data disturbing gravity defined formula well known in the art are calculated as the disturbing gravity of benchmark unanimity in theory; Utilize boat measurement disturbing gravity point value data validation satellite to survey the precision of high disturbing gravity data (boat measurement disturbing gravity data precision is higher than satellite and surveys high disturbing gravity) then, carrying out system deviation extracts, promptly calculating boat measurement disturbing gravity and satellite, to survey the system of high disturbing gravity data poor, and satellite is surveyed high disturbing gravity data system difference correct (constant correction), make it not exist system poor with boat measurement disturbing gravity point Value Data; Land and coastal zone disturbing gravity point Value Data and ocean disturbing gravity data should be carried out system's difference analysis and correction respectively based on a certain high precision earth gravity field model (for example EGM2008), promptly adopt the disturbing gravity data of utilizing earth gravity field model to derive to compare with above three kinds of disturbing gravity data, then obtain the system deviation value on the statistical significance, and utilize this value to carry out system's difference and correct (constant correction); Then form land, coastal zone and ocean disturbing gravity data at last.

Two, the unified disturbing gravity data graticule mesh processing in sea, land

Land with first step processing, coastal zone and ocean disturbing gravity point Value Data (can regard ocean graticule mesh data as the point value data processing at this) obtain point value Bouguer disturbing gravity respectively after gravity reduction, it is carried out rough error surveys (can select several different methods for use) and selects suitable approximating method with the processing of point value Bouguer disturbing gravity graticule mesh, be treated to equidistant longitude and latitude graticule mesh numerical model, utilize drawing software drawing isoline figure then, analyze in edge fit zone, sea, land whether have saltus step phenomenon (saltus step of indication of the present invention is similar to the discontinuous phenomenon of toroidal function at a certain interface).If any, then utilize part land sea to overlap area data computing system poor (if do not overlap zone can suitably be extended to the ocean analytic system poor) and be that standard corrects marine gravity data (constant correction) with land Bouguer disturbing gravity data according to Bouguer disturbing gravity isogram tendency.Then form the consistent Bouguer disturbing gravity graticule mesh data in sea, land after finishing correction, thereby form the consistent disturbing gravity graticule mesh data in sea, needed land by recovering the graticule mesh Bouguer correction with topographic correction again.

Three, the unified gravity quasigeoid in sea, land calculates

We adopt the Hotine integral formula of taking the single order item into account well known in the art and remove-recovery technology in calculating, and the Hotine integral formula of taking the single order item into account is:

$\mathrm{\ζ}=\frac{R}{4\mathrm{\π\γ}}{\∫}_{\mathrm{\σ}}(\mathrm{\δg}+\mathrm{\δ}{g}_1)H\left(\mathrm{\ψ}\right)\mathrm{d\σ}$

Wherein ψ is the angular distance between calculation level and the pour point;

The Hotine nuclear that H (ψ) is;

R is an earth mean radius

σ is a unit sphere

γ is a normal gravity

And δ g ₁Expression formula be

$\mathrm{\δ}{g}_1=\frac{R^2}{2\mathrm{\π}}{\∫}_{\mathrm{\σ}}\frac{h-h_p}{l_0^3}[\mathrm{\δg}-\frac{1}{8\mathrm{\π}}{\∫}_{\mathrm{\σ}}\mathrm{\δgH}\left(\mathrm{\ψ}\right)\mathrm{d\σ}]\mathrm{d\σ}$

In the formula, h and h _PGeodetic height for pour point and calculation level.

But Treatment of Singular Integration method of the present invention is different.Existing Treatment of Singular Integration formula is

Different with it is, we have proposed tight singular integral formula at this, and its derivation is as follows:

We know that the tight integral formula of δ N is

$\mathrm{\δN}=\frac{R}{4\mathrm{\π\γ}}\underset{\mathrm{\α}=0}{\overset{2\mathrm{\π}}{\∫}}\underset{\mathrm{\ψ}=0}{\overset{{\mathrm{\ψ}}_0}{\∫}}\mathrm{\δgH}\left(\mathrm{\ψ}\right)\sin \left(\mathrm{\ψ}\right)\mathrm{d\ψd\α}---\left(2\right)$

In the formula, α represents the position angle, and ψ represents the spherical angle distance, and H (ψ) is the Hotine kernel function, and its expression formula can be found in many textbooks, is not providing here.When ψ → 0, the Hotine kernel function occurs unusual, denominator promptly occurs and be 0 phenomenon, can't directly obtain δ N.In theory, see that from formula disturbance δ g should continuous distribution, but in the actual measurement, we can only measure discrete gravity point value, can not make gravity point value continuous distribution, this just means that we can average disturbance gravity in bead hat zone

Replace answering in theory the point value of continuous distribution, promptly in little spherical crown, can think that disturbing gravity is a constant.Formula (2) just can be expressed as so

$\mathrm{\δN}=\frac{R\stackrel{\‾}{\mathrm{\δg}}}{4\mathrm{\π\γ}}\underset{\mathrm{\α}=0}{\overset{2\mathrm{\π}}{\∫}}\underset{\mathrm{\ψ}=0}{\overset{{\mathrm{\ψ}}_0}{\∫}}H\left(\mathrm{\ψ}\right)\sin \left(\mathrm{\ψ}\right)\mathrm{d\ψd\α}---\left(3\right)$

Derive through tight, can obtain

$\underset{\mathrm{\ψ}=0}{\overset{{\mathrm{\ψ}}_0}{\∫}}H\left(\mathrm{\ψ}\right)\sin \left(\mathrm{\ψ}\right)\mathrm{d\ψ}={\left|\begin{array}{c}\cos \left(\mathrm{\ψ}\right)+\frac{3{\cos }^2\left(\mathrm{\ψ}\right)}{4}+\cos \left(\mathrm{\ψ}\right)\ln [1+\csc \left(\frac{\mathrm{\ψ}}{2}\right)]\\ +2\ln [\cos \left(\frac{\mathrm{\ψ}}{4}\right)+\sin \left(\frac{\mathrm{\ψ}}{4}\right)]+\ln \left[\sin \left(\frac{\mathrm{\ψ}}{2}\right)\right]+2\sin \left(\frac{\mathrm{\ψ}}{2}\right)\end{array}\right|}_{\mathrm{\ψ}=0}^{\mathrm{\ψ}={\mathrm{\ψ}}_0}---\left(4\right)$

When ψ=0, following formula the right formula is unusual, but shows weak singularity characteristics, and its ultimate value is constant, promptly

$\underset{\mathrm{\ψ}\→0}{\mathrm{limit}}\left\{\begin{array}{c}\cos \left(\mathrm{\ψ}\right)+\frac{3{\cos }^2\left(\mathrm{\ψ}\right)}{4}+\cos \left(\mathrm{\ψ}\right)\ln [1+\csc \left(\frac{\mathrm{\ψ}}{2}\right)]\\ +2\ln [\cos \left(\frac{\mathrm{\ψ}}{4}\right)+\sin \left(\frac{\mathrm{\ψ}}{4}\right)]+\ln \left[\sin \left(\frac{\mathrm{\ψ}}{2}\right)\right]+2\sin \left(\frac{\mathrm{\ψ}}{2}\right)\end{array}\right\}=\frac{7}{4}---\left(5\right)$

With following formula substitution formula (3), then obtain

$\mathrm{\δN}=\frac{R\·\stackrel{\‾}{\mathrm{\δg}}}{2\mathrm{\γ}}\left\{\begin{array}{c}\cos \left({\mathrm{\ψ}}_0\right)+\frac{3{\cos }^2\left({\mathrm{\ψ}}_0\right)}{4}+\cos \left({\mathrm{\ψ}}_0\right)\ln [1+\csc \left(\frac{{\mathrm{\ψ}}_0}{2}\right)]\\ +2\ln [\cos \left(\frac{{\mathrm{\ψ}}_0}{4}\right)+\sin \left(\frac{{\mathrm{\ψ}}_0}{4}\right)]+\ln \left[\sin \left(\frac{{\mathrm{\ψ}}_0}{2}\right)\right]+2\sin \left(\frac{{\mathrm{\ψ}}_0}{2}\right)-\frac{7}{4}\end{array}\right\}---\left(6\right)$

By little spherical crown and through meridional difference graticule mesh (longitude mesh spacing Δ λ and latitude mesh spacing

) homalographic relation Can obtain ψ ₀Computing formula, promptly

(7)

Both differences are to compare in the past by our formula, and formula is tight in theory, but form shows complexity slightly.

Four, utilize near the GPS level data extract land in land and shore line sea gravity quasigeoid system poor

Utilize the height anomaly value on the gravity quasigeoid interpolation GPS leveling point, compare, can obtain statistical informations such as the standard deviation of height anomaly difference and mean value with the high precision height anomaly value of utilizing GPS level data computation.Whether criterion difference size satisfies the design accuracy requirement.

Five, carry out the system difference and correct, realize a kind of land-sea seamless splicing of the quasigeoid based on disturbing gravity

If utilize the standard deviation of GPS level data validation to satisfy the design accuracy requirement, then directly carry out the difference correction of constant system and get final product.As check standard deviation and do not satisfy accuracy requirement, then need analytic system difference cloth rule, select suitable approximating method to finish sea, land quasigeoid and correct, thereby realize the land-sea seamless splicing of quasigeoid.And approximating method can selectivity constant or the combination of multiple mathematical model such as linear fit, fitting of a polynomial, spherical function match, neural network match or several models.

Claims (3)

1. the quasi-geoid land-sea seamless splicing method based on disturbing gravity is characterized in that, utilizes the disturbing gravity data to carry out quasi-geoid land-sea seamless splicing, and this method may further comprise the steps:

(1) with the gravimetric data pre-service of sea, land is sea, land disturbing gravity data;

(2) the marine gravity field data is treated to the ocean disturbing gravity data consistent, utilizes boat measurement disturbing gravity data validation ocean disturbing gravity data whether to have system poor,, then carry out system's difference and correct if having with the land benchmark;

(3) based on existing high precision earth gravity field model land disturbing gravity and the corrected ocean of warp (2) step disturbing gravity data are carried out system's difference analysis, and system's difference correction is carried out on land and ocean disturbing gravity;

(4) be disturbing gravity data with the consistent coastal zone of land benchmark with coastal zone disturbing gravity data through the difference correction aftertreatment of same gravity field model system;

(5) the unified disturbing gravity data graticule mesh processing in sea, land;

(6) the unified gravity quasigeoid in sea, land calculates;

(7) utilize land and coastal zone GPS level data extract land sea gravity quasigeoid system poor;

(8) carry out the system difference and correct, realize a kind of land-sea seamless splicing of the quasigeoid based on disturbing gravity.

2. the quasi-geoid land-sea seamless splicing method based on disturbing gravity according to claim 1, it is characterized in that, in the described step (5), carry out the unified Bouguer disturbing gravity graticule mesh processing in sea, land, and judge whether graticule mesh Bouguer disturbing gravity data have the saltus step phenomenon at the edge fit place, if sea, land benchmark unanimity should not have the saltus step phenomenon through the unified disturbing gravity data in the sea, land of graticule mesh processing at the edge fit place so; If any the saltus step phenomenon, should be standard detection system difference size then, and carry out corresponding system difference and correct according to land disturbing gravity data.

3. the quasi-geoid land-sea seamless splicing method based on disturbing gravity according to claim 1 is characterized in that, in the described step (6), has adopted a kind of disposal route of tight Hotine integration singular point, and singular point is handled formula and is

$\mathrm{\δN}=\frac{R\·\stackrel{\‾}{\mathrm{\δg}}}{2\mathrm{\γ}}\left\{\begin{array}{c}\cos \left({\mathrm{\ψ}}_0\right)+\frac{3{\cos }^2\left({\mathrm{\ψ}}_0\right)}{4}+\cos \left({\mathrm{\ψ}}_0\right)\ln [1+\csc \left(\frac{{\mathrm{\ψ}}_0}{2}\right)]\\ +2\ln [\cos \left(\frac{{\mathrm{\ψ}}_0}{4}\right)+\sin \left(\frac{{\mathrm{\ψ}}_0}{4}\right)]+\ln \left[\sin \left(\frac{{\mathrm{\ψ}}_0}{2}\right)\right]+2\sin \left(\frac{{\mathrm{\ψ}}_0}{2}\right)-\frac{7}{4}\end{array}\right\}.$

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