CN106125149A - The Point-mass Model middle-shallow layer optimal buried depth of high-resolution point mass determines method - Google Patents

Abstract

The present invention relates to a kind of Point-mass Model middle-shallow layer optimal buried depth of high-resolution point mass and determine method, including: utilize existing Gravity Models and different resolution gravimetric data to build low resolution layering residue points quality model, vertical gravity gradient and exact position are measured, Depth Inverse is carried out according to measurement data, determine point mass buried depth scope, multiple buried depth values are selected with a fixed step size, carry out Point-mass Model resolving respectively, the data at non-grid midpoint are recovered, compare with actual measured value, statistics restoration errors, the restoration errors of all node correspondence degree of depth is carried out lateral comparison, determine the optimal buried depth of Shallow High Resolution point mass that minimum restoring error is corresponding.The present invention can more accurately obtain the buried depth of Shallow High Resolution point mass, improves the degree of accuracy of demixing point mass combination Model approximation Spatial Disturbing Gravity near the ground.

Description

The Point-mass Model middle-shallow layer optimal buried depth of high-resolution point mass determines method

Technical field

The present invention relates to point mass buried depth approximation technique field in outside of the earth disturbance gravitation, particularly to one point matter The amount model middle-shallow layer optimal buried depth of high-resolution point mass determines method.

Background technology

Point-mass Model method is a kind of method grown up to calculate spacecraft disturbance gravitation, the method Advantage be kernel function simple in construction, and when low-altitude track point direct integral can be avoided to calculate occur singularity, this exterior point The superposability of quality model can carry out frequency-division section calculating to disturbing gravity field more neatly.In Point-mass Model side Method research and application aspect, needing a key issue to be processed is the buried depth selecting different resolution point mass.In the past Mostly the domestic Selecting research to point mass buried depth is directly to use for reference existing theoretical conclusion, is selecting Shallow High Resolution point Also it is according to following empirical representation during buried depth D of quality:

D=a_e·θ

Wherein a_eBeing terrestrial equator mean radius, θ is that grid resolution (is presented as, list in the earth centre of sphere angle that grid is corresponding Position is radian).Thus obtaining the buried depth that the grid commonly used is corresponding, see shown in Fig. 2 and Fig. 3, deep layer point mass refers to point Resolution is 1 ° × 1 °, the point mass of 20 ' × 20 ', 5 ' × 5 ', and Shallow Point quality then refers exclusively to the point mass that resolution is 1 ' × 1 '. Owing to Shallow Point quality is near earth's surface, improper the choosing of its buried depth will cause when recovering the disturbance gravitation in space near the ground Bigger error occurs, as main in " mapping journal " volume 39 the 5th phase " structure of three layers of point mass of gravity and analysis " to deeper The building method of layer point mass is studied, the structure of low resolution Point-mass Model in solution, but without reference to shallow-layer high score Structure and the degree of depth of resolution Point-mass Model determine, lack the research and analysis to Shallow Point mass effect, it is impossible to effectively select Shallow High Resolution point mass buried depth.Therefore, a kind of structure to Shallow High Resolution Point-mass Model and the degree of depth are needed badly The technology determined, improves the recovery effects that disturbance gravitational field is overall.

Summary of the invention

For the deficiencies in the prior art, the present invention provides a kind of Point-mass Model middle-shallow layer high-resolution point mass most preferably to bury Hide depth determination method, compared with prior art, it is possible to recover ground and neighbouring Spatial Disturbing Gravity field thereof with degree of precision.

According to design provided by the present invention, a kind of Point-mass Model middle-shallow layer high-resolution point mass is most preferably buried Depth determination method, comprises the steps of:

Gravity anomaly data construct low resolution layering residue points quality model in the range of step 1, foundation selection area；

Step 2, in the Point-mass Model grid that step 1 builds, carry out vertical gravity gradiometry and exact position survey Amount, calculates gravity anomaly and the disturbing gravity vertical gradient in Earth ' data at Shallow High Resolution Point-mass Model grid midpoint；

Step 3, to the Shallow High Resolution gravity anomaly data in the range of selection area and disturbing gravity vertical gradient in Earth ' number According to carrying out Depth Inverse, determine point mass buried depth scope；

Step 4, the Point-mass Model built according to step 1, obtain according to high-resolution gravity anomaly data and step 2 The disturbing gravity vertical gradient in Earth ' data at Shallow High Resolution Point-mass Model grid midpoint, with step-length L in point mass buried depth In the range of select multiple buried depth value, resolve Point-mass Model one by one according to buried depth value, recover selected with calculation result The gravity anomaly data at non-grid midpoint and disturbing gravity vertical gradient in Earth ' data in regional extent, add up restoration errors, until point The degree of depth that in the range of quality buried depth, all nodes are corresponding completes Point-mass Model one by one and resolves, it is thus achieved that all nodes are corresponding deep The Point-mass Model restoration errors of degree；

Step 5, to obtain Point-mass Model restoration errors carry out lateral comparison, determine corresponding to minimum restoring error The degree of depth, is the optimal buried depth of Shallow High Resolution point mass.

Above-mentioned, step 1 specifically comprises the steps of:

Step 1.1, utilize low-order bit Modulus Model calculate each 1 ° × 1 ° of grid mean gravity riod data Residual error observation:Solve 1 ° × 1 ° point mass M₁As first group of point mass；Step 1.2, The mean gravity riod of each 20 ' × 20 ' grids is calculated with potential coefficient modelBy 1 ° × 1 ° point mass M₁Calculate average AbnormalResidual error observation:

${\stackrel{\‾}{\mathrm{\Δ}g}}_{{20}^{\′}\×{20}^{\′}}^e={\stackrel{\‾}{\mathrm{\Δ}g}}_{{20}^{\′}\×{20}^{\′}}-{\stackrel{\‾}{\mathrm{\Δ}g}}_{{20}^{\′}\×{20}^{\′}}^S-{\stackrel{\‾}{\mathrm{\Δ}g}}_{{20}^{\′}\×{20}^{\′}}^{M_1}$

, solve 20 ' × 20 ' point masses M₂As second group of point mass；

Step 1.3, use potential coefficient model calculate the mean gravity riod of each 5 ' × 5 ' gridsWith first group, Two groups of point masses calculate average exception respectivelyResidual error observation:

${\stackrel{\‾}{\mathrm{\Δ}g}}_{5^{\′}\×5^{\′}}^e={\stackrel{\‾}{\mathrm{\Δ}g}}_{5^{\′}\×5^{\′}}-{\stackrel{\‾}{\mathrm{\Δ}g}}_{5^{\′}\×5^{\′}}^S-{\stackrel{\‾}{\mathrm{\Δ}g}}_{5^{\′}\×5^{\′}}^{M_1}-{\stackrel{\‾}{\mathrm{\Δ}g}}_{5^{\′}\×5^{\′}}^{M_2}$

, solve 5 ' × 5 ' point masses M₃As the 3rd group of point mass.

Above-mentioned, step 2 calculates the gravity anomaly at each 1 ' × 1 ' grid midpoint with potential coefficient modelAnd disturbance Vertical gradient of gravity

Above-mentioned, step 4 specifically comprises following content:

Step 4.1, with first group, second group, the 3rd group of point mass calculate Shallow High Resolution Point-mass Model net respectively Lattice midpoint gravity anomalyAnd disturbing gravity vertical gradient in Earth ' Residual error observation:

${\stackrel{\‾}{\mathrm{\Δ}g}}_{1^{\′}\×1^{\′}}^e={\stackrel{\‾}{\mathrm{\Δ}g}}_{1^{\′}\×1^{\′}}-{\stackrel{\‾}{\mathrm{\Δ}g}}_{1^{\′}\×1^{\′}}^S-{\stackrel{\‾}{\mathrm{\Δ}g}}_{1^{\′}\×1^{\′}}^{M_1}-{\stackrel{\‾}{\mathrm{\Δ}g}}_{1^{\′}\×1^{\′}}^{M_2}-{\stackrel{\‾}{\mathrm{\Δ}g}}_{1^{\′}\×1^{\′}}^{M_3}$

${\stackrel{\‾}{\mathrm{\δ}g}}_{\mathrm{\ρ}\mathrm{\ρ}(1^{\′}\×1^{\′})}^e={\stackrel{\‾}{\mathrm{\δ}g}}_{\mathrm{\ρ}\mathrm{\ρ}(1^{\′}\×1^{\′})}-{\stackrel{\‾}{\mathrm{\δ}g}}_{\mathrm{\ρ}\mathrm{\ρ}(1^{\′}\×1^{\′})}^S-{\stackrel{\‾}{\mathrm{\δ}g}}_{\mathrm{\ρ}\mathrm{\ρ}(1^{\′}\×1^{\′})}^{M_1}-{\stackrel{\‾}{\mathrm{\δ}g}}_{\mathrm{\ρ}\mathrm{\ρ}(1^{\′}\×1^{\′})}^{M_2}-{\stackrel{\‾}{\mathrm{\δ}g}}_{\mathrm{\ρ}\mathrm{\ρ}(1^{\′}\×1^{\′})}^{M_3}$

, two kinds of residual error observations combine and constitute vector:

$G=\left[\begin{array}{c}{\stackrel{\‾}{\mathrm{\Δ}g}}_{1^{\′}\×1^{\′}}^e\\ {\mathrm{\δg}}_{\mathrm{\ρ}\mathrm{\ρ}(1^{\′}\×1^{\′})}^e\end{array}\right];$

Step 4.2, according to buried depth scope determined by step 3, in the range of each node depth value, according to Little square law resolves point mass M corresponding to solving equations all nodes buried depth₄；

Step 4.3, by point mass M corresponding for each node buried depth₄Slicing fully mechanized face is constituted with deep layer point mass, Recover gravity anomaly data and the disturbing gravity vertical gradient in Earth ' data at non-grid midpoint in the range of ground selection area, at measuring point Actual observed value poor, the error that is restored also is added up.

Above-mentioned, step 4.3 is recovered gravity anomaly data and the disturbance at non-grid midpoint in the range of the selection area of ground Vertical gradient of gravity data formula is:

Wherein, n_maxAnd n_layerRepresenting exponent number and the number of plies of residue points quality of low-order bit model respectively, R represents radius of sphericity, Represent corresponding potential coefficient model, ρ represent the earth's core to footpath,Represent the earth's core of i-th ground gravity abnormity point place sphere Radius, r_ijRepresenting the distance between i-th ground gravity abnormity point and jth point mass, K represents point mass number, and M represents by K The vector that individual point mass is constituted, a represents terrestrial equator radius, M_ijRepresent i-th layer of jth point mass.

Beneficial effects of the present invention:

It is residual that the present invention utilizes existing Gravity Models and survey region different resolution gravimetric data to build low resolution layering Not good enough quality model, and in model meshes, vertical gravity gradient and exact position are measured, carry out according to measurement data Depth Inverse, so that it is determined that the scope of point mass buried depth, with a fixed step size in the range of select multiple buried depth value, and Carry out Point-mass Model resolving respectively, the data at non-grid midpoint are recovered, compares with actual measured value, add up extensive Multiple error, carries out lateral comparison to the restoration errors of all node correspondence degree of depth obtained, determines that minimum restoring error is corresponding The degree of depth, is the optimal buried depth of Shallow High Resolution point mass, effectively reduces the tradition shallow-layer that rule of thumb rule obtains The uncertainty of high-resolution point mass buried depth, can more accurately obtain the buried depth of Shallow High Resolution point mass, carry High stratification point mass model approaches the degree of accuracy of Spatial Disturbing Gravity near the ground.

Accompanying drawing illustrates:

Fig. 1 is Shallow High Resolution point mass distribution schematic diagram；

Fig. 2 is that low resolution is layered residue points quality model depthwise construction schematic diagram；

Fig. 3 is that low resolution is layered residue points quality model grid correspondence degree of depth schematic diagram；

Fig. 4 is the schematic flow sheet of the present invention；

Fig. 5 be in test block measuring point coordinate and its gravity anomaly and disturbing gravity vertical gradient in Earth ' observation compare figure；

Fig. 6 be utilize gravity anomaly and disturbing gravity vertical gradient in Earth ' and buried depth compare figure；

Fig. 7 is the error statistics result schematic diagram of all nodes of lateral comparison；

Fig. 8 is the present invention and the hierarchical mode Comparative result schematic diagram of transmission empirical law foundation in Experimental Area.

Detailed description of the invention:

The present invention is further detailed explanation with technical scheme below in conjunction with the accompanying drawings, and detailed by preferred embodiment Describe bright embodiments of the present invention in detail, but embodiments of the present invention are not limited to this.

Embodiment one, sees shown in Fig. 1～4, and a kind of Point-mass Model middle-shallow layer high-resolution point mass is most preferably buried deeply Degree determines method, comprises the steps of:

Gravity anomaly data construct low resolution layering residue points quality model in the range of step 1, foundation selection area；

Step 2, in the Point-mass Model grid that step 1 builds, carry out vertical gravity gradiometry and exact position survey Amount, calculates gravity anomaly and the disturbing gravity vertical gradient in Earth ' data at Shallow High Resolution Point-mass Model grid midpoint；

Step 3, to the Shallow High Resolution gravity anomaly data in the range of selection area and disturbing gravity vertical gradient in Earth ' number According to carrying out Depth Inverse, determine point mass buried depth scope；

Step 4, the Point-mass Model built according to step 1, obtain according to high-resolution gravity anomaly data and step 2 The disturbing gravity vertical gradient in Earth ' data at Shallow High Resolution Point-mass Model grid midpoint, with step-length L in point mass buried depth In the range of select multiple buried depth value, resolve Point-mass Model one by one according to buried depth value, recover selected with calculation result The gravity anomaly data at non-grid midpoint and disturbing gravity vertical gradient in Earth ' data in regional extent, add up restoration errors, until point The degree of depth that in the range of quality buried depth, all nodes are corresponding completes Point-mass Model one by one and resolves, it is thus achieved that all nodes are corresponding deep The Point-mass Model restoration errors of degree；

Step 5, to obtain Point-mass Model restoration errors carry out lateral comparison, determine corresponding to minimum restoring error The degree of depth, is the optimal buried depth of Shallow High Resolution point mass.

By building low resolution layering residue points quality model, and in model meshes to vertical gravity gradient and accurately Position measures, and carries out Depth Inverse according to measurement data, so that it is determined that the scope of point mass buried depth, with a fixed step size Select multiple buried depth value in the range of, and carry out Point-mass Model resolving respectively, the data at non-grid midpoint are carried out extensive Multiple, compare with actual measured value, add up restoration errors, the restoration errors of all node correspondence degree of depth obtained is carried out horizontal stroke To comparing, determine the degree of depth that minimum restoring error is corresponding, be the optimal buried depth of Shallow High Resolution point mass, effectively drop The uncertainty of the Shallow High Resolution point mass buried depth that low tradition rule of thumb rule obtains, can more accurately obtain shallow-layer The buried depth of high-resolution point mass.

Embodiment two, sees shown in Fig. 1～8, and a kind of Point-mass Model middle-shallow layer high-resolution point mass is most preferably buried deeply Degree determines method, comprises the steps of:

Gravity anomaly data construct low resolution layering residue points quality model in the range of step 1, foundation selection area, Specifically comprise following content:

Step 1.1, utilize low-order bit Modulus Model calculate each 1 ° × 1 ° of grid mean gravity riod data Residual error observation:Solve 1 ° × 1 ° point mass M₁As first group of point mass, wherein, low order 36 rank elected as by potential coefficient model, and it is equivalent to 5 ° × 5 ° mean gravity riods in the whole world；

Step 1.2, use potential coefficient model calculate the mean gravity riod of each 20 ' × 20 ' gridsWith 1 ° × 1 ° Point mass M₁Calculate average abnormalResidual error observation:

${\stackrel{\‾}{\mathrm{\Δ}g}}_{{20}^{\′}\×{20}^{\′}}^e={\stackrel{\‾}{\mathrm{\Δ}g}}_{{20}^{\′}\×{20}^{\′}}-{\stackrel{\‾}{\mathrm{\Δ}g}}_{{20}^{\′}\×{20}^{\′}}^S-{\stackrel{\‾}{\mathrm{\Δ}g}}_{{20}^{\′}\×{20}^{\′}}^{M_1}$

, solve 20 ' × 20 ' point masses M₂As second group of point mass；

Step 1.3, use potential coefficient model calculate the mean gravity riod of each 5 ' × 5 ' gridsWith first group, Two groups of point masses calculate average exception respectivelyResidual error observation:

${\stackrel{\‾}{\mathrm{\Δ}g}}_{5^{\′}\×5^{\′}}^e={\stackrel{\‾}{\mathrm{\Δ}g}}_{5^{\′}\×5^{\′}}-{\stackrel{\‾}{\mathrm{\Δ}g}}_{5^{\′}\×5^{\′}}^S-{\stackrel{\‾}{\mathrm{\Δ}g}}_{5^{\′}\×5^{\′}}^{M_1}-{\stackrel{\‾}{\mathrm{\Δ}g}}_{5^{\′}\×5^{\′}}^{M_2}$

, solve 5 ' × 5 ' point masses M₃As the 3rd group of point mass.

Step 2, in the Point-mass Model grid that step 1 builds, carry out vertical gravity gradiometry and exact position survey Amount, calculates gravity anomaly and the disturbing gravity vertical gradient in Earth ' data at Shallow High Resolution Point-mass Model grid midpoint, specifically Refer to: calculate the gravity anomaly at each 1 ' × 1 ' grid midpoint with potential coefficient modelAnd disturbing gravity vertical gradient in Earth 'At measuring point, between 2 some positions of vertical direction, measure Shanxi Province value dg, and accurately measure hanging down between 2 Straight discrepancy in elevation Δ h, then use formulaDetermine the vertical gradient of gravity in above-mentioned observation station；Coordinate according to measuring point is according to public affairs FormulaCalculating normal gravity vertical gradient, in formula, B is the geodetic latitude of measuring point；H is for surveying The geodetic height of point；Further by the definition of gravity, according to formulaCalculate the disturbing gravity on measuring point vertical Gradient data.

Step 3, to the Shallow High Resolution gravity anomaly data in the range of selection area and disturbing gravity vertical gradient in Earth ' number According to carrying out Depth Inverse, determine point mass buried depth scope, specifically refer to: theoretical according to potential field, a radius is R, center Buried depth is D, residual density is the uniform spherome of κ, in the gravity anomaly that its space outerpace arbitrfary point causes, with the residue matter of spheroid Amount M=4 π R³The particle situation that κ/3 all concentrate on the centre of sphere is identical；If with the centre of sphere at floor projection point as zero, z-axis hang down Straight downward, x-axis overlaps with selected measurement section, then in x-axis, between arbitrfary point and buried depth D, relational expression is:

$\mathrm{\Δ}g(x,0)=GM\frac{D}{{(x^2+D^2)}^{3/2}}$

Relation between P (x, 0) place gravity anomaly first derivative (i.e. vertical gradient) and buried depth D is:

${\mathrm{\Δg}}_z=GM\frac{2D^2-x^2}{{(x^2+D^2)}^{5/2}}$

According to gravity anomaly and disturbing gravity vertical gradient in Earth ' inverting buried depth D, and consider point mass and bury and deeply cross Empirical law, determine the interval of a buried depth, as the point mass buried depth scope that next step is used.

Step 4, the Point-mass Model built according to step 1, obtain according to high-resolution gravity anomaly data and step 2 The disturbing gravity vertical gradient in Earth ' data at Shallow High Resolution Point-mass Model grid midpoint, with step-length L in point mass buried depth In the range of select multiple buried depth value, resolve Point-mass Model one by one according to buried depth value, recover selected with calculation result The gravity anomaly data at non-grid midpoint and disturbing gravity vertical gradient in Earth ' data in regional extent, add up restoration errors, until point The degree of depth that in the range of quality buried depth, all nodes are corresponding completes Point-mass Model one by one and resolves, it is thus achieved that all nodes are corresponding deep The Point-mass Model restoration errors of degree, specifically comprises content as follows:

Step 4.1, with first group, second group, the 3rd group of point mass calculate Shallow High Resolution Point-mass Model net respectively Lattice midpoint gravity anomalyAnd disturbing gravity vertical gradient in Earth ' ? Residual error observation:

${\stackrel{\‾}{\mathrm{\Δ}g}}_{1^{\′}\×1^{\′}}^e={\stackrel{\‾}{\mathrm{\Δ}g}}_{1^{\′}\×1^{\′}}-{\stackrel{\‾}{\mathrm{\Δ}g}}_{1^{\′}\×1^{\′}}^S-{\stackrel{\‾}{\mathrm{\Δ}g}}_{1^{\′}\×1^{\′}}^{M_1}-{\stackrel{\‾}{\mathrm{\Δ}g}}_{1^{\′}\×1^{\′}}^{M_2}-{\stackrel{\‾}{\mathrm{\Δ}g}}_{1^{\′}\×1^{\′}}^{M_3}$

${\stackrel{\‾}{\mathrm{\δ}g}}_{\mathrm{\ρ}\mathrm{\ρ}(1^{\′}\×1^{\′})}^e={\stackrel{\‾}{\mathrm{\δ}g}}_{\mathrm{\ρ}\mathrm{\ρ}(1^{\′}\×1^{\′})}-{\stackrel{\‾}{\mathrm{\δ}g}}_{\mathrm{\ρ}\mathrm{\ρ}(1^{\′}\×1^{\′})}^S-{\stackrel{\‾}{\mathrm{\δ}g}}_{\mathrm{\ρ}\mathrm{\ρ}(1^{\′}\×1^{\′})}^{M_1}-{\stackrel{\‾}{\mathrm{\δ}g}}_{\mathrm{\ρ}\mathrm{\ρ}(1^{\′}\×1^{\′})}^{M_2}-{\stackrel{\‾}{\mathrm{\δ}g}}_{\mathrm{\ρ}\mathrm{\ρ}(1^{\′}\×1^{\′})}^{M_3}$

, two kinds of residual error observations combine and constitute vector:

$G=\left[\begin{array}{c}{\stackrel{\‾}{\mathrm{\Δ}g}}_{1^{\′}\×1^{\′}}^e\\ {\mathrm{\δg}}_{\mathrm{\ρ}\mathrm{\ρ}(1^{\′}\×1^{\′})}^e\end{array}\right];$

Step 4.2, according to buried depth scope determined by step 3, in the range of each node depth value, according to Little square law resolves point mass M corresponding to solving equations all nodes buried depth₄；

Step 4.3, by point mass M corresponding for each node buried depth₄Slicing fully mechanized face is constituted with deep layer point mass, Recover gravity anomaly data and the disturbance weight at non-Shallow High Resolution Point-mass Model grid midpoint in the range of ground selection area Power vertical gradient data, poor with the actual observed value at measuring point, the error that is restored also is added up, and wherein, recovers ground choosing The gravity anomaly data at non-Shallow High Resolution Point-mass Model grid midpoint and disturbing gravity vertical gradient in Earth ' in determining regional extent Data formula is:

Wherein, n_maxAnd n_layerRepresenting exponent number and the number of plies of residue points quality of low-order bit model respectively, R represents radius of sphericity, Represent corresponding potential coefficient model, ρ represent the earth's core to footpath,Represent i-th ground gravity abnormity point place sphere The earth's core radius, r_ijRepresenting the distance between i-th ground gravity abnormity point and jth point mass, K represents point mass number, M table Showing the vector being made up of K point mass, a represents terrestrial equator radius, M_ijRepresent i-th layer of jth point mass.

Step 5, to obtain Point-mass Model restoration errors carry out lateral comparison, determine corresponding to minimum restoring error The degree of depth, is the optimal buried depth of Shallow High Resolution point mass.

Wherein, the computing formula about gravity anomaly data and disturbing gravity vertical gradient in Earth ' data used is as follows:

Utilize potential coefficient model calculate mean gravity riod formula:

Wherein,Be one group complete The bit model coefficient of full normalization；

Point mass is utilized to calculate average abnormal formula:

${\mathrm{\Δg}}_i=\frac{1}{2r_i}\underset{j=1}{\overset{K}{\Σ}}(\frac{r_i^2-R_B^2}{l_{ij}^3}-\frac{3}{l_{ij}})M_j;$

Utilize the formula of potential coefficient model calculation perturbation vertical gradient of gravity:

Utilize the formula of point mass calculation perturbation vertical gradient of gravity:

${\mathrm{\δg}}_{\mathrm{\ρ}\mathrm{\ρ}}=-\underset{j=1}{\overset{K}{\Σ}}\left(\frac{r_j^2-3{(\mathrm{\ρ}-R_j{\mathrm{cos\ψ}}_j)}^2}{r_j^5}\right)M_j$

After choosing low order reference field composition layering residue points quality model, the computing formula of disturbing gravity vertical gradient in Earth ' For:

Wherein, n_maxAnd n_layerRepresent exponent number and the number of plies of residue points quality of low-order bit model respectively.

For verifying the effect of the present invention, below in conjunction with concrete example, the present invention is described further:

According to above-mentioned step, make full use of the existing gravitational field mould higher with China's domestic gravity data matching degree Type, the gravimetric data of survey region different resolution, set up the demixing point quality model of survey region；Utilize high-precision CG-5 Relative gravity instrument and GRS RTK equipment are observed some vertical gravity gradiometry and a precision measurement, it is thus achieved that selected scope 1 ' × 1 ' interior grid midpoint and the vertical gravity gradient information of internal a certain amount of point；According to principle, the vertical gravity ladder of a bit Degree is equal to normal gravity vertical gradient and the disturbing gravity vertical gradient in Earth ' sum of this point, vertical by calculating the normal gravity of measuring point Gradient, may thereby determine that the disturbing gravity vertical gradient in Earth ' on measuring point；High-resolution weight according to scope selected in survey region The disturbing gravity vertical gradient in Earth ' information that power is abnormal and previously obtained, while carrying out underground density anomaly Depth Inverse, estimates The empirical law of point mass buried depth, determines the interval of point mass buried depth；Certain step-length is selected in buried depth interval, Multiple depth value is set, resolves 1 ' × 1 ' or higher resolution Point-mass Model respectively according to each depth value, then to calculate Point-mass Model recover survey region center selected in the range of the gravity anomaly at non-grid midpoint and disturbing gravity vertical gradient in Earth ', Restoration errors is carried out statistical analysis；The statistical result of each degree of depth higher slice Point-mass Model restoration errors of Integrated comparative, root Optimal burying depth is selected according to minimum error.

Choosing observation experiment district near Song Shan, Zhengzhou, its size is 8km × 8km, and upper left corner longitude is 113 ° 38 ', latitude Degree is 34 ° 46 '.In test block uniform cloth surveyed 16 points, the coordinate of these measuring points and gravity anomaly thereof and disturbing gravity hang down Vertical ladder degree observation is as shown in Figure 5；(resolution is followed successively by 1 ° from low to high to set up four kinds of resolution according to test block according to Fig. 1 × 1 °, 20 ' × 20 ', 5 ' × 5 ', 1 ' × 1 ') Point-mass Model graduation, arrange in these different range and resolution Gravity data, sets up the low order point mass model that resolution is by 5 ' × 5 '.The gravity anomaly money in comprehensive 1 ' × 1 ' region Material and the disturbing gravity vertical gradient in Earth ' of above-mentioned measuring point, be utilized respectively between gravity anomaly and disturbing gravity vertical gradient in Earth ' and buried depth Relation determines buried depth D of corresponding particle₁And D₂, and calculate mean depth D=(D₁+D₂)/2, as shown in Figure 6, binding site matter The empirical law of amount buried depth sets up buried depth interval for (1300m, 2400m)；Multiple degree of depth node is set, often in buried depth interval The individual node degree of depth combines low order Point-mass Model and ground 1 ' × 1 ' residual gravity anomaly and disturbing gravity vertical gradient in Earth ' data, solves Calculating ground high-resolution Point-mass Model, the disturbing gravity utilizing complete Point-mass Model above-mentioned 16 points of recovery resolved is vertical Gradient, and compare acquisition error statistics result (with ∑ (v with measured value_Calculate-v_Amount)²For index, wherein v_CalculateRecover for calculating Value, v_AmountFor measured value)；Error statistics result on all nodes of lateral comparison, selects the result that error is minimum, and determines that it is right The buried depth answered, according to Fig. 7, in figure, secondary series statistical result can determine whether out that 1 ' × 1 ' point mass optimal burying depth is about 1900 meters.

In the various documents calculated about outside of the earth disturbance gravitation, utilizing demixing point quality model to carry out approaching is one Plant significantly method, but when determining the buried depth of Shallow Point quality, almost all of way is all to utilize this Invent above-mentioned empirical law, say, that empirical law is to determine the traditional method of Shallow Point quality buried depth at present.For The present invention is relative to the advantage of Conventional wisdom rule in explanation, compares used here as following process:

Choose base reference data, for comparison reference: the aviation weight of 10 points of the about 1500 meters of eminences in overhead, Experimental Area Power measurement data (has been processed into gravity anomaly)；Set up four layers of Point-mass Model of Experimental Area, the point mass of its middle-shallow layer Buried depth empirically rule determines, then utilizes the layering point mass model set up to recover reference point Gravity anomaly, and poor with measured value；Set up four layers of Point-mass Model of Experimental Area, the point mass buried depth of its middle-shallow layer It is that the method proposed according to the present invention determines, then utilizes the layering point mass model set up to recover reference point Gravity anomaly, and poor with measured value；Being analyzed above-mentioned poor outcome, as shown in Figure 8, in figure, unit is 10^-5ms^-2, According to the poor comparative result in figure, the error that the demixing point quality model utilizing the present invention to be set up recovers measured data is obvious Restoration result less than the hierarchical mode that rule of thumb rule is set up.

Thus, demonstrate further compared with traditional method, present invention have the advantage that: determining Shallow Point quality Buried depth time, employ novel observation data, i.e. disturbing gravity vertical gradient in Earth ' observation data, therefore, its modeling process The known gravity field information in outside used is more comprehensive；Utilize the demixing point quality model that the present invention sets up, recovering outside the earth During portion's gravitational field, the precision of its result is higher than the demixing point quality model utilizing Conventional wisdom rule to set up.

The invention is not limited in above-mentioned detailed description of the invention, those skilled in the art also can make multiple change accordingly, But any with the present invention equivalent or similar change all should contain within the scope of the claims.

Claims (5)

1. the Point-mass Model middle-shallow layer optimal buried depth of high-resolution point mass determines method, it is characterised in that: comprise Following steps:

Gravity anomaly data construct low resolution layering residue points quality model in the range of step 1, foundation selection area；

Step 2, in the Point-mass Model grid that step 1 builds, carry out vertical gravity gradiometry and exact position measure, meter Calculate gravity anomaly and the disturbing gravity vertical gradient in Earth ' data at Shallow High Resolution Point-mass Model grid midpoint；

Step 3, the Shallow High Resolution gravity anomaly data in the range of selection area and disturbing gravity vertical gradient in Earth ' data are entered Row Depth Inverse, determines point mass buried depth scope；

Step 4, the Point-mass Model built according to step 1, the shallow-layer obtained according to high-resolution gravity anomaly data and step 2 The disturbing gravity vertical gradient in Earth ' data at high-resolution Point-mass Model grid midpoint, with step-length L in point mass buried depth scope Interior selection multiple buried depth value, resolves Point-mass Model one by one according to buried depth value, recovers selection area with calculation result In the range of the gravity anomaly data at non-grid midpoint and disturbing gravity vertical gradient in Earth ' data, add up restoration errors, until point mass The degree of depth that in the range of buried depth, all nodes are corresponding completes Point-mass Model one by one and resolves, it is thus achieved that all node correspondence degree of depth Point-mass Model restoration errors；

Step 5, the Point-mass Model restoration errors obtained being carried out lateral comparison, determine corresponding to minimum restoring error is deep Degree, is the optimal buried depth of Shallow High Resolution point mass.

The Point-mass Model middle-shallow layer optimal buried depth of high-resolution point mass the most according to claim 1 determines method, It is characterized in that: step 1 specifically comprises the steps of:

Step 1.1, utilize low-order bit Modulus Model calculate each 1 ° × 1 ° of grid mean gravity riod dataObtain residual Difference observation:Solve 1 ° × 1 ° point mass M₁As first group of point mass；

Step 1.2, use potential coefficient model calculate the mean gravity riod of each 20 ' × 20 ' gridsBy 1 ° × 1 ° some matter Amount M₁Calculate average abnormalResidual error observation:

${\stackrel{\‾}{\mathrm{\Δ}g}}_{{20}^{\′}\×{20}^{\′}}^e={\stackrel{\‾}{\mathrm{\Δ}g}}_{{20}^{\′}\×{20}^{\′}}-{\stackrel{\‾}{\mathrm{\Δ}g}}_{{20}^{\′}\×{20}^{\′}}^S-{\stackrel{\‾}{\mathrm{\Δ}g}}_{{20}^{\′}\×{20}^{\′}}^{M_1}$ ,

Solve 20 ' × 20 ' point masses M₂As second group of point mass；

Step 1.3, use potential coefficient model calculate the mean gravity riod of each 5 ' × 5 ' gridsWith first group, second group Point mass calculates average exception respectivelyResidual error observation:

${\stackrel{\‾}{\mathrm{\Δ}g}}_{5^{\′}\×5^{\′}}^e={\stackrel{\‾}{\mathrm{\Δ}g}}_{5^{\′}\×5^{\′}}-{\stackrel{\‾}{\mathrm{\Δ}g}}_{5^{\′}\×5^{\′}}^S-{\stackrel{\‾}{\mathrm{\Δ}g}}_{5^{\′}\×5^{\′}}^{M_1}-{\stackrel{\‾}{\mathrm{\Δ}g}}_{5^{\′}\×5^{\′}}^{M_2}$ ,

Solve 5 ' × 5 ' point masses M₃As the 3rd group of point mass.

The Point-mass Model middle-shallow layer optimal buried depth of high-resolution point mass the most according to claim 1 determines method, It is characterized in that: described step 2 calculates the gravity anomaly at each 1 ' × 1 ' grid midpoint with potential coefficient modelAnd disturbance Vertical gradient of gravity

The Point-mass Model middle-shallow layer optimal buried depth of high-resolution point mass the most according to claim 2 determines method, It is characterized in that: described step 4 specifically comprises following content:

Step 4.1, with first group, second group, the 3rd group of point mass calculate in Shallow High Resolution Point-mass Model grid respectively Point gravity anomalyAnd disturbing gravity vertical gradient in Earth ' ? Residual error observation:

${\stackrel{\‾}{\mathrm{\Δ}g}}_{1^{\′}\×1^{\′}}^e={\stackrel{\‾}{\mathrm{\Δ}g}}_{1^{\′}\×1^{\′}}-{\stackrel{\‾}{\mathrm{\Δ}g}}_{1^{\′}\×1^{\′}}^S-{\stackrel{\‾}{\mathrm{\Δ}g}}_{1^{\′}\×1^{\′}}^{M_1}-{\stackrel{\‾}{\mathrm{\Δ}g}}_{1^{\′}\×1^{\′}}^{M_2}-{\stackrel{\‾}{\mathrm{\Δ}g}}_{1^{\′}\×1^{\′}}^{M_3}$

${\stackrel{\‾}{\mathrm{\δ}g}}_{\mathrm{\ρ}\mathrm{\ρ}\left(1^{\′}\×1^{\′}\right)}^e={\stackrel{\‾}{\mathrm{\δ}g}}_{\mathrm{\ρ}\mathrm{\ρ}\left(1^{\′}\×1^{\′}\right)}-{\stackrel{\‾}{\mathrm{\δ}g}}_{\mathrm{\ρ}\mathrm{\ρ}\left(1^{\′}\×1^{\′}\right)}^S-{\stackrel{\‾}{\mathrm{\δ}g}}_{\mathrm{\ρ}\mathrm{\ρ}\left(1^{\′}\×1^{\′}\right)}^{M_1}-{\stackrel{\‾}{\mathrm{\δ}g}}_{\mathrm{\ρ}\mathrm{\ρ}\left(1^{\′}\×1^{\′}\right)}^{M_2}={\stackrel{\‾}{\mathrm{\δ}g}}_{\mathrm{\ρ}\mathrm{\ρ}\left(1^{\′}\×1^{\′}\right)}^{M_3}$ ,

Combined by two kinds of residual error observations and constitute vector:

$G=\left[\begin{array}{c}{{\stackrel{\‾}{\mathrm{\Δ}g}}^e}_{1^{\′}\×1^{\′}}\\ {\mathrm{\δg}}_{\mathrm{\ρ}\mathrm{\ρ}(1^{\′}\×1^{\′})}^e\end{array}\right];$

Step 4.2, according to buried depth scope determined by step 3, in the range of each node depth value, according to a young waiter in a wineshop or an inn Multiplication resolves point mass M corresponding to solving equations all nodes buried depth₄；

Step 4.3, by point mass M corresponding for each node buried depth₄Constitute slicing fully mechanized face with deep layer point mass, recover In the range of the selection area of ground, gravity anomaly data and the disturbing gravity at non-Shallow High Resolution Point-mass Model grid midpoint hang down Vertical ladder degrees of data, poor with the actual observed value at measuring point, the error that is restored also is added up.

The Point-mass Model middle-shallow layer optimal buried depth of high-resolution point mass the most according to claim 4 determines method, It is characterized in that: in described step 4.3 in the range of the selection area of recovery ground in non-Shallow High Resolution Point-mass Model grid Point gravity anomaly data and disturbing gravity vertical gradient in Earth ' data formula be:

Wherein, n_maxWith n_layerRepresenting exponent number and the number of plies of residue points quality of low-order bit model respectively, R represents radius of sphericity, Table Show correspondence potential coefficient model, ρ represent the earth's core to footpath,Represent the earth's core half of i-th ground gravity abnormity point place sphere Footpath, r_ijRepresenting the distance between i-th ground gravity abnormity point and jth point mass, K represents point mass number, and M represents by K The vector that point mass is constituted, a represents terrestrial equator radius, M_ijRepresent i-th layer of jth point mass.