CN106125149B - The optimal buried depth of Point-mass Model middle-shallow layer high-resolution point mass determines method - Google Patents
The optimal buried depth of Point-mass Model middle-shallow layer high-resolution point mass determines method Download PDFInfo
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Abstract
The present invention relates to a kind of optimal buried depth of Point-mass Model middle-shallow layer high-resolution point mass to determine method, including：Utilize existing Gravity Models and different resolution gravimetric data structure low resolution layering residual error Point-mass 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, Point-mass Model resolving is carried out respectively, the data at non-grid midpoint are recovered, compared with actual measured value, count restoration errors, the restoration errors that all nodes are corresponded to depth carry out lateral comparison, determine the optimal buried depth of Shallow High Resolution point mass corresponding to minimum restoring error.The present invention can more accurately obtain the buried depth of Shallow High Resolution point mass, improve the accuracy of demixing point mass combination Model approximation Spatial Disturbing Gravity near the ground.
Description
Technical field
The present invention relates to point mass buried depth approximation technique field in outside of the earth disturbance gravitation, more particularly to a kind of point matter
The amount optimal buried depth of model middle-shallow layer high-resolution point mass determines method.
Background technology
Point-mass Model method is to calculate a kind of method that spacecraft disturbs gravitation and grown up, this method
The advantages of be that kernel function is simple in construction, and the singularity that occurs when can avoid the low-altitude track point direct integral from calculating, this exterior point
The superposability of quality model more neatly can carry out frequency-division section calculating to disturbing gravity field.In Point-mass Model side
Method research and application aspect are, it is necessary to which a key issue of processing is to select the buried depth of different resolution point mass.In the past
The domestic Selecting research to point mass buried depth is mostly directly to use for reference existing theoretical conclusion, in selection Shallow High Resolution point
It is also according to following empirical representation during the buried depth D of quality：
D=ae·θ
Wherein aeIt is terrestrial equator mean radius, θ is that earth centre of sphere angle corresponding to grid (is presented as grid resolution ratio, list
Position is radian).Thus buried depth corresponding to conventional grid is obtained, referring to shown in Fig. 2 and Fig. 3, deep layer point mass refers to point
Resolution is 1 ° × 1 °, 20 ' × 20 ', 5 ' × 5 ' point mass, and shallow-layer point mass then refers exclusively to the point mass that resolution ratio is 1 ' × 1 '.
Due to shallow-layer point mass, closely table, the improper selection of its buried depth will cause when recovering the disturbance gravitation of near-earth space of planes
There is larger error, such as《Survey and draw journal》The 5th phase of volume 39《The construction of three layers of point mass of gravity and analysis》Mainly 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
The structure and depth of resolution Point-mass Model determine, lack the research and analysis to Shallow Point mass effect, can not effectively select
Shallow High Resolution point mass buried depth.Therefore, a kind of structure and depth to Shallow High Resolution Point-mass Model is needed badly
The technology of determination, to improve the overall recovery effects of disturbance gravitational field.
The content of the invention
In view of the shortcomings of the prior art, the present invention provides a kind of Point-mass Model middle-shallow layer high-resolution point mass and most preferably buried
Depth determination method is hidden, compared with prior art, ground and its neighbouring Spatial Disturbing Gravity field can be recovered 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, comprise the following steps：
Step 1, low resolution layering residual error Point-mass Model is built according to the gravity anomaly data in the range of selection area；
Step 2, vertical gravity gradiometry and exact position survey are carried out in the Point-mass Model grid that step 1 is built
Amount, calculate the gravity anomaly and 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 and disturbing gravity vertical gradient in Earth ' number in the range of selection area
According to Depth Inverse is carried out, point mass buried depth scope is determined；
Step 4, the Point-mass Model built according to step 1, obtained 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 values, Point-mass Model is resolved according to buried depth value one by one, recovers selected with calculation result
The gravity anomaly data and disturbing gravity vertical gradient in Earth ' data at non-grid midpoint in regional extent, restoration errors are counted, until point
Depth corresponding to all nodes completes Point-mass Model resolving one by one in the range of quality buried depth, and it is corresponding deep to obtain all nodes
The Point-mass Model restoration errors of degree；
Step 5, the Point-mass Model restoration errors to acquisition carry out lateral comparison, determine corresponding to minimum restoring error
Depth, the as optimal buried depth of Shallow High Resolution point mass.
Above-mentioned, step 1 specifically comprises the following steps：
Step 1.1, the mean gravity riod data using each 1 ° × 1 ° grid of low-order bit Modulus Model calculating
Obtain 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 ' grid is calculated with potential coefficient modelWith 1 ° × 1 ° point mass M1Calculate average
It is abnormalObtain residual error observation：
, solve 20 ' × 20 ' point mass M2As second group of point mass；
Step 1.3, the mean gravity riod with each 5 ' × 5 ' grid of potential coefficient model calculatingWith first group,
Two groups of point masses calculate average exception respectivelyObtain residual error observation：
, solve 5 ' × 5 ' point mass M3As the 3rd group of point mass.
Above-mentioned, with the gravity anomaly at each 1 ' × 1 ' grid midpoint of potential coefficient model calculating in step 2And disturbance
Vertical gradient of gravity
Above-mentioned, step 4 specifically includes following content：
Step 4.1, with first group, second group, the 3rd group of point mass Shallow High Resolution Point-mass Model net is calculated respectively
Lattice midpoint gravity anomalyAnd disturbing gravity vertical gradient in Earth '
Obtain residual error observation：
,
Combined by two kinds of residual error observations and form vector：
Step 4.2, the buried depth scope according to determined by step 3, each node depth value in the range of, according to most
Small square law resolves the point mass M corresponding to all node buried depths of solving equations4；
Step 4.3, by point mass M corresponding to each node buried depth4Slicing fully mechanized face is formed with deep layer point mass,
Recover the gravity anomaly data and disturbing gravity vertical gradient in Earth ' data at non-grid midpoint in the range of the selection area of ground, at measuring point
Actual observed value make it is poor, the error that is restored simultaneously counts.
Above-mentioned, recover the gravity anomaly data at non-grid midpoint and disturbance in the range of the selection area of ground in step 4.3
Vertical gradient of gravity data formula is：
Wherein, nmaxAnd nlayerThe exponent number of low order bit model and the number of plies of residual error point mass are represented respectively, R represents radius of sphericity, Potential coefficient model corresponding to expression, ρ represent the earth's core to footpath,Represent i-th of ground gravity abnormity point place
The earth's core radius of sphere, rijThe distance between i-th of ground gravity abnormity point and j-th point mass are represented, K represents point mass
Number, M represent the vector being made up of K point mass, and a represents terrestrial equator radius, MijRepresent i-th layer of j-th of point mass.
Beneficial effects of the present invention：
The present invention is residual using existing Gravity Models and the structure low resolution layering of survey region different resolution gravimetric data
Not good enough quality model, and vertical gravity gradient and exact position are measured in model meshes, carried out according to measurement data
Depth Inverse, so that it is determined that the scope of point mass buried depth, multiple buried depth values are selected with a fixed step size in the range of, and
Point-mass Model resolving is carried out respectively, the data at non-grid midpoint are recovered, and compared with actual measured value, statistics is extensive
Multiple error, the restoration errors progress lateral comparison of depth is corresponded to all nodes of acquisition, determined corresponding to minimum restoring error
The optimal buried depth of depth, as Shallow High Resolution point mass, effectively reduce the tradition shallow-layer that rule of thumb rule obtains
The uncertainty of high-resolution point mass buried depth, the buried depth of Shallow High Resolution point mass can be more accurately obtained, is carried
High stratification point mass model approaches the accuracy of Spatial Disturbing Gravity near the ground.
Brief description of the drawings：
Fig. 1 is Shallow High Resolution point mass distribution schematic diagram；
Fig. 2 is that low resolution is layered residual error Point-mass Model depthwise construction schematic diagram；
Fig. 3 is that low resolution layering residual error Point-mass Model grid corresponds to depth schematic diagram；
Fig. 4 is the schematic flow sheet of the present invention；
Fig. 5 is measuring point coordinate and its gravity anomaly and the compares figure of disturbing gravity vertical gradient in Earth ' observation in test block；
Fig. 6 is the compares figure using gravity anomaly and disturbing gravity vertical gradient in Earth ' and buried depth；
Fig. 7 is the error statistics result schematic diagram of all nodes of lateral comparison；
Fig. 8 is the hierarchical mode Comparative result schematic diagram that the present invention establishes with the transmission rule of thumb in Experimental Area.
Embodiment：
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, referring to shown in Fig. 1~4, a kind of Point-mass Model middle-shallow layer high-resolution point mass most preferably buries depth
Determination method is spent, is comprised the following steps：
Step 1, low resolution layering residual error Point-mass Model is built according to the gravity anomaly data in the range of selection area；
Step 2, vertical gravity gradiometry and exact position survey are carried out in the Point-mass Model grid that step 1 is built
Amount, calculate the gravity anomaly and 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 and disturbing gravity vertical gradient in Earth ' number in the range of selection area
According to Depth Inverse is carried out, point mass buried depth scope is determined；
Step 4, the Point-mass Model built according to step 1, obtained 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 values, Point-mass Model is resolved according to buried depth value one by one, recovers selected with calculation result
The gravity anomaly data and disturbing gravity vertical gradient in Earth ' data at non-grid midpoint in regional extent, restoration errors are counted, until point
Depth corresponding to all nodes completes Point-mass Model resolving one by one in the range of quality buried depth, and it is corresponding deep to obtain all nodes
The Point-mass Model restoration errors of degree；
Step 5, the Point-mass Model restoration errors to acquisition carry out lateral comparison, determine corresponding to minimum restoring error
Depth, the as optimal buried depth of Shallow High Resolution point mass.
Residual error Point-mass Model is layered by building low resolution, and to vertical gravity gradient in model meshes and accurately
Position is measured, and Depth Inverse is carried out according to measurement data, so that it is determined that the scope of point mass buried depth, with a fixed step size
Multiple buried depth values are selected in the range of, and carry out Point-mass Model resolving respectively, the data progress to non-grid midpoint is extensive
It is multiple, compared with actual measured value, restoration errors are counted, the restoration errors progress horizontal stroke of depth is corresponded to all nodes of acquisition
To comparing, the optimal buried depth of depth corresponding to minimum restoring error, as Shallow High Resolution point mass is determined, effectively drop
The uncertainty of low traditional rule of thumb Shallow High Resolution point mass buried depth that rule obtains, can more accurately obtain shallow-layer
The buried depth of high-resolution point mass.
Embodiment two, referring to shown in Fig. 1~8, a kind of Point-mass Model middle-shallow layer high-resolution point mass most preferably buries depth
Determination method is spent, is comprised the following steps：
Step 1, low resolution layering residual error Point-mass Model is built according to the gravity anomaly data in the range of selection area,
Specifically include following content：
Step 1.1, the mean gravity riod data using each 1 ° × 1 ° grid of low-order bit Modulus Model calculating
Obtain residual error observation：Solve 1 ° × 1 ° point mass M1As first group of point mass, wherein, low order
Potential coefficient model elects 36 ranks as, and it is equivalent to global 5 ° × 5 ° mean gravity riods；
Step 1.2, the mean gravity riod with each 20 ' × 20 ' grid of potential coefficient model calculatingWith 1 ° × 1 °
Point mass M1Calculate average abnormalObtain residual error observation：
, solve 20 ' × 20 ' point mass M2As second group of point mass；
Step 1.3, the mean gravity riod with each 5 ' × 5 ' grid of potential coefficient model calculatingWith first group,
Two groups of point masses calculate average exception respectivelyObtain residual error observation：
, solve 5 ' × 5 ' point mass M3As the 3rd group of point mass.
Step 2, vertical gravity gradiometry and exact position survey are carried out in the Point-mass Model grid that step 1 is built
Amount, the gravity anomaly and disturbing gravity vertical gradient in Earth ' data at Shallow High Resolution Point-mass Model grid midpoint are calculated, be specifically
Refer to：The gravity anomaly at each 1 ' × 1 ' grid midpoint is calculated with potential coefficient modelAnd disturbing gravity vertical gradient in Earth '
Shanxi Province value dg is determined at the measuring point between 2 point positions of vertical direction, and accurately measures the vertical discrepancy in elevation Δ between 2 points
H, then use formulaDetermine the vertical gradient of gravity in above-mentioned observation station；According to the coordinate of measuring point according to formulaNormal gravity vertical gradient is calculated, B is the geodetic latitude of measuring point in formula；H is the big of measuring point
Ground is high；Further by the definition of gravity, according to formulaCalculate the disturbing gravity vertical gradient in Earth ' number on measuring point
According to.
Step 3, to the Shallow High Resolution gravity anomaly data and disturbing gravity vertical gradient in Earth ' number in the range of selection area
According to carry out Depth Inverse, determine point mass buried depth scope, in particular to：Theoretical according to potential field, a radius is R, center
The uniform spherome that buried depth is D, residual density is κ, in gravity anomaly caused by its exterior space arbitrfary point, the remaining matter with spheroid
Measure M=4 π R3The particle situation that κ/3 all concentrate on the centre of sphere is identical；If using the centre of sphere in floor projection point as the origin of coordinates, z-axis is hung down
Straight downward, x-axis overlaps with selected measurement section, then relational expression is between arbitrfary point and buried depth D in x-axis：
Relation between P (x, 0) place's gravity anomaly first derivative (i.e. vertical gradient) and buried depth D is：
According to gravity anomaly and disturbing gravity vertical gradient in Earth ' inverting buried depth D, and consider point mass and bury deep cross
The rule of thumb, the section of a buried depth is determined, as the point mass buried depth scope used in next step.
Step 4, the Point-mass Model built according to step 1, obtained 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 values, Point-mass Model is resolved according to buried depth value one by one, recovers selected with calculation result
The gravity anomaly data and disturbing gravity vertical gradient in Earth ' data at non-grid midpoint in regional extent, restoration errors are counted, until point
Depth corresponding to all nodes completes Point-mass Model resolving one by one in the range of quality buried depth, and it is corresponding deep to obtain all nodes
The Point-mass Model restoration errors of degree, it is specifically as follows comprising content：
Step 4.1, with first group, second group, the 3rd group of point mass Shallow High Resolution Point-mass Model net is calculated respectively
Lattice midpoint gravity anomalyAnd disturbing gravity vertical gradient in Earth '
Residual error observation：
, combined by two kinds of residual error observations and form vector：
Step 4.2, the buried depth scope according to determined by step 3, each node depth value in the range of, according to most
Small square law resolves the point mass M corresponding to all node buried depths of solving equations4；
Step 4.3, by point mass M corresponding to each node buried depth4Slicing fully mechanized face is formed with deep layer point mass,
Recover the gravity anomaly data at non-Shallow High Resolution Point-mass Model grid midpoint and disturbance weight in the range of the selection area of ground
Power vertical gradient data, it is poor to make with the actual observed value at measuring point, and the error that is restored simultaneously counts, wherein, recover ground choosing
Determine the gravity anomaly data and disturbing gravity vertical gradient in Earth ' at non-Shallow High Resolution Point-mass Model grid midpoint in regional extent
Data formula is：
Wherein, nmaxAnd nlayerThe exponent number of low order bit model and the number of plies of residual error point mass are represented respectively, R represents radius of sphericity, Potential coefficient model corresponding to expression, ρ represent the earth's core to footpath,Represent i-th of ground gravity abnormity point place
The earth's core radius of sphere, rijThe distance between i-th of ground gravity abnormity point and j-th point mass are represented, K represents point mass
Number, M represent the vector being made up of K point mass, and a represents terrestrial equator radius, MijRepresent i-th layer of j-th of point mass.
Step 5, the Point-mass Model restoration errors to acquisition carry out lateral comparison, determine corresponding to minimum restoring error
Depth, the as optimal buried depth of Shallow High Resolution point mass.
Wherein, the calculation formula on gravity anomaly data and disturbing gravity vertical gradient in Earth ' data used is as follows：
The formula of mean gravity riod is calculated using potential coefficient model：
Wherein,It is complete for one group
The bit model coefficient of full normalization；
Average abnormal formula is calculated using point mass：
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：
After choosing low order reference field and forming layering residual error Point-mass Model, the calculation formula of disturbing gravity vertical gradient in Earth '
For:
Wherein, nmaxAnd nlayerThe exponent number of low order bit model and the number of plies of residual error point mass are represented respectively.
For the effect of the checking present invention, with reference to specific example, the present invention is described further：
According to above-mentioned step, the existing and higher gravitational field mould of the domestic gravity data matching degree in China is made full use of
The gravimetric data of type, survey region different resolution, establish the layering Point-mass Model of survey region；Utilize high-precision CG-5
Relative gravity instrument and GRS RTK equipment are observed vertical gravity gradiometry and a precision measurement, obtain selected scope
The grid midpoint of interior 1 ' × 1 ' 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 the normal gravity vertical gradient and disturbing gravity vertical gradient in Earth ' sum of the point, vertical by the normal gravity for calculating measuring point
Gradient, it may thereby determine that the disturbing gravity vertical gradient in Earth ' on measuring point；According to the high-resolution weight that scope is selected in survey region
The abnormal and previously obtained disturbing gravity vertical gradient in Earth ' information of power, while underground density anomaly Depth Inverse is carried out, estimation
The rule of thumb of point mass buried depth, determine the section of point mass buried depth；Certain step-length is selected in buried depth section,
Multiple depth values are set, 1 ' × 1 ' or higher resolution Point-mass Model are resolved respectively according to each depth value, then to calculate
Point-mass Model recover gravity anomaly and disturbing gravity vertical gradient in Earth ' that non-grid midpoint in scope is selected at survey region center,
Statistical analysis is carried out to restoration errors；The statistical result of each depth higher slice Point-mass Model restoration errors of Integrated comparative, root
Optimal burying depth is selected according to the error of minimum.
Observation experiment area is chosen near the Song Shan of Zhengzhou, its size is 8km × 8km, and upper left corner longitude is 113 ° 38 ', latitude
Spend for 34 ° 46 '.Uniform cloth has surveyed 16 points in test block, and the coordinate and its gravity anomaly and disturbing gravity of these measuring points hang down
Vertical ladder degree observation is as shown in Figure 5；According to Fig. 1 establishing four kinds of resolution ratio according to test block, (resolution ratio is followed successively by 1 ° from low to high
× 1 °, 20 ' × 20 ', 5 ' × 5 ', 1 ' × 1 ') Point-mass Model graduation, arrange in these different range and resolution
Gravity data, establish low order point mass model of the resolution ratio by 5 ' × 5 '.The gravity anomaly money in comprehensive 1 ' × 1 ' region
The disturbing gravity vertical gradient in Earth ' of material and above-mentioned measuring point, is utilized respectively between gravity anomaly and disturbing gravity vertical gradient in Earth ' and buried depth
Relation determines the buried depth D of corresponding particle1And D2, and calculate mean depth D=(D1+D2)/2, as shown in fig. 6, binding site matter
It is (1300m, 2400m) that the rule of thumb of amount buried depth, which establishes buried depth section,；Multiple depth nodes are set in buried depth section, every
The residual gravity anomaly of individual node depth joint low order Point-mass Model and ground 1 ' × 1 ' and disturbing gravity vertical gradient in Earth ' data, solution
Ground high-resolution Point-mass Model is calculated, the disturbing gravity for recovering above-mentioned 16 points using the complete Point-mass Model of resolving is vertical
Gradient, and error statistics result is obtained (with ∑ (v compared with measured valueCalculate-vAmount)2For index, wherein vCalculateRecover to calculate
Value, vAmountFor measured value)；Error statistics result on all nodes of lateral comparison, the minimum result of error is selected, and determine that its is right
The buried depth answered, according to Fig. 7, secondary series statistical result can determine whether out that 1 ' × 1 ' point mass optimal burying depth is about in figure
1900 meters.
It is one using being layered Point-mass Model and approach in the various documents calculated on outside of the earth disturbance gravitation
Kind significantly method, however it is determined that shallow-layer point mass buried depth when, almost all of way is all to utilize this
Invent the above-mentioned rule of thumb, that is to say, that the rule of thumb is the current traditional method for determining shallow-layer point mass buried depth.For
The explanation present invention is compared used here as following process relative to the advantage of Conventional wisdom rule：
Base reference data is chosen, for comparison reference：The aviation weight of 10 points of about 1500 meters of Experimental Area overhead eminence
Power measurement data (has been processed into gravity anomaly)；Establish four layers of Point-mass Model of Experimental Area, the point mass of its middle-shallow layer
Buried depth is that empirically rule determines, then recovers reference point using the layering point mass model established
Gravity anomaly, and it is poor with measured value work；Establish four layers of Point-mass Model of Experimental Area, the point mass buried depth of its middle-shallow layer
It is to be determined according to method proposed by the present invention, then recovers reference point using the layering point mass model established
Gravity anomaly, and it is poor with measured value work；Above-mentioned poor outcome is analyzed, as shown in figure 8, unit is 10 in figure-5ms-2,
Poor comparative result in figure, the error that the layering Point-mass Model established using the present invention recovers measured data are obvious
The restoration result for the hierarchical mode established less than rule of thumb rule.
Thus, further demonstrate compared with conventional method, the present invention has the advantage that：It is determined that shallow-layer point mass
Buried depth when, used new observation data, i.e. disturbing gravity vertical gradient in Earth ' observation data, therefore, its modeling process
Gravity field information known to the outside used is more comprehensive；The layering Point-mass Model established using the present invention, recovering outside the earth
During portion's gravitational field, the precision of its result is higher than the layering Point-mass Model established using Conventional wisdom rule.
The invention is not limited in above-mentioned embodiment, those skilled in the art can also make a variety of changes accordingly,
It is but any all to cover within the scope of the claims with equivalent or similar change of the invention.
Claims (5)
1. a kind of optimal buried depth of Point-mass Model middle-shallow layer high-resolution point mass determines method, it is characterised in that：Comprising
Following steps：
Step 1, low resolution layering residual error Point-mass Model is built according to the gravity anomaly data in the range of selection area；
Step 2, vertical gravity gradiometry and exact position measurement, meter are carried out in the Point-mass Model grid that step 1 is built
Calculate the gravity anomaly and 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, determine 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
The interior multiple buried depth values of selection, Point-mass Model is resolved according to buried depth value one by one, recovers selection area with calculation result
In the range of non-grid midpoint gravity anomaly data and disturbing gravity vertical gradient in Earth ' data, restoration errors are counted, until point mass
Depth corresponding to all nodes completes Point-mass Model resolving one by one in the range of buried depth, obtains all nodes and corresponds to depth
Point-mass Model restoration errors；
Step 5, the Point-mass Model restoration errors to acquisition carry out lateral comparison, determine the depth corresponding to minimum restoring error
Degree, the as optimal buried depth of Shallow High Resolution point mass.
2. the optimal buried depth of Point-mass Model middle-shallow layer high-resolution point mass according to claim 1 determines method,
It is characterized in that：Step 1 specifically comprises the following steps：
Step 1.1, the mean gravity riod data using each 1 ° × 1 ° grid of low-order bit Modulus Model calculatingObtain residual
Poor observation：Solve 1 ° × 1 ° point mass M1As first group of point mass；
Step 1.2, the mean gravity riod with each 20 ' × 20 ' grid of potential coefficient model calculatingWith 1 ° × 1 ° point matter
Measure M1Calculate average abnormalObtain residual error observation：
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Solve 20 ' × 20 ' point mass M2As second group of point mass；
Step 1.3, the mean gravity riod with each 5 ' × 5 ' grid of potential coefficient model calculatingWith first group, second group
Point mass calculates average exception respectivelyObtain residual error observation：
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,
Solve 5 ' × 5 ' point mass M3As the 3rd group of point mass.
3. the optimal buried depth of Point-mass Model middle-shallow layer high-resolution point mass according to claim 1 determines method,
It is characterized in that：The gravity anomaly at each 1 ' × 1 ' grid midpoint is calculated in the step 2 with potential coefficient modelAnd disturbance
Vertical gradient of gravity
4. the optimal buried depth of Point-mass Model middle-shallow layer high-resolution point mass according to claim 2 determines method,
It is characterized in that：The step 4 specifically includes following content：
Step 4.1, calculated respectively in Shallow High Resolution Point-mass Model grid with first group, second group, the 3rd group of point mass
Point gravity anomalyAnd disturbing gravity vertical gradient in Earth '
Residual error observation：
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Combined by two kinds of residual error observations and form vector：
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Step 4.2, the buried depth scope according to determined by step 3, each node depth value in the range of, according to a most young waiter in a wineshop or an inn
Multiplication resolves the point mass M corresponding to all node buried depths of solving equations4；
Step 4.3, by point mass M corresponding to each node buried depth4Slicing fully mechanized face is formed with deep layer point mass, is recovered
The gravity anomaly data at non-Shallow High Resolution Point-mass Model grid midpoint and disturbing gravity hang down in the range of the selection area of ground
Vertical ladder degrees of data, it is poor to make with the actual observed value at measuring point, and the error that is restored simultaneously counts.
5. the optimal buried depth of Point-mass Model middle-shallow layer high-resolution point mass according to claim 4 determines method,
It is characterized in that：Recover in the step 4.3 in the range of the selection area of 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, nmaxAnd nlayerThe exponent number of low order bit model and the number of plies of residual error point mass are represented respectively, R represents radius of sphericity, Potential coefficient model corresponding to expression, ρ represent the earth's core to footpath,Represent i-th of ground gravity abnormity point place
The earth's core radius of sphere, rijThe distance between i-th of ground gravity abnormity point and j-th point mass are represented, K represents point mass
Number, M represent the vector being made up of K point mass, and a represents terrestrial equator radius, MijRepresent i-th layer of j-th of point mass.
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