CN103984015A - Potential field separation method and potential field separation system based on forward coefficient filtering - Google Patents

Potential field separation method and potential field separation system based on forward coefficient filtering Download PDF

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CN103984015A
CN103984015A CN201410230416.2A CN201410230416A CN103984015A CN 103984015 A CN103984015 A CN 103984015A CN 201410230416 A CN201410230416 A CN 201410230416A CN 103984015 A CN103984015 A CN 103984015A
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potential field
underground space
coefficient
filter
grid
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CN103984015B (en
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荆磊
杨亚斌
陆桂福
郜晓亮
陈亮
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Institute of Geophysical and Geochemical Exploration of CAGS
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Institute of Geophysical and Geochemical Exploration of CAGS
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Abstract

The invention relates to a potential field separation method and a potential field separation system, in particular to a potential field separation method and a potential field separation system based on forward coefficient filtering. The potential field separation method based on forward coefficient filtering includes the steps that a corresponding forward coefficient filter is constructed according to a forward coefficient obtained in the three-dimensional forward process and a horizontal scale of a scheduled target model; after the forward coefficient filter filters a potential field abnormal signal, potential fields of a model proximately the same as a scheduled target in size in different depth layers are obtained, and a relatively obvious corresponding relation of a potential field separation result and a field source depth can be obtained due to the fact that the filter has depth meaning. The forward coefficient filter used in the method is built through the forward coefficient with a certain depth, so that the filtering result can correspond to the depth of the corresponding forward coefficient, and remarkable physical significance is achieved.

Description

Potential field separation method and potential field piece-rate system based on just drilling coefficient filtering
Technical field
The present invention relates to a kind of potential field separation method and potential field piece-rate system, particularly a kind of potential field separation method and potential field piece-rate system based on just drilling coefficient filtering.
Background technology
Potential field exploration is main by extract the local anomaly relevant with objective body from potential field anomaly, to find scale, form and the buried depth of plastid unevenly.Potential field anomaly has comprised the effect that all anomalous bodys cause from earth's surface to deep, so insensitive to the degree of depth of field source.The division in the heavy magnetic field of different depth can improve the vertical resolution in heavy magnetic field, and tool is of great significance.In pseudodensity inverting, the accuracy of potential field separation is one of basis of pseudodensity inverting accuracy.
The explanation of potential field data is conventionally regarded real gravity anomaly by regional anomaly and local anomaly as and is formed.Regional anomaly refers to the gravity anomaly being caused by wider, the relatively dark geologic agent of distribution range; Local anomaly refers to than the little research object of areal geology factor scope as rock mass, ore body etc.Conventional potential field separation method comprises window technique, upward continuation method, Multiscale Wavelet Decomposition method etc., the application prerequisite of these methods is different extremely there are differences in " frequency ", therefore can adopt the method based on filtering that the discrepant frequency of this tool is carried out to separation, and difference is larger, separated effect is better.Window technique, the regional anomaly obtaining by the method and residual anomaly are as " basic data " of qualitative interpretation, and the key of the method is choosing of window size.Upward continuation method, is greater than the abnormal rate of decay principle in deep according to the rate of decay of superficial part exception response, reaches the object of outstanding deep off-note, because it is low-pass filter, can not well show the anomalous body feature of a certain degree of depth.In addition also have Multiscale Wavelet Decomposition, wavelet decomposition can be meticulous decomposites the abnormal of different frequency bands, and its weak point is that filtering result lacks corresponding physical significance.In addition, the corresponding relation between these separation methods and the field source degree of depth not obvious, is difficult to obtain the potential field anomaly that objective body causes at the different depth layer of the underground space.
Summary of the invention
The invention provides a kind of potential field separation method and potential field piece-rate system based on just drilling coefficient filtering, solved corresponding relation unconspicuous technical matters between separation method and the field source degree of depth in prior art.
A kind of potential field separation method based on just drilling coefficient filtering of the present invention, comprises the following steps:
Step 1, definition sizing grid and mesh spacing, according to Meshing Method, by underground space layering, and the transverse and longitudinal number of the every one deck online of definite described underground space lattice;
Step 2, the size of objective body and mesh spacing, set up model dimension wave filter Q on the estimation model;
Step 3, according to the sizing grid of definition in grid Forward Formula and step 1, calculate underground space different layers corresponding just drill coefficient Q p, and according to the described coefficient Q that just drilling pset up bandpass filter F p1; The bandpass filter sum that described underground space different layers is corresponding is 0, i.e. Σ F p1=0,1<p<P, P is the number of plies that the described underground space is divided, p is each layer that the described underground space is divided;
Step 4, according to described bandpass filter and described model dimension wave filter, what build each layer of the underground space just drills coefficient filter, is describedly just drilling the convolution that coefficient filter is described bandpass filter and described model dimension wave filter;
Step 5, obtains the original potential field abnormal signal of the described underground space, adopts the described coefficient filter of just drilling to carry out filtering to described original potential field abnormal signal, obtains the potential field separating resulting of each layer of the underground space.
Further, described step 5 is specially: described original potential field abnormal signal is expanded to limit and obtain expanding the potential field anomaly signal behind limit, adopt the described potential field anomaly signal of coefficient filter after to described expansion limit of just drilling to carry out filtering and generate filtering result, and to obtaining the potential field separating resulting of each layer of the underground space after described filtering result cissing.
Further, in step 1, by the transverse and longitudinal spacing of grid data and self-defining grid height, determine sizing grid; Align with grid data in the horizontal center of described grid.
Further, in step 2, described model dimension wave filter Q modelbe specially:
Wherein, q=(A * B)/(4a * b), A is the length of described scheduled target body in X-axis, B is the length of described scheduled target body in Y-axis, a be described mesh spacing in X-axis numerical value 1/2, b be described mesh spacing on y axle numerical value 1/2.
Further, in step 3, the described coefficient Q that just drilling pcomputing formula be:
Q p ( mp , np ) = G &Sigma; i = 1 2 &Sigma; j = 1 2 &Sigma; k = 1 2 ( - 1 ) i + j + k [ &xi; i l n ( &eta; j + r i , j , k ) + &eta; j ln ( &xi; i + r i , j , k ) + &zeta; k tan - 1 &zeta; k r i , j , k &xi; i &eta; j ]
, wherein, G is universal gravitational constant, m and n are the transverse and longitudinal number of the every one deck online of described underground space lattice; ξ 1, ξ 2be respectively the end points coordinate of described grid in X-direction; η 1, η 2be respectively the end points coordinate of described grid in Y direction; ζ 1, ζ 2be respectively the end points coordinate of described grid in Z-direction, p is each layer that the described underground space is divided;
ξ 1=(mp-m-1/2)*Δx;
ξ 2=(mp-m+1/2)*Δx;
η 1=(np-n-1/2)*Δy;
η 2=(np-n+1/2)*Δy;
ζ 1=h p-z, ζ 2=h p+ l-z, z is the elevation of gravity inspection surface, h pthe end face degree of depth for every layer of grid;
r i , j , k = [ &xi; i 2 + &eta; j 2 + &zeta; k 2 ] 1 2 .
Further, in step 3, described bandpass filter F p1(p)=Q p-Q p+1, wherein, 1≤p≤P-1, P is the number of plies that the described underground space is divided, p is each layer that the described underground space is divided.
A potential field piece-rate system based on just drilling coefficient filtering, comprises that underground space hierarchical block, model dimension wave filter build module, bandpass filter and build module, just drill coefficient filter and build module and potential field separation module,
Described underground space hierarchical block is used for defining sizing grid and mesh spacing, and according to Meshing Method, by underground space layering, determines the transverse and longitudinal number of the every one deck online of described underground space lattice;
Described model dimension wave filter builds module and is used for size and the mesh spacing of objective body on the estimation, sets up model dimension wave filter Q model;
Described bandpass filter builds mould for according to grid Forward Formula and described sizing grid, calculate underground space different layers corresponding just drill coefficient Q p, and according to the described coefficient Q that just drilling p, set up bandpass filter F p1;
The described coefficient filter of just drilling builds module for according to described bandpass filter and described model dimension wave filter, what build each layer of the underground space just drills coefficient filter, is describedly just drilling the convolution that coefficient filter is described bandpass filter and described model dimension wave filter;
Described potential field separation module obtains expanding the potential field anomaly signal behind limit for the described original potential field abnormal signal obtaining is expanded to limit, and adopt the described potential field anomaly signal of coefficient filter after to described expansion limit of just drilling to carry out filtering and obtain filtering result, to obtaining the potential field separating resulting of each layer of the underground space after described filtering result cissing.
Further, described model dimension wave filter Q modelbe specially:
Wherein, q=(A * B)/(4a * b), A is the length of described scheduled target body in X-axis, B is the length of described scheduled target body in Y-axis, a be described mesh spacing in X-axis numerical value 1/2, b be described mesh spacing on y axle numerical value 1/2.
Further, the described coefficient Q that just drilling pcomputing formula be:
Q p ( mp , np ) = G &Sigma; i = 1 2 &Sigma; j = 1 2 &Sigma; k = 1 2 ( - 1 ) i + j + k [ &xi; i l n ( &eta; j + r i , j , k ) + &eta; j ln ( &xi; i + r i , j , k ) + &zeta; k tan - 1 &zeta; k r i , j , k &xi; i &eta; j ]
, wherein, G is universal gravitational constant, m and n are the transverse and longitudinal number of the every one deck online of described underground space lattice; ξ 1, ξ 2be respectively the end points coordinate of described grid in X-direction; η 1, η 2be respectively the end points coordinate of described grid in Y direction; ζ 1, ζ 2be respectively the end points coordinate of described grid in Z-direction, p is each layer that the described underground space is divided;
ξ 1=(mp-m-1/2)*Δx;
ξ 2=(mp-m+1/2)*Δx;
η 1=(np-n-1/2)*Δy;
η 2=(np-n+1/2)*Δy;
ζ 1=h p-z, ζ 2=h p+ l-z, z is the elevation of gravity inspection surface, h pthe end face degree of depth for every layer of grid;
r i , j , k = [ &xi; i 2 + &eta; j 2 + &zeta; k 2 ] 1 2 .
Further, described bandpass filter F p1(p)=Q p-Q p+1, wherein, 1≤p≤P-1, P is the number of plies that the described underground space is divided, p is each layer that the described underground space is divided.
Beneficial effect of the present invention is: the present invention proposes a kind of potential field separation method based on just drilling coefficient filtering, first on the estimation the size of objective body and three-dimensional are just being drilled the cube Forward Formula obtaining in process, structure is just being drilled coefficient filter accordingly, adopt this just drilling coefficient filter and carry out approximately after filtering obtaining the potential field that the model identical with corresponding scheduled target body size produces at different depth layer, therefore can make the result of potential field separation obtain relative obvious corresponding relation with the field source degree of depth; And in potential field separation method of the present invention, use just drill coefficient filter by certain depth just drill coefficients to construct, therefore filtering result is corresponding with the corresponding degree of depth of just drilling coefficient, there is obvious physical significance.
Accompanying drawing explanation
Fig. 1 is the schematic flow sheet of potential field separation method of the present invention;
Fig. 2 is single grid forward model schematic diagram;
Fig. 3 is the structural representation of invention potential field piece-rate system;
Fig. 4 is the potential field anomaly figure that the present embodiment relates to related area;
Fig. 5~Fig. 7 is the layering potential field separating effect figure in the related area of the present embodiment.
Embodiment
Below in conjunction with accompanying drawing, principle of the present invention and feature are described, example, only for explaining the present invention, is not intended to limit scope of the present invention.
As shown in Figure 1, be a kind of schematic flow sheet based on just drilling the potential field separation method of coefficient filtering of the present embodiment, wherein need to utilize the grid Forward Formula obtaining based on the process of just drilling, described grid Forward Formula derivation is as follows:
If the density of right prism body is ρ (ξ, η, ζ), as shown in Figure 2, prism Density inhomogeneity, the end face length of prism, width are respectively 2a and 2b, and the end face degree of depth is h, and the vertical thickness of prism is l.Making (ξ, η, ζ) is the coordinate of any body unit dv=d ξ d η d ζ in prism, and this mass unit dm=ρ (ξ, η, ζ) dv in the gravitation position of arbitrfary point, space (x, y, z) is
dV = G dm r = G&rho; ( &xi; , &eta; , &zeta; ) d&xi;d&eta;d&zeta; r - - - ( 1 )
G universal gravitational constant in formula, its value is 6.67 * 10 -11m 3/ (kgs 2);
r = [ ( x - &xi; ) 2 + ( y - &eta; ) 2 + ( z - &zeta; ) 2 ] 1 2 , For the distance of mass-element to arbitrfary point, space.
To obtaining the gravity anomaly of Density inhomogeneity prism after the integration of formula (1), be:
V z ( x , y , z ) = G &Integral; h h + l &Integral; - a a &Integral; - b b &rho; ( &xi; , &eta; , &zeta; ) &zeta; [ ( x - &xi; ) 2 + ( y - &eta; ) 2 + ( z - &zeta; ) 2 ] 3 2 d&xi;d&eta;d&zeta; - - - ( 2 )
When h and l are fixedly time, and a and b be during much larger than l, and formula (2) becomes the gravity anomaly formula of Density inhomogeneity tabular body:
V z ( x , y , z ) = &Integral; - a a &Integral; - b b &rho; ( &xi; , &eta; ) Q ( x - &xi; , y - &eta; ) d&xi;d&eta; - - - ( 3 )
Wherein:
Q ( x - &xi; , y - &eta; ) = G &Integral; h h + l &zeta;d&zeta; [ ( x - &xi; ) 2 + ( y - &eta; ) 2 + ( z - &zeta; ) 2 ] 3 2
According to the definition of convolution, above-mentioned formula can be decomposed into the convolution of two signals, i.e. V z=ρ * Q.
Wherein: the density attributes that ρ is a certain sheaf space, is called model signals; It is that h, length are the gravity Forward Formula of l, the density perpendicular line volume elements that is 1 that Q can regard the degree of depth as, is called depth filtering device.With reference to this decomposition method, can build the coefficient filter of just drilling of the present invention, by the described coefficient filter of just drilling, potential field abnormal signal is carried out to separation, obtain the separating resulting of each layer of the underground space.
When heavy magnetic three-dimensional model is just being drilled, can by mesh spacing Δ x, Δ y and thickness l subdivision, be equal-sized prism by the underground space, the underground space be divided into P layer; By each prism, give corresponding density attributes and form three-dimensional model; Calculate the horizontal center superposition of pendulum point and prism; The end face degree of depth of every layer of prism is h p; The gravity anomaly that three-dimensional model produces on earth's surface is:
V z ( mp , np ) = &Sigma; p = 1 P &Sigma; m = 1 M &Sigma; n = 1 N &rho; p ( m , n ) Q p ( mp - m , np - n ) - - - ( 4 )
In formula: M and N are the number of every one deck prism, z is the elevation of gravity inspection surface;
ξ 1=(mp-m-1/2)*Δx ξ 2=(mp-m+1/2)*Δ
η 1=(np-n-1/2)*Δy η 2=(np-n+1/2)*Δy
ζ 1=h p-z ζ 2=h p+l-z r i , j , k = [ &xi; i 2 + &eta; j 2 + &zeta; k 2 ] 1 2
Q p ( mp , np ) = G &Sigma; i = 1 2 &Sigma; j = 1 2 &Sigma; k = 1 2 ( - 1 ) i + j + k [ &xi; i l n ( &eta; j + r i , j , k ) + &eta; j ln ( &xi; i + r i , j , k ) + &zeta; k tan - 1 &zeta; k r i , j , k &xi; i &eta; j ]
, Q pbe the grid Forward Formula using in the inventive method, just drilling coefficient Q pcomputing formula.
As shown in Figure 1, for potential field separation method of the present invention comprises the following steps:
(1) according to the transverse and longitudinal spacing of grid data (X-axis is long is 2a, and Y-axis is long is 2b) and self-defining grid height l, determining sizing grid, and with this grid, the underground space is divided into P layer, aligns with grid data in the horizontal center of described grid; Determine transverse and longitudinal number m, the n of the every one deck online of described underground space lattice;
(2) size (long in X-axis is 2a, and long in Y-axis is 2b) of the size of objective body (long in X-axis is A, and long in Y-axis is B) and mesh spacing on the estimation, sets up model dimension wave filter Q model(m, n), m wherein, the transverse and longitudinal number of the every one deck online of underground space lattice described in n; When-int (A/4a)≤m≤int (A/4a), during-int (B/4b)≤n≤int (B/4b), described model dimension wave filter Q model(m, n)=1/int (q), wherein, q=(A * B)/(4a * b), A is the length of described scheduled target body in X-axis, B is the length of described scheduled target body in Y-axis, a be described mesh spacing in X-axis numerical value 1/2, b be described mesh spacing on y axle numerical value 1/2; When m and n be not during in the above scope, described Q model(m, n)=0;
(3) according to the sizing grid of definition in the grid Forward Formula of aforementioned derivation and step (1), calculate underground space different layers corresponding just drill coefficient Q p, and according to just drilling coefficient Q pset up bandpass filter F p1; The bandpass filter sum that underground space different layers is corresponding is 0, i.e. Σ F p1=0,1<p<P, the bandpass filter of described foundation is F p1(p)=Q p-Q p+1, wherein, 1≤p≤P-1, P is the number of plies that the described underground space is divided, p is each layer that the described underground space is divided;
(4), according to described bandpass filter and model dimension wave filter, what build each layer of the underground space just drills coefficient filter F p, the described convolution that coefficient filter is bandpass filter and model dimension wave filter, the i.e. F of just drilling p=F p1* Q model.
(5) obtain the original potential field abnormal signal of the described underground space, and described original potential field abnormal signal is expanded to limit obtain expanding the potential field anomaly signal behind limit; Adopt the described coefficient filter F that just drilling ppotential field anomaly signal behind described expansion limit is carried out to filtering and obtain filtering result, and to obtaining each layer of the underground space at the potential field separating resulting on earth's surface after described filtering result cissing.
In filtering of the present invention, also comprise and stablize downward continuation wave filter, downward continuation is after potential field decomposition step, object is to make the anomalous body of underground certain one deck under the potential field of earth's surface generation, be extended down to the top of anomalous body, the potential field value at every one deck abnormal layer top can be put together and is drawn as sectional view like this, convenient longitudinally contrast.
The coefficient Q that just drilling of the present invention prepresent a kind of low-pass filter, its filtering result can weaken frequency in raw bits field information higher than the radio-frequency component of this wave filter, outstanding remaining low-frequency component.Based on this, can be by Q p-Q p+1as bandpass filter F p1.Just drilling in process and also comprising and determine scheduled target body Model signal, will after model signals energy normalized, obtain model dimension wave filter Q model.By bandpass filter F p1with model signals wave filter Q modelafter convolution, obtain just drilling coefficient filter F p, its filtering result has been given prominence to p layer and has been had the anomalous body of scheduled target body characteristics in the potential field of ground generation.When model signals is consistent with objective body signal, separating effect is best.
Because wave filter is slower with the decay of lateral separation, spatial resolution is low, and therefore can choose applicable threshold values directly blocks or be multiplied by suitable attenuation function.
The present embodiment also comprises a kind of potential field piece-rate system based on just drilling coefficient filtering, as shown in Figure 3, described potential field piece-rate system comprises that underground space hierarchical block, model dimension wave filter build module, bandpass filter and build module, just drill coefficient filter and build module and potential field separation module
Described underground space hierarchical block is used for defining sizing grid and mesh spacing, according to Meshing Method, and by underground space layering, and the transverse and longitudinal number of the every one deck online of definite described underground space lattice;
Described model dimension wave filter builds module and is used for size and the mesh spacing of objective body on the estimation, sets up model dimension wave filter Q model;
Described bandpass filter builds module for according to grid Forward Formula and described sizing grid, calculate underground space different layers corresponding just drill coefficient Q p, and according to just drilling coefficient Q pset up bandpass filter F p1;
The described coefficient filter of just drilling builds module for according to described bandpass filter and described model dimension wave filter, what build each layer of the underground space just drills coefficient filter, is describedly just drilling the convolution that coefficient filter is described bandpass filter and described model dimension wave filter;
Described potential field separation module obtains expanding the potential field anomaly signal behind limit for the described original potential field abnormal signal obtaining is expanded to limit, and adopt the described potential field anomaly signal of coefficient filter after to described expansion limit of just drilling to carry out filtering and obtain filtering result, to obtaining the potential field separating resulting of each layer of the underground space after described filtering result cissing.
With embodiment, explain below the actual effect of potential field separation method of the present invention.The present embodiment data are the actual measurement potential field data in somewhere, and mesh coordinate transverse and longitudinal spacing is equal, and data coordinates is unit distance after treatment.The 3D grid spacing that structure is just being drilled coefficient filter is 1 * 1 * 3.The moving average filter that the model signals wave filter that filtering is selected is 3 * 3.
The raw bits field pattern of Tu4Wei this area.Fig. 5~7 are layering filtering result figure, be the potential field separating effect figure of different depth, the map of the different depth showing in figure be by different depth just drill the resulting result of coefficient filter filtering, reacted the gravity separation result that the geologic body shape of this area's different depth produces on earth's surface.
Fig. 5 be 1~3 unit depth just drill the resulting potential field separating resulting of coefficient filter filtering, reflected the gravity separation result that geologic body shape corresponding to 1~3 of this area unit depth produces on earth's surface; Fig. 6 be 3~6 unit depth just drill the resulting potential field separating resulting of coefficient filter filtering, reflected the gravity separation result that geologic body shape corresponding to 3~6 of this areas unit depth produces on earth's surface; Fig. 7 be 6~9 unit depth just drill the resulting potential field separating resulting of coefficient filter filtering, reflected the gravity separation result that geologic body shape corresponding to 6~9 of this areas unit depth produces on earth's surface.
The present invention proposes a kind of potential field separation method based on just drilling coefficient filtering, first on the estimation the size of objective body and three-dimensional are just being drilled the cube Forward Formula obtaining in process, structure is just being drilled coefficient filter accordingly, adopt this just drilling coefficient filter and carry out approximately after filtering obtaining the potential field that the model identical with corresponding scheduled target body size produces at different depth layer, therefore can make the result of potential field separation obtain relative obvious corresponding relation with the field source degree of depth; And in potential field separation method of the present invention, use just drill coefficient filter by certain depth just drill coefficients to construct, therefore filtering result is corresponding with the corresponding degree of depth of just drilling coefficient, there is obvious physical significance.
The foregoing is only preferred embodiment of the present invention, in order to limit the present invention, within the spirit and principles in the present invention not all, any modification of doing, be equal to replacement, improvement etc., within all should being included in protection scope of the present invention.

Claims (10)

1. the potential field separation method based on just drilling coefficient filtering, comprises the following steps:
Step 1, definition sizing grid and mesh spacing, according to Meshing Method, by underground space layering, and the transverse and longitudinal number of the every one deck online of definite described underground space lattice;
Step 2, the size of objective body and mesh spacing, set up model dimension wave filter Q on the estimation model;
Step 3, according to the sizing grid of definition in grid Forward Formula and step 1, calculate underground space different layers corresponding just drill coefficient Q p, and according to just drilling coefficient Q pset up bandpass filter F p1; The bandpass filter sum that described underground space different layers is corresponding is 0, i.e. Σ F p1=0,1<p<P, P is the number of plies that the described underground space is divided, p is each layer that the described underground space is divided;
Step 4, according to described bandpass filter and described model dimension wave filter, what build each layer of the underground space just drills coefficient filter, is describedly just drilling the convolution that coefficient filter is described bandpass filter and described model dimension wave filter;
Step 5, obtains the original potential field abnormal signal of the described underground space, adopts the described coefficient filter of just drilling to carry out filtering to described original potential field abnormal signal, obtains the potential field separating resulting of each layer of the underground space.
2. potential field separation method according to claim 1, it is characterized in that: described step 5 is specially: described original potential field abnormal signal is expanded to limit and obtain expanding the potential field anomaly signal behind limit, adopt the described potential field anomaly signal of coefficient filter after to described expansion limit of just drilling to carry out filtering and generate filtering result, and to obtaining the potential field separating resulting of each layer of the underground space after described filtering result cissing.
3. potential field separation method according to claim 1, is characterized in that: in step 1, by the transverse and longitudinal spacing of grid data and self-defining grid height, determine sizing grid; Align with grid data in the horizontal center of described grid.
4. potential field separation method according to claim 1, is characterized in that: in step 2, and described model dimension wave filter Q modelbe specially:
Wherein, q=(A * B)/(4a * b), A is the length of described scheduled target body in X-axis, B is the length of described scheduled target body in Y-axis, a be described mesh spacing in X-axis numerical value 1/2, b be described mesh spacing on y axle numerical value 1/2.
5. potential field separation method according to claim 1, is characterized in that: in step 3, and the described coefficient Q that just drilling pcomputing formula be:
Q p ( mp , np ) = G &Sigma; i = 1 2 &Sigma; j = 1 2 &Sigma; k = 1 2 ( - 1 ) i + j + k [ &xi; i l n ( &eta; j + r i , j , k ) + &eta; j ln ( &xi; i + r i , j , k ) + &zeta; k tan - 1 &zeta; k r i , j , k &xi; i &eta; j ]
Wherein, G is universal gravitational constant, and m and n are the transverse and longitudinal number of the every one deck online of described underground space lattice; ξ 1, ξ 2be respectively the end points coordinate of described grid in X-direction; η 1, η 2be respectively the end points coordinate of described grid in Y direction; ζ 1, ζ 2be respectively the end points coordinate of described grid in Z-direction, p is each layer that the described underground space is divided;
ξ 1=(mp-m-1/2)*Δx;
ξ 2=(mp-m+1/2)*Δx;
η 1=(np-n-1/2)*Δy;
η 2=(np-n+1/2)*Δy;
ζ 1=h p-z, ζ 2=h p+ l-z, z is the elevation of gravity inspection surface, h pthe end face degree of depth for every layer of grid;
r i , j , k = [ &xi; i 2 + &eta; j 2 + &zeta; k 2 ] 1 2 .
6. potential field separation method according to claim 5, is characterized in that: in step 3, and described bandpass filter F p1(p)=Q p-Q p+1, wherein, 1≤p≤P-1, P is the number of plies that the described underground space is divided, p is each layer that the described underground space is divided.
7. the potential field piece-rate system based on just drilling coefficient filtering, is characterized in that: comprise that underground space hierarchical block, model dimension wave filter build module, bandpass filter and build module, just drill coefficient filter and build module and potential field separation module,
Described underground space hierarchical block is used for defining sizing grid and mesh spacing, and according to Meshing Method, by underground space layering, determines the transverse and longitudinal number of the every one deck online of described underground space lattice;
Described model dimension wave filter builds module and is used for size and the mesh spacing of objective body on the estimation, sets up model dimension wave filter Q model;
Described bandpass filter builds mould for according to grid Forward Formula and described sizing grid, calculate underground space different layers corresponding just drill coefficient Q p, and according to the described coefficient Q that just drilling p, set up bandpass filter F p1;
The described coefficient filter of just drilling builds module for according to described bandpass filter and described model dimension wave filter, what build each layer of the underground space just drills coefficient filter, is describedly just drilling the convolution that coefficient filter is described bandpass filter and described model dimension wave filter;
Described potential field separation module obtains expanding the potential field anomaly signal behind limit for the described original potential field abnormal signal obtaining is expanded to limit, and adopt the described potential field anomaly signal of coefficient filter after to described expansion limit of just drilling to carry out filtering and obtain filtering result, to obtaining the potential field separating resulting of each layer of the underground space after described filtering result cissing.
8. potential field piece-rate system according to claim 7, is characterized in that: described model dimension wave filter Q modelbe specially:
Wherein, q=(A * B)/(4a * b), A is the length of described scheduled target body in X-axis, B is the length of described scheduled target body in Y-axis, a be described mesh spacing in X-axis numerical value 1/2, b be described mesh spacing on y axle numerical value 1/2.
9. potential field piece-rate system according to claim 7, is characterized in that: the described coefficient Q that just drilling pcomputing formula be:
Q p ( mp , np ) = G &Sigma; i = 1 2 &Sigma; j = 1 2 &Sigma; k = 1 2 ( - 1 ) i + j + k [ &xi; i ln ( &eta; j + r i , j , k ) + &eta; j ln ( &xi; i + r i , j , k ) + &zeta; k tan - 1 &zeta; k r i , j , k &xi; i &eta; j ]
, wherein, G is universal gravitational constant, m and n are the transverse and longitudinal number of the every one deck online of described underground space lattice; ξ 1, ξ 2be respectively the end points coordinate of described grid in X-direction; η 1, η 2be respectively the end points coordinate of described grid in Y direction; ζ 1, ζ 2be respectively the end points coordinate of described grid in Z-direction, p is each layer that the described underground space is divided;
ξ 1=(mp-m-1/2)*Δx;
ξ 2=(mp-m+1/2)*Δx;
η 1=(np-n-1/2)*Δy;
η 2=(np-n+1/2)*Δy;
ζ 1=h p-z, ζ 2=h p+ l-z, z is the elevation of gravity inspection surface, h pthe end face degree of depth for every layer of grid;
r i , j , k = [ &xi; i 2 + &eta; j 2 + &zeta; k 2 ] 1 2 .
10. potential field piece-rate system according to claim 9, is characterized in that: described bandpass filter F p1(p)=Q p-Q p+1, wherein, 1≤p≤P-1, P is the number of plies that the described underground space is divided, p is each layer that the described underground space is divided.
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