CN105608338B - The geostatistics method that variogram for seamount space surface data is simulated - Google Patents
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Abstract
The invention discloses a kind of geostatistics methods that the variogram for seamount space surface data is simulated, and define 3D Surface regionalized variables；It is calculated using based on the variogram of " apart from the gradient " or " apart from relative water depth "：Change journey is fitted to the continuous function of the gradient；Carry out KRIGING valuations.
Description
Technical field
The present invention relates to geostatistics, variogram, and Marine Geology, Quantitative Assessment of Mineral Resources field are a passes
In " variogram " of spatial data and the new calculation method of geostatistics, it is mainly used for the variation of seamount space surface data
Functional simulation and geostatistics interpolation.
Background technology
Currently, being that model defines three-dimensional surface (3D-Surface) compartmentalization by the mineral resources data of seamount surface output
Variable：Continuous value on two-dimentional geographical coordinate, the geographical coordinate points of only unique value only correspond to third dimension space on three dimensions
Unique value, i.e. bathymetric data longitudinal upper continuous value unlike 3d space data, only unique value in certain geo point；In addition
The parameter distribution of three-dimensional surface spatially is not by direction controlling, only by the opposite variation control of third dimension space；Traditional variation letter
Number calculating method is no longer appropriate for this kind of spatial data；New variogram computational methods are needed to be adapted therewith.
Traditional " distance-direction " variogram, is not suitable for using seamount surface mineral resources as the 3D- of data model
Surface spatial datas because seamount mineral resources data distribution is by direction controlling, and are controlled by the depth of water.
Traditional geostatistics (KRIGING) estimation method, is also no longer appropriate for the space parallax of 3D-Surface spatial datas
Value.
Define 3D-Surface regionalized variables；Three-dimensional surface area variable has its particularity, leads to conventional method not
Can be effective, to 3D-Surface regionalized variables such as seamount space surface data, variogram calculating is carried out, it can not be into
Row KRIGING valuations.
Variogram concept and computational methods of this case definition based on " distance-gradient " or " distance-relative water depth "；This
Model method is based on the variogram in " distance-direction " than tradition, is more suitable for the variation letter of 3D-Surface regionalized variables
Number calculates.
The depth of water is only treated as longitudinal coordinate by KRIGING valuations, conventional method, and this case sees relative water depth or the gradient point
At point to variational independent variable.
Invention content
The purpose of the present invention is in view of the deficiencies of the prior art, propose a kind of variation letter for seamount space surface data
The quasi- geostatistics method of digital-to-analogue.
Purpose to realize the present invention, the present invention is achieved by the following scheme：
The geostatistics method that a kind of variogram for seamount space surface data is simulated, using following formula into
Row calculates：
Assuming that there is n data information point Z (xi, yi, dpi), i=1 ..., n
As head point Z (xh, yh, dph) determine, according to certain gradient and apart from tail point is searched, as follows：
Space length：ds′ht=sqart [(xh-xt)2+(yh-yt)2+(dph-dpt)2]
Horizontal distance：dsht=sqart [(xh-xt)2+(yh-yt)2] (3)
Since gradient calculating will use horizontal distance, use horizontal distance that space length is replaced to join as the measurement of distance
It counts, hereinafter involved distance refers both to horizontal distance.
The gradient：
N experimental point sharesA Gradient, ruling grade value gmax, minimum grade value gmin
By value of slope size, it is divided into three groups of equal frequency, is referred to as heavy grade gradient3 groups, middle gradient gradient2
Group and light grade gradient1 groups.The boundary gradient g of heavy grade group and middle gradient groupbig, point of light grade group and middle gradient group
Boundary's value of slope is gsmall
Point is carried out to searching by three groups of gradient principles：
It is identical that distance searches principle and document (Claytonet al., 1998), according to step-length lag distance and step-length
Tolerance lag tolerance search the point pair in particular step size；Last statistics step-length takes the average value in each group.
For determining distance ds and gradient g, N (ds, dp) a point pair is obtained, by formula (2) experiment with computing variogram；With
Corresponding distance ds, gradient g be average distance and mean inclination in the group respectively；It is achieved in that the distance-of three gradient groups
Become difference data, as shown in Fig. 5, Fig. 6 and Fig. 7：
Distance-variation two dimension scatter plot of three gradient groups is made, as shown in Figure 5；Then it is tried with artificial curve Preliminary Simulation
Test variogram；Finally, according to experiment variogram curve, variance c, block gold c are estimated0It is each group with change journey a, gradient g
Mean inclination.
Experiment variogram as shown in Figure 7 is grouped based on the gradient rather than is grouped based on direction；Fig. 5 is certain seamount richness
" distance-gradient " Experiment variogram figure of cobalt crusts thickness.
Three groups of mean inclinations are respectively 1.6 °, 5.8 °, 16.1 °, and corresponding change journey is respectively 7.5km, 5.5km and 4.5km,
Base station value is close to 1.0, block gold c0It is 0.0.
Journey will be become and be fitted to the continuous function of the gradient, the functional relation being fitted between the gradient-change journey with rectangular coordinate system,
Three groups of gradients of Experiment variogram and change journey (1.6,7.5), (5.8,5.5), (16.1,4.5) are projected into the gradient-change journey
In rectangular coordinate system, Fig. 8 is seen；As seen from the figure, become journey and the gradient substantially inversely.
The relationship being inversely proportional substantially due to becoming journey and the gradient, utilizes reciprocal functionIt is fallen using the extension of such as formula (6)
Function is counted to be fitted change journey-gradient function.
A is the change eikonal number using gradient g as independent variable, wherein a0, p be undetermined constant；As gradient g=0, change journey is a0+
p；When the gradient is very big, become journey close to a0；There are two undetermined constants for functional expression (6), only need two known points on function, energy
Constant a0, p, which is solved, to be come.We use two groups of data (g of heavy grade group gradient3 and light grade group gradient13,
a3), (g1, a1), it is substituted into formula (7) and obtains undetermined constant a0And p：
Formula (7), which is substituted into formula (6), must become journey-gradient analog function.
In order to examine the functional simulation effect, we are by one group of data (g of middle gradient group2, a2) substitute into formula (6) and formula
(7), it acquires the theoretical of middle gradient group and becomes journey a '2, then compare a '2And a2Relative error, judge become journey-gradient function mould
Quasi- effect；Or by this group of data (g2, a2) input functional expression (6) rectangular coordinate system, see Fig. 6, observe (g2, a2) whether fall
On becoming journey-gradient simulation curve, with this, the simulation effect for becoming journey-gradient function is judged.
For experiment Seamount Co-rich crust thickness data, by two groups of data (1.6,7.5) of heavy grade group and light grade group
(16.1,4.5) formula (6) is substituted into, a is acquired0=4.0, p=9.2；Become journey-gradient analog function into：
The curve of functional expression (8) is shown in Fig. 6；It regard the change journey of middle gradient group-Gradient (5.5,5.8) as Function Fitting again
The check point of effect, by the gradient 5.8 substitute into formula (8) theoretical changes journey 5.4, with experiment become journey 5.5 error be 0.1, relatively miss
Difference is 1.8%, and inspection result illustrates that functional simulation effect is pretty good.
(5.5,5.8) are put into and become journey-gradient rectangular coordinate system, it has been found that the point is fallen on theoretical curve substantially,
Change journey-gradient functional simulation effect is affirmed.
The extension reciprocal function for change journey-gradient that simulation is obtained, substitutes among the theoretical model of variogram；Here only
Spherical model function is selected to illustrate.
Formula (6) is substituted into formula (9) and obtains the theoretical variogram based on the distance-gradient, as shown in formula (10) formula.
Formula (10) does not consider nugget effect (nugget effect)；a0, p be undetermined constant, by the change of experiment variogram
Journey fitting obtains.
If it is considered that nugget effect, formula (10) becomes formula (11)
Covariance function can also be converted to：
Judge whether stochastic variable is steady using the method for normal distribution, logarithm normal distribution hypothesis testing；If research
Area's data fit normal distribution is regarded as not stringent random plateau region variable.Experiment variation letter can be carried out to it
Number calculates and Kriging estimations.
Using formula, the relative slope of landform between area grid node to be estimated is calculated, while also calculating erect-position information station
The gradient between 2 points pairs of position；Ruling grade, minimum grade, gradient mean value, the standard deviation of the gradient are extracted in statistical analysis, are the gradient
Grouping provides reference data；Bathymetric data is generally the high-precision bathymetric data of multi-beam Sonar Sounding instrument acquisition.
According to (5) formula, with reference to the statistical information of terrain slope, information erect-position is grouped by three groups of gradients.
Light grade group (gradient1) represents the search direction of substantially isobath；Intermediate (-)grade group (gradient2), generation
The search direction of compensation grade between table isobath and greatest gradient；Heavy grade group (gradient3) represents substantially terrain gradients
The search direction in direction.The change journey of wherein gradient1, gradient3, value of slope participate in " become journey-gradient " fitting of function,
Inspection data of the change journey, value of slope of gradient2 as fitting effect, verification become the fitting effect of journey-gradient function.
Variogram of the present invention for seamount space surface data is simulated, its advantage is that：Method demonstration in this case is answered
Cobalt bearing crust thickness for seamount Spatial outlier work in, successfully obtain experiment variogram, and extract become journey, base station,
The parameters such as block gold；Success has carried out Spatial outlier or simulation to the spatial distribution of two Seamount Co-rich crust thickness, to actual
Resource assessment provides foundation, obtains potential benefit.
Description of the drawings
In order to more clearly explain the embodiment of the invention or the technical proposal in the existing technology, to embodiment or will show below
There is attached drawing needed in technology description to be briefly described, it should be apparent that, the accompanying drawings in the following description is only this
Some embodiments of invention for those of ordinary skill in the art without creative efforts, can be with
Obtain other attached drawings according to these attached drawings.
Fig. 1 is the function of random variable of 3D systems.
Fig. 2 is the surfaces 3D function of random variable.
Fig. 3 is traditional variogram pair.
Fig. 4 is point to searching three groups of slope maps.
Fig. 5 is the experiment variogram 1 based on " distance-gradient ".
Fig. 6 is the experiment variogram 2 based on " distance-gradient ".
Fig. 7 is the experiment variogram 3 based on " distance-gradient ".
Fig. 8 be three testing sites (g, a) and the gradient-change journey functional simulation.
Specific implementation mode
Following will be combined with the drawings in the embodiments of the present invention, and technical solution in the embodiment of the present invention carries out clear, complete
Site preparation describes, it is clear that described embodiments are only a part of the embodiments of the present invention, instead of all the embodiments.It is based on
Embodiment in the present invention, it is obtained by those of ordinary skill in the art without making creative efforts every other
Embodiment shall fall within the protection scope of the present invention.
Embodiment：
It is the function of coordinate as shown in Figure 1, representing stochastic variable with Z, is expressed with Z (x, y, v), is typical three-dimensional seat
Vector function in mark system；For example, this stochastic variable can represent certain three-dimensional marine siteInterior salinity, in domainInterior appoints
Meaning, which is selected, determining salt angle value；The domain or random field of this typical three random variables, existing length, width,
Also there is thickness, i.e., it all can continuous value on tri- coordinate directions of z.
As shown in Fig. 2, regarding the cobalt bearing crust parameter of seamount ramped surfaces as stochastic variable, belong to the surfaces 3D stochastic variable
(3D Surface Random Variable) is expressed with Z (x, y, dp), and for test data, Z (x, y, dp) represents geography
The cobalt bearing crust thickness data on slope that position is (x, y), the depth of water is dp.
There is following property on the surfaces 3D stochastic variable Z (x, y, dp) in addition to the property for having usual stochastic variable：
(1) domainIt is some curved surface of 3d space, sees Fig. 2；
(2) when (x, y) is determined, dp only has unique value matching；
(3) desired value of stochastic variable Z (x, y, dp) does not change with the variation of position；Its spatial variability not only with
Distance dependent, it is also related to relative water depth Δ dp or gradient g, and independent of direction.
Since it is not 3D the or 2D stochastic variables of stricti jurise, then common variogram cannot be recycled to test
Its variogram is calculated with the method for fitting.Hereafter, it is proposed that a kind of its new suitable variogram experiment and fitting
Method.
It is similar to the hypothesis of stochastic variable stationarity to GSLIB, it is assumed that：
1. the surfaces 3D expectation of a random variable does not change with specific location and is changed；
2. the mean square deviation function of stochastic variable exists, and only related to space distance, relative water depth or the gradient, and with
Direction is unrelated.
Traditional variogram is defined as：" half of the point that distance-direction vector h is defined to the mean square deviation of (see Fig. 3 a) ",
Formula (1) can be used to express.
Corresponding, the surfaces 3D stochastic variable variogram is defined as：" the mean square deviation for the point pair that the distance-gradient defines
Half ", with formula (2) express.It is this kind of point pair shown in Fig. 3 b, if delineating relationship a little pair with right angled triangle, when
After distance ds is determined, relative water depth dp, gradient g need to only know one, and right angled triangle determines that, and put the space between
Relationship also just can determine that.Dp and g should be of equal value, only discuss that the variogram based on " distance-gradient (ds-g) " is real herein
It tests and analogy method.
It is calculated using following formula：
Assuming that there is n data information point Z (xi, yi, dpi), i=1 ..., n
As head point Z (xh, yh, dph) determine, according to certain gradient and apart from tail point is searched, as follows：
Space length：ds′ht=sqart [(xh-xt)2+(yh-yt)2+(dph-dpt)2]
Horizontal distance：dsht=sqart [(xh-xt)2+(yh-yt)2] (3)
Since gradient calculating will use horizontal distance, use horizontal distance that space length is replaced to join as the measurement of distance
It counts, hereinafter involved distance refers both to horizontal distance.
The gradient：
N experimental point sharesA Gradient, ruling grade value gmax, minimum grade value gmin
By value of slope size, it is divided into three groups of equal frequency, is referred to as heavy grade gradient3 groups, middle gradient gradient2
Group and light grade gradient1 groups.The boundary gradient g of heavy grade group and middle gradient groupbig, point of light grade group and middle gradient group
Boundary's value of slope is gsmall
Point is carried out to searching by three groups of gradient principles：
It is identical that distance searches principle and document (Claytonet al., 1998), according to step-length lag distance and step-length
Tolerance lag tolerance search the point pair in particular step size；Last statistics step-length takes the average value in each group.
For determining distance ds and gradient g, N (ds, dp) a point pair is obtained, by formula (2) experiment with computing variogram；With
Corresponding distance ds, gradient g be average distance and mean inclination in the group respectively；It is achieved in that the distance-of three gradient groups
Become difference data, as shown in Fig. 5, Fig. 6 and Fig. 7：
Distance-variation two dimension scatter plot of three gradient groups is made, as shown in Figure 5；Then it is tried with artificial curve Preliminary Simulation
Test variogram；Finally, according to experiment variogram curve, variance c, block gold c are estimated0It is each group with change journey a, gradient g
Mean inclination.
Experiment variogram as shown in Figure 7 is grouped based on the gradient rather than is grouped based on direction；Fig. 5 is certain seamount richness
" distance-gradient " Experiment variogram figure of cobalt crusts thickness.
Three groups of mean inclinations are respectively 1.6 °, 5.8 °, 16.1 °, and corresponding change journey is respectively 7.5km, 5.5km and 4.5km,
Base station value is close to 1.0, block gold c0It is 0.0.
Journey will be become and be fitted to the continuous function of the gradient, the functional relation being fitted between the gradient-change journey with rectangular coordinate system,
Three groups of gradients of Experiment variogram and change journey (1.6,7.5), (5.8,5.5), (16.1,4.5) are projected into the gradient-change journey
In rectangular coordinate system, Fig. 8 is seen；As seen from the figure, become journey and the gradient substantially inversely.
The relationship being inversely proportional substantially due to becoming journey and the gradient, contemplates reciprocal function hereUsing such as formula (6)
Reciprocal function is extended to be fitted change journey-gradient function.
A is the change eikonal number using gradient g as independent variable, wherein a0, p be undetermined constant；As gradient g=0, change journey is a0+
p；When the gradient is very big, become journey close to a0；There are two undetermined constants for functional expression (6), only need two known points on function, energy
Constant a0, p, which is solved, to be come.We use two groups of data (g of heavy grade group gradient3 and light grade group gradient13,
a3), (g1, a1), it is substituted into formula (7) and obtains undetermined constant a0And p：
Formula (7), which is substituted into formula (6), must become journey-gradient analog function.
In order to examine the functional simulation effect, we are by one group of data (g of middle gradient group2, a2) substitute into formula (6) and formula
(7), it acquires the theoretical of middle gradient group and becomes journey a '2, then compare a '2And a2Relative error, judge become journey-gradient function mould
Quasi- effect；Or by this group of data (g2, a2) input functional expression (6) rectangular coordinate system, see Fig. 6, observe (g2, a2) whether fall
On becoming journey-gradient simulation curve, with this, the simulation effect for becoming journey-gradient function is judged.
For experiment Seamount Co-rich crust thickness data, we by two groups of data of heavy grade group and light grade group (1.6,
7.5) (16.1,4.5) substitute into formula (6), acquire a0=4.0, p=9.2；Become journey-gradient analog function into：
The curve of functional expression (8) is shown in Fig. 6；It regard the change journey of middle gradient group-Gradient (5.5,5.8) as Function Fitting again
The check point of effect, by the gradient 5.8 substitute into formula (8) theoretical changes journey 5.4, with experiment become journey 5.5 error be 0.1, relatively miss
Difference is 1.8%, and inspection result illustrates that functional simulation effect is pretty good.
(5.5,5.8) are put into and become journey-gradient rectangular coordinate system, it has been found that the point is fallen on theoretical curve substantially,
Change journey-gradient functional simulation effect is affirmed.
The extension reciprocal function for change journey-gradient that simulation is obtained, substitutes among the theoretical model of variogram；Here only
Spherical model function is selected to illustrate.
Formula (6) is substituted into formula (9) and obtains the theoretical variogram based on the distance-gradient, as shown in formula (10) formula.
Formula (10) does not consider nugget effect (nugget effect)；a0, p be undetermined constant, by the change of experiment variogram
Journey fitting obtains.
If it is considered that nugget effect, formula (10) becomes formula (11)
Covariance function can also be converted to：
Judge whether variable is steady immediately using the method for normal distribution, logarithm normal distribution hypothesis testing；If research
Area's data fit normal distribution is regarded as not stringent random plateau region variable.Experiment variation letter can be carried out to it
Number calculates and Kriging estimations.
Using formula, the relative slope of landform between Krige area grid nodes to be estimated is calculated, while also calculating erect-position letter
Cease the gradient between 2 points pairs of erect-position；Ruling grade, minimum grade, gradient mean value, the standard deviation of the gradient are extracted in statistical analysis, are
Gradient grouping provides reference data.
According to (5) formula, with reference to the statistical information of terrain slope, information erect-position is grouped by three groups of gradients.
Light grade group (gradient1) represents the search direction of substantially isobath；Intermediate (-)grade group (gradient2), generation
The search direction of compensation grade between table isobath and greatest gradient；Heavy grade group (gradient3) represents substantially terrain gradients
The search direction in direction.The change journey of wherein gradient1, gradient3, value of slope participate in " become journey-gradient " fitting of function,
Inspection data of the change journey, value of slope of gradient2 as fitting effect, verification become the fitting effect of journey-gradient function.
The gradient of heavy grade group is combined using light grade and becomes the journey test data fitting gradient-change eikonal number；In recycling
Change journey, the ramp test data of gradient group test to the gradient-change eikonal number of fitting；If effect is bad, adjustment extension
Reciprocal function formula (6), for example make (g+1) in formula (6) into (g+1) n, n is desirable1,2,3,4,5 etc..
Certainly, above description is not limitation of the present invention, and the present invention is also not limited to the example above, the art
Those of ordinary skill, the present invention essential scope in, the variations, modifications, additions or substitutions made, should all belong to the present invention
Protection domain.
Claims (1)
1. the geostatistics method that the variogram for seamount space surface data is simulated, it is characterised in that：
(1) 3D-Surface regionalized variables are defined：Confirm some curved surface of 3d space as domainAnd it is sat using three-dimensional
It marks vector function Z (x, y, dp) to quantify, wherein (x, y) represents geographical location, dp is the depth of water；
(2) it is calculated using the variogram based on " distance-gradient " or " distance-relative water depth "：As head point Z (xh, yh, dph) really
It is fixed, according to certain gradient and apart from search tail point Z (xt, yt, dpt), as follows：
Space length：ds′ht=sqart [(xh-xt)2+(yh-yt)2+(dph-dpt)2] horizontal distance：dsht=sqart [(xh-xt)2+
(yh-yt)2]..............................(3)
The gradient：
N experimental point sharesA Gradient, ruling grade value gmax, minimum grade value gmin, by value of slope size, it is divided into
Three groups of equal frequency is referred to as heavy grade gradient3 groups, middle gradient gradient2 groups and light grade gradient1 groups；
The boundary gradient g of heavy grade group and middle gradient groupbig, the boundary value of slope of light grade group and middle gradient group is gsmallPoint pair
It searches and is carried out by three groups of gradient principles：
For determining distance ds and gradient g, N (ds, dp) a point pair is obtained, by formula (2) experiment with computing variogram；It is right therewith
The distance ds, the gradient g that answer are average distance and mean inclination in the group respectively；
Preliminary Simulation tests variogram；Finally, according to experiment variogram curve, variance c, block gold c are estimated0With become journey a,
Gradient g is the mean inclination of each group；
(3) change journey is fitted to the continuous function of the gradient：The relationship being inversely proportional substantially due to becoming journey and the gradient, utilizes letter reciprocal
Number；Using the extension reciprocal function of such as formula (6)It is fitted change journey-gradient function,
A is the change eikonal number using gradient g as independent variable, wherein a0, p be undetermined constant；As gradient g=0, change journey is a0+p；When
When the gradient is very big, become journey close to a0；There are two undetermined constants for functional expression (6), only need two known points on function, can be normal
Number a0, p, which is solved, to be come；Using two groups of data (g of heavy grade group gradient3 and light grade group gradient13, a3), (g1,
a1), it is substituted into formula (7) and obtains undetermined constant a0And p：
Formula (7), which is substituted into formula (6), must become journey-gradient analog function；
The extension reciprocal function for change journey-gradient that simulation is obtained, substitutes among the theoretical model of variogram,
Formula (6) is substituted into formula (9) and obtains the theoretical variogram based on the distance-gradient, as shown in formula (10) formula；
Formula (10) does not consider nugget effect (nugget effect)；a0, p be undetermined constant, intended by the change journey of experiment variogram
It closes and obtains；
If it is considered that nugget effect, formula (10) becomes formula (11)
Covariance function can also be converted to：
Judge whether stochastic variable is steady using the method for normal distribution, logarithm normal distribution hypothesis testing；If studying area's number
According to normal distribution is met, it is regarded as not stringent random plateau region variable；Experiment variogram meter can be carried out to it
It calculates and Kriging estimates；
Using formula, the relative slope of landform between Krige area grid nodes to be estimated is calculated, while also calculating erect-position information station
The gradient between 2 points pairs of position；Ruling grade, minimum grade, gradient mean value, the standard deviation of the gradient are extracted in statistical analysis, are the gradient
Grouping provides reference data；
According to (5) formula, with reference to the statistical information of terrain slope, information erect-position is grouped by three groups of gradients；
Light grade group (gradient1) represents the search direction of substantially isobath；Intermediate (-)grade group (gradient2), represent etc.
The search direction of compensation grade between deep line and greatest gradient；Heavy grade group (gradient3) represents substantially landform gradient direction
Search direction；Change journey therein, value of slope participate in that " becoming journey-gradient, " fitting of function becomes journey, value of slope as fitting effect
Inspection data, verification become journey-gradient function fitting effect.
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| "表层沉积物元素地球化学数据平差方法及在渤海的应用";闫仕娟等;《海洋地质与第四纪地质》;20140428;第34卷(第2期);第177-182页 * |
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