CN100350273C - Full well wall restoring method for electric imaging logging map - Google Patents

Abstract

The present invention relates to a full well wall restoring method for electric image logs, which belongs to the field of logging technique data processing and has the patent classification number of G01V 1/40. A resistivity scan measurer is used for scanning well logging; image data is calculated and processed by using the following method: step 1, resistivity scanned imagery well logging pole plate data is input; step 2, space positions of points which are not measured are calculated; step 3, the influence range of the points to be calculated is slelected; step 4, the factor of each of influence points is calculated; step 5, the number of the points is calculated; step 6, steps from the step 3 to the step 5 are repeated till all the points which are not measured; step 7, the electric image logs are output. The method can be used for restoring the image of the whole well wall with the coverage rate of 100% and effectively increasing the quality of the images; the preset invention lays the foundation for the subsequent processing of the images, clearly reflects the structure of subsurface geology, simplifies a restoring process and reduces the risk of repeat well logging operation.

Description

A kind of full well wall restoring method for electric imaging logging map

Technical field

The present invention relates to a kind of full well wall restoring method for electric imaging logging map, belong to the logging technology data processing field; Patent classificating number: G01V 1/40.

Background technology

In the well logging process, usually the log that uses resistivity scanning well logger to measure and make is owing to hole structure and the structural reason of resistivity scanning well logger, when measuring, instrument is in open configuration, cause when the borehole wall scans, not energy measurement of the part borehole wall is arranged, coverage rate can not reach 100%, on electric imaging logging map, produce white ribbon, influenced the quality of image, as shown in Figure 6, in calculation processes, made troubles.Remediable method is in identical well depth position, resistivity is scanned well logger rotate different angles, and duplicate measurements repeatedly in order to remedy the white ribbon that produces on the former imaging logging map, is not promptly surveyed data division.Shortcoming is that the course of work is complicated, and loses time, and increases construction operation input and risk.

Summary of the invention

The purpose of this invention is to provide a kind of full well wall restoring method for electric imaging logging map, the data of using the wall part of having logged well to obtain are estimated the wall part data of not logging well, and make full borehole wall image data recovery, make the borehole wall image coverage rate reach 100%, can improve picture quality effectively; Processing procedure is simplified, saved time; Handle to lay the foundation for the successive image of well-log information, more clearly react the structure of subsurface geology.

The technical scheme of a kind of full well wall restoring method for electric imaging logging map of the present invention is: a kind of full well wall restoring method for electric imaging logging map:

When well logging, adopt the resistivity imaging well logger scanning borehole wall, owing to the reason on instrument and the shaft wall structure, instrument is in open configuration when measuring, cause when the borehole wall scans, not energy measurement of the part borehole wall is arranged, produce white ribbon on the image, for fear of duplicate measurements and make borehole wall coverage rate reach 100%, employing has been surveyed the partial data estimation and has not been surveyed partial data, make the imaging logging map full well wall restoring, its well-log information is handled and is characterised in that, carries out the log data computing by the following method;

＜1〉input resistance rate scanning imagery well logging pole plate data;

Wherein resistivity scanning imagery log data is 4 image data to 36 pole plates, and each data is the value that a corresponding pole plate is gathered at the different mining sampling point;

＜2〉calculating take-off spot and the not locus of measuring point;

According to apparatus structure and hole diameter parameter, can determine to have surveyed the locus of data point, calculate not measuring point number and locus;

＜3〉survey of measuring point influences point range to select to wait to calculate not;

As required, select calculating to wait to calculate the not scope of the take-off spot of measuring point needs;

＜4〉calculating each has surveyed and has influenced dot factor: promptly each surveyed data point to this size of the contribution of measuring point not, anti-distance weighted method is: calculate the distance of each influence point to this point, ask reciprocal then, ask again influential some inverse distance and, each coefficient of having surveyed influence point for this influence point arrive this inverse of putting distance divided by an influential inverse distance with;

According to different situations, also can adopt the method for deriving by anti-distance weighted method, calculate each and surveyed and influence dot factor;

＜5〉calculate this not measuring point numerical value, multiply by the coefficient sum for all surveys influence point value, formula is:

$y_i=\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{\mathrm{\λ}}_i\×x_i$

In the formula: y _jBe measuring point numerical value not, λ _iThe coefficient of representing i point take-off spot, x _iRepresent i point take-off spot numerical value, N is the total influence of survey some number;

＜6〉the next not measuring point that does not calculate of selection repeats the＜3〉go on foot to the＜5 the step, to having calculated all not measuring point;

＜7〉data with the not measuring point after take-off spot and the calculating are presented on the display with corresponding method, or print and publish picture;

For the data after having calculated, an available curve data store whole take-off spots and not measuring point data in data file, and carry out follow-up data processing.

A kind of full well wall restoring method for electric imaging logging map is characterized in that, calculates the coefficient that each influences several points: promptly each data point can adopt golden algorithm in the gram, glug Lang Ri algorithm to the computing method of the size of the contribution of this point;

The Lagrange's interpolation algorithmic formula is as follows:

$\mathrm{\λ}\left[j\right]\left[i\right]=\frac{(x_{b,a}-x_{\mathrm{1,1}})\·\·\·(x_{b,a}-x_{b,a-1})(x_{b,a}-x_{b,a+1})\·\·\·(x_{b,a}-x_{n,m})}{(x_{j,i}-x_{\mathrm{1,1}})\·\·\·(x_{j,i}-x_{b,a-1})(x_{j,i}-x_{b,a+1})\·\·\·(x_{j,i}-x_{n,m})}$

X in the formula _{B, a}The capable a of b that expression requires is listed as the not position of measuring point, the capable i row of λ [j] [i] expression j surveyed data point to this measuring point coefficient not, (x _{B, a}-x _1,1) be the distance that the capable a of b is listed as 2 at measuring point to the 1 row the 1st columns strong point not, other and the like;

Wherein also can adopt the interpolation polynomial of Aitken interpolation, Hermite interpolation, and the piecewise linear interpolation of low order, splines interpolation;

Golden method of interpolation in wherein restraining, method is as follows:

At first, experiment variation function can calculate by following formula:

$\mathrm{\γ}\left(h\right)=\frac{1}{2N\left(h\right)}\underset{i=1}{\overset{N\left(h\right)}{\mathrm{\Σ}}}{[X\left(u_i\right)-X(u_i+h)]}^2$

X (u in the formula _i) represent the not locus of measuring point, X (u _i+ h) be the locus of take-off spot, N (h) counts for total influence; γ (h) is variation function (variation function);

The experiment variation function that calculates spherical model commonly used, exponential model, Gauss model, power model come match; Wherein spherical model is the variation model that the most generally adopts, and its normalized form is:

${\mathrm{\γ}}_{\mathrm{sph}}\left(h\right)=\left\{\begin{array}{cc}C[\frac{3}{2}\left(\frac{h}{a}\right)-\frac{1}{2}{\left(\frac{h}{a}\right)}^3]& h\≤a\\ C& h\≥a\end{array}\right.$

After the match, calculate C, a;

By the second-order stationary hypothesis down, variation function and covariance satisfy following relational expression:

C(h)＝C(0)-γ(h)

According to following system of equations:

$\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{\mathrm{\λ}}_{j}C(u_i,u_j)=C(u_i,u_0)$ I=1 wherein, 2 ..., n

C (u wherein _i, u ₀) represent not measuring point u ₀With take-off spot u _iBetween covariance, C (u _i, u _j) expression take-off spot u _iAnd u _jBetween covariance;

Just can calculate weighting coefficient λ after solving an equation _i

Wherein, also can obtain similar results according to the derivative algorithm of golden algorithm in the gram;

Wherein according to above-mentioned glug Lang Ri algorithm, golden algorithm and other algorithm of polynomial expression that derived by said method, approximate all are existing mathematic calculation in the gram, all belong to the present invention and are used within the total design scope of the technological means of deal with data.

Log by above-mentioned full well wall restoring method processing, eliminated white ribbon part on the image, made borehole wall coverage rate reach 100%, picture quality obviously improves, lay a good foundation for the successive image processing of well-log information, more clearly reflected the structure of subsurface geology.Needn't repeat to measure, subsequent processes is simplified, save time, reduce cost, reduce the logging operation risk.

Description of drawings

Fig. 1 is the flow chart of a kind of full well wall restoring method for electric imaging logging map of the present invention.

Fig. 2 is a button structural representation on pole plate of resistivity imaging logging instrumentation.

Instrument electrode plate structure figure when Fig. 3 is the measurement of resistivity imaging logging instrumentation.

Fig. 4 is a depth point before a kind of electric preimage log of the present invention is handled, do not survey data and surveyed the DATA DISTRIBUTION synoptic diagram, data are not surveyed in the white point representative among the figure, and data have been surveyed in the black color dots representative, at a certain degree of depth place 6 * 6 take-off spots are arranged among the figure, 6 * 4 measuring points not.

Fig. 5 is in the present embodiment, the take-off spot and the distribution explanation synoptic diagram of measuring point not.The depth point is 400 among the figure, and having surveyed data is 6 * 24 * 400, and not surveying data is 6 * 10 * 400.

Before Fig. 6 is the processing of a kind of full well wall restoring method for electric imaging logging map of the present invention, the design sketch of Fig. 5 data, every gray scale is proportional to resistivity among the figure, and promptly black color dots is represented low-resistivity, and the light color point is represented high resistivity.

Fig. 7 is after adopting a kind of full well wall restoring method for electric imaging logging map computing of the present invention, the design sketch of log full well wall restoring, and white ribbon partly is eliminated among the figure, and coverage rate reaches 100%.

Fig. 8 is the coverage point synoptic diagram in the embodiments of the invention, the coverage point of stain for selecting, and white point is a not measuring point to be calculated, shadow spots is the not measuring point that present embodiment calculates.

Embodiment

Below in conjunction with drawings and Examples,, be described in detail a kind of full well wall restoring method for electric imaging logging map of the present invention.When using resistivity sweep measuring instrument imaging logging, owing to the reason on hole structure and the resistivity scanner structure, instrument is in open configuration when measuring, cause when the borehole wall scans, not energy measurement (part between button shown in Figure 3) of the part borehole wall is arranged, and coverage rate can not reach 100%, produces white ribbon on image, (as shown in Figure 6), directly influenced the quality of image.Black represents to survey data among Fig. 4, and data are not surveyed in the white expression.

Adopt computing method of the present invention (as shown in Figure 1), can restore full borehole wall electric imaging logging map, its method is:

1. input resistance rate scanning imagery well logging pole plate data;

To scan the pole plate data input of well logger well logging with resistivity; Six resistivity scanning curve p1btn～p6btn of present embodiment input are respectively the matrix data that 400 row 24 are listed as, and promptly each curve has 9600 sampled points.

2. calculate the not locus of measuring point

Among this embodiment, apparatus structure and hole diameter parameter are respectively, and button is two rows, 12 button electrodes of every row, and spacing is 0.2 inch.Instrument has 6 pole plates, and apparatus measures borehole wall scope is 0.2 * 12.5 * 6=15 inch, and 12 is row's button length, because two row's buttons are staggered up and down, as shown in Figure 2, so total length is 12.5,6 to be 6 pole plates.1 expression button, first row among Fig. 2,2 expression buttons, second row, Fig. 2 is a synoptic diagram, a row has only shown 8.Pole plate of 3 expressions among Fig. 3,4 another pole plates of expression have only shown two pole plates among the figure.Hole diameter is 6.7 inch, so interpolation is the data of 6 400 row 10 row.Get that a part is described as shown in Figure 8 in this example.

Be followed successively by a little among Fig. 8

x[1][1] x[1][2] … x[1][14] x[1][15] x[1][16]

… … … … … …

… … … … … …

… … … … … …

x[5][1] x[5][2] … x[5][14] x[5][15] x[5][16]

x[6][1] x[6][2] … x[6][14] x[6][15] x[6][16]

The first row x[1 wherein] [1]～x[1] [3] represent the 22nd～24 column data of pole plate 1, x[1 respectively] [14]～x[1] [16] represent the 1st～3 column data of pole plate 2, middle x[1] [4]～x[1] [13] 10 classify as and do not survey data.Second goes.

Among Fig. 8, black represents to survey data, and data are not surveyed in the white expression.What this example will be calculated has 60 points, and the position as shown in the figure.This figure is a plane outspread drawing, and reality is three-dimensional cylindric figure, and in order to simplify computation process, the approximate planimetric coordinates that adopts of this example calculates.

3. select this to wait to calculate a little coverage

Suppose to calculate the numerical value (shadow spots among Fig. 8) of first white point of fourth line, can select coverage point to be 36 stains in the full figure; Also can a fourth line, data point of the 3rd stain is selected whole stains in this example.

4. calculate the coefficient that each influences several points: promptly each data point is to the size of the contribution of this point.Calculation Method, golden algorithm in the available gram, glug Lang Ri algorithm, anti-distance weighted etc.Present embodiment adopts anti-distance weighted method.

The parameter of input institute coverage, the mathematical algorithm of selection design factor.

For example to x[4] calculating of [4] point, influence point is x[1] [1]～x[6] [3] and x[1] [14]～x[6] [16] 36 points.

Adopt the method for anti-distance weighted algorithm computation coefficient.X[1] [1] to x[3] distance of [4] is,

$\sqrt{{(1-4)}^2+{(1-4)}^2}\≈4.24$ X[1] [2] to x[4] distance of [4] is,

$\sqrt{{(1-4)}^2+{(2-4)}^2}\≈3.60$ X[6] [16] to x[4] distance of [4] is,

$\sqrt{{(6-4)}^2+{(16-4)}^2}\≈12.16$ 。Ask inverse to obtain 0.23,0.27 to each distance ... 0.08, then divided by 36 inverse distances and (0.23+0.27+ ... + 0.08), obtains matrix of coefficients

λ[1][1] λ[1][2] … λ[1][14] λ[1][15] λ[1][16]

… … … … … …

… … … … … …

… … … … … …

λ[5][1] λ[5][2] … λ[5][11] λ[5][15] λ[5][16]

λ[6][1] λ[6][2] … λ[6][14] λ[6][15] λ[61[16]

According to different situations, also can adopt by anti-distance weighted method derive as distance square etc. method, design factor λ.

When each influences the coefficient of several points in calculating, also can adopt the Lagrange's interpolation algorithm, formula is as follows:

$\mathrm{\λ}\left[j\right]\left[i\right]=\frac{(x_{\mathrm{4,4}}-x_{\mathrm{1,1}})\·\·\·(x_{\mathrm{4,4}}-x_{\mathrm{4,3}})(x_{\mathrm{4,4}}-x_{4.5})\·\·\·(x_{\mathrm{4,4}}-x_{\mathrm{6,16}})}{(x_{j,i}-x_{\mathrm{1,1}})\·\·\·(x_{j,i}-x_{\mathrm{4,3}})(x_{j,i}-x_{\mathrm{4,5}})\·\·\·(x_{j,i}-x_{\mathrm{6,16}})}---\left(1\right)$

The coefficient of the capable i row of λ in the formula [j] [i] expression j, (x _4,4-x _1,1) be the distance that the 4th row the 4th is listed as 2 of the 1st row the 1st row.

Can certainly adopt the interpolation polynomial of Aitken interpolation, Hermite interpolation etc., and the piecewise linear interpolation of low order, splines interpolation.

When each influences the coefficient of several points in calculating, also can adopt golden method of interpolation in the gram, method is as follows:

At first, experiment variation function can calculate by following formula:

$\mathrm{\γ}\left(h\right)=\frac{1}{2N\left(h\right)}\underset{i=1}{\overset{N\left(h\right)}{\mathrm{\Σ}}}{[X\left(u_i\right)-X(u_i+h)]}^2---\left(2\right)$

X (u in the formula _i) represent the not locus of measuring point, X (u _i+ h) be the locus of take-off spot, N (h) counts for total influence.γ (h) is variation function (variation function).

The experiment variation function that calculates spherical model commonly used, exponential model, Gauss model, power model come match.Wherein spherical model is the variation model that the most generally adopts, and its normalized form is:

${\mathrm{\γ}}_{\mathrm{sph}}\left(h\right)=\left\{\begin{array}{cc}C[\frac{3}{2}\left(\frac{h}{a}\right)-\frac{1}{2}{\left(\frac{h}{a}\right)}^3]& h\≤a\\ C& h\≥a\end{array}\right.---\left(3\right)$

After the match, calculate C, a.

By the second-order stationary hypothesis down, variation function and covariance satisfy following relational expression:

C(h)＝C(0)-γ(h) (4)

According to following system of equations:

$\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{\mathrm{\λ}}_{j}C(u_i,u_j)=C(u_i,u_0)$ Its i=1,2 ..., n (5)

C (u wherein _i, u ₀) represent not measuring point u ₀With take-off spot u _iBetween covariance, C (u _i, u _j) expression take-off spot u _iAnd u _jBetween covariance.

Represent that with matrix form (5) formula is:

$\left[\begin{array}{ccc}C(u_i,u_1)& \·\·\·& C(u_1,u_n)\\ \·& & \·\\ \·& & \·\\ \·& & \·\\ C(u_n,u_1)& \·\·\·& C(u_n,u_n)\end{array}\right]\left[\begin{array}{c}{\mathrm{\λ}}_1\\ \·\\ \·\\ \·\\ {\mathrm{\λ}}_n\end{array}\right]\left[\begin{array}{c}C(u_1,u_0)\\ \·\\ \·\\ \·\\ C(u_n,u_0)\end{array}\right]---\left(6\right)$

Just can calculate weighting coefficient λ after solving an equation _i

According to the derivative algorithm of golden algorithm in the gram, for example piece can in method such as gold, also can obtain similar results.

In a word, according to above-mentioned anti-distance weighted method, glug Lang Ri algorithm, golden algorithm and other algorithm of polynomial expression that derive by said method, approximate in the gram, all be existing mathematic calculation, all belong to the present invention and be used within the total design scope of the technological means of deal with data.

5. calculate this point value, by the numerical value of influential point multiply by the coefficient sum, calculating not, the formula of measuring point number is:

$y_i=\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{\mathrm{\λ}}_i\×x_i---\left(7\right)$

Wherein: y _jBe measuring point numerical value not, λ _iRepresent that the i point surveyed coefficient, x _iRepresent that the i point surveyed numerical value, N is the total influence of a survey some number.

The concrete formula that is transformed into present embodiment is:

$x\left[4\right]\left[4\right]=\underset{i=1}{\overset{3}{\mathrm{\Σ}}}\underset{j=1}{\overset{6}{\mathrm{\Σ}}}x\left[j\right]\left[i\right]\×\mathrm{\λ}\left[j\right]\left[i\right]+\underset{i=14}{\overset{16}{\mathrm{\Σ}}}\underset{j=1}{\overset{6}{\mathrm{\Σ}}}x\left[j\right]\left[i\right]\×\mathrm{\λ}\left[j\right]\left[i\right]---\left(8\right)$

Obtain x[4] [4] numerical value.

6. and the like, calculate all not measuring point data, add that original take-off spot data just obtain the imaging data of full well wall restoring.Referring to the flow chart Fig. 1 that uses this method.

7. after having calculated, with the numerical value that calculates, promptly the size of resistivity changes into gray scale or uses correlation technique, just obtains full well wall restoring figure, as shown in Figure 7.Also can adopt the pseudo-colours demonstration or be printed as colored log.As can be seen from Figure 7, full well wall restoring figure has made borehole wall coverage rate reach 100%.

Borehole wall data are being carried out subsequent treatment, and when for example graph image strengthened, total data can be with a matrix representation, need not a plurality of matrix representations.And when calculating, considered each matrix in the past respectively, and between contact, process is loaded down with trivial details.

Through certain is distinguished the full well wall restoring figure at 1345.1-1345.2m place and the contrast of borehole wall acoustic imaging figure and this degree of depth sidewall sampling photo, the result shows that both relevant anastomose properties are better.Thereby proved accuracy of the present invention.

In conjunction with practical condition, the expense that adopts imaging technique to measure a bite well at present approximately is 80,000 U.S. dollars, and the time is about 15 hours.And duplicate measurements time and expense also will increase greatly, and have increased the operating risk of well logging process.Adopt the inventive method, not only solved the recovery problem of the full borehole wall image of electric imaging logging map effectively, and, greatly reduce construction cost avoiding duplicate measurements and reducing the operating risk purpose simultaneously.

In sum, the technical problem to be solved in the present invention provides a kind of full well wall restoring method of electric imaging logging map, the data of having used the wall part of logging well to obtain, estimate the wall part data of not logging well, make the technological means of full well wall restoring, produced and make borehole wall coverage rate reach 100%, improved the effect of the technology of picture quality effectively.Therefore, the invention belongs within the scope of patent protection.

Allly conceive identical technical scheme, all within this claim protection domain with the present invention.

Claims (2)

1. full well wall restoring method for electric imaging logging map:

When well logging, adopt the resistivity imaging well logger scanning borehole wall, owing to the reason on instrument and the shaft wall structure, instrument is in open configuration when measuring, cause when the borehole wall scans, not energy measurement of the part borehole wall is arranged, produce white ribbon on the image, for fear of duplicate measurements and make borehole wall coverage rate reach 100%, employing has been surveyed the partial data estimation and has not been surveyed partial data, make the imaging logging map full well wall restoring, its well-log information is handled and is characterised in that, carries out the log data computing by the following method;

＜1〉input resistance rate scanning imagery well logging pole plate data;

Wherein resistivity scanning imagery log data is 4 image data to 36 pole plates, and each data is the value that a corresponding pole plate is gathered at the different mining sampling point;

＜2〉calculating take-off spot and the not locus of measuring point;

According to apparatus structure and hole diameter parameter, can determine to have surveyed the locus of data point, calculate not measuring point number and locus;

＜3〉survey of measuring point influences point range to select to wait to calculate not;

As required, select calculating to wait to calculate the not scope of the take-off spot of measuring point needs;

＜4〉calculating each has surveyed and has influenced dot factor: promptly each surveyed data point to this size of the contribution of measuring point not, anti-distance weighted method is: calculate the distance of each influence point to this point, ask reciprocal then, ask again influential some inverse distance and, each coefficient of having surveyed influence point for this influence point arrive this inverse of putting distance divided by an influential inverse distance with;

According to different situations, also can adopt the method for deriving by anti-distance weighted method, calculate each and surveyed and influence dot factor;

＜5〉calculate this not measuring point numerical value, multiply by the coefficient sum for all surveys influence point value, formula is:

$y_i=\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{\mathrm{\λ}}_i\×x_i$

In the formula: y _jBe measuring point numerical value not, λ _iThe coefficient of representing i point take-off spot, x _iRepresent i point take-off spot numerical value, N is the total influence of survey some number;

＜6〉the next not measuring point that does not calculate of selection repeats the＜3〉go on foot to the＜5 the step, to having calculated all not measuring point;

＜7〉data with the not measuring point after take-off spot and the calculating are presented on the display with corresponding method, or print and publish picture;

For the data after having calculated, an available curve data store whole take-off spots and not measuring point data in data file, and carry out follow-up data processing.

2. according to the described a kind of full well wall restoring method for electric imaging logging map of claim 1, it is characterized in that, calculate the coefficient that each influences several points: promptly each data point can adopt golden algorithm in the gram, glug Lang Ri algorithm to the computing method of the size of the contribution of this point;

The Lagrange's interpolation algorithmic formula is as follows:

$\mathrm{\λ}\left[j\right]\left[i\right]=\frac{(x_{b,a}-x_{\mathrm{1,1}})\·\·\·(x_{b,a}-x_{b,a-1})(x_{b,a}-x_{b,a+1})\·\·\·(x_{b,a}-x_{n,m})}{(x_{j,i}-x_{\mathrm{1,1}})\·\·\·(x_{j,i}-x_{b,a-1})(x_{j,i}-x_{b,a+1})\·\·\·(x_{j,i}-x_{n,m})}$

X in the formula _{B, a}The capable a of b that expression requires is listed as the not position of measuring point, the capable i row of λ [j] [i] expression j surveyed data point to this measuring point coefficient not, (x _{B, a}-x _1,1) be the distance that the capable a of b is listed as 2 at measuring point to the 1 row the 1st columns strong point not, other and the like;

Wherein also can adopt the interpolation polynomial of Aitken interpolation, Hermite interpolation, and the piecewise linear interpolation of low order, splines interpolation;

Golden method of interpolation in wherein restraining, method is as follows:

At first, experiment variation function can calculate by following formula:

$\mathrm{\γ}\left(h\right)=\frac{1}{2N\left(h\right)}\underset{i=1}{\overset{N\left(h\right)}{\mathrm{\Σ}}}{[X\left(u_i\right)-X(u_i+h)]}^2$

X (u in the formula _i) represent the not locus of measuring point, X (u _i+ h) be the locus of take-off spot, N (h) counts for total influence; γ (h) is variation function (variation function);

The experiment variation function that calculates spherical model commonly used, exponential model, Gauss model, power model come match; Wherein spherical model is the variation model that the most generally adopts, and its normalized form is:

${\mathrm{\γ}}_{\mathrm{sph}}\left(h\right)=\left\{\begin{array}{cc}C[\frac{3}{2}\left(\frac{h}{a}\right)-\frac{1}{2}{\left(\frac{h}{a}\right)}^3]& h\≤a\\ C& h\≥a\end{array}\right.$

After the match, calculate C, a;

By the second-order stationary hypothesis down, variation function and covariance satisfy following relational expression:

C(h)＝C(0)-γ(h)

According to following system of equations:

$\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{\mathrm{\λ}}_{j}C(u_i,u_j)=C(u_i,u_0)$

I=1 wherein, 2 ..., n is C (u wherein _i, u ₀) represent not measuring point u ₀With take-off spot u _iBetween covariance, C (u _i, u _j) expression take-off spot u _iAnd u _jBetween covariance;

Just can calculate weighting coefficient λ after solving an equation _i

Wherein, also can obtain similar results according to the derivative algorithm of golden algorithm in the gram;

Wherein according to above-mentioned glug Lang Ri algorithm, golden algorithm and other algorithm of polynomial expression that derived by said method, approximate all are existing mathematic calculation in the gram, all belong to the present invention and are used within the total design scope of the technological means of deal with data.

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