CN1873444A - Method for carrying out comparison of member by using wavelet pair of Mexico cap to measure open curve - Google Patents

Abstract

The invention relates to a method to take member contrast to well logging by using Mexico cap wavelet that includes the following steps: taking sampling to the well logging, and taking spectral analysis to the well logging to gain the frequency distribution range, calculating the range of wavelet transformation size factor and straggling the factor in the range, taking Mexico cap wavelet transformation to the well logging to gain the transformation curve under different size, taking partition to the low frequency section curve and using the thickness as relative contrast length, finding the corresponding point and removing the crossing link contrast point, the rest contrast point is the member contrasting result. The invention could take member contrasting under not abundant the prior information situation.

Description

Logging trace is carried out the method for the detail correlation of reservoir bed with mexican hat wavelet

Technical field

The present invention relates to a kind of method of logging trace being carried out the detail correlation of reservoir bed with mexican hat wavelet.

Background technology

At present, the known logging trace detail correlation of reservoir bed all needs more geology prior imformation, be based on and extract layer attribute feature (rock signature, thickness characteristics, position feature, tracing pattern feature, adjacent bed feature etc.), adopt dynamic programming, pattern-recongnition method, neural network method, grey pairing comparision, fuzzy clustering algorithm, expert system analysis method etc. to compare then.These methods need more geology prior imformation, can't provide certain any comparative information, and should use convenient inadequately.

Summary of the invention

The objective of the invention is in order not have geology prior imformation or prior imformation less to carry out the logging trace detail correlation of reservoir bed under the situation, and can realize the contrast of point-to-point stratum.

To achieve these goals, the invention provides a kind of method of logging trace being carried out the detail correlation of reservoir bed with mexican hat wavelet, the step of this method is:

1) logging trace is carried out the sampling of certain intervals, the different morphological feature of sampling reflection curve of different interval;

2) the described logging trace after the sampling is carried out gorgeous leaf spectrum analysis, obtain the frequency distribution scope of described logging trace;

3), be vector with the wavelet transformation factor is discrete in above-mentioned scope according to the scope of the frequency distribution range computation wavelet transform dimension factor of described logging trace;

4) according to described vector described logging trace is carried out the mexican hat wavelet conversion, obtain the transformation curve under the different scale, the different characteristic that has reflected logging trace by low frequency to high frequency, low frequency part has reflected the general characteristic of curve substantially, and HFS has reflected the detail characteristic of logging trace;

5) to the low frequency part curve of described transformation curve, divide according to minimum point, with the zone thickness after dividing as relevant correlation window;

6), finding the point corresponding on the curve to be contrasted with any point on the described transformation curve according to described correlation window;

7) remove the contrast points that those layer position intersection occurs the point corresponding on the correlation curve from described treating, remaining contrast points is point-to-point detail correlation of reservoir bed result.

The method according to the scope of the frequency distribution range computation wavelet transform dimension factor of described logging trace described in the said method step 3) is:

When the frequency distribution scope of logging trace is [f _Min, f _Max], then

Mexican hat wavelet is defined as:

$\mathrm{\&Psi;}\left(t\right)=\frac{2}{\sqrt{3}}{\mathrm{\&pi;}}^{1/4}(1-t^2)e^{-{\mathrm{<figure-callout\; id="2"\; label="t"\; filenames="A20051007481100131.png"\; state="\{\{state\}\}">t</figure-callout>}}^2/2}---\left(3\right)$

Wherein

Be the frequency center and the frequency range of mexican hat wavelet, , then the distribution range of wavelet transformation factor a is [a ₁, a ₂];

In the said method step 4) to the method that described logging trace carries out the mexican hat wavelet conversion be according to described vector:

$W_f(a,b)=\frac{1}{\sqrt{a}}{\&Integral;}_{-\&infin;}^{\&infin;}\mathrm{\&Psi;}\left(\frac{t-b}{a}\right)f\left(t\right)\mathrm{dt}=<f\left(t\right),{\mathrm{\&Psi;}}_{\mathrm{ab}}\left(t\right)>,a,b\&Element;R---\left(4\right)$

(4) in the formula, a ≠ 0 is flexible parameter, and shifting parameter when b is, function Ψ (t) are called female small echo, and selecting mexican hat wavelet here is the represented function of formula (3).Constitute following wavelet basis function with different a and b:

${\mathrm{\&Psi;}}_{\mathrm{ab}}\left(t\right)=\frac{1}{\sqrt{a}}\mathrm{\&Psi;}\left(\frac{t-b}{a}\right)---\left(5\right)$

The method finding the point corresponding with any point on the described transformation curve on the curve to be contrasted described in the said method step 6) is:

The both direction up and down at any point A place on curve is got long (l) the data A of window _On=(A ₁, A ₂..., A _l), A _Down=(A _L+1, A _L+2..., A _2l) and logging trace B to be contrasted ₁=(B ₁, B ₂..., B _n), n is the data point number, according to formula (6) from top to bottom carry out correlation computations successively,

${\left(r_{\mathrm{AB}}\right)}_k=\frac{\underset{i=k}{\overset{k+l}{\mathrm{\&Sigma;}}}{A}_i{B}_i}{\sqrt{\underset{i=k}{\overset{k+l}{\mathrm{\&Sigma;}}}{A_i}^2\underset{i=k}{\overset{k+l}{\mathrm{\&Sigma;}}}{B_i}^2}}---\left(6\right)$

Wherein, k=(1,2 ..., n-l), obtain two related coefficient curves among the figure, r at the every bit on the curve of the right _On=(r ₁, r ₂... r _N-l), r _Down=(r ₁, r ₂... r _N-l).If curve A place and curve B place are same stratum, so, two related coefficient curves reach maximum value simultaneously at the B point, and some B is exactly the point corresponding with the A point.To the every bit on the logging trace, all carry out top analysis, just can on curve to be contrasted, find corresponding point

The well section that the layer position that occurs in the substratum stratum comparing result described in the said method step 7) intersects, under described detail correlation of reservoir bed result's constraint, again carry out step 1) to step 4), the HFS of the transformation curve that wavelet transformation is obtained compares, this step is a recursive definition, finishes up to whole interval correlations.

Can also may further comprise the steps behind the said method: at described some points that do not have comparative information for the treatment of on the correlation curve, under described detail correlation of reservoir bed result's control, the HFS of the transformation curve that obtains behind the selection wavelet transformation, calculate the correlation window, provide correlation logging curve depth range, the comparative analysis of in this scope, being correlated with, according to the correlation window according to both direction from top to bottom and from the bottom to top with treat that correlation curve calculates two related coefficient curves, related coefficient is very big and amass the point that will look for exactly for maximum point, so that obtain the single-point comparing result on stratum.

The advantage that adopts the inventive method to carry out logging trace is carried out the detail correlation of reservoir bed is:

1. obtain comparing result fast, use convenient, flexible.

Only understand geology prior imformations such as work area overview or type formation data seldom situation under just can compare.

3. can carry out the stratum contrast of single-point.

4. the extreme point of logging signal and flex point all have good embodiment in the wavelet transformation under the different scale, and the direction indication of zero crossing the crest in the virgin curve, trough information, the size of extreme point has reflected the variation severe degree of virgin curve.

Description of drawings

Fig. 1 is the wavelet transformation curve under the different scale in the inventive method;

Fig. 2 is for comparing the synoptic diagram of the long division of window in the inventive method;

Fig. 3 is a relevant comparative analysis synoptic diagram in the inventive method;

Fig. 4 is a logging trace single-point comparing result synoptic diagram in the inventive method;

Fig. 5 is a logging trace comparing result synoptic diagram in the inventive method.

Embodiment

Describe method of the present invention in detail below in conjunction with accompanying drawing:

The spontaneous potential curve of choosing two mouthfuls of wells is carried out the sampling of certain intervals as logging trace to it, the different morphological feature of sampling reflection curve of different interval.This logging trace is at first carried out gorgeous leaf transformation, obtain the frequency distribution scope [f of two curves _Min, f _Max], according to this frequency range wavelet transform scale factor:

Mexican hat wavelet is defined as:

$\mathrm{\&Psi;}\left(t\right)=\frac{2}{\sqrt{3}}{\mathrm{\&pi;}}^{1/4}(1-t^2)e^{-{\mathrm{<figure-callout\; id="2"\; label="t"\; filenames="A20051007481100131.png"\; state="\{\{state\}\}">t</figure-callout>}}^2/2}---\left(3\right)$

Wherein Be the frequency center and the frequency range of mexican hat wavelet,

, with wavelet transformation factor a at interval [a ₁, a ₂] loosing is vectorial a={a ₁, a ₂..., a _n;

The vector that generates according to the described wavelet transform dimension factor carries out the mexican hat wavelet conversion to logging trace.The wavelet transformation formula is:

$W_f(a,b)=\frac{1}{\sqrt{a}}{\&Integral;}_{-\&infin;}^{\&infin;}\mathrm{\&Psi;}\left(\frac{t-b}{a}\right)f\left(t\right)\mathrm{dt}=<f\left(t\right),{\mathrm{\&Psi;}}_{\mathrm{ab}}\left(t\right)>,a,b\&Element;R---\left(4\right)$

(4) in the formula, a ≠ 0 is flexible parameter, and shifting parameter when b is, function Ψ (t) are called female small echo, and selecting mexican hat wavelet here is the represented function of formula (3).Constitute following wavelet basis function with different a and b:

${\mathrm{\&Psi;}}_{\mathrm{ab}}\left(t\right)=\frac{1}{\sqrt{a}}\mathrm{\&Psi;}\left(\frac{t-b}{a}\right)---\left(5\right)$

The wavelet transformation curve of the different scale that obtains through wavelet transformation as shown in Figure 1, curve 1 is a logging trace, curve 2,3,4,5 and 6 is that low frequency after the logging trace conversion is to the curve of high frequency, low frequency part has reflected the general characteristic of curve substantially, and HFS has reflected the detail characteristic of logging trace.

To the low frequency part curve of described transformation curve, divide according to minimum point, as relevant correlation window, as shown in Figure 2, the data 22 among the figure are the depth value of logging trace with the zone thickness after dividing, line 7 and 8 is correlation window's separatrix up and down.Carry out the logging trace comparative analysis then, as shown in Figure 3, upwards get the correlation window A shown in the arrow at arbitrfary point A on the low frequency curve 2 after logging trace 1 conversion _On=(A ₁, A ₂..., A _l) and logging trace B to be contrasted ₁=(B ₁, B ₂..., B _n), the related coefficient curve 9 that (n is the data point number) calculates; Get the correlation window A shown in the arrow downwards at an A _Down=(A _L+1, A _L+2..., A _2l) and the described related coefficient curve 10 for the treatment of that correlation curve calculates, curve 11 is the product of above-mentioned two related coefficient curves.The method of above-mentioned calculating related coefficient curve is:

According to formula (6) from top to bottom carry out correlation computations successively,

${\left(r_{\mathrm{AB}}\right)}_k=\frac{\underset{i=k}{\overset{k+l}{\mathrm{\&Sigma;}}}{A}_i{B}_i}{\sqrt{\underset{i=k}{\overset{k+l}{\mathrm{\&Sigma;}}}{A_i}^2\underset{i=k}{\overset{k+l}{\mathrm{\&Sigma;}}}{B_i}^2}}---\left(6\right)$

Wherein, k=(1,2 ..., n-l), obtain two related coefficient curves, r at the every bit on the curve to be measured _On=(r ₁, r ₂... r _N-l), r _Down=(r ₁, r ₂... r _N-l).If curve A place and curve B place are same stratum, so, two related coefficient curves reach maximum value simultaneously at the B point, and some B is exactly the point corresponding with the A point.To the every bit on the logging trace, all carry out top analysis, just can on curve to be contrasted, find corresponding point.

Remove those and the contrast points that layer position intersects occurs in the result of contrast, remaining contrast points is point-to-point stratum comparing result.

The well section that the layer position that occurs in the comparing result of described substratum stratum intersects under described detail correlation of reservoir bed result's constraint, is carried out spectrum analysis again, wavelet transformation, HFS to wavelet transformation compares, and this step is a recursive definition, finishes up to whole interval correlations.

At described some points that do not have comparative information for the treatment of on the correlation curve, as Fig. 4, under described detail correlation of reservoir bed result's control, the HFS 14 of the transformation curve that behind wavelet transformation, obtains according to a bite well natural potential logging curve 12, calculate correlation window C, thus, the HFS 15 of the transformation curve that obtains behind wavelet transformation at another mouthful well natural potential logging curve 13 provides treats correlation logging curve depth range D, the comparative analysis of in this scope, being correlated with, according to the correlation window according to both direction from top to bottom and from the bottom to top with treat that correlation curve calculates two related coefficient curves, related coefficient is very big and amass the point that will look for exactly for maximum point, so that obtain the single-point comparing result 16 on stratum.The comparing result that obtains above is consistent with the stratum comparing result of real data with point-to-point comparing result.In being applied to the processing procedure of real data, obtain good effect, not only provided the comparative information on stratum, and obtained point-to-point comparing result, and comparative information is more more specifically detailed, and as Fig. 5, curve 17 and 18 is the natural potential logging curve of two mouthfuls of wells among the figure, curve 19 and 20 for curve 17 and 18 behind wavelet transformation, obtain the low frequency part curve respectively, serial line 21 is the comparing result line.

It should be noted last that: above embodiment is the unrestricted technical scheme of the present invention in order to explanation only, although the present invention is had been described in detail with reference to the foregoing description, those of ordinary skill in the art is to be understood that, still can to the present invention make amendment and or be equal to replacement, and do not break away from the spirit and scope of the present invention.

Claims (6)

1, a kind ofly use the method that mexican hat wavelet carries out the detail correlation of reservoir bed to logging trace, comprising following steps:

1) logging trace is carried out the sampling of certain intervals, the different morphological feature of sampling reflection curve of different interval;

2) the described logging trace after the sampling is carried out gorgeous leaf spectrum analysis, obtain the frequency distribution scope of described logging trace;

3), be vector with the wavelet transformation factor is discrete in above-mentioned scope according to the scope of the frequency distribution range computation wavelet transform dimension factor of described logging trace;

4) according to described vector described logging trace is carried out the mexican hat wavelet conversion, obtain the transformation curve under the different scale, the different characteristic that has reflected logging trace by low frequency to high frequency, low frequency part has reflected the general characteristic of curve substantially, and HFS has reflected the detail characteristic of logging trace;

5) to the low frequency part curve of described transformation curve, divide according to minimum point, with the zone thickness after dividing as relevant correlation window;

6), finding the point corresponding on the curve to be contrasted with any point on the described transformation curve according to described correlation window;

7) remove the contrast points that those layer position intersection occurs the point corresponding on the correlation curve from described treating, remaining contrast points is point-to-point detail correlation of reservoir bed result.

2, application mexican hat wavelet according to claim 1 is to the method that logging trace carries out the detail correlation of reservoir bed, it is characterized in that the method for the scope of the described frequency distribution range computation wavelet transform dimension factor according to described logging trace of step 3) is:

When the frequency distribution scope of logging trace is [f _Min, f _Max], then

Mexican hat wavelet is defined as:

$\mathrm{\&Psi;}\left(t\right)=\frac{2}{\sqrt{3}}{\mathrm{\&pi;}}^{1/4}\left({1-t}^2\right)e^{-t^2/2}---\left(3\right)$

Wherein Be the frequency center and the frequency range of mexican hat wavelet, Then the distribution range of wavelet transformation factor a is [a ₁, a ₂].

3, application mexican hat wavelet according to claim 1 is characterized in that in the step 4) according to described vector to the method that described logging trace carries out the mexican hat wavelet conversion being to the method that logging trace carries out the detail correlation of reservoir bed:

$W_f(a,b)=\frac{1}{\sqrt{a}}{\&Integral;}_{-\&infin;}^{\&infin;}\mathrm{\&Psi;}\left(\frac{t-b}{a}\right)f\left(t\right)\mathrm{dt}=<f\left(t\right),{\mathrm{\&Psi;}}_{\mathrm{ab}}\left(t\right)>,a,b\&Element;R---\left(4\right)$

In the formula, a ≠ 0 is flexible parameter, and shifting parameter when b is, function Ψ (t) are called female small echo, and selecting mexican hat wavelet here is the represented function of formula (3).Constitute following wavelet basis function with different a and b:

${\mathrm{\&Psi;}}_{\mathrm{ab}}\left(t\right)=\frac{1}{\sqrt{a}}\mathrm{\&Psi;}\left(\frac{t-b}{a}\right)---\left(5\right)$

4, application mexican hat wavelet according to claim 1 is characterized in that to the method that logging trace carries out the detail correlation of reservoir bed method finding the point corresponding with any point on the described transformation curve on the curve to be contrasted described in the step 6) is:

The both direction up and down at any point A place on curve is got long (l) the data A of window _On=(A ₁, A ₂..., A _l), A _Down=(A _L+1, A _L+2..., A _2l) and logging trace B to be contrasted ₁=(B ₁, B ₂..., B _n), n is the data point number, according to formula (6) from top to bottom carry out correlation computations successively,

${\left(r_{\mathrm{AB}}\right)}_k=\frac{\underset{i=k}{\overset{k+l}{\mathrm{\&Sigma;}}}{A}_i{B}_i}{\sqrt{\underset{i=k}{\overset{k+l}{\mathrm{\&Sigma;}}}{A_i}^2\underset{i=k}{\overset{k+l}{\mathrm{\&Sigma;}}}{B_i}^2}}---\left(6\right)$

Wherein, k=(1,2 ..., n-l), obtain two related coefficient curves among the figure, r at the every bit on the curve of the right _On=(r ₁, r ₂... r _N-l), r _Down=(r ₁, r ₂... r _N-l); If curve A place and curve B place are same stratum, so, two related coefficient curves reach maximum value simultaneously at the B point, and some B is exactly the point corresponding with the A point; To the every bit on the logging trace, all carry out top analysis, just can on curve to be contrasted, find corresponding point.

5, application mexican hat wavelet according to claim 1 carries out the method for the detail correlation of reservoir bed to logging trace, it is characterized in that well section to the layer position intersection that occurs in the substratum stratum comparing result described in the step 7), under described detail correlation of reservoir bed result's constraint, repeat step 1) to step 4), the HFS of the transformation curve that wavelet transformation is obtained compares, this step is a recursive definition, finishes up to whole interval correlations.

6, application mexican hat wavelet according to claim 1 carries out the method for the detail correlation of reservoir bed to logging trace, it is characterized in that also having following steps after the step 7): at described some points that do not have comparative information for the treatment of on the correlation curve, under described detail correlation of reservoir bed result's control, the HFS of the transformation curve that obtains behind the selection wavelet transformation, calculate the correlation window, provide correlation logging curve depth range, the comparative analysis of in this scope, being correlated with, according to the correlation window according to both direction from top to bottom and from the bottom to top with treat that correlation curve calculates two related coefficient curves, related coefficient is very big and amass the point that will look for exactly for maximum point, so that obtain the single-point comparing result on stratum.

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