CN106199726A - Orbital period recognition methods based on wavelet transformation module maximum algorithm - Google Patents

Abstract

The present invention relates to orbital period recognition methods based on wavelet transformation module maximum algorithm, belong to technical field of physical geography.Which solve the qualitative and quantitative directly perceived difference that prior art exists, and realize the problems such as difficulty.The present invention comprises the steps: to ask for the Continuous Wavelet Transform Coefficients matrix of one-dimensional log model；Wavelet conversion coefficient matrix in step one is taken absolute value；Every a line of absolute value matrix in step 2 is averaged, then one column vector of composition；Obtain the column vector extrema in a sequence point in step 3；In step 4, yardstick corresponding to extreme point is the response of Predominant period, the size in cycle of being gained the upper hand by the corresponding relation formula conversion of wavelet analysis medium frequency with yardstick；Obtain energy spectrogram through wavelet analysis, and then obtain the ratio of energy ring number.The present invention carries out module maximum computing by continuous wavelet transform energy spectrogram, not only accomplishes combination of qualitative and quantitative analysis directly perceived, and implements convenient and swift.

Description

Orbital period recognition methods based on wavelet transformation module maximum algorithm

Technical field

The present invention relates to orbital period recognition methods based on wavelet transformation module maximum algorithm, belong to geophysical techniques neck Territory.

Background technology

Wavelet transformation theory is the new signal processing technology grown up the nearly more than ten years, because it is in time domain and frequency domain It is all up high resolution, is referred to as " school microscop ".One Dimension Continuous Wavelet Transform involved in the present invention can be by one-dimensional survey Log signal is transformed into time domain and scale domain two-dimensional signal power spectrum, although can give expression to the spectrum structure of signal the most intuitively, but Owing to data redundancy phenomenon can be there is by spectrogram, it is difficult to accurately point out its frequency (cycle) quantitative values.In prior art, survey from stratum The research Chinese scholars of well extracting data orbital period information all did much work.But past or inquire into the most in detail How quantitatively to ask for cycle information from One Dimension Continuous Wavelet Transform wave spectrum, or need to enter in conjunction with fast Fourier transform (FFT) Line frequency analysis of spectrum, or application wavelet transform, but need to determine the problem of Decomposition order.

Summary of the invention

It is an object of the invention to the drawbacks described above overcoming existing recognition methods to exist, it is proposed that a kind of based on wavelet transformation The orbital period recognition methods of module maximum algorithm, by wavelet conversion coefficient matrix is done as follows computing, can obtain excellent The average quantitative information of gesture cycle.

The present invention is to use following technical scheme to realize: a kind of orbital period based on wavelet transformation module maximum algorithm Recognition methods, comprises the steps:

Step one: according to one-dimensional log model f (x) ∈ L²(R) Continuous Wavelet Transform Coefficients matrix is calculated:

According to

Wherein,For the conjugate function of ψ (x), if ψ (x) is real function, then

Draw coefficient matrix after wavelet transformation:

Step 2: the wavelet conversion coefficient matrix in step one is taken absolute value:

Step 3: every a line of absolute value matrix in step 2 is averaged, then one column vector of composition:

$\stackrel{\‾}{C_i}=\left[\begin{array}{c}{\mathrm{\ΣC}}_{1j}/n\\ {\mathrm{\ΣC}}_{2j}/n\\ \·\\ \·\\ \·\\ {\mathrm{\ΣC}}_{mj}/n\end{array}\right]=\left[\begin{array}{c}\stackrel{\‾}{C_1}\\ \stackrel{\‾}{C_2}\\ \·\\ \·\\ \·\\ \stackrel{\‾}{C_m}\end{array}\right],i=1,2,...,m;j=1,2,...,n;$

Step 4: obtain the column vector extrema in a sequence point in step 3；

Step 5: in step 4, yardstick corresponding to extreme point is the response of Predominant period, by wavelet analysis intermediate frequency Corresponding relation formula (1) conversion of rate and yardstick is gained the upper hand the size in cycle,

$F_a=\frac{F_c}{a\·\mathrm{\Δ}}$

In formula: a is the yardstick corresponding to extreme point, Δ is the sampling period, F_cFor the mid frequency of small echo, F_aFor yardstick a's Quasi-frequency；

Step 6: obtain energy spectrogram through wavelet analysis, and then obtain the ratio of energy ring number.

Further, in step one, one-dimensional log model constructs as follows:

The first step: take major cycle of orbital period than for 20:40:100:400ka ≈ 1:2:5:20, it is intended that 2 π, pi/2 divide Not representing the eccentrically connecting 400 of earth 's orbit, 100ka, π/5 represent the period of change of ecliptic obliquity, and π/10 represent year Difference period of change 20ka；

Second step: by function y=sinx, y=sin4x, y=sin10x, y=sin20x realize, four functions Be combined with each other and just obtain the log model in Michaelis cycle, i.e. y=sinx+sin4x+sin10x+sin20x,

Wherein, the x of the log model in Michaelis cycle is uniformly to take from 2000 point values between 0 to 10 π, dot spacing It is 2 π/400；Specify sample point to be spaced 2 π/400 and represent actual samples spacing 0.125m, be analogue signal after conversion corresponding The degree of depth row.

Further, in the second step of step one, the time cycle included in the log model in Michaelis cycle divides Not being 0.314,0.628,1.571 and 6.283, the corresponding thickness cycle is 2.5m, 5m, 12.5m and 50m respectively, number of cycles It it is 100,50,20 and 5.

Further, in step 2, it is thus achieved that time cycle be 0.3093,0.6187,1.5660 and 6.3798 respectively, right The thickness cycle answered is 2.46m, 4.923m, 12.46m and 50.77m.

Further, in step 5, in certain range of error, quasi-frequency F_aIt is the true frequency of yardstick a.

Further, in step 5, when Δ is actual samples thickness gap, in calculating gained frequency is unit thickness Number of cycles.

Further, step 5 is based on Morlet Wavelet Expansions, F_c=0.8125Hz, quasi-frequency F_aInverse be advantage The size in cycle.

Further, in step 5, the maximum point of the mould meansigma methods of wavelet coefficient scale-value is the response in cycle, and The size in cycle can be obtained by conversion.

Further, in step 6, add the face that the data after making an uproar are exactly energy ring after analyzing in the embodiment of energy spectrogram Complexion changed, utilizes the ratio of energy ring number, and the model of structure has credibility in the range of certain error.

The invention has the beneficial effects as follows: orbital period identification side based on wavelet transformation module maximum algorithm of the present invention Method, directly carries out module maximum computing by continuous wavelet transform energy spectrogram and asks for advantage cycle, not only accomplishes the most qualitative and fixed Amount combines, and implements convenient and swift.

Accompanying drawing explanation

Fig. 1 is orbital period signal model construction process figure.

Fig. 2 is the wavelet transformation energy spectrogram of Michaelis periodic model.

Fig. 3 is wavelet coefficient module Mean curve figure.

Fig. 4 is wavelet coefficient curve chart.

Fig. 5 is to add one of before and after's signal contrast figure of making an uproar.

Fig. 6 be add make an uproar before one of Wavelet Energy Spectrum figure.

Fig. 7 be add make an uproar after Wavelet Energy Spectrum figure two.

Fig. 8 is to add the two of before and after's signal contrast figure of making an uproar.

Fig. 9 be add make an uproar before Wavelet Energy Spectrum figure three.

Figure 10 be add make an uproar after Wavelet Energy Spectrum figure four.

Figure 11 is to add the three of before and after's signal contrast figure of making an uproar.

Figure 12 be add make an uproar before Wavelet Energy Spectrum figure five.

Figure 13 be add make an uproar after Wavelet Energy Spectrum figure six.

Figure 14 is the schematic flow sheet of the present invention.

Detailed description of the invention

The invention will be further described below in conjunction with the accompanying drawings.

As shown in figure 14, by wavelet conversion coefficient matrix is done as follows computing, the equal of cycle of can gaining the upper hand Value quantitative information:

(1) One Dimension Continuous Wavelet Transform coefficient matrix is asked for；

(2) matrix of wavelet coefficients is taken absolute value；

(3) every string is averaged, then one row matrix of composition；

(4) extreme point of row matrix is obtained；

(5) yardstick corresponding to extreme point is the response of Predominant period, right by wavelet analysis medium frequency and yardstick Relational expression (1) conversion is answered to gain the upper hand the size in cycle.

$F_a=\frac{F_c}{a\·\mathrm{\Δ}}---\left(1\right)$

In formula: a is yardstick, Δ is the sampling period, F_cFor the mid frequency of small echo, F_aQuasi-frequency for yardstick a.Necessarily Range of error in, it is believed that quasi-frequency F_aIt is the true frequency of yardstick a.If during Δ actual samples thickness gap, then counting Calculation gained frequency is the number of cycles in unit thickness.

By being then based on Morlet Wavelet Expansions, so F_c=0.8125, unit is Hz.Quasi-frequency F_aInverse be The size of Predominant period.The method is referred to as WAVELET TRANSFORM MODULUS extremum method.

In order to verify the effectiveness of said method, establish and utilize the periodicity of SIN function or cosine function to construct Michaelis cycle log model.Owing to the major cycle of orbital period is than for 20:40:100:400ka ≈ 1:2:5:20, therefore refer to Fixed 2 π, pi/2 represent the eccentrically connecting 400 of earth 's orbit, 100ka respectively, and π/5 represent the period of change of ecliptic obliquity, π/10 represent precession of the equinoxes period of change 20ka, and respectively by function y=sinx, y=sin4x, y=sin10x, y=sin20x come real Existing, four fonction composition are the most just obtained the well logging reaction in Michaelis cycle, such as Fig. 1, i.e. y=sinx+sin4x+sin10x+ sin20x.Wherein x is uniformly to take from 2000 point values between 0 to 10 π, and dot spacing is 2 π/400.For the ease of with every meter 8 The conventional logging signal of individual sampled data compares, it is intended that sample point is spaced 2 π/400 and represents actual samples spacing 0.125m, changes The degree of depth row that analogue signal is corresponding it are after calculation.So, the time cycle included in model is respectively 0.314, and 0.628, 1.571,6.283, the corresponding thickness cycle is 2.5m, 5m, 12.5m, 50m respectively, and number of cycles is 100,50,20,5.

The application WAVELET TRANSFORM MODULUS extremum method simulation curve to being set up carries out Periodic identification, such as Fig. 2 and Fig. 3, obtains Time cycle is 0.3093,0.6187,1.5660,6.3798 respectively, the corresponding thickness cycle be 2.46m, 4.923m, 12.46m, 50.77m, and number of cycles is with the number of modelling is, such as Fig. 4.

In sum, Michaelis cycle log model can identify exactly after the one-dimensional continuous transformation of small echo and wherein deposit Cycle, it may be determined that the ratio in cycle, the maximum point of the mould meansigma methods of wavelet coefficient scale-value is the response in cycle, and The size in cycle can be obtained by conversion.

It is above the identification situation under the conditions of ideal signal, but in actual practice, owing to geological condition is intricate, Geological structure is complicated and changeable, and influence factor is varied, and Michaelis cycle combination actual in stratum and the situation that presents want complexity Many.Therefore, construct the most again the model of the Michaelis cycle combination adding noise signal, the most only list four kinds of periodic groups Close add noise signal model construction process and with do not add noise signal model contrast situation.

The structure of figure is to add a random number on the basis of y value (GR), now obtains adding the figure after making an uproar and artwork shape To such as Fig. 5.

Can be seen that data waveform change is not the most greatly.By what wavelet analysis process obtained can spectrogram be, such as Fig. 6 and Fig. 7.

It is therefore seen that, owing to noise data is inconspicuous, the most how many analysis results adding the data after making an uproar significantly changes Become, the power of influence of noise data is strengthened the figure obtained, such as Fig. 8.

These group data are analyzed again, is obtained following figure, such as Fig. 9 and Figure 10.

It can be seen that graphics shape does not the most change, but the color of energy ring there occurs substantially change.Add again Big noise data impact, artwork at this moment and add the figure after making an uproar, such as Figure 11.

Following energy spectrogram is obtained, such as Figure 12 and Figure 13 after program analysis.

By above-mentioned analysis process it can be seen that adding the embodiment at energy spectrogram after analyzing of the data after making an uproar is exactly energy ring Color there occurs change, cause fuzzy situation occurring spectrogram, but the number ratio of energy ring do not have anything to change substantially. And in practical study, need research and utilize is exactly the ratio of energy ring number, thus illustrate, the mould constructed at this Type has credibility in the range of certain error.

Certainly, foregoing is only presently preferred embodiments of the present invention, it is impossible to be considered for limiting the enforcement to the present invention Example scope.The present invention is also not limited to the example above, and those skilled in the art are in the essential scope of the present invention Interior made impartial change and improvement etc., all should belong in the patent covering scope of the present invention.

Claims (9)

1. an orbital period recognition methods based on wavelet transformation module maximum algorithm, it is characterised in that: comprise the steps:

Step one: according to one-dimensional log model f (x) ∈ L²(R) Continuous Wavelet Transform Coefficients matrix is calculated:

According to

Wherein,For the conjugate function of ψ (x), if ψ (x) is real function, then

Draw coefficient matrix after wavelet transformation:

Step 2: the wavelet conversion coefficient matrix in step one is taken absolute value:

Step 3: every a line of absolute value matrix in step 2 is averaged, then one column vector of composition:

$\stackrel{\‾}{C_i}=\left[\begin{array}{c}{\mathrm{\ΣC}}_{1j}/n\\ {\mathrm{\ΣC}}_{2j}/n\\ \begin{array}{c}.\\ .\\ .\end{array}\\ {\mathrm{\ΣC}}_{mj}/n\end{array}\right]=\left[\begin{array}{c}\stackrel{\‾}{C_1}\\ \stackrel{\‾}{C_2}\\ \begin{array}{c}.\\ .\\ .\end{array}\\ \stackrel{\‾}{C_m}\end{array}\right],i=1,2,...,m;j=1,2,...,n;$

Step 4: obtain the column vector extrema in a sequence point in step 3；

Step 5: in step 4, yardstick corresponding to extreme point is the response of Predominant period, by wavelet analysis medium frequency with Corresponding relation formula (1) conversion of yardstick is gained the upper hand the size in cycle,

$F_a=\frac{F_c}{a\·\mathrm{\Δ}}$

In formula: a is the yardstick corresponding to extreme point, Δ is the sampling period, F_cFor the mid frequency of small echo, F_aQuasi-frequency for yardstick a Rate；

Step 6: obtain energy spectrogram through wavelet analysis, and then obtain the ratio of energy ring number.

Orbital period recognition methods based on wavelet transformation module maximum algorithm the most according to claim 1, it is characterised in that: In step one, one-dimensional log model constructs as follows:

The first step: take major cycle of orbital period than for 20:40:100:400ka ≈ 1:2:5:20, it is intended that 2 π, pi/2 generation respectively The eccentricity long and short cycle 400 of table earth 's orbit, 100ka, π/5 represent the period of change of ecliptic obliquity, and π/10 represent year Difference period of change 20ka；

Second step: by function y=sinx, y=sin4x, y=sin10x, y=sin20x realize, four fonction composition The most just the log model in Michaelis cycle, i.e. y=sinx+sin4x+sin10x+sin20x are obtained；

Wherein, the x of the log model in Michaelis cycle is uniformly to take from 2000 point values between 0 to 10 π, and dot spacing is 2π/400；Specify sample point to be spaced 2 π/400 and represent actual samples spacing 0.125m, after conversion, be corresponding deep of analogue signal Degree row.

Orbital period recognition methods based on wavelet transformation module maximum algorithm the most according to claim 2, it is characterised in that: In the second step of step one, the time cycle included in the log model in Michaelis cycle is respectively 0.314,0.628, 1.571 and 6.283, the corresponding thickness cycle is 2.5m, 5m, 12.5m and 50m respectively, and number of cycles is 100,50,20 and 5.

Orbital period recognition methods based on wavelet transformation module maximum algorithm the most according to claim 1, it is characterised in that: In step 2, it is thus achieved that time cycle be 0.3093,0.6187,1.5660 and 6.3798 respectively, the corresponding thickness cycle is 2.46m, 4.923m, 12.46m and 50.77m.

Orbital period recognition methods based on wavelet transformation module maximum algorithm the most according to claim 1, it is characterised in that: In step 5, in certain range of error, quasi-frequency F_aIt is the true frequency of yardstick a.

Orbital period recognition methods based on wavelet transformation module maximum algorithm the most according to claim 1, it is characterised in that: In step 5, when Δ is actual samples thickness gap, calculating gained frequency is the number of cycles in unit thickness.

Orbital period recognition methods based on wavelet transformation module maximum algorithm the most according to claim 1, it is characterised in that: Step 5 is based on Morlet Wavelet Expansions, F_c=0.8125Hz, quasi-frequency F_aInverse be the size of Predominant period.

Orbital period recognition methods based on wavelet transformation module maximum algorithm the most according to claim 1, it is characterised in that: In step 5, the maximum point of the mould meansigma methods of wavelet coefficient scale-value is the response in cycle, and can be obtained by conversion The size in cycle.

Orbital period recognition methods based on wavelet transformation module maximum algorithm the most according to claim 1, it is characterised in that: In step 6, add the color change that the data after making an uproar are exactly energy ring after analyzing in the embodiment of energy spectrogram, utilize energy ring The ratio of number, the model of structure has credibility in the range of certain error.