CN104635263A - Method for extracting mixed-phase seismic wavelets - Google Patents

Abstract

The invention provides a method for extracting mixed-phase seismic wavelets. The method includes the steps of 1, selecting a seismic channel and a time range; 2, subjecting the selected seismic channel and seismic data within the time range to high-order statistics analysis; 3, establishing the target function; 4, calculating the target function with a genetic algorithm; 5, outputting the extracted mixed-phase seismic wavelets. With the method, the mixed-phase seismic wavelets can be extracted, the seismic data can be subjected to convolution processing by adopting the extracted wavelets, and seismic data higher in resolution can be acquired.

Description

Extract the method for mixed-phase seismic wavelet

Technical field

The present invention relates to oil exploration technology field, particularly relate to a kind of method extracting mixed-phase seismic wavelet.

Background technology

Seismic wavelet extraction is seismic prospecting data process and a problem very crucial in explaining, in forward problem, need to form forward simulation geological data by wave equation or convolution model in conjunction with seismic wavelet, in inverting and deconvolution problem, also need the wavelet being extracted by seismic trace, different wavelets often has different impacts to inversion result.The basic framework of seismic wavelet extraction is convolution model, namely comprise the seismic trace that wavelet and reflection coefficient sequence add noise, extracting method mainly comprises two large classes, the first kind is determinate wavelet pickup method, Equations of The Second Kind is statistic wavelet pickup method, determinate wavelet pickup method refers to and utilizes well-log information first to calculate reflection coefficient sequence, then obtains seismic wavelet in conjunction with seismic trace near well by convolution model.

Statistically wavelet extraction method estimates wavelet by seismic trace self, can be divided into again based on second-order statistic with based on high-order statistic two kinds of methods.First second-order statistics metering method is proposed by Robinson (1975), it is based on such hypothesis, namely it is constant when seismic wavelet is, there is during the reflection of underground the random series of white noise spectrum, an autocorrelative estimation of seismic wavelet that the auto-correlation of the seismic trace then observed is just given, namely there is known the spectral amplitude of seismic wavelet, for the phase spectrum of wavelet, then must provide certain hypothesis, as supposed, seismic wavelet is zero phase, minimum phase, maximum phase, and in fact seismic wavelet is a kind of mixed-phase, therefore, the wavelet that the method for adding up based on the auto-correlation of second-order statistic is extracted also is inaccurate.Since the later stage eighties, many scholars bring into use higher-order statistical method to solve the problem of seismic wavelet estimation, these methods come from the semi-invariant and multispectral theory that grow up the sixties mostly, they are used for the estimation of mixed-phase seismic wavelet by T.Matsuoka and T.J.Ulrych (1984) the earliest, the new thought of high-order statistic seismic wavelet extraction is proposed by G.D.Lazear (1993) and D.R.Velis (1996), fourth order cumulant in non-Gaussian signal process is used for the estimation of wavelet by them, a brand-new thinking is provided for solving mixed phase wavelet estimation problem.

But the multi-solution of seismic wavelet extraction result is the difficult problem faced at present, makes wavelet extraction well do not applied always, therefore, in actual seism processing, need methods of seismic wavelet extraction more accurately and reliably.

Because high-order statistic remains the phase information of signal, therefore many methods of seismic wavelet extractions based on high-order statistic had been developed in recent years, but, the multi-solution of seismic wavelet extraction result is the difficult problem faced at present always, and high-order statistic wavelet extraction is not well applied.We have invented a kind of method of extraction mixed-phase seismic wavelet newly for this reason, solve above technical matters.

Summary of the invention

The object of this invention is to provide one and can extract mixed-phase seismic wavelet, to obtain the method for the extraction mixed-phase seismic wavelet of the higher seismic data of resolution.

Object of the present invention realizes by following technical measures: the method extracting mixed-phase seismic wavelet, and the method for this extraction mixed-phase seismic wavelet comprises: step 1, chooses seismic trace and time range; Step 2, carries out higher order statistic analysis to the geological data in the seismic trace chosen and time range; Step 3, sets up objective function; Step 4, uses genetic algorithm for solving objective function; And step 5, export the mixed-phase seismic wavelet extracted.

Object of the present invention also realizes by following technical measures:

In step 1, first input seismic data, select as required to need the seismic trace carrying out seismic wavelet extraction, then according to the situation in research work area, determine the time range needing to carry out seismic wavelet extraction.

When selecting to need the seismic trace carrying out seismic wavelet extraction, select structure mild, lineups select seismic trace close to the place of level, and ensure that seismic data has certain signal to noise ratio (S/N ratio).

When determining the time range needing to carry out seismic wavelet extraction, the length of this time range should be at least more than 2 times of wavelet lengths, and time window border be not stuck on strong lineups, be placed in the transitional zone of seismic response.

In step 2, the fourth order cumulant of geological data is calculated.

In step 3, consider the computing formula of three spectrums, and select the fourth order statistic of geological data, obtain the objective function extracting wavelet, and in objective function, add the hard constraint to wavelet, reduce the multi-solution of wavelet extraction.

In step 3, genetic algorithm mixed phase wavelet extracts the thought of mating with wavelet High Order Moment based on seismic trace Higher Order Cumulants, considers following convolution model:

d(n)=x(n)+n(n)=w(n)*r(n)+n(n) (1)

Wherein: d (n) to make an uproar seismologic record for band, x (n) is without making an uproar seismologic record, w (n) is seismic wavelet, r (n) represents additive noise, assuming that noise is white Gaussian noise or gaussian colored noise for stratum reflection coefficient, n (n), and with r (n) statistical iteration, then its high-order statistic is zero, and hypothesis stratum reflection coefficient r (n) is super-Gaussian white noise further, can obtain formula below:

$\begin{array}{c}{c}_{\mathrm{kd}}({\mathrm{\τ}}_1,L,{\mathrm{\τ}}_{k-1})=c_{\mathrm{kx}}({\mathrm{\τ}}_1,L,{\mathrm{\τ}}_{k-1})+c_{\mathrm{kn}}({\mathrm{\τ}}_1,L,{\mathrm{\τ}}_{k-1})\\ =\underset{i_1=-\∞}{\overset{\∞}{\mathrm{\Σ}}}L\underset{i_k=-\∞}{\overset{\∞}{\mathrm{\Σ}}}w\left(i_1\right)\mathrm{Lw}\left(i_k\right)\·c_{\mathrm{kr}}({\mathrm{\τ}}_1+i_1-i_2,L,{\mathrm{\τ}}_{k-1}+i_1-i_k)\\ {=\mathrm{\γ}}_{\mathrm{dr}}\·\underset{i_1=-\∞}{\overset{\∞}{\mathrm{\Σ}}}L\underset{i_k=-\∞}{\overset{\∞}{\mathrm{\Σ}}}w\left(i_1\right)\mathrm{Lw}\left(i_k\right)\\ ={\mathrm{\γ}}_{\mathrm{dr}}\·m_{\mathrm{kw}}\end{array}---\left(2\right)$

Wherein: c _kdfor the High-order Cumulant of real seismic record, c _kxfor the High-order Cumulant of noiseless seismologic record, c _knfor the High-order Cumulant of noise, m _kwfor the High Order Moment of seismic wavelet, γ _drfor the High-order Cumulant of reflection coefficient, w is seismic wavelet, and τ is the delay of time; As can be seen from the above equation, if stratum reflection coefficient is super-Gaussian white noise, then the High-order Cumulant of seismologic record only differs a constant with the High Order Moment of seismic wavelet, finally can obtain objective function below:

$\begin{array}{c}\min \mathrm{\φ}=\underset{{\mathrm{\τ}}_1,{\mathrm{\τ}}_2,{\mathrm{\τ}}_3}{\mathrm{\Σ}}{[\mathrm{\α}({\mathrm{\τ}}_1,{\mathrm{\τ}}_2,{\mathrm{\τ}}_3)\·c_{4d}({\mathrm{\τ}}_1,{\mathrm{\τ}}_2,{\mathrm{\τ}}_3)-{\mathrm{\γ}}_{4r}{m}_{4w}({\mathrm{\τ}}_1,{\mathrm{\τ}}_2,{\mathrm{\τ}}_3)]}^2\\ s.t.\\ v_{\mathrm{down}}\≤w\≤v_{\mathrm{up}}\\ \mathrm{\Σw}=0\end{array}---\left(3\right)$

Wherein: min represents and minimizes, c _4d(τ ₁, τ ₂, τ ₃) be the fourth order statistic of seismologic record, m _4w(τ ₁, τ ₂, τ ₃) be the Fourth-order moment of wavelet to be asked, γ _4rthe kurtosis of reflection coefficient, a (τ ₁, τ ₂, τ ₃) be three-dimensional window function, w is wavelet vector, v _downand v _upfor the span of wavelet, namely to the hard constraint of wavelet waveforms, add the multi-solution that hard constraint solves with lower wavelet, ∑ w=0 represent the wavelet that requirement extracts and be zero, reacted seismic wavelet a kind of shake and decay to zero characteristic, s.t. represents and is tied in (subject to).

Have employed Revised genetic algorithum in step 4, algorithm design three kinds of crossover operators, when carrying out intersecting the operation of link, the interlace operation that two filial generations of cycling each time will carry out three times could produce corresponding two parents; Devise three different mutation operators, namely each filial generation will carry out the mutation operation of three times.

The method of the extraction mixed-phase seismic wavelet in the present invention, be mainly used in the extraction of seismic wavelet in seismic data interpretation in petroleum prospecting, the objective function extracting seismic wavelet is established based on the thought that higher order statistical is flux matched, and the hard constraint added in objective function wavelet waveforms of novelty, thus well reduce the multi-solution of wavelet extraction, then this objective function of genetic algorithm for solving is applied, finally extract mixed-phase seismic wavelet, apply the wavelet extracted and deconvolution process is carried out to geological data, the seismic data that resolution is higher can be obtained.The method belongs to statistics class methods of seismic wavelet extraction, stable, seismic wavelet accurately can be obtained, the seismic wavelet extracted can be used for the demarcation of seismic data, deconvolution and refutation process, effective accuracy and the reliability ensureing these explanatory treatment technologies.

Accompanying drawing explanation

Fig. 1 is the process flow diagram of a specific embodiment of the method for extraction mixed-phase seismic wavelet of the present invention;

Fig. 2 is the schematic diagram of seismic trace Higher Order Cumulants in a specific embodiment of the present invention;

Fig. 3 is the schematic diagram of the section of seismic trace Higher Order Cumulants in a specific embodiment of the present invention;

Fig. 4 is the wavelet extraction result after genetic algorithm iteration of the present invention 10 times;

Fig. 5 is the wavelet extraction result after genetic algorithm iteration of the present invention 30 times;

Fig. 6 is the wavelet extraction result after genetic algorithm iteration of the present invention 50 times;

Fig. 7 is the wavelet extraction result after genetic algorithm iteration of the present invention 70 times;

Fig. 8 is the wavelet extraction result after genetic algorithm iteration of the present invention 90 times;

Fig. 9 is the wavelet extraction result after genetic algorithm iteration of the present invention 200 times;

Figure 10 is the schematic diagram of actual seismic wavelet and the hard constraint thereof extracted in a specific embodiment of the present invention.

Embodiment

For making above and other object of the present invention, feature and advantage can become apparent, cited below particularly go out preferred embodiment, and coordinate institute's accompanying drawings, be described in detail below.

As shown in Figure 1, Fig. 1 is the process flow diagram of the method for extraction mixed-phase seismic wavelet of the present invention.

In step 101, choose seismic trace and time range.

Seismic data mainly comprises Prestack seismic data and poststack seismic data two kinds, and method of the present invention is mainly used in the extraction of poststack seismic wavelet.First seismic data is inputted, select as required to need the seismic trace carrying out seismic wavelet extraction, preferably mild at structure, lineups select seismic trace close to the place of level, and ensure that seismic data has certain signal to noise ratio (S/N ratio), then according to the situation in research work area, determine the time range needing to carry out seismic wavelet extraction, it should be noted that, this time range is too short, its length should be at least more than 2 times of wavelet lengths, and time window border be not stuck on strong lineups, be placed in the transitional zone of seismic response.Flow process enters into step 102.

In step 102, calculate Higher Order Cumulants.

Higher order statistic analysis is carried out to the geological data in the seismic trace of specifying and time range.High-order Cumulant, High-order Cumulant spectrum, High Order Moment, Higher-Order Moment Spectra are four kinds of main high-order statistics.Generally, High-order Cumulant and the High-order Cumulant of using is composed more, and High Order Moment and Higher-Order Moment Spectra then seldom use, therefore often compose High-order Cumulant referred to as higher-order spectrum.Higher-order spectrum is also named multispectral, the spectrum of meaning and multiple frequency.The most frequently used higher-order spectrum is three rank spectrum and fourth order spectrum, is referred to as two spectrum (Bispectum) and three spectrums (Trispectum).It is the fourth order cumulant calculating geological data in this method.Fig. 2 is seismic trace fourth order cumulant 3-D display, τ ₁, τ ₂, τ ₃be three different time delays respectively, Fig. 3 is a section of Fig. 2 seismic trace fourth order cumulant.Flow process enters into step 103.

In step 103, set up objective function.

Consider the computing formula of three spectrums, and select the fourth order statistic of geological data, obtain the objective function extracting wavelet, and in objective function, add the hard constraint to wavelet, reduce the multi-solution of wavelet extraction.

A large amount of non-gaussian, non-minimum phase, non-causal, non-stationary signal is usually faced in seismic data process, high-order statistic is utilized to be the Main Means addressed these problems, high-order statistic comprises Higher Order Cumulants and High Order Moment, the multidimensional fourier transform of Higher Order Cumulants is defined as higher-order spectrum (or claiming multispectral), and high-order statistic has the three significant advantages in aspect compared with second-order statistic (autocorrelation function):

(a) Higher Order Cumulants have gaussian colored noise perseverance be zero feature, thus can be used for extracting the non-Gaussian signal in gaussian colored noise;

B () Higher Order Cumulants, containing systematic phase information, thus can be used for non-minimum phase system identification;

C () high-order statistic can be used for detecting and descriptive system non-linear, as detection gaussian signal or non-Gaussian signal.

Genetic algorithm mixed phase wavelet extracts the thought of mating with wavelet High Order Moment based on seismic trace Higher Order Cumulants, considers following convolution model:

d(n)=x(n)+n(n)=w(n)*r(n)+n(n) (1)

Wherein: d (n) to make an uproar seismologic record for band, x (n) is without making an uproar seismologic record, w (n) is seismic wavelet, r (n) represents additive noise, assuming that noise is white Gaussian noise or gaussian colored noise for stratum reflection coefficient, n (n), and with r (n) statistical iteration, then its high-order statistic is zero, and hypothesis stratum reflection coefficient r (n) is super-Gaussian white noise further, can obtain formula below:

$\begin{array}{c}{c}_{\mathrm{kd}}({\mathrm{\τ}}_1,L,{\mathrm{\τ}}_{k-1})=c_{\mathrm{kx}}({\mathrm{\τ}}_1,L,{\mathrm{\τ}}_{k-1})+c_{\mathrm{kn}}({\mathrm{\τ}}_1,L,{\mathrm{\τ}}_{k-1})\\ =\underset{i_1=-\∞}{\overset{\∞}{\mathrm{\Σ}}}L\underset{i_k=-\∞}{\overset{\∞}{\mathrm{\Σ}}}w\left(i_1\right)\mathrm{Lw}\left(i_k\right)\·c_{\mathrm{kr}}({\mathrm{\τ}}_1+i_1-i_2,L,{\mathrm{\τ}}_{k-1}+i_1-i_k)\\ {=\mathrm{\γ}}_{\mathrm{dr}}\·\underset{i_1=-\∞}{\overset{\∞}{\mathrm{\Σ}}}L\underset{i_k=-\∞}{\overset{\∞}{\mathrm{\Σ}}}w\left(i_1\right)\mathrm{Lw}\left(i_k\right)\\ ={\mathrm{\γ}}_{\mathrm{dr}}\·m_{\mathrm{kw}}\end{array}---\left(2\right)$

Wherein: c _kdfor the High-order Cumulant of real seismic record, c _kxfor the High-order Cumulant of noiseless seismologic record, c _knfor the High-order Cumulant of noise, m _kwfor the High Order Moment of seismic wavelet, γ _drfor the High-order Cumulant of reflection coefficient, w is seismic wavelet, and τ is the delay of time.As can be seen from the above equation, if stratum reflection coefficient is super-Gaussian white noise, then the High-order Cumulant of seismologic record only differs a constant with the High Order Moment of seismic wavelet, finally can obtain objective function below:

$\begin{array}{c}\min \mathrm{\φ}=\underset{{\mathrm{\τ}}_1,{\mathrm{\τ}}_2,{\mathrm{\τ}}_3}{\mathrm{\Σ}}{[\mathrm{\α}({\mathrm{\τ}}_1,{\mathrm{\τ}}_2,{\mathrm{\τ}}_3)\·c_{4d}({\mathrm{\τ}}_1,{\mathrm{\τ}}_2,{\mathrm{\τ}}_3)-{\mathrm{\γ}}_{4r}{m}_{4w}({\mathrm{\τ}}_1,{\mathrm{\τ}}_2,{\mathrm{\τ}}_3)]}^2\\ s.t.\\ v_{\mathrm{down}}\≤w\≤v_{\mathrm{up}}\\ \mathrm{\Σw}=0\end{array}---\left(3\right)$

Wherein: min represents and minimizes, c _4d(τ ₁, τ ₂, τ ₃) be the fourth order statistic of seismologic record, m _4w(τ ₁, τ ₂, τ ₃) be the Fourth-order moment of wavelet to be asked, γ _4rthe kurtosis of reflection coefficient, a (τ ₁, τ ₂, τ ₃) be three-dimensional window function, w is wavelet vector, v _downand v _upfor the span of wavelet, namely to the hard constraint of wavelet waveforms, add the multi-solution that hard constraint solves with lower wavelet, ∑ w=0 represent the wavelet that requirement extracts and be zero, reacted seismic wavelet a kind of shake and decay to zero characteristic, s.t. represents and is tied in (subject to).

Seismic wavelet often one section there is initial time, the finite energy and have the signal of certain continuity length determined, it is the elementary cell in seismologic record, it is generally acknowledged, the seismic event produced during seismic focus shooting is only extremely short spike pulse perdurability, along with spike pulse is propagated in viscoelastic medium, the radio-frequency component of spike pulse is decayed very soon, waveform increases thereupon, just seismic wavelet is defined, a seismic wavelet generally has the continuity length of two to three phase places, then with the form of seismic wavelet at underground propagation.

In poststack seismic data, zero phase rectification is carried out to seismic wavelet, therefore often seismic wavelet has now been thought a kind of wavelet being similar to zero phase, namely shake from zero amplitude, energy becomes large gradually, starts again to diminish gradually, until energy is zero to energy time maximum.According to this feature, different forms can be selected to carry out windowing process to wavelet to be estimated, such as: rectangular window, Gaussian window, window index etc., Figure 10 is the schematic diagram of seismic wavelet of the present invention and hard constraint thereof, mainly add when applying genetic algorithm for solving objective function, controlled the hunting zone of genetic algorithm by windowing, namely only carry out the search of solution space in window function inside.Flow process enters into step 104.

In step 104, use genetic algorithm for solving objective function.

Have employed Revised genetic algorithum, greatly reduce the generation for precocious phenomenon, enhance the local search ability of algorithm, finally improve the probability finding optimum solution, simultaneously the stability of algorithm and speed of convergence there has also been certain raising.Along with circulation solves the increase of iterations, the actual wavelet of wavelet meeting Step wise approximation extracted, when genetic algorithm for solving is to more generation, the wavelet of the wavelet extracted and reality is closely similar, the spectral amplitude extracting wavelet is also more consistent with actual wavelet, just amplitude has some difference, this is mainly owing to extracting the energy of wavelet a little less than actual wavelet, but their phase spectrum is consistent in the effective band of wavelet.

Genetic algorithm is the parameter search optimization technology be based upon in natural genetics mechanism based, because it has lot of advantages, if do not needed objective function differentiate, can global optimizing etc., and be thus introduced in geophysics field, and achieve certain achievement.But genetic algorithm is also not bery ripe when processing actual seismic data, and the problem that existence own much need solve, is mainly manifested in: (1) precocious phenomenon; (2) later stage search is blunt; (3) local search ability is weak; (4) algorithm the convergence speed is low etc.For these weak points, this patent have employed a kind of Revised genetic algorithum, algorithm design three kinds of crossover operators, when carrying out the operation of intersection link, the interlace operation that two filial generations of cycling each time will carry out three times could produce corresponding two parents, so just greatly reduces the generation for precocious phenomenon; For mutation operator, devise three different operators equally, namely each filial generation will carry out the mutation operation of three times, which enhances the local search ability of algorithm, finally improve the probability finding optimum solution, simultaneously the stability of algorithm and speed of convergence there has also been certain raising.

Fig. 4 is the wavelet extraction result after genetic algorithm iteration 10 times, Fig. 5 is the wavelet extraction result after genetic algorithm iteration 30 times, Fig. 6 is the wavelet extraction result after genetic algorithm iteration 50 times, Fig. 7 is the wavelet extraction result after genetic algorithm iteration 70 times, Fig. 8 is the wavelet extraction result after genetic algorithm iteration 90 times, wherein solid black lines is wavelet model, and black dotted lines is the wavelet extracted after corresponding iterations.Fig. 9 is the seismic wavelet extraction result after iteration 200 times, can find out, along with the increase of iterations, the wavelet of extraction close to wavelet model, when arrival 200 times, has just had good extraction effect unlimited.Flow process enters into step 105.

In step 105, export the mixed-phase seismic wavelet extracted.Flow process terminates.

Claims (8)

1. extract the method for mixed-phase seismic wavelet, it is characterized in that, the method for this extraction mixed-phase seismic wavelet comprises:

Step 1, chooses seismic trace and time range;

Step 2, carries out higher order statistic analysis to the geological data in the seismic trace chosen and time range;

Step 3, sets up objective function;

Step 4, uses genetic algorithm for solving objective function; And

Step 5, exports the mixed-phase seismic wavelet extracted.

2. the method for extraction mixed-phase seismic wavelet according to claim 1, it is characterized in that, in step 1, first seismic data is inputted, select as required to need the seismic trace carrying out seismic wavelet extraction, then according to the situation in research work area, the time range needing to carry out seismic wavelet extraction is determined.

3. the method for extraction mixed-phase seismic wavelet according to claim 2, it is characterized in that, when selecting to need the seismic trace carrying out seismic wavelet extraction, selecting structure mild, lineups select seismic trace close to the place of level, and ensure that seismic data has certain signal to noise ratio (S/N ratio).

4. the method for extraction mixed-phase seismic wavelet according to claim 2, it is characterized in that, when determining the time range needing to carry out seismic wavelet extraction, the length of this time range should be at least more than 2 times of wavelet lengths, and time window border be not stuck on strong lineups, be placed in the transitional zone of seismic response.

5. the method for extraction mixed-phase seismic wavelet according to claim 1, is characterized in that, in step 2, calculates the fourth order cumulant of geological data.

6. the method for extraction mixed-phase seismic wavelet according to claim 5, it is characterized in that, in step 3, consider the computing formula of three spectrums, and select the fourth order statistic of geological data, obtain the objective function extracting wavelet, and in objective function, add the hard constraint to wavelet, reduce the multi-solution of wavelet extraction.

7. the method for extraction mixed-phase seismic wavelet according to claim 6, is characterized in that, in step 3, genetic algorithm mixed phase wavelet extracts the thought of mating with wavelet High Order Moment based on seismic trace Higher Order Cumulants, considers following convolution model:

d(n)=x(n)+n(n)=w(n)*r(n)+n(n) (1)

Wherein: d (n) to make an uproar seismologic record for band, x (n) is without making an uproar seismologic record, w (n) is seismic wavelet, r (n) represents additive noise, assuming that noise is white Gaussian noise or gaussian colored noise for stratum reflection coefficient, n (n), and with r (n) statistical iteration, then its high-order statistic is zero, and hypothesis stratum reflection coefficient r (n) is super-Gaussian white noise further, can obtain formula below:

$\begin{array}{c}{c}_{\mathrm{kd}}({\mathrm{\τ}}_1,L,{\mathrm{\τ}}_{k-1})=c_{\mathrm{kx}}({\mathrm{\τ}}_1,L,{\mathrm{\τ}}_{k-1})+c_{\mathrm{kn}}({\mathrm{\τ}}_1,L,{\mathrm{\τ}}_{k-1})\\ =\underset{i_1=-\∞}{\overset{\∞}{\mathrm{\Σ}}}L\underset{i_k=-\∞}{\overset{\∞}{\mathrm{\Σ}}}w\left(i_1\right)\mathrm{Lw}\left(i_k\right)\·c_{\mathrm{kr}}({\mathrm{\τ}}_1+i_1-i_2,L,{\mathrm{\τ}}_{k-1}+i_1-i_k)\\ {=\mathrm{\γ}}_{\mathrm{dr}}\·\underset{i_1=-\∞}{\overset{\∞}{\mathrm{\Σ}}}L\underset{i_k=-\∞}{\overset{\∞}{\mathrm{\Σ}}}w\left(i_1\right)\mathrm{Lw}\left(i_k\right)\\ ={\mathrm{\γ}}_{\mathrm{dr}}\·m_{\mathrm{kw}}\end{array}---\left(2\right)$

Wherein: c _kdfor the High-order Cumulant of real seismic record, c _kxfor the High-order Cumulant of noiseless seismologic record, c _knfor the High-order Cumulant of noise, m _kwfor the High Order Moment of seismic wavelet, γ _drfor the High-order Cumulant of reflection coefficient, w is seismic wavelet, and τ is the delay of time; As can be seen from the above equation, if stratum reflection coefficient is super-Gaussian white noise, then the High-order Cumulant of seismologic record only differs a constant with the High Order Moment of seismic wavelet, finally can obtain objective function below:

$\begin{array}{c}\min \mathrm{\φ}=\underset{{\mathrm{\τ}}_1,{\mathrm{\τ}}_2,{\mathrm{\τ}}_3}{\mathrm{\Σ}}{[\mathrm{\α}({\mathrm{\τ}}_1,{\mathrm{\τ}}_2,{\mathrm{\τ}}_3)\·c_{4d}({\mathrm{\τ}}_1,{\mathrm{\τ}}_2,{\mathrm{\τ}}_3)-{\mathrm{\γ}}_{4r}{m}_{4w}({\mathrm{\τ}}_1,{\mathrm{\τ}}_2,{\mathrm{\τ}}_3)]}^2\\ s.t.\\ v_{\mathrm{down}}\≤w\≤v_{\mathrm{up}}\\ \mathrm{\Σw}=0\end{array}---\left(3\right)$

Wherein: min represents and minimizes, c _4d(τ ₁, τ ₂, τ ₃) be the fourth order statistic of seismologic record, m _4w(τ ₁, τ ₂, τ ₃) be the Fourth-order moment of wavelet to be asked, γ _4rthe kurtosis of reflection coefficient, a (τ ₁, τ ₂, τ ₃) be three-dimensional window function, w is wavelet vector, v _downand v _upfor the span of wavelet, namely to the hard constraint of wavelet waveforms, add the multi-solution that hard constraint solves with lower wavelet, ∑ w=0 represent the wavelet that requirement extracts and be zero, reacted seismic wavelet a kind of shake and decay to zero characteristic, s.t. represents and is tied in (subject to).

8. the method for extraction mixed-phase seismic wavelet according to claim 6, it is characterized in that, have employed Revised genetic algorithum in step 4, algorithm design three kinds of crossover operators, when carrying out intersecting the operation of link, the interlace operation that two filial generations of cycling each time will carry out three times could produce corresponding two parents; Devise three different mutation operators, namely each filial generation will carry out the mutation operation of three times.