CN106772573B - Seismic wavelet method for extracting signal based on maximal correlation entropy - Google Patents
Seismic wavelet method for extracting signal based on maximal correlation entropy Download PDFInfo
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- G01—MEASURING; TESTING
- G01V—GEOPHYSICS; GRAVITATIONAL MEASUREMENTS; DETECTING MASSES OR OBJECTS; TAGS
- G01V1/00—Seismology; Seismic or acoustic prospecting or detecting
- G01V1/28—Processing seismic data, e.g. analysis, for interpretation, for correction
- G01V1/288—Event detection in seismic signals, e.g. microseismics
Abstract
The invention discloses a kind of seismic wavelet method for extracting signal based on maximal correlation entropy, maximal correlation entropy criterion is combined during Method for Seismic Wavelet Estimation in exploration geophysics is learnt with information theory, original criterion of least squares is replaced using maximal correlation entropy criterion so that object function can preferably overcome non-Gaussian noise.The present invention is stronger relative to traditional least square method robustness, precision higher, is more advantageous to carrying out the data processing in geological prospecting.
Description
Technical field
The invention belongs to Seismic Data Processing Technique fields, and in particular to a kind of seismic wavelet letter based on maximal correlation entropy
The design of number extracting method.
Background technology
Seismic wavelet is the basis for carrying out High resolution seismic data processing, forward simulation and reservoir parameter inversion.Wavelet
Inaccuracy can cause the impedance that inverting is obtained unreliable, and then cause seismic data High-resolution Processing ideal
High-fidelity section.Therefore, the accurate estimation of seismic wavelet is always one of key problem of exploration geophysics field concern.Ground
The basic framework for shaking wavelet extraction is convolution model, including wavelet, reflection coefficient sequence, Noise seismic channel.For earthquake
Wave estimates that current common method can be divided into two classes：One kind is statistical extracting method, one kind being to determine property extracting method.
Determinate wavelet pickup method needs well-log information and seismic data participates in jointly, is calculated first by log data
Go out reflection coefficient sequence, seismic wavelet is then obtained by well bypass road inverting.Determinate wavelet pickup method can be obtained compared with subject to
True wavelet, but be easy to be influenced by various logging errors, especially Sonic Logging Data be not allowed caused by velocity error
It can lead to wavelet amplitude distortion and phase blending algorithm.Main method has Wiener Filter Method, linear inversion method, Bayes side at present
Method etc..
Another extracting method is called statistical wavelet extraction method, and this method does not need to well logging information, similar to signal
Blind identification problem in processing.If regarding stratum reflectance factor as input, regard wavelet as system function, then it is statistical
Wavelet extraction is exactly in the case of stratum reflectance factor and all unknown wavelet, according to seismic data estimation earthquake observed
The problem of wave.Such method does not need to log data participation, but needs to divide seismic data and underlying reflection coefficient sequence
Cloth carries out certain it is assumed that acquired wavelet precision is related with the satisfaction degree of assumed condition.At present main method have correlation method,
Higher order Statistics, intermediary heat Power estimation method etc..When having log data in exploration work area, Liu Jie etc. compared certainty most
Show to use deterministic wavelet extraction method in real data after square method, statistical intermediary heat spectrum and bispectrum method advantage and disadvantage
It is substantially better than statistical method.
The basic principle of certainty sub wave method of estimation is based on convolution model：
S=w (t) * r (t)+n (t)
It if, can be according to the seismic data of observation using least square from log data extraction reflectance factor r (t)
Mode builds that object function is minimum to be solved：
Local derviation is asked to above formula, equation below can be built：
Wherein φrrRepresent reflectance factor auto-correlation function, ψxrRepresent the earthquake record cross-correlation function similar to reflection,
The seismic wavelet that direct solution equation is estimated with regard to that can obtain needs.But since algorithm influence can be led during solving result
It causes wavelet side lobe effect apparent, obtains initial wavelet using multiple tracks correlation computations for this wide intelligence etc., pass through Inverse iteration method
It is fine to solve well bypass road seismic wavelet.But the seismic data of actual observation is there are noise, and reflectance factor also has calibration
The factors such as inaccurate and calculating error, in the presence of these can all lead to wavelet calculating there are error, especially non-Gaussian noise, how
Obtaining high-precision seismic wavelet estimation result needs to further investigate.
For the concept of joint entropy most early in 2006 by Santamaria et al. propositions, idea is initially to solve information reason
The problem of by random sequence time structure and its statistical distribution cannot be handled in study in same measurement functions, one kind of proposition
The generalized related function is generalized to the situation of two stochastic variables by generalized related function, further, Liu et al. again, so as to shape
Into the concept of joint entropy, joint entropy has been successfully applied to signal processing and engineering as a non linear robust algorithm
The multiple fields such as habit, such as robust regression analysis, filtering, dimensionality reduction, classification and recognition of face etc..Recent study shows maximum phase
Non-Gaussian noise can effectively be suppressed by closing entropy criterion, and the basic principle of maximal correlation entropy is briefly described below.
If two stochastic variables are X, Y, their joint entropy is defined as：
Vσ(X, Y)=E [kσ(X-Y)]=∫ K (x, y) dFXY(x,y)
Wherein E represents expectation operator, kσ() represents the positive definite kernel function for meeting Mercer conditions, FXY(x, y) represents two
The joint distribution function of a stochastic variable.The joint probability density function is often unknown in practical problem, at this time can profit
With finite sample data pairTo obtain joint entropy estimator：
The kernel function in above formula uses Gaussian kernel under normal circumstances, then above formula can be write as：
Wherein σ ＞ 0 are wide for core.Work as X, when the similarity between Y is higher, the value of above formula is bigger, and it is most to maximize above formula
Big joint entropy criterion (Maximum Correntropy Criterion, MCC).
Compared to other similarity measurement criterion, such as criterion of least squares, joint entropy criterion has the following advantages：
(1) criterion includes all even-order squares and available for the processing of non-linear and non-Gaussian signal；
(2) kernel function effectively can control High Order Moment to weight；
(3) criterion is really a local similarity measurement criterion, therefore the criterion has preferable Shandong to outlier
Stick.
Invention content
The purpose of the present invention is to solve the certainty higher-order spectra methods in the prior art based on least square method to exist
Since seismic data is there are noise in practical measurement process, and reflectance factor also exist calibration it is inaccurate and calculate error etc. because
A kind of the problem of element causes wavelet to calculate there are error, and precision is relatively low, it is proposed that seismic wavelet signal based on maximal correlation entropy
Extracting method.
The technical scheme is that：Seismic wavelet method for extracting signal based on maximal correlation entropy, includes the following steps：
S1, by the use of Gaussian kernel as kernel function, build discrete joint entropy expression formula；
S2, seismic inversion model, existing observation data and reflectance factor are substituted into joint entropy expression formula, obtains target letter
Number；
S3, object function is converted to minimalization form；
S4, object function is solved using plan conjugate gradient inversion algorithm, obtains the seismic wavelet for needing to estimate.
Further, the discrete joint entropy expression formula built in step S1 is：
σ is that core is wide in formula and σ ＞ 0, N represent the length of data X and Y, xiAnd yiI-th of data X and Y is represented respectively.
Further, step S2 is specially：
By seismic inversion model s=w (t) * r (t)+n (t), existing observation data x (t)obsAnd reflectance factor r (t) generations
Enter joint entropy expression formula, wherein, observation data x (t)obsS i.e. in seismic inversion model, w (t) will calculate solution for the present invention
Seismic wavelet, r (t) is the vector for characterizing formation characteristics, i.e. reflectance factor, n (t) is present in characterization seismic inversion model
Additive noise；
Obtain object function：
Further, it is expressed as after object function being converted to minimalization form in step S3：
Further, step S4 specifically include it is following step by step：
S41, initialization process, setting initial model x0=w, w be need the seismic wavelet estimated and using null vector as
Initial value puts iterations k=0；
The gradient g of S42, calculating target function objk；
S43, update intend the direction of search of conjugate gradient inversion algorithm：If k=0, pk=-gk, otherwise have：
P in formulakRepresent the direction of search, yk-1Represent gradient increment, zk-1Represent conjugate direction, βkForgetting for the direction of search
The factor, bkFor the gradient increment coefficient in the direction of search more new formula；
S44, step-size in search α is calculatedk：
Matrixes of the G for reflectance factor auto-correlation function construction, e in formulakRepresent kth time iterative estimate residual error；
S45, update model parameter：
xk+1=xk+αkpk (6)
S46, it checks whether algorithm meets the condition of convergence, if then terminating iteration, exports inversion result x*=xk+1As need
Otherwise the seismic wavelet w to be estimated enables k=k+1, return to step S42 be iterated.
The beneficial effects of the invention are as follows：The present invention manages the Method for Seismic Wavelet Estimation in exploration geophysics and information
It is combined by maximal correlation entropy criterion in study, it is proposed that the Method for Seismic Wavelet Estimation based on maximal correlation entropy, using most
Big joint entropy criterion replaces original criterion of least squares so that object function can preferably overcome non-Gaussian noise.Model and
Real data shows, precision higher stronger relative to traditional least square method robustness of the invention, is more advantageous to carrying out ground
Data processing in matter exploration.
Description of the drawings
Fig. 1 is the seismic wavelet method for extracting signal flow chart provided by the invention based on maximal correlation entropy.
Fig. 2 is the flow chart step by step of step S4 of the present invention.
Fig. 3 is the mixed-phase seismic wavelet model of the embodiment of the present invention and model reflectance factor schematic diagram.
Fig. 4 is the noise free synthetic seismogram of the embodiment of the present invention and distinct methods inversion result contrast schematic diagram.
Fig. 5 is that the synthetic seismogram of Gaussian noise containing 6db of the embodiment of the present invention and the comparison of distinct methods inversion result are shown
It is intended to.
Fig. 6 is the synthetic seismogram of Laplacian noise containing 6db of the embodiment of the present invention and distinct methods inversion result pair
Compare schematic diagram.
Fig. 7 is that wavelet Comparative result schematic diagram is estimated in the practical work area of the embodiment of the present invention.
Fig. 8 is that the practical work area of the embodiment of the present invention estimates that wavelet composite traces is illustrated with true earthquake record Comparative result
Figure.
Specific embodiment
The embodiment of the present invention is further described below in conjunction with the accompanying drawings.
The present invention provides a kind of seismic wavelet method for extracting signal based on maximal correlation entropy, as shown in Figure 1, including with
Lower step：
S1, by the use of Gaussian kernel as kernel function, build discrete joint entropy expression formula：
σ is that core is wide in formula and σ ＞ 0, N represent the length (data Y length is equal to X) of data X, xiAnd yiData X is represented respectively
With i-th of Y.
S2, by seismic inversion model s=w (t) * r (t)+n (t), it is existing observation data x (t)obsAnd reflectance factor r (t)
Substitute into joint entropy expression formula.Wherein, observation data x (t)obsS i.e. in seismic inversion model, w (t) will be calculated for the present invention and be asked
The seismic wavelet of solution, r (t) are the vector for characterizing formation characteristics, i.e. reflectance factor, and n (t) is has in characterization seismic inversion model
Additive noise, be 6dB Gaussian noises or 6dB Laplacian noises in the embodiment of the present invention.
Obtain object function：
S3, object function is converted to minimalization form：
S4, object function is solved using plan conjugate gradient inversion algorithm, obtains the seismic wavelet for needing to estimate.
In the step, it is with the reason of intending conjugate gradient inversion algorithm, from the point of view of formula (3) structure, which is high
Spend it is nonlinear, if immediate derivation hardly results in analytic solutions, therefore we using iterative solution mode to the object function into
Row solves.
In the ill optimization problem of processing, conjugate gradient algorithms and quasi-Newton iteration method algorithm are all common algorithms.Usually
In the case of, the former convergence rate is low compared with the latter, but the latter needs to spend larger memory space in the calculating Hessian matrix inverse time.Cause
This, the present invention is based on derivation algorithm stability, low storage and iterative rates etc. to consider, using Zhang et.al
(2013) the plan conjugate gradient inversion algorithm (it combines conjugate gradient algorithms and quasi-Newton iteration method algorithm) proposed is solved
Operation.Further, since it needs come material calculation not had according to different generalized extreme value distribution object functions in primal algorithm general
Adaptive, we are directly using the code revision of step length searching of Dianne (1991) the offers step, due to the searching method
Two functions of value and gradient for providing calculating target function is needed just can to search for obtain step-length, therefore can cause above-mentioned calculation
Method adapts to arbitrary target function situation.
As shown in Fig. 2, the step include it is following step by step：
S41, initialization process, setting initial model x0=w, w be need the seismic wavelet estimated and using null vector as
Initial value puts iterations k=0.
The gradient g of S42, calculating target function objk。
S43, update intend the direction of search of conjugate gradient inversion algorithm：If k=0, pk=-gk, otherwise have：
P in formulakRepresent the direction of search, yk-1Represent gradient increment, zk-1Represent conjugate direction, βkForgetting for the direction of search
The factor (coefficient of Polak-Ribiere-Polyak (PRP) conjugate gradient method searching algorithms), bkTo search
Gradient increment coefficient in Suo Fangxiang more new formulas.
S44, step-size in search α is calculatedk：
Matrixes of the G for reflectance factor auto-correlation function construction, e in formulakRepresent kth time iterative estimate residual error.ek=xk*r
(t)-d, xkFor the wavelet that kth time iterative estimate goes out, r (t) is reflectance factor, and d is observes data, i.e. x (t)obs。
S45, update model parameter：
xk+1=xk+αkpk (6)
S46, check whether algorithm meets the condition of convergence, in the embodiment of the present invention, the condition of convergence is | | gk| |≤ε, ε mono-
A minimum positive number.If then terminating iteration, inversion result x is exported*=xk+1As the seismic wavelet w that needs are estimated, otherwise enable
K=k+1, return to step S42 are iterated.
The extraction effect of the present invention is illustrated with two specific embodiments below：
Embodiment one：
We and extract this using the seismic wavelet of arteface with maximal correlation entropy in the embodiment of the present invention
Wavelet.
In real seismic record, seismic wavelet is often mixed-phase, therefore we directly (are schemed with mixed phase wavelet
3) synthetic seismogram is calculated for model, it is known that reflectance factor by reflectance factor and seismic wavelet convolution as shown in figure 4, form ground
Shake record as shown in figure 5, below we according to maximal correlation entropy criterion Test extraction wavelet as a result, the robust for verification algorithm
Property, while compared estimating wavelet result under least square condition.Fig. 4 is synthetic seismogram and extraction under noise-free environment
For wavelet as a result, it can be found that under noise-free environment, two ways can obtain preferable estimation effect.
For the robustness that analysis maximal correlation entropy criterion records Noise, we are analyzed first containing 6db Gausses
(Fig. 5 a) wavelet inversion result (Fig. 5 b) under interference scenarios.Similarly, when synthesis seismic signal, to contain 6db Laplacian noises (non-
Gaussian noise) when (Fig. 6 a), inversion result is as shown in Figure 6 b.From the point of view of Noise result, in the case where there is noise conditions, least square
Wavelet oscillatory estimated by criterion is stronger, and maximal correlation entropy estimate result matches preferably with preliminary wavelet, especially to non-height
This noise, resultant error is more apparent obtained by criterion of least squares, and maximal correlation entropy can preferably restore seismic wavelet
True form, it can be seen that Method for Seismic Wavelet Estimation has stronger than criterion of least squares under the conditions of maximal correlation entropy criterion
Robustness.
Embodiment two：
In the embodiment of the present invention, we have carried out seismic wavelet estimation using the practical work area of China's reservoirs in one oilfield in western China.First
Well earthquake record was extracted, and piecemeal is done to well curve and handles to obtain reflection coefficient sequence, then passes through maximal correlation entropy criterion
Seismic wavelet is estimated with criterion of least squares, obtains that the results are shown in Figure 7.For verification result validity, Wo Mentong
Composite traces is crossed to compare to be verified with composite traces by well.Fig. 8 is maximal correlation entropy criterion extraction wavelet synthesis earthquake note
Record, criterion of least squares extraction wavelet composite traces and seismic trace near well compare, it can be found that maximal correlation entropy criterion extraction
Wave composite traces and well bypass road difference are smaller, and whole mean square error is 2.3, and seismic wavelet synthesis is obtained under criterion of least squares
The whole mean square error of record is 3.6, it can be seen that, the methods of seismic wavelet extraction based on maximal correlation entropy criterion than it is traditional most
Small two to multiply wavelet extraction method precision higher, robustness under criterion stronger.
Those of ordinary skill in the art will understand that the embodiments described herein, which is to help reader, understands this hair
Bright principle, it should be understood that protection scope of the present invention is not limited to such specific embodiments and embodiments.This field
Those of ordinary skill can make according to these technical inspirations disclosed by the invention various does not depart from the other each of essence of the invention
The specific deformation of kind and combination, these deform and combine still within the scope of the present invention.
Claims (4)
1. a kind of seismic wavelet method for extracting signal based on maximal correlation entropy, which is characterized in that include the following steps：
S1, by the use of Gaussian kernel as kernel function, build discrete joint entropy expression formula；
S2, seismic inversion model, existing observation data and reflectance factor are substituted into joint entropy expression formula, obtains object function；
S3, object function is converted to minimalization form；
S4, object function is solved using plan conjugate gradient inversion algorithm, obtains the seismic wavelet for needing to estimate；The step S4 tools
Body include it is following step by step：
S41, initialization process, setting initial model x0=w, w are to need the seismic wavelet estimated and using null vector as initially
Value, puts iterations k=0；
The gradient g of S42, calculating target function objk；
S43, update intend the direction of search of conjugate gradient inversion algorithm：If k=0, pk=-gk, otherwise have：
P in formulakRepresent the direction of search, yk-1Represent gradient increment, zk-1Represent conjugate direction, βkFor the forgetting factor of the direction of search,
bkFor the gradient increment coefficient in the direction of search more new formula；
S44, step-size in search α is calculatedk：
Matrixes of the G for reflectance factor auto-correlation function construction, e in formulakRepresent kth time iterative estimate residual error；
S45, update model parameter：
xk+1=xk+αkpk (6)
S46, it checks whether algorithm meets the condition of convergence, if then terminating iteration, exports inversion result x*=xk+1Estimate as needs
Otherwise the seismic wavelet w of meter enables k=k+1, return to step S42 be iterated.
2. the seismic wavelet method for extracting signal according to claim 1 based on maximal correlation entropy, which is characterized in that described
The discrete joint entropy expression formula built in step S1 is：
σ is core is wide and σ in formula>0, N represents the length of data X and Y, xiAnd yiI-th of data X and Y is represented respectively.
3. the seismic wavelet method for extracting signal according to claim 2 based on maximal correlation entropy, which is characterized in that described
Step S2 is specially：
By seismic inversion model s=w (t) * r (t)+n (t), existing observation data x (t)obsAnd reflectance factor r (t) substitutes into phase
Close entropy expression formula；Wherein, observation data x (t)obsS i.e. in seismic inversion model, w (t) are the ground that the present invention will calculate solution
Wavelet is shaken, r (t) is the vector for characterizing formation characteristics, i.e. reflectance factor, and n (t) is additivity present in characterization seismic inversion model
Noise；
Obtain object function：
4. the seismic wavelet method for extracting signal according to claim 3 based on maximal correlation entropy, which is characterized in that described
It is expressed as after object function is converted to minimalization form in step S3：
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| CN108120598B (en) * | 2017-12-19 | 2019-09-13 | 胡文扬 | Square phase-couple and the bearing incipient fault detection method for improving bispectrum algorithm |
| CN116755141B (en) * | 2023-04-18 | 2024-03-29 | 成都捷科思石油天然气技术发展有限公司 | Depth domain seismic wavelet extraction method |
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| US6597994B2 (en) * | 2000-12-22 | 2003-07-22 | Conoco Inc. | Seismic processing system and method to determine the edges of seismic data events |
| CN102707314B (en) * | 2012-05-28 | 2014-05-28 | 中国石油集团川庆钻探工程有限公司地球物理勘探公司 | Deconvolution method of multi-path double-spectral domain mixed phase wavelets |
| CN103645500B (en) * | 2013-11-08 | 2015-05-27 | 中国石油大学(北京) | Method for estimating mixed-phase seismic wavelets of frequency domain |
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