Wavelet extraction method based on fractional number order Fourier
Technical field
The present invention relates to seismic exploration technique field. More particularly, relate to a kind of in seismic prospecting, use based onThe wavelet extraction method in fractional order Fourier (FRFT) territory.
Background technology
Seismic exploration technique is gradually to high accuracy, high-resolution future development, and accurately extracting wavelet is deconvolution, wave resistanceThe basis of anti-inverting and forward simulation. In nearly twenty or thirty year, people have proposed the algorithm of a lot of wavelet extractions, and have obtained certainEffect, but existing methods of seismic wavelet extraction all has deficiency separately, and the wavelet precision of extracting is not high, makes waveletExtractive technique becomes affects one of further key factor improving of seismic inversion. Conventional algorithm all supposes that stratum is individualTime-invariant system, but because subsurface formations information is along with the variation of the degree of depth changes, therefore it is a time-varying system, soDescribing it by linear time invariant system must be not accurate enough, thereby causes wavelet extraction precision poor, wave impedance inversion resultMisfit reservoir prediction difficulty with drilling geology. Therefore, find a kind of method, describe subsurface formations by time-varying system and believeBreath, make up conventional Fourier can not process when non-become, the deficiency of non-stationary process, improve the precision of wavelet extraction, improve intoThe accuracy of row seismic layer labeling and the resolution ratio of seismic inversion, carry out bonding layer prediction and fluid identification more accurately.
The extracting method of seismic wavelet comprises two large classes at present, and the first kind is that certainty is extracted wavelet, and Equations of The Second Kind is statisticsProperty extract wavelet. The first kind refers to that hypothesis reflectance factor can have well logging to calculate, and in conjunction with seismic trace near well, is asked by convolution theoryGo out seismic wavelet, seismographic record is regarded as to the convolution of wavelet and reflectance factor. Equations of The Second Kind is that hypothesis seismic wavelet is constant while being, underground reflection coefficient sequence has white noise random sequence, does not need to calculate reflection coefficient sequence, and according to seismic channelStatistical information (second-order statistic, high-order statistic), estimates seismic wavelet. Common wavelet extraction method has:
(1) auto-correlation algorithm
The method is extracted seismic wavelet based on second-order statistic (auto-correlation function) method, first by Robinson (1975)Propose, suppose when seismic wavelet is constantly, underground reflectivity is the random sequence with white noise spectrum, and these hypothesis are meaned and landedThe shake amplitude spectrum of data and the amplitude spectrum of seismic wavelet only differ a constant, namely can be in the hope of the amplitude of seismic waveletSpectrum, for the phase spectrum of wavelet, must provide some hypothesis (minimum phase, zero phase or maximum phase), then by negatingFourier transformation can be tried to achieve wavelet, but the method can not be extracted the phase information of wavelet.
(2) homomorphism method
The method basic thought is that convolution signal is carried out to Fourier transform, obtains the product of two signals, then to take the logarithm be two lettersNumber and, namely the nonlinear properties in time domain are converted to the linear signal in frequency domain, in frequency domain, separated. OneIt is the logarithm of its Fourier transformation that the intermediary heat of critical sequences is composed. Supposed that seismic wavelet is metastable, it is correspondingIntermediary heat spectrum is also approximate constant, and stratum reflectance factor thinks that it is change at random, and corresponding intermediary heat spectrum is to change. Carry outWhen multiple tracks stack, stable because the seismic wavelet on per pass is all similar to, thus in the time of stack, obtain reinforcement, and reflectance factor isChange, what in the time of stack, just may be similar to balances out, thereby the cepstrum of whole earthquake model has just become seismic waveletIntermediary heat spectrum. The method is very sensitive to noise, and the effect of the lower geological data of signal to noise ratio being extracted to wavelet is poor.
(3) RoyWhite wavelet extraction method
The method is that well data is demarcated and made to a kind of employing and geological data is interrelated obtains earthquake from waveletThe method of excellent estimation, belongs to determinate wavelet pickup method, and it does not need to suppose the phase place of wavelet. Ideally, this algorithm dividesTwo steps: determine the optimum position of extracting wavelet well used; On this position, determine best wavelet. Its supposition has with geological dataThe drilling well position of closing may not be the ideal position that extracts wavelet, and seismic sweep algorithm can be effectively near fixed well positionFind new position. Because this algorithm is used log data, so extract the precision of wavelet, the precision of log data is relied on veryGreatly.
(4) Higher order Statistics
High-order statistic (higher-order spectrum) is compared with second-order statistic (power spectrum), except comprising the abundanter information of signalOutside amount (as complete phase information), also has any Gaussian noise signal characteristic blindly, coloured Gauss that can be under intensity arbitrarilyIn noise, extract the phase information of non-Gaussian signal, broken away from some hypothesis of sub-wave phase and additive noise, this has solved veryThe problem that multiplex other method cann't be solved. The shortcoming of this algorithm is that amount of calculation is very large.
Summary of the invention
The present invention uses time-varying system (Fourier Transform of Fractional Order FrFT) to describe formation information, more realisticThe true medium situation of stratum geological system, can improve the precision of seismic wavelet extraction, further improves seismic inversion, reservoirResolution ratio and the precision of prediction. Method of the present invention utilizes the FrFT second-order cumulant of seismographic record, log data to extract earthquakeWavelet, has avoided using calculating numerous and diverse, and the Higher-order Cumulants that operand is huge extracts seismic wavelet.
According to an aspect of the present invention, provide a kind of wavelet extraction method based on fractional number order Fourier, having comprised: buildVertical formation information initial model; Utilize the reflectance factor synthetic seismogram of input wavelet and formation information initial model; CalculateInput wavelet and the synthetic cross-correlation matrix of seismographic record data and the autocorrelation matrix of seismographic record data, and to describedCross-correlation matrix and autocorrelation matrix carry out Fourier Transform of Fractional Order; To described cross-correlation matrix and autocorrelation matrix application pointThe optimal filtering algorithm of number rank Fourier calculates optimal order and the optimal filter operator of mean square error minimum; Based on describedExcellent filter operator and optimal order extract wavelet, and wherein, optimum operator f (m) is represented by following equation:
Wherein,WithRepresent respectively the Fourier Transform of Fractional Order of described cross-correlation matrix and autocorrelation matrix,And extract wavelet by following equation
Wherein, y represents the column vector of the sample sequence of seismic signal, y=Hx+n, and p represents optimal order;
Wherein, x is the column vector that represents the sample sequence of inputting wavelet, and n represents the column vector of the sample sequence of noise, HRepresent reflectance factor matrix.
According to an aspect of the present invention, described wavelet extraction method also comprises: by the wavelet of extracting and original inputRipple compares.
According to an aspect of the present invention, the formation information initial model becoming when described formation information initial model is.
According to an aspect of the present invention, described input wavelet is to carry in theoretical wavelet or actual seismic data and well-log informationThe true wavelet of getting.
According to an aspect of the present invention, search optimal order p in the scope of (2,2).
Brief description of the drawings
By the description of carrying out below in conjunction with accompanying drawing, above and other object of the present invention and feature will become more clearChu, wherein:
Fig. 1 is the flow chart illustrating according to the wavelet extraction method based on FRFT territory of the present invention;
Fig. 2 is the schematic diagram illustrating according to the original input wavelet of the embodiment of the present invention;
Fig. 3 illustrates that input wavelet is by synthetic after time-varying system, the schematic diagram of the seismographic record of plus noise not;
Fig. 4 is illustrated in the schematic diagram of traditional Fourier to the wavelet that synthetic seismogram of plus noise is not extracted;
Fig. 5 illustrates to use according to the wavelet extraction method based on FRFT territory of the embodiment of the present invention closing of plus noise notBecome the schematic diagram of the wavelet of seismographic record extraction;
Fig. 6 is the schematic diagram that seismographic record synthetic, that be added with Gaussian noise after input wavelet is by time-varying system is shown;
Fig. 7 is illustrated in the schematic diagram of wavelet that traditional Fourier has extracted having added the synthetic seismogram of noise;
Fig. 8 illustrates to use according to the wavelet extraction method based on FRFT territory of the embodiment of the present invention having added noiseThe schematic diagram of the wavelet that synthetic seismogram is extracted;
Fig. 9 illustrates to use according to the wavelet extraction method based on FRFT territory of the embodiment of the present invention having added different lettersMake an uproar than the schematic diagram of wavelet that extracts of the synthetic seismogram of Gaussian noise.
Detailed description of the invention
Provide the description carried out with reference to accompanying drawing to contribute to complete understanding to be limited as claim and equivalent thereof belowExemplary embodiment of the present invention. Described description comprises that various detailed details understand contributing to, and these descriptions will be byThink only for exemplary. Therefore, those of ordinary skill in the art will recognize do not departing from the scope of the present invention and spiritSituation under can make various change described here and modification. In addition, for clear and succinct, can omit known function andThe description of structure.
Fig. 1 is the flow chart illustrating according to the wavelet extraction method based on FRFT territory of the present invention.
First,, at step S101, set up formation information initial model. This formation information initial model is remembered for generation of earthquakeRecord reflectance factor. Preferably, according to the present invention, the stratum initial model becoming can set up time. The formation information becoming when employing is initialThe benefit of model is the truth of more realistic stratum system. According to one embodiment of present invention, can adoptThe formation information initial model that following equation becomes while simulation as the linear time varying system representing:
h(t,t′)=exp(-j2πt(t-t′))sinc(t-t′)(1)
Should be understood that the formation information initial model becoming when above is only an example, also can adopt other time becomeSystem builds formation information initial model.
Next,, at step S102, utilize the synthetic earthquake note of reflectance factor of input wavelet and formation information initial modelRecord. According to one embodiment of present invention, input wavelet can be theoretical wavelet, for example, and Ricker wavelet as shown in Figure 2. RootAccording to another embodiment of the present invention, input wavelet can be the true wavelet of extracting in actual seismic data and well-log information.
Then, at step S103, calculate the correlation matrix of input wavelet and synthetic seismographic record data, and to Correlation MomentBattle array is carried out p rank fractional fourier transform. Particularly, conventionally, the observation model of seismic signal can be represented by following equation (2):
y=Hx+n(2)
Wherein, y is that column vector, the x that represents the sample sequence of seismic signal is the row that represent the sample sequence of inputting waveletVector, n represents the column vector of the sample sequence of noise, H represents reflectance factor matrix. Calculate input wavelet and seismographic record dataCross-correlation matrix Rxy=E[xyH] and the autocorrelation matrix Ryy=E[yy of seismographic record dataH]. Suppose input wavelet and make an uproarThe autocorrelation matrix of sound is respectively RxxAnd Rnn, correlation matrix RyyAnd RxyP rank fractional fourier transform can be expressed as withUnder equation (3) and (4):
Next,, at step S104, based on the correlation matrix of input wavelet and synthetic seismographic record data, utilize markThe optimal filtering algorithm of rank Fourier calculates the optimal order that makes mean square error minimum, and calculates optimal filter operator f (m).Particularly, can pass through p value to be searched for to calculate in the scope of (2,2) optimal order of mean square error minimum, and can pass throughFollowing equation (5) calculates optimum operator f (m):
Then,, at step S105, extract wavelet based on optimal order and optimum operator. Can calculate wavelet by equation (6)
Finally, can also show the wavelet of extracting at step S106, thereby by the wavelet of extracting and original input waveletCompare analysis.
Fig. 2-Fig. 9 shows respectively the not input wavelet of plus noise and closes with input wavelet, the input wavelet of having added noiseThe seismographic record becoming and the schematic diagram of wavelet extracting according to traditional Fourier with according to FRFT of the present invention territory respectively. ItsIn, Fig. 3 illustrates that input wavelet is by synthetic after time-varying system, the schematic diagram of the seismographic record of plus noise not; Fig. 4 illustratesSchematic diagram at traditional Fourier to the wavelet that synthetic seismogram of plus noise is not extracted; Fig. 5 illustrates to use according to thisThe signal of the wavelet extraction method based on FRFT territory of inventive embodiments to the wavelet that synthetic seismogram of plus noise is not extractedFigure; Fig. 6 is the schematic diagram that seismographic record synthetic, that be added with Gaussian noise after input wavelet is by time-varying system is shown; Fig. 7 isBe illustrated in the schematic diagram of wavelet that traditional Fourier has extracted having added the synthetic seismogram of noise; Fig. 8 illustrates useThe son having extracted having added the synthetic seismogram of noise according to the wavelet extraction method based on FRFT territory of the embodiment of the present inventionThe schematic diagram of ripple; Fig. 9 illustrates to use according to the wavelet extraction method based on FRFT territory of the embodiment of the present invention having added notThe schematic diagram of the wavelet of extracting with the synthetic seismogram of the Gaussian noise of signal to noise ratio.
Contrast by above accompanying drawing can find out, according to the wavelet extraction method based on FRFT territory of the present invention is no matterAt plus noise or not in plus noise seismographic record, can more intactly extract the Main Morphology of original wavelet, and extract sonThe effect of ripple is all effective than conventional Fourier transform method. Especially, in Fig. 9, added the Gaussian noise of different signal to noise ratiosAfter, can more intactly extract the Main Morphology of original wavelet according to wavelet extraction method of the present invention, there is certain anti-noiseAbility.
Wavelet extraction method according to the present invention can be recorded in and comprise the journey of carrying out by computer implemented various operationsIn the computer-readable medium of order instruction. Medium also can only include programmed instruction or comprise the number combining with programmed instructionAccording to file, data structure etc. The example of computer-readable medium comprises magnetizing mediums (for example hard disk, floppy disk and tape); Optics is situated betweenMatter (for example CD-ROM and DVD); Magnet-optical medium (for example, CD); And special preparation is for storing and execution of program instructionsHardware unit (for example, read-only storage (ROM), random access memory (RAM), flash memory etc.). Medium can be also to comprise biographyThe transmission medium (such as optical line or metal wire, waveguide etc.) of the carrier wave of the signal of defeated established procedure instruction, data structure etc. JourneyThe example of order instruction comprises the machine code for example being produced by compiler and comprises can use interpreter to be carried out by computer seniorThe file of code.
Although specifically shown with reference to exemplary embodiment of the present invention and described the present invention, the skill of this areaArt personnel should be appreciated that, in the case of not departing from the spirit and scope of the present invention that are defined by the claims, can enter itVarious changes in row form and details.