CN108646289B - A method of estimation earthquake quality factor - Google Patents
A method of estimation earthquake quality factor Download PDFInfo
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- G—PHYSICS
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- 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. for interpretation or for event detection
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- 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. for interpretation or for event detection
- G01V1/36—Effecting static or dynamic corrections on records, e.g. correcting spread; Correlating seismic signals; Eliminating effects of unwanted energy
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Abstract
The invention discloses a kind of methods for estimating earthquake quality factor, the following steps are included: the earthquake reflective data of S1, acquisition poststack earthquake record, obtain smooth local time's frequency amplitude spectrum using shaping regularization and least-square inversion technology according to the earthquake reflective data；S2, the crest frequency decomposed based on Ricker wavelet is calculated according to local time's frequency amplitude spectrum；S3, seismic attenuation quality factor is estimated according to the relationship of the Ricker wavelet crest frequency and Q value.The invention has the benefit that influence that can be relevant etc. to avoid seismic noise, reflection, improves stability, the reliability and accuracy of the quality factor of acquisition.
Description
Technical field
The present invention relates to seismic data processing technical field more particularly to a kind of methods for estimating earthquake quality factor.
Background technique
Seismic wave in actual formation Propagation, geometrical attenuation, transmission, reflection loss and medium it is non-fully elastic
The decaying of seismic wave can be caused.And natural attenuation and stratum inner structural features caused by the non-fully elasticity of medium, containing stream
Volume property (porosity, permeability, saturation degree etc.) is closely related, general stores material prime factor Q description.Q value is in prediction lithology, oil gas
Have great importance in terms of the position of hiding and distribution, is a kind of very promising seismic properties.
Presently, there are a variety of Q value estimation methods, such as wavelet or frequency spectrum simulation, frequency spectrum ratio method, Rise time and
Analytic signal method etc..The method that these methods are generally divided into time-domain and frequency domain, due to depending on the calculation method of frequency
It is simple and reliable, it is widely used in geophysical exploration.The method that local time-frequency conversion passes through least-square inversion
Smooth local time-frequency spectrum is obtained, provides preferable time-frequency spectrum for the estimation of Q value.But seismic noise reflects the equal energy such as relevant
Local time-frequency feature is influenced, to influence the precision of earthquake Q value estimation, therefore, the embodiment of the present application is in time-frequency
The stability and precision for proposing high q-factor estimation are decomposed on the basis of spectrum using Ricker wavelet.
Summary of the invention
The present invention provides a kind of method for estimating earthquake quality factor, can be concerned with to avoid seismic noise, reflection etc.
It influences, improves stability, the reliability and accuracy of the quality factor of acquisition.
In order to solve the above technical problems, the embodiment of the present application provides a kind of method for estimating earthquake quality factor, including
Following steps:
S1, the earthquake reflective data for obtaining poststack earthquake record utilize shaping regularization according to the earthquake reflective data
Smooth local time's frequency amplitude spectrum is obtained with least-square inversion technology；
S2, the crest frequency decomposed based on Ricker wavelet is calculated according to local time's frequency amplitude spectrum；
S3, seismic attenuation quality factor is estimated according to the relationship of the Ricker wavelet crest frequency and Q value.
Wherein, in the present embodiment, local time's frequency amplitude spectrum, packet are calculated according to earthquake reflective data in the step S1
Include following steps:
S11, shaping regularization method is introduced on the basis of Fourier transformation, calculate local time's frequency amplitude spectrum, comprising:
Unstable state recurrence and Fourier analysis are combined, time-frequency spectrum is defined with the Fourier coefficient of time-varying, utilizes shaping
The continuity and slickness of regularization constraint time-varying Fourier coefficient；
Fourier transformation can be expressed as
In formula: CkFor Fourier coefficient；ΦkIt (x) is Fourier basis functions, if frequency is limited, the range of k
Become [0, N], N=kmax=fmax/Δf,CkFor frequency sampling interval, in optimum theory, CkIt can be asked by following least square
Topic solves
In formula, | | | |2The L2 norm of representative function；Assuming that CkX changes at any time, as the function of time variable x, fixed
Justice
Fourier coefficient Ck(x) be time x function, the range of frequency f is zero between Nyquist frequency,
Above-mentioned least-squares problem is mathematically ill, because it is to owe fixed least-squares problem: unknown quantity
Number is far longer than the number of constraint condition, considers constraint factor Ck(x) have certain characteristic, such as slickness, therefore
R indicates shaping regularizing operator in formula, and shaping regularization provides a kind of iteration optimization algorithms of simplicity, Ke Yiwen
Fixed solution indirect problem, being typically chosen Gauss smoothing operator is shaping regularizing operator, and smooth radius is adjustable parameter, control
Make coefficient Ck(x) smooth degree；
By extending above-mentioned equation, reversible local time-frequency conversion has following form
Wherein, in the present embodiment, it is calculated according to local time's frequency amplitude spectrum based on rake in the step S2
The crest frequency of Wave Decomposition, comprising the following steps:
S22, a series of sum that earthquake time-frequency spectrum is expressed as to different Ricker wavelet components
Wherein d (t, f) is the time-frequency spectrum of seismic channel, ai(t) and mi(t) be respectively i-th of Ricker wavelet spectrum component vibration
Width and crest frequency, spectrum component are represented by
The model is a linear combination of Ricker wavelet frequency spectrum, determines comprising nonlinear function and by multiple parameters, is
Estimation Ricker wavelet frequency spectrum, needs to seek parameter a={ a1,a2,...,anAnd m={ m1,m2,...,mn, it can be by such as
Under optimization least-squares estimation
Wherein, in the present embodiment, according to the pass of Ricker wavelet crest frequency and Q value in the step S3
System's estimation seismic attenuation quality factor, comprising the following steps:
S31, the amplitude spectrum according to Ricker wavelet
Wherein m is the crest frequency of Ricker wavelet, is obtained to frequency derivation
Instantaneous spectrum is after seismic travel time t
A (f, t)=G (t) F (f) exp (- π ftQ-1),
Wherein Q is quality factor, and G (t) is and propagates and the unrelated factor that decays, available to above formula frequency derivation
F ' (f)=π tF (f) Q-1
It is available by the above-mentioned equation of simultaneous
Wherein fpIndicate the crest frequency of received direct wave；
After obtaining the estimation method of accumulative Q, to obtain end layer Q value, it can be obtained by following publicity
Wherein TnAnd Tn-1Respectively different observation moment, QnAnd Qn-1Respectively TnAnd Tn-1The accumulative Q value at place, Qn' be
The layer Q value of n-th layer.
One or more technical solutions provided in the embodiments of the present application have at least the following technical effects or advantages:
Influence that can be relevant etc. to avoid seismic noise, reflection, improve the stability of the quality factor of acquisition, reliability and
Accuracy.
Detailed description of the invention
In order to more clearly explain the embodiment of the invention or the technical proposal in the existing technology, to embodiment or will show below
There is attached drawing needed in technical description to be briefly described, it should be apparent that, the accompanying drawings in the following description is only this hair
Bright some embodiments for those of ordinary skill in the art without any creative labor, can be with
It obtains other drawings based on these drawings.
After Fig. 1 is the seismic channel (a) for the decaying simulated in one embodiment for providing of this specification and does automatic gain
Display figure (b)；
Local time-frequency spectrum (a) and the Ricker wavelet point of seismic channel are simulated in one embodiment that Fig. 2 provides for this specification
Solve the spectrum (b) of simulation；
The Q value (solid line) of the Q value (dotted line) and theory estimated in one embodiment that Fig. 3 provides for this specification；
Practical post-stack seismic data in one embodiment that Fig. 4 provides for this specification；
The Q value that real data is estimated in one embodiment that Fig. 5 provides for this specification.
Specific embodiment
In order to better understand the above technical scheme, in conjunction with appended figures and specific embodiments to upper
Technical solution is stated to be described in detail.
A kind of method of estimation earthquake quality factor described in the present embodiment, comprising the following steps:
S1, the earthquake reflective data for obtaining poststack earthquake record utilize shaping regularization according to the earthquake reflective data
Smooth local time's frequency amplitude spectrum is obtained with least-square inversion technology；
S2, the crest frequency decomposed based on Ricker wavelet is calculated according to local time's frequency amplitude spectrum；
S3, seismic attenuation quality factor is estimated according to the relationship of the Ricker wavelet crest frequency and Q value.
In one embodiment of this specification, unstable state recurrence and Fourier analysis are combined, in Fu of time-varying
Leaf system number defines time-frequency spectrum, utilizes the continuity and slickness of shaping regularization constraint time-varying Fourier coefficient.
Fourier transformation can be expressed as
In formula: CkFor Fourier coefficient；ΦkIt (x) is Fourier basis functions.If frequency is limited, the range of k
Become [0, N], N=kmax=fmax/Δf,CkFor frequency sampling interval.In optimum theory, CkIt can be by following least square
Problem solving
In formula, | | | |2The L2 norm of representative function；Assuming that CkX changes at any time, as the function of time variable x, fixed
Justice
Fourier coefficient Ck(x) be time x function.The range of frequency f is zero between Nyquist frequency.In reality
In, frequency range can be provided according to specific practical problem.
Above-mentioned least-squares problem is mathematically ill, because it is to owe fixed least-squares problem: unknown quantity
Number is far longer than the number of constraint condition.To solve this ill-conditioning problem, constraint factor C is consideredk(x) there is certain characteristic,
Such as slickness.Therefore
R indicates shaping regularizing operator in formula.Shaping regularization provides a kind of iteration optimization algorithms of simplicity, Ke Yiwen
Fixed solution indirect problem, being typically chosen Gauss smoothing operator is shaping regularizing operator, and smooth radius is adjustable parameter, control
Make coefficient Ck(x) smooth degree.
By extending above-mentioned equation, reversible local time-frequency conversion has following form
Parameter smooth radius is the ginseng of a Controlling model (coefficient of time-frequency conversion) smooth degree in local time-frequency conversion
Number, and window Fourier transform and the window function of S-transformation are the parameters of data field, by the way that data (original input signal) are divided into
The window of different moments completes local addresses analysis.Also different from small echo class Time-Frequency Analysis Method, it is local time-frequency conversion
The simple extension of Fourier analysis, the selection of basic function are different from other small echo class Time-Frequency Analysis Methods.
After obtaining local time-frequency conversion, frequency spectrum and crest frequency after being decomposed using Ricker wavelet decomposition technique.Tool
Body is implemented as follows:
Earthquake time-frequency spectrum is expressed as to a series of sum of different Ricker wavelet components
Wherein d (t, f) is the time-frequency spectrum of seismic channel, ai(t) and mi(t) be respectively i-th of Ricker wavelet spectrum component vibration
Width and crest frequency, spectrum component are represented by
The model is a linear combination of Ricker wavelet frequency spectrum, determines comprising nonlinear function and by multiple parameters, is
Estimation Ricker wavelet frequency spectrum, needs to seek parameter a={ a1,a2,...,anAnd m={ m1,m2,...,mn, it can be by such as
Under optimization least-squares estimation
The specific method using separable least-squares estimation solves above-mentioned parameter, and separation is referred to linear segment and non-
Linear segment separately solves, it is assumed that nonlinear parameter m and linear dimensions a can be asked by solving Linear least squares minimization problem
It takes
A=ψ (m)*d
Wherein ψ (m) is by ψi[mi(t), f] composition matrix, ψ (m) * is the generalized inverse of matrix ψ (m), and a is substituted into former letter
Number, minimization problem are converted into
With Gauss-Newton algorithm by the problem linearization
According to mi(t) initial value finds out ai(t) and ai' (t) then finds out mi(t), after successive ignition, mi
(t) accumulated value can converge to estimated value, and Gauss-Newton algorithm is high-efficient, by 20 available acceptables of iteration
Convergency value.
The method of the determination earthquake quality factor of the embodiment of the present application, it is described according to Ricker wavelet crest frequency and quality because
The relationship of sub- Q value estimates seismic attenuation quality factor.
According to the amplitude spectrum of Ricker wavelet
Wherein m is the crest frequency of Ricker wavelet.Frequency derivation is obtained
Instantaneous spectrum is after seismic travel time t
A (f, t)=G (t) F (f) exp (- π ftQ-1),
Wherein Q is quality factor, G (t) be with the factor (including geometrical attenuation etc.) propagating and decay unrelated, to above formula frequency
Rate derivation is available
F ' (f)=π tF (f) Q-1
It is available by the above-mentioned equation of simultaneous
Wherein fpIndicate the crest frequency of received direct wave.This results in the estimation methods of accumulative Q, if to obtain
End layer Q value can be obtained by following formula
Wherein TnAnd Tn-1Respectively different observation moment, QnAnd Qn-1Respectively TnAnd Tn-1The accumulative Q value at place, Qn' be
The layer Q value of n-th layer.
Fig. 1 (a) is one of seismic data of simulation, which has a very strong decay characteristics, in theoretical Q value such as Fig. 3
Realization shown in.In order to show the signal of deep layer, we are display such as Fig. 1 (b) after automatic gain, and comparison is it can be found that earthquake letter
Number by deep fades.To the road, seismic data does local time-frequency conversion, obtains time-frequency amplitude spectrum such as Fig. 2 (a), it can be seen that part
Time-frequency spectrum is not very smooth, and frequency limit has seriously affected the feature of its decaying, therefore the estimation of Q value is relatively difficult.It utilizes
Spectrum such as Fig. 2 (b) after Ricker wavelet is decomposed and reconstituted, it can be seen that frequency spectrum is smooth, conducive to being used to calculate Q value.Utilize crest frequency
With the relationship of Q value, the Q value being calculated is as shown by dotted lines in figure 3, it can be seen that the method energy provided by this specification embodiment
It is enough to obtain and the much the same result of theoretical value.
This explanation additionally provides the embodiment of a real data.Fig. 4 is actual seismic poststack data；Fig. 5 is actual number
The Q value obtained according to estimates, it can be seen that the Q value shallow-layer of estimation is higher, and deep layer Q value is smaller, illustrates that deep layer decaying is serious.
The above described is only a preferred embodiment of the present invention, be not intended to limit the present invention in any form, though
So the present invention has been disclosed as a preferred embodiment, and however, it is not intended to limit the invention, any technology people for being familiar with this profession
Member, without departing from the scope of the present invention, when the technology contents using the disclosure above make a little change or modification
For the equivalent embodiment of equivalent variations, but anything that does not depart from the technical scheme of the invention content, according to the technical essence of the invention
Any simple modification, equivalent change and modification to the above embodiments, all of which are still within the scope of the technical scheme of the invention.
Claims (2)
1. a kind of method for estimating earthquake quality factor, which comprises the following steps:
S1, the earthquake reflective data for obtaining poststack earthquake record, according to the earthquake reflective data using shaping regularization and most
Small square inversion technique obtains smooth local time's frequency amplitude spectrum；
S2, the crest frequency decomposed based on Ricker wavelet is calculated according to local time's frequency amplitude spectrum, comprising the following steps:
Earthquake time-frequency spectrum is expressed as to a series of sum of different Ricker wavelet components
Wherein d (t, f) is the time-frequency spectrum of seismic channel, ai(t) and mi(t) be respectively i-th of Ricker wavelet spectrum component amplitude and
Crest frequency, spectrum component are represented by
The model is a linear combination of Ricker wavelet frequency spectrum, is determined comprising nonlinear function and by multiple parameters, in order to estimate
Ricker wavelet frequency spectrum is calculated, needs to seek parameter a={ a1,a2,...,anAnd m={ m1,m2,...,mn, it can be by following
Optimize least-squares estimation
The specific method using separable least-squares estimation solves above-mentioned parameter, and separation is referred to linear segment and non-linear
Part separately solves, it is assumed that nonlinear parameter m and linear dimensions a can be sought by solving Linear least squares minimization problem
A=ψ (m)*d
Wherein ψ (m) is by ψi[mi(t), f] composition matrix, ψ (m) * is the generalized inverse of matrix ψ (m), a is substituted into original function, most
Smallization problem is converted into
With Gauss-Newton algorithm by the problem linearization
According to mi(t) initial value finds out ai(t) and ai' (t) then finds out mi(t), after successive ignition, mi(t)
Accumulated value can converge to estimated value, and Gauss-Newton algorithm is high-efficient, restrain by the available acceptable of 20 iteration
Value；
S3, according to the relationship of the Ricker wavelet crest frequency and Q value estimate seismic attenuation quality factor, including with
Lower step:
According to the amplitude spectrum of Ricker wavelet
Wherein m is the crest frequency of Ricker wavelet, is obtained to frequency derivation
Instantaneous spectrum is after seismic travel time t
A (f, t)=G (t) F (f) exp (- π ftQ-1),
Wherein Q is quality factor, and G (t) is and propagates and the unrelated factor that decays, available to above formula frequency derivation
F ' (f)=π tF (f) Q-1
It is available by the above-mentioned equation of simultaneous
Wherein fpIndicate the crest frequency of received direct wave；
After obtaining the estimation method of accumulative Q, to obtain end layer Q value, it can be obtained by following formula
Wherein TnAnd Tn-1Respectively different observation moment, QnAnd Qn-1Respectively TnAnd Tn-1The accumulative Q value at place, Qn' it is n-th layer
Layer Q value.
2. a kind of method for estimating earthquake quality factor according to claim 1, which is characterized in that in the step S1
Local time's frequency amplitude spectrum is calculated according to earthquake reflective data, comprising the following steps:
S11, shaping regularization method is introduced on the basis of Fourier transformation, calculate local time's frequency amplitude spectrum, comprising:
Unstable state recurrence and Fourier analysis are combined, time-frequency spectrum is defined with the Fourier coefficient of time-varying, utilizes shaping canonical
Change the continuity and slickness of constraint time-varying Fourier coefficient；
Fourier transformation can be expressed as
In formula: CkFor Fourier coefficient；ΦkIt (x) is Fourier basis functions, if frequency is limited, the range of k becomes
[0, N], N=kmax=fmax/Δf,CkFor time-varying coefficient, in optimum theory, CkIt can be solved by following least-squares problem
In formula, | | | |2The L2 norm of representative function；Assuming that CkX changes at any time, as the function of time variable x, definition
Fourier coefficient Ck(x) be time x function, the range of frequency f is zero between Nyquist frequency,
Above-mentioned least-squares problem is mathematically ill, because it is to owe fixed least-squares problem: the number of unknown quantity
It is far longer than the number of constraint condition, considers constraint factor Ck(x) have certain characteristic, such as slickness, therefore
R indicates shaping regularizing operator in formula, and shaping regularization provides a kind of iteration optimization algorithms of simplicity, can be stable
Indirect problem is solved, selects Gauss smoothing operator for shaping regularizing operator, smooth radius is adjustable parameter, controls coefficient
Ck(x) smooth degree；
By extending above-mentioned equation, reversible local time-frequency conversion has following form
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| CN110187388B (en) * | 2019-06-06 | 2021-01-05 | 成都信息工程大学 | Stable seismic quality factor Q estimation method based on variational modal decomposition |
| CN112415587B (en) * | 2019-08-21 | 2024-06-18 | 中国石油化工股份有限公司 | Reservoir seismic wave attenuation characteristic analysis method and reservoir reflection coefficient inversion method |
| CN112883326B (en) * | 2021-03-19 | 2022-07-08 | 吉林大学 | Self-adaptive time-frequency transformation method based on stream algorithm |
| CN113625341A (en) * | 2021-08-04 | 2021-11-09 | 中化地质矿山总局地质研究院 | Quality factor estimation method, device and system based on cepstrum analysis |
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