CN104570071B - A kind of linear AVA and AVF inversion methods of viscous acoustic medium Bayes - Google Patents
A kind of linear AVA and AVF inversion methods of viscous acoustic medium Bayes Download PDFInfo
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- CN104570071B CN104570071B CN201310476278.1A CN201310476278A CN104570071B CN 104570071 B CN104570071 B CN 104570071B CN 201310476278 A CN201310476278 A CN 201310476278A CN 104570071 B CN104570071 B CN 104570071B
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Abstract
The invention provides a kind of viscous linear AVA and AVF inversion methods of acoustic medium Bayes, belong to field of petroleum geophysical exploration.This method includes：The first step, input angle domain geological data, frequency domain geological data and log data；Second step, sets up the prior information and likelihood function of log data；3rd step, using the prior information and likelihood function, carries out the linear AVA and AVF invertings of Bayes, obtains speed and quality factor.
Description
Technical field
The invention belongs to field of petroleum geophysical exploration, and in particular to a kind of viscous acoustic medium Bayes linear AVA and AVF
Inversion method, SVEL and decay factor are obtained based on viscous acoustic medium using bayesian theory to carry out AVA and AVF invertings.
Background technology
Traditional AVO (amplitude is with offset distance) or AVA (Amplitudeversusangle) are always based on the complete bullet of underground medium
The hypothesis of property.And the Petrophysical measurement in VSP records, log data and laboratory shows seismic wave in communication process
Decay and dispersion phenomenon occurs, especially for the stratum containing hydrocarbon, the decay of seismic wave becomes apparent.It is actual
On, huge risk will be carried out to AVO analytic bands by ignoring the influence of the attenuation of seismic wave.
Base area earthquake wave propagation theory, external some scholars are attributed to the reflectance factor that underground medium absorbs by force.
White (1975), De Hoop (1991), Ursin (2002) etc. are giving one in terms of how calculating absorption reflectance factor
Series is theoretic to be discussed, general absorption inverse Problem is reduced to the single boundary of inverting by Innanen and Weglein (2007)
Reflectance factor at face, when Innanen (2011) has derived seismic wave and incide absorbing medium by elastic non-attenuation medium in detail
Reflection and the expression formula of transmission coefficient.In fact, the reflectance factor absorbed in complete description or inverting underground medium, both needs to examine
Change (AVA) of the amplitude with angle is considered, while also to consider variation relation (AVF) of the amplitude with frequency.Although having built at present
Some mechanism have been found to explain variation relation of the reflectance factor with frequency, but how to solve indirect problem is still one international
Problem.
Domestic scholars notice the amplitude anomaly in gas-bearing reservoir regional earthquake low frequency part very early, and based on broad sense S
Conversion or the method such as wavelet transformation have carried out correlative study, but not yet someone enters row amplitude and changed with frequency always) system grind
Study carefully.Appoint (2009) to carry out pore media amplitude in University of Houston to study with the mutation analysis of frequency, and derived in detail vertical
When straight incident reflectance factor with frequency change.With reference to AVO classification, appoint (2009) that AVF is equally divided into three classes and corresponded to respectively
Different gas-bearing reservoirs.This research work is paid attention to by some domestic scholars quickly, on the basis of Liu (2011) etc. is in office
Amplitude and achieves some beneficial understanding with the variation relation of frequency when further having derived inclined seismic wave.Even if
In this way, still still belonging to blank at home on the research for gluing acoustic medium AVA/AVF invertings work.
The content of the invention
It is an object of the invention to solve problem present in above-mentioned prior art, there is provided a kind of viscous acoustic medium Bayes line
Property AVA and AVF inversion methods, the geophysics fine description for reservoir is target, linear using viscous acoustic medium Bayes
AVA/AVF invertings obtain the speed and dampening information of underground medium, improve the reliability and accuracy of reservoir oil and gas prediction,
With the strong bright characteristics of face the practice, application.
The present invention is achieved by the following technical solutions：
A kind of linear AVA and AVF inversion methods of viscous acoustic medium Bayes, including：
The first step, input angle domain geological data, frequency domain geological data and log data
Second step, sets up the prior information and likelihood function of log data；
3rd step, using the prior information and likelihood function, carries out the linear AVA and AVF invertings of Bayes, obtains speed
And quality factor.
Angle domain geological data and the geological data of frequency domain are expressed as d in the first stepobs, the data be the time,
The 3D data volume of angle and frequency；Log data is expressed as：M=[lnc, α ,]T, wherein, m be elastic parameter constitute to
Amount, lncThe logarithm of speed is represented respectively, and α represents decay factor, and the two is obtained from well-log information.
What the second step was realized in：
The prior information for setting up log data is as follows：
Wherein,Represent the n sampling point Normal Distributions on m, μm, ∑mM expectation and variance is represented respectively, is led to
Cross what the statistics for sampling point of logging well was obtained；
Set up likelihood function as follows：
Wherein,Represent that observation geological data meets Gaussian Profile,The expectation of geological data is represented,
Represent the variance of geological data；
Expect to meet respectively with variance：
∑″mRepresent to ask second order to lead the statistical variance of elastic parameter, ∑eRepresent the variance of noise；
Wherein, S is：
It can be write as each S：
For AVA invertings, use：
For AVF invertings, use：
Wherein, s1(θi, ωi) expression incidence angle be θi, dominant frequency is ωiWavelet；Subscript 1,2 is until nwave represents son
The delay of ripple；Ac(θnθ, ωfix) represent frequencies omegafixIt is fixed, dependent on incidence angle θnθVelocity coeffficient；Aα(θnθ, ωfix) represent
Frequencies omegafixIt is fixed, dependent on incidence angle θnθDecay factor coefficient；Ac(θfix, ωnω) represent incidence angle θfixIt is fixed, rely on
In frequencies omeganωVelocity coeffficient；Aα(θfix, ωnω) represent incidence angle θfixIt is fixed, dependent on frequencies omeganωDecay factor system
Number.
What the 3rd step was realized in：
Earthquake record and elastic parameter meet Joint Distribution：
Wherein
In given dobsIn the case of m Posterior probability distribution be：
Posterior error and variance are respectively：
M maximum a posteriori solution (MAP) is equal to posterior error valueCovariance matrix is used
To evaluate the final uncertainty of inversion result.
Formula (23) is m expectation and variance, and that m expression is velocities Vp and quality factor q p, therefore obtains m's
Expect to have obtained the expectation of velocities Vp and quality factor q p, that is, maximum probability solution；And variance is then to assess the two
The uncertainty of parameter.
Compared with prior art, the beneficial effects of the invention are as follows：Relative to existing technology, invention introduces earthquake number
According to frequency-domain information, the prior information needed for inverting and the likelihood function of frequency dependence are built under the guidance of bayesian theory,
Inversion result not only can obtain the speed of underground medium but also can obtain the decay factor change of medium；Provided in the form of probability
Result provide possibility for follow-up analysis of uncertainty, more comprehensively evaluated while also being provided for reservoir prediction.
Brief description of the drawings
Fig. 1 gas-bearing sandstone reservoir model schematics.
Fig. 2 reservoirs top interface accurate reflection coefficient with incidence angle and frequency change.
The approximate reflectance factor in Fig. 3 reservoirs top interface with incidence angle and frequency change.
The interface reflection coefficients error analysis of Fig. 4 reservoirs top.
Fig. 5-1 simulated seismograms with incidence angle and frequency change (angle-frequency domain reflection record data volume).
Fig. 5-2 simulated seismograms with incidence angle and frequency change (for the incidence section of 10 ° of angles and 20hz frequency slices).
Fig. 6-1 glues acoustic medium Bayes's AVA inversion results.
Fig. 6-2 glues acoustic medium Bayes's AVF inversion results.
Fig. 7 is the step block diagram of the inventive method.
Embodiment
The present invention is described in further detail below in conjunction with the accompanying drawings：
Viscous acoustic medium AVA and AVF approximate expression is combined by the present invention with bayesian theory, not merely with amplitude with entering
The information of firing angle conversion, and take full advantage of information converting of the amplitude with frequency, by build the expectation under probability meaning and
Covariance matrix carries out the linear AVA/AVF invertings of Bayes, obtains the speed and decay factor of target zone.
The inventive method is specifically included：
(1) derivation and application of acoustic medium AVA/AVF approximate expressions are glued
For gluing acoustic medium, phase velocity formula can be labeled as：
H (ω)=1+Q-1F (ω),
Wherein c (ω) is phase velocity, and c is the speed of reference frequency.For normal density medium, by the stress of reflecting interface
Strain continuous condition, reflectance factor can be written as：
Acoustic medium reflectance factor is linearized：
Place carries out Taylor expansion, and retains single order (weak speed difference is approximate)：
Phase velocity formula is substituted into, obtained：
Place carries out Talor expansion, and retains single order：
Wherein, c is the speed of reference frequency, and θ, ω is respectively angle and frequency, and H is the intermediate variable with frequency dependence,
It is specifically shown in formula (1).
Formula (6) is the approximate expression used in viscous acoustic medium Bayes AVA/AVF invertings.
(2) prior information of Bayes's inverting and likelihood function are set up；
1. prior information is set up：
Bayes is in Bayesian frame, and what prior model was defined is the statistical models of elastic parameter prior information, leads to
Cross the form expression of probability density function.Meanwhile, prior information must be independently of geological data, can only pass through other channels
Obtain (such as well logging information and geologic knowledge).Acoustic medium, which is glued, for Chang Midu describes ground with speed c and attenuation factor=1/Q
Lower medium, and assume that parameter { ln c (t), α (t) } meets Gaussian Profile.On the one hand it is using this hypothesis because it is to compare
Meet the fact, substantial amounts of well-log information shows the logarithm and decay factor of speed all close to Gaussian Profile；On the other hand, it is high
The hypothesis of this distribution can bring great convenience to calculating.
A continuous Gaussian vector field being made up of elastic parameter is defined first：
M (t)=[ln c (t), α (t)]T (7)
It is contemplated to be：
E [m (t)]=μ (t)=[μc, μα]T (8)
Lnc (t), α (t) are in time sampling point t and s variance：
Cov [m (t), m (s)]=∑ (t, s)=∑0vt(τ) (9)
Wherein vt(τ) is a time correlation function, and that τ is represented is time delay τ=t-s, and ∑0What is represented is one
When constant covariance matrix：
In the matrix, diagonal entry represents the variance of wave velocity and decay factor, v respectivelycαRepresentation speed and density
Coefficient correlation.Time correlation function vt(τ) must be a positive definite integral form, and value is in [- 1,1], and vt(0)=1.Such as two
Rank exponential function can be expressed as：
Wherein d is the parameter for portraying temporal correlation.Thus, discrete elastic parameter prior information can be write as：
Wherein, m is the vector that elastic parameter is constituted, and lnc represents to take the logarithm to speed respectively, and α represents decay factor,
Represent the n sampling point Normal Distributions on m, μm, ∑mM expectation and variance is represented respectively.
2. likelihood function is set up：
Based on viscous acoustic medium AVA/AVF approximate expressions, the equation both sides of formula (6) are obtained into the equation to the derivation of time t and opened up
Open up the situation to continuous time interface：
In Bayes's AVA/AVF invertings, likelihood function is defined as obtaining earthquake sight in the case of setting models parameter m
Survey data dobsProbability, can be write as p (dobs|m).It, which describes to what extent these model parameters, can obtain earthquake
Observe data.It is written as with a matrix type：
R=Am ' (14)
Wherein m ' is derivatives of the m to the time, and A is the sparse matrix that coefficient is constituted in equation,
For AVA invertings：
For AVF invertings：
The earthquake record that forward modeling is obtained is expressed as：
dobs=SR+e=SAm '+e (16)
Wherein e is the noise in earthquake record, and S is：
It can be write as each S：
It is assumed that noise e, which is met, is desired for 0, variance is ∑eGaussian Profile：So observe data
Meet Gaussian Profile, likelihood function is written as：
Formula (18) is exactly the likelihood function used in AVA and AVF, wherein, dobsObservation geological data is represented, m represents bullet
Property parameter,Represent that observation geological data meets Gaussian Profile,The expectation of geological data is represented,Table
Show the variance of geological data.So-called likelihood function, is, in known underground parameter m, to obtain observation geological data dobsProbability have
It is much.Due to meeting Gaussian Profile, therefore likelihood function here can be expected and variance difference with expecting and variance be expressed
Meet：
(3) for speed and the linear AVA/AVF invertings of Bayes of decay；
Earthquake record and elastic parameter meet Joint Distribution：
Wherein
In given dobsIn the case of m Posterior probability distribution be：
Posterior error and variance are respectively：
M maximum a posteriori solution (MAP) should just be equal to posterior error valueCovariance matrix
To evaluate the final uncertainty of inversion result.
As shown in fig. 7, the inventive method includes：
The first step, input angle domain geological data, frequency domain geological data and log data；Angle domain geological data and frequency
The geological data in rate domain is expressed as dobs, the data are the 3D data volume of time, angle and frequency, and user is carrying out AVA
Corresponding data, d can be extracted out during with AVF invertingsobsSpecifically angle domain geological data or frequency domain geological data, are depended on
User uses any inversion method.Log data is expressed as：M=[lnc, α ,]T, m is the vector that elastic parameter is constituted, lnc
The logarithm of speed is represented respectively, and α represents decay factor, and the two is obtained from well-log information；
Second step, calculates the prior information of log data；
3rd step, using prior information and likelihood function, carries out the linear AVA and AVF invertings of Bayes, obtains speed and product
Prime factor.
Illustrate the effect of the present invention below by a synthesis trace gather, algorithm is shown a C language, picture Matlab systems
Make.Model is that shale layer is sandwiched between sandstone reservoir (as shown in Figure 1), and the parameter of three bed boundarys is set to：Vp1=300m/
S, Qp1=100；Vp2=4000, Qp2=10；Vp3=3500, Qp3=80.Wavelet is ricker wavelets, dominant frequency 35hz；Time
Sampling interval is：2ms；Angular range changes from 0 ° -45 °, and frequency range is：2hz-80hz.
The viscous acoustic medium AVA/AVF approximate expressions of comparative analysis and error (such as Fig. 2, Fig. 3 and the figure of accurate reflectance factor first
Shown in 4), be as a result shown in that speed difference above and below reflecting interface is little, quality factor it is poor less in the case of, degree of approximation is very
It is high.And this 2 approximate conditions are easier to meet, therefore the viscous acoustic medium AVA/AVF approximate expressions derived have very high essence
Degree and application value.Then, by convolution model obtain record that seismic amplitude changes with incidence angle and frequency (such as Fig. 5-1 and
Shown in Fig. 5-2).Next it is utilized respectively amplitude linear in frequency-domain information progress Bayes in incidence angle domain information and amplitude
AVA/AVF invertings, the speed and decay factor for obtaining underground medium changes (as shown in Fig. 6-1 and Fig. 6-2), the value of initial model
For the average of medium velocity.It is not difficult to find out, the viscous linear AVA invertings of acoustic medium Bayes can accurately be finally inversed by medium velocity
Conversion, but it is limited for the inversion accuracy of decay factor；And the linear AVF invertings of Bayes then can be finally inversed by ground with point-device
The speed and decay factor of lower medium.
With the aggravation of oil-gas exploration difficulty, people have to sight be turned to from structural deposit more hidden lithology
Oil-gas reservoir.Therefore, traditional structure imaging has been difficult to the demand of current oil-gas exploration.And the wide-azimuth developed on this basis is adopted
Collection technology and relative amplitude preserved processing technology achieve significant progress, while being also prestack inversion including AVO technologies in storage
Great function, which is provided, played in layer prediction ensures.However, traditional AVO analyses always assume that underground medium is perfect elasticity
's.Petrophysical measurement in VSP data, well-log information and laboratory shows that seismic wave can be sent out during actual propagation
Raw decay and velocity dispersion phenomenon.Especially for the region containing hydrocarbon, decay is clearly.Ignore seismic wave
Decay can bring huge risk to AVO analyses and reservoir prediction.
The present invention brings the attenuation by absorption of seismic wave into whole inverting framework and got off, while make use of seismic reflection data
The information of angle domain and frequency domain, has derived the Reflection Efficient Approximation of frequency angle domain and by it and Bayes's inversion method knot
The new prior information of structure and likelihood function are closed, inversion result can not only obtain the change of viscous acoustic medium medium velocity, while can
To obtain the change of underground medium decay factor.This invention is not only outstanding to seism processing work meaning, more finds
Subterranean oil gas reservoir provides important indicate.
Above-mentioned technical proposal is one embodiment of the present invention, for those skilled in the art, at this
On the basis of disclosure of the invention application process and principle, it is easy to make various types of improvement or deformation, this is not limited solely to
Invent the method described by above-mentioned embodiment, therefore previously described mode is preferred, and and without limitation
The meaning of property.
Claims (2)
1. a kind of linear AVA and AVF inversion methods of viscous acoustic medium Bayes, it is characterised in that：Methods described includes：
The first step, input angle domain geological data, frequency domain geological data and log data；
Second step, sets up the prior information and likelihood function of log data；
3rd step, using the prior information and likelihood function, carries out the linear AVA and AVF invertings of Bayes, obtains speed and product
Prime factor；
Angle domain geological data and frequency domain geological data are expressed as d in the first stepobs, the data be the time, angle and
The 3D data volume of frequency；Log data is expressed as：M=[lnc, α ,]T, wherein, m is the vector that elastic parameter is constituted, ln c
The logarithm of speed is represented respectively, and α represents decay factor, and the two is obtained from well-log information；
What the second step was realized in：
The prior information for setting up log data is as follows：
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For AVA invertings, use：
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<mi>&omega;</mi>
<mrow>
<mi>n</mi>
<mi>&omega;</mi>
</mrow>
</msub>
<mo>)</mo>
</mrow>
</mrow>
</mtd>
</mtr>
</mtable>
</mfenced>
<mo>,</mo>
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<mn>15</mn>
<mi>b</mi>
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</mrow>
</mrow>
Wherein, s1(θi,ωi) expression incidence angle be θi, dominant frequency is ωiWavelet；Subscript 1,2 is until nwave represents wavelet
Delay；Ac(θnθ,ωfix) represent frequencies omegafixIt is fixed, dependent on incidence angle θnθVelocity coeffficient；Aα(θnθ,ωfix) represent frequency
ωfixIt is fixed, dependent on incidence angle θnθDecay factor coefficient；Ac(θfix,ωnω) represent incidence angle θfixIt is fixed, dependent on frequency
Rate ωnωVelocity coeffficient；Aα(θfix,ωnω) represent incidence angle θfixIt is fixed, dependent on frequencies omeganωDecay factor coefficient.
2. the linear AVA and AVF inversion methods of viscous acoustic medium Bayes according to claim 1, it is characterised in that：Described
What three steps were realized in：
Earthquake record and elastic parameter meet Joint Distribution：
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<mn>20</mn>
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Wherein
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In given dobsIn the case of m Posterior probability distribution be：
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Posterior error and variance are respectively：
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</mrow>
</mrow>
M maximum a posteriori solution (MAP) is equal to posterior error valueCovariance matrix is to anti-
The final uncertainty of result is drilled to be evaluated.
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| "Inversion of the seismic AVF/AVA signatures of highly attenuative targets";Kristopher A. Innanen;《Geophysics》;20110228;第76卷(第1期);第R12页左栏第6段及附图1-8 * |
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