CN104570071A - Bayesian linear AVA and AVF retrieval method of sticky sound medium - Google Patents
Bayesian linear AVA and AVF retrieval method of sticky sound medium Download PDFInfo
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Abstract
The invention provides a Bayesian linear AVA and AVF retrieval method of a sticky sound medium and belongs to the field of geophysical prospecting for petroleum. The method comprises the following steps: S1, inputting angle-domain seismic data, frequency-domain seismic data and log data; S2, establishing prior information and a likelihood function of the log data; S3, carrying out Bayesian linear AVA and AVF retrieval by using the prior information and the likelihood function so as to obtain a velocity and a quality factor.
Description
Technical Field
The invention belongs to the field of petroleum geophysical exploration, and particularly relates to a Bayesian linear AVA and AVF retrieval method for a sticky acoustic medium.
Background
Conventional AVO (amplitude versus offset) or AVA (amplitude versus angle of incidence) is always based on the assumption that the subsurface medium is completely elastic. VSP records, well logging data and rock physics measurements in a laboratory all show that seismic waves can be attenuated and dispersed in the propagation process, and particularly for formations containing hydrocarbons, the attenuation of the seismic waves is more obvious. Indeed, neglecting the effects of seismic wave attenuation will pose a significant risk to AVO analysis.
According to the seismic wave propagation theory, foreign preschool attribute it to the reflection coefficient of strong absorption of the underground medium. White (1975), De hop (1991), Ursin (2002) and the like give a series of theoretical discussions on how to calculate the absorption reflection coefficient, Innanen and Weglein (2007) simplify the general absorption backscattering problem to invert the reflection coefficient at a single interface, and Innanen (2011) derives in detail the expression of the reflection and transmission coefficients of seismic waves incident from an elastic non-attenuating medium to an absorbing medium. In fact, a complete description or inversion of the reflection coefficient absorbed in the subsurface medium requires consideration of both the Amplitude Versus Angle (AVA) and the Amplitude Versus Frequency (AVF). Although some mechanisms have been established to explain the variation of the reflection coefficient with frequency, how to solve the inverse problem is still an international problem.
The national scholars have noticed the amplitude abnormality of the earthquake low-frequency part in the gas-bearing reservoir area for a long time, and have conducted related researches based on the methods of generalized S transformation or wavelet transformation, etc., but no systematic research has been conducted on the change of the amplitude with the frequency). Anybody (2009) performed an analytical study of the change of the amplitude of the pore medium with frequency at houston university and derived in detail the change of the reflection coefficient with frequency at normal incidence. Referring to the AVO classification, any (2009) equally classifies AVFs into three classes and corresponds to different gas reservoirs, respectively. The research work is quickly valued by some scholars in China, Liu (2011) and the like further deduce the change relation of the amplitude along with the frequency when the seismic waves are obliquely incident on the basis of any theory, and obtain some beneficial understanding. Even so, research on the inversion work of the viscoelastic medium AVA/AVF still remains blank in China.
Disclosure of Invention
The invention aims to solve the problems in the prior art, provides a Bayesian linear AVA and AVF inversion method for a sticky acoustic medium, aims at geophysical fine description of a reservoir, utilizes the Bayesian linear AVA/AVF inversion of the sticky acoustic medium to obtain the speed and attenuation information of an underground medium, improves the reliability and accuracy of oil-gas content prediction of the reservoir, and has the distinct characteristics of practice orientation and strong applicability.
The invention is realized by the following technical scheme:
a Bayesian linear AVA and AVF inversion method for a viscous acoustic medium comprises the following steps:
first, inputting angle domain seismic data, frequency domain seismic data and logging data
Secondly, establishing prior information and a likelihood function of the logging data;
and thirdly, carrying out Bayesian linear AVA and AVF inversion by utilizing the prior information and the likelihood function to obtain speed and quality factors.
In the first step, the seismic data of the angle domain and the seismic data of the frequency domain are both expressed as dobsThe data is a three-dimensional data volume of time, angle and frequency; the log data is expressed as: m is one of [ lnc, α,]Twhere m is a vector consisting of elastic parameters, lncRespectively, the logarithm of the velocity and the attenuation factor, both derived from the log data.
The second step is realized by:
the prior information to establish the well log data is as follows:
wherein,means that n samples with respect to m follow a normal distribution, μm，∑mRespectively representing the expectation and the variance of m, which are obtained by counting logging sampling points;
the likelihood function is established as follows:
wherein,indicating that the observed seismic data satisfies a gaussian distribution,a representation of the expectation of the seismic data,representing the variance of the seismic data;
the expectation and variance satisfy:
∑″mrepresents the calculation of second derivative, sigma, of the statistical variance of the elastic parameterseRepresents the variance of the noise;
wherein S is:
for each S can be written:
for the AVA inversion, use is made of:
for AVF inversion, use:
wherein s is1(θi，ωi) Representing an angle of incidence of thetaiDominant frequency is omegaiThe wavelet of (2); subscripts 1, 2 up to nwave denote the delay of the wavelet; a. thec(θnθ，ωfix) Representing frequency omegafixFixed, dependent on angle of incidence θnθThe velocity coefficient of (a); a. theα(θnθ，ωfix) Representing frequency omegafixFixed, dependent on angle of incidence θnθThe attenuation factor coefficient of (a); a. thec(θfix，ωnω) Represents the incident angle thetafixFixed, dependent on frequency ωnωThe velocity coefficient of (a); a. theα(θfix，ωnω) Represents the incident angle thetafixFixed, dependent on frequency ωnωThe attenuation factor coefficient of (2).
The third step is realized by:
the seismic record and the elastic parameter satisfy joint distribution:
wherein
At a given dobsThe posterior probability distribution of m in case (a) is:
the posterior expectation and variance are:
the maximum a posteriori solution (MAP) of m is equal to the A posteriori expected valueThe covariance matrix is used to evaluate the final uncertainty of the inversion result.
Equation (23) is the expectation and variance of m, and m expresses velocity Vp and quality factor Q p, so the expectation of m, i.e. the expectation of velocity Vp and quality factor Q p, i.e. the most probable solution, is obtained; and the variance is used to evaluate the uncertainty of these two parameters.
Compared with the prior art, the invention has the beneficial effects that: compared with the prior art, the method introduces seismic data frequency domain information, constructs prior information and frequency-related likelihood functions required by inversion under the guidance of Bayesian theory, and obtains the velocity of the underground medium and the attenuation factor change of the medium according to the inversion result; the results given in the form of probabilities provide the possibility for subsequent uncertainty analysis, and also provide a more comprehensive evaluation for reservoir prediction.
Drawings
Figure 1 schematic representation of a gas sand reservoir model.
Figure 2 the exact reflection coefficient of the reservoir top interface varies with angle of incidence and frequency.
FIG. 3 approximate reflection coefficient of the reservoir top interface as a function of incident angle and frequency.
FIG. 4 analysis of error in the reflection coefficient of the top interface of the reservoir.
Fig. 5-1 simulates the variation of seismic recordings with angle of incidence and frequency (angle-frequency domain reflection recording data volume).
Fig. 5-2 simulates the variation of seismic recordings with angle of incidence and frequency (10 deg. angle of incidence slice and 20hz frequency slice).
FIG. 6-1 myxoacoustic medium Bayesian AVA inversion results.
FIG. 6-2 myxoacoustic medium Bayesian AVF inversion results.
Fig. 7 is a block diagram of the steps of the method of the present invention.
Detailed Description
The invention is described in further detail below with reference to the accompanying drawings:
the invention combines the approximate expression of the viscous sound media AVA and AVF with the Bayes theory, not only utilizes the information of the amplitude changing along with the incident angle, but also fully utilizes the information of the amplitude changing along with the frequency, and carries out Bayesian linear AVA/AVF inversion by constructing the expectation and covariance matrix under the probability meaning, thereby obtaining the speed and the attenuation factor of the target layer.
The method specifically comprises the following steps:
(1) derivation and application of AVA/AVF approximate expression of sticky sound medium
For a visco-acoustic medium, the phase velocity formula can be labeled:
H(ω)＝1+Q-1F(ω)，
where c (ω) is the phase velocity and c is the velocity of the reference frequency. For a medium of constant density, the reflection coefficient can be written as:
linearizing the acoustic medium reflection coefficient:
in thatTaylor expansion is performed and the first order term (weak velocity difference approximation) is retained:
substituting the phase velocity formula yields:
in thatTalor expansion is performed and the first order term is retained:
where c is the velocity of the reference frequency, θ, ω are the angle and frequency, respectively, and H is an intermediate variable related to the frequency, see equation (1).
Equation (6) is the approximate equation used for the Bayesian AVA/AVF inversion of the sticky acoustic medium.
(2) Establishing prior information and a likelihood function of Bayesian inversion;
establishing prior information:
bayes in a Bayes framework, a prior model defines a statistical model of elastic parameter prior information, and is expressed by a probability density function. Meanwhile, the prior information must be independent of seismic data and can only be obtained through other channels (such as well logging information and geological knowledge). The subsurface medium is described with a velocity c and an attenuation factor α of 1/Q for a constant density viscoelastic medium, and the parameters { ln c (t), α (t) } are assumed to satisfy a gaussian distribution. This assumption is used on the one hand because it is relatively true that a large number of well logs indicate that both the logarithm of the velocity and the attenuation factor are close to gaussian; on the other hand, the assumption of gaussian distribution can bring great convenience to the calculation.
First, a continuous gaussian vector field is defined, which consists of elastic parameters:
m(t)＝[ln c(t)，α(t)]T (7)
its expectations are:
E[m(t)]＝μ(t)＝[μc，μα]T (8)
lnc (t), the variance of α (t) at time samples t and s is:
Cov[m(t)，m(s)]＝∑(t，s)＝∑0vt(τ) (9)
wherein v ist(τ) is a time-dependent function, and τ represents the time delay τ t-s, and Σ0Represented is a time-invariant covariance matrix:
in the matrix, the diagonal elements represent the variance of the wave velocity and attenuation factor, vcαRepresenting the correlation coefficient of velocity and density. Time correlation function vt(τ) must be a positive definite function, with a value of [ -1, 1 [ ]]And v ist(0) 1. For example, a second order exponential function may be expressed as:
where d is a parameter characterizing the temporal correlation. Thus, discrete elastic parameter prior information can be written as:
wherein m is a vector formed by elastic parameters, lnc respectively represents the logarithm of the speed, alpha represents an attenuation factor,means that n samples with respect to m follow a normal distribution, μm，∑mRespectively representing the expectation and variance of m.
Establishing a likelihood function:
and (3) deriving the time t on two sides of the equation of the formula (6) based on the AVA/AVF approximate expression of the sticky sound medium to obtain the condition that the equation is expanded to a continuous time interface:
in Bayesian AVA/AVF inversion, a likelihood function is defined to obtain seismic observation data d given a model parameter mobsCan be written as p (d)obs| m). It describes to what extent these model parameters can be derived from seismic observations. Written in matrix form as:
R＝Am′ (14)
where m' is the derivative of m with respect to time, A is a sparse matrix consisting of the coefficients in the equation,
for the AVA inversion:
for AVF inversion:
the forward derived seismic records are expressed as:
dobs＝SR+e＝SAm′+e (16)
wherein e is the noise in the seismic record, and S is:
for each S can be written:
assuming that the noise e satisfies the expectation of 0, the variance is ΣeGaussian distribution of (a):thus the observed data is also gaussian-distributed, and the likelihood function is written as:
equation (18) is the likelihood function used for AVA and AVF, where dobsRepresenting observed seismic data, m representing an elastic parameter,indicating that the observed seismic data satisfies the gaussian distribution,a representation of the expectation of the seismic data,representing the variance of the seismic data. The likelihood function is the acquisition of observed seismic data d when the subsurface parameter m is knownobsHow large the probability of (c) is. Since a gaussian distribution is satisfied, the likelihood function herein can be expressed in terms of expectation and variance, which satisfy:
(3) bayesian linear AVA/AVF inversion for velocity and attenuation;
the seismic record and the elastic parameter satisfy joint distribution:
wherein
At a given dobsThe posterior probability distribution of m in case (a) is:
the posterior expectation and variance are:
the maximum a posteriori solution (MAP) of m should be equal to the expected a posteriori valueThe covariance matrix is used to evaluate the final uncertainty of the inversion result.
As shown in fig. 7, the method of the present invention comprises:
firstly, inputting angle domain seismic data, frequency domain seismic data and logging data; seismic data in both the angle domain and the frequency domain are expressed as dobsThe data is three-dimensional data volume of time, angle and frequency, corresponding data can be extracted by a user when AVA and AVF inversion is carried out, dobsAnd in particular, angle domain seismic data or frequency domain seismic data, depends on what inversion method is used by the user. The log data is expressed as: m is one of [ lnc, α,]Tm is a vector formed by elastic parameters, lnc respectively represents the logarithm of the speed, and alpha represents an attenuation factor, and the two are obtained from logging data;
secondly, calculating prior information of the logging data;
and thirdly, carrying out Bayesian linear AVA and AVF inversion by utilizing the prior information and the likelihood function to obtain speed and quality factors.
The effect of the invention is illustrated by a composite gather, the algorithm is written in C language, and the picture is made by Matlab. The model is a sandstone reservoir clamped in the middle of a mudstone layer (as shown in figure 1), and the parameters of three layers of interfaces are respectively set as follows: vp 1-300 m/s, Qp 1-100; vp2 is 4000, Qp2 is 10; vp 3-3500 and Qp 3-80. The wavelet is ricker wavelet with dominant frequency 35 hz; the time sampling interval is: 2 ms; the angle ranges from 0 ° to 45 °, the frequency ranges are: 2hz-80 hz.
First, the error between the approximation formula of the sticky acoustic medium AVA/AVF and the accurate reflection coefficient is compared and analyzed (as shown in fig. 2, fig. 3, and fig. 4), and the result shows that the approximation degree is very high when the difference between the upper and lower speeds of the reflection interface is not large and the difference between the quality factors is not large. Both the two approximation conditions are easy to satisfy, so that the derived AVA/AVF approximation formula of the sticky sound medium has very high precision and application value. Then, the seismic amplitude versus angle of incidence and frequency is recorded by convolution modeling (as shown in FIGS. 5-1 and 5-2). And then carrying out Bayesian linear AVA/AVF inversion respectively by utilizing the information of the amplitude in the incidence angle domain and the information of the amplitude in the frequency domain to obtain the velocity and attenuation factor change of the underground medium (as shown in figures 6-1 and 6-2), wherein the value of the initial model is the average value of the velocity of the medium. It can be seen that the Bayesian linear AVA inversion of the sticky acoustic medium can accurately invert the medium velocity transformation, but the inversion accuracy of the attenuation factor is limited; and the Bayesian linear AVF inversion can accurately invert the velocity and attenuation factor of the underground medium.
With the increasing difficulty of oil and gas exploration, people have to look away from the constructed reservoir to more concealed lithological reservoirs. Therefore, conventional formation imaging has been difficult to meet the requirements of oil and gas exploration today. The wide azimuth acquisition technology and the amplitude preservation processing technology developed on the basis make great progress, and meanwhile guarantee is provided for the great effect of prestack inversion including the AVO technology in reservoir prediction. However, conventional AVO analysis always assumes that the subsurface media is fully elastic. VSP data, well logging data and laboratory petrophysical measurements all show that seismic waves are attenuated and velocity dispersed in the actual propagation process. Especially for hydrocarbon containing areas, the attenuation is very significant. Neglecting seismic wave attenuation brings a huge risk to AVO analysis and reservoir prediction.
The invention brings the absorption attenuation of seismic waves into the whole inversion framework, simultaneously utilizes the information of the angle domain and the frequency domain of the reflected seismic data, deduces the reflection coefficient approximate expression of the frequency angle domain, combines the reflection coefficient approximate expression with a Bayesian inversion method to construct new prior information and a likelihood function, and obtains the velocity change in the sticky sound medium and the change of the attenuation factor of the underground medium through the inversion result. The invention not only has remarkable significance for seismic data processing work, but also provides important indication for searching underground oil and gas reservoirs.
The above-described embodiment is only one embodiment of the present invention, and it will be apparent to those skilled in the art that various modifications and variations can be easily made based on the application and principle of the present invention disclosed in the present application, and the present invention is not limited to the method described in the above-described embodiment of the present invention, so that the above-described embodiment is only preferred, and not restrictive.
Claims (4)
1. A Bayesian linear AVA and AVF inversion method for a viscous acoustic medium is characterized in that: the method comprises the following steps:
first, inputting angle domain seismic data, frequency domain seismic data and logging data
Secondly, establishing prior information and a likelihood function of the logging data;
and thirdly, carrying out Bayesian linear AVA and AVF inversion by utilizing the prior information and the likelihood function to obtain speed and quality factors.
2. The myxoacoustic media bayes linear AVA and AVF inversion method of claim 1, characterized in that: in the first step, the seismic data of the angle domain and the seismic data of the frequency domain are both expressed as dobsThe data is a three-dimensional data volume of time, angle and frequency; the log data is expressed as: m is one of [ lnc, α,]Twherein m is a vector formed by elastic parameters, lnc respectively represents the logarithm of the velocity, and alpha represents an attenuation factor, and the two are obtained from logging data.
3. The myxoacoustic media bayes linear AVA and AVF inversion method of claim 2, characterized in that: the second step is realized by:
the prior information to establish the well log data is as follows:
wherein,means that n samples with respect to m follow a normal distribution, μm，∑mRespectively representing the expectation and the variance of m, which are obtained by counting logging sampling points;
the likelihood function is established as follows:
wherein,indicating that the observed seismic data satisfies a gaussian distribution,a representation of the expectation of the seismic data,representing the variance of the seismic data;
the expectation and variance satisfy:
∑″mrepresents the calculation of second derivative, sigma, of the statistical variance of the elastic parameterseRepresents the variance of the noise;
wherein S is:
for each S can be written:
for the AVA inversion, use is made of:
for AVF inversion, use:
wherein s is1(θi，ωi) Representing an angle of incidence of thetaiDominant frequency is omegaiThe wavelet of (2); subscripts 1, 2 up to nwave denote the delay of the wavelet; a. thec(θnθ，ωfix) Representing frequency omegafixFixed, dependent on angle of incidence θnθThe velocity coefficient of (a); a. theα(θnθ，ωfix) Representing frequency omegafixFixed, dependent on angle of incidence θnθThe attenuation factor coefficient of (a); a. thec(θfix，ωnω) Represents the incident angle thetafixFixed, dependent on frequency ωnωThe velocity coefficient of (a); a. theα(θfix，ωnω) Represents the incident angle thetafixFixed, dependent on frequency ωnωThe attenuation factor coefficient of (2).
4. The myxoacoustic media bayes linear AVA and AVF inversion method of claim 3, wherein: the third step is realized by:
the seismic record and the elastic parameter satisfy joint distribution:
wherein
At a given dobsThe posterior probability distribution of m in case (a) is:
the posterior expectation and variance are:
the maximum a posteriori solution (MAP) of m is equal to the A posteriori expected valueThe covariance matrix is used to evaluate the final uncertainty of the inversion result.
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