CN104570071A - Bayesian linear AVA and AVF retrieval method of sticky sound medium - Google Patents

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

A kind of sticky linear AVA and AVF inversion method of acoustic medium Bayes

Technical field

The invention belongs to field of petroleum geophysical exploration, be specifically related to a kind of sticky linear AVA and AVF inversion method of acoustic medium Bayes, utilize bayesian theory to carry out AVA and AVF inverting based on sticky acoustic medium and obtain acoustic velocity and decay factor.

Background technology

Traditional AVO (amplitude offset distance) or AVA (Amplitudeversusangle) is always based on the perfectly elastic hypothesis of underground medium.And VSP record, Petrophysical measurement in log data and laboratory all explicitly seismic wave in communication process, there will be decay and dispersion phenomenon, especially for the stratum containing hydrocarbon, the decay of seismic event is more obvious.In fact, the impact ignoring seismic wave attenuation brings huge risk by analyzing AVO.

Base area earthquake wave propagation theory, the reflection coefficient that it absorbs by force owing to underground medium by external some scholars.White (1975), De Hoop (1991), Ursin (2002) etc. are about how calculating the discussion absorbing and to give in reflection coefficient in series of theories, general absorption inverse Problem is reduced to the reflection coefficient of the single interface of inverting by Innanen and Weglein (2007), and Innanen (2011) has derived the expression formula of seismic event reflection and transmission coefficient when inciding absorbing medium by the non-attenuation medium of elasticity in detail.In fact, the reflection coefficient absorbed in complete description or inverting underground medium, had both needed the change (AVA) considering amplitude angle, also will consider the variation relation (AVF) of amplitude frequency simultaneously.Although established some mechanism to explain the variation relation of reflection coefficient with frequency at present, how to solve indirect problem and remained an international difficult problem.

Domestic scholars notices the amplitude anomaly in gas-bearing reservoir regional earthquake low frequency part very early, and has carried out correlative study based on the method such as generalized S-transform or wavelet transformation, but not yet someone carries out amplitude frequency change always) systematic study.Appoint (2009) to carry out the mutation analysis research of pore media amplitude frequency in University of Houston, and derived in detail vertical incidence time reflection coefficient with the change of frequency.With reference to AVO classification, appoint (2009) to be divided three classes equally by AVF and distinguish corresponding different gas-bearing reservoirs.This research work is subject to the attention of more domestic scholars very soon, derived further in the basis that Liu (2011) etc. are in office inclined seismic wave time amplitude frequency variation relation, and achieve some useful understanding.Nonetheless, the research about sticky acoustic medium AVA/AVF inverting work still still belongs to blank at home.

Summary of the invention

The object of the invention is to solve the difficult problem existed in above-mentioned prior art, a kind of sticky linear AVA and AVF inversion method of acoustic medium Bayes is provided, geophysics fine description for reservoir is target, the sticky linear AVA/AVF inverting of acoustic medium Bayes is utilized to obtain speed and the dampening information of underground medium, improve reliability and the accuracy of reservoir oil and gas prediction, there is face the practice, bright characteristics that application is strong.

The present invention is achieved by the following technical solutions:

A kind of sticky linear AVA and AVF inversion method of acoustic medium Bayes, comprising:

The first step, input angle territory geological data, frequency field geological data and log data

Second step, sets up prior imformation and the likelihood function of log data;

3rd step, utilizes described prior imformation and likelihood function, carries out linear AVA and the AVF inverting of Bayes, obtains speed and quality factor.

In the described first step, the geological data of angle domain geological data and frequency field is all expressed as d _obs, these data are the 3-D data volume of time, angle and frequency; Log data is expressed as: m=[lnc, α ,] ^t, wherein, m is the vector of elastic parameter composition, l _ncrepresent the logarithm of speed respectively, α represents decay factor, and the two all obtains from well-log information.

Described second step is achieved in that

The prior imformation setting up log data is as follows:

$m={[\ln c,\mathrm{\α}]}^T{~N}_{n_m}({\mathrm{\μ}}_m,{\mathrm{\Σ}}_m),---\left(12\right)$

Wherein, represent n the sampling point Normal Distribution about m, μ _m, ∑ _mrepresent the expectation and variance of m respectively, by what obtain the statistics of well logging sampling point;

Set up likelihood function as follows:

$p\left(d_{\mathrm{obs}}\right|m)=N_{n_d}({\mathrm{\μ}}_{d_{\mathrm{obs}}},{\mathrm{\Σ}}_{d_{\mathrm{obs}}})---\left(18\right)$

Wherein, represent that observation geological data meets Gaussian distribution, represent the expectation of geological data, represent the variance of geological data;

Expectation and variance meets respectively:

${\mathrm{\μ}}_{d_{\mathrm{obs}}}=\mathrm{SA}{\mathrm{\μ}}_m^{\′},$

${\mathrm{\Σ}}_{d_{\mathrm{obs}}}=\mathrm{SA}{\mathrm{\Σ}}_m^{\′\′}{A}^T{S}^T+{\mathrm{\Σ}}_e---\left(19\right)$

∑ " _mrepresenting asks second order to lead to the statistical variance of elastic parameter, ∑ _erepresent the variance of noise;

Wherein, S is:

Can be write as each S:

For AVA inverting, adopt:

$A=\left[\begin{array}{cc}{A}_c({\mathrm{\θ}}_1,{\mathrm{\ω}}_{\mathrm{fix}})& A_{\mathrm{\α}}({\mathrm{\θ}}_1,{\mathrm{\ω}}_{\mathrm{fix}})\\ ......& ......\\ A_c({\mathrm{\θ}}_{\mathrm{n\θ}},{\mathrm{\ω}}_{\mathrm{fix}})& A_{\mathrm{\α}}({\mathrm{\θ}}_{\mathrm{n\θ}},{\mathrm{\ω}}_{\mathrm{fix}})\end{array}\right],---\left(15a\right)$

For AVF inverting, adopt:

$A=\left[\begin{array}{cc}{A}_c({\mathrm{\θ}}_{\mathrm{fix}},{\mathrm{\ω}}_1)& A_{\mathrm{\α}}({\mathrm{\θ}}_{\mathrm{fix}},{\mathrm{\ω}}_1)\\ ......& ......\\ A_c({\mathrm{\θ}}_{\mathrm{fix}},{\mathrm{\ω}}_{\mathrm{n\ω}})& A_{\mathrm{\α}}({\mathrm{\θ}}_{\mathrm{fix}},{\mathrm{\ω}}_{\mathrm{n\ω}})\end{array}\right],---\left(15b\right)$

Wherein, s ₁(θ _i, ω _i) expression incident angle is θ _i, dominant frequency is ω _iwavelet; Subscript 1,2 until nwave represents the time delay of wavelet; A _c(θ _{n θ}, ω _fix) represent frequencies omega _fixfixing, depend on incidence angle θ _{n θ}velocity coefficient; A _α(θ _{n θ}, ω _fix) represent frequencies omega _fixfixing, depend on incidence angle θ _{n θ}decay factor coefficient; A _c(θ _fix, ω _{n ω}) represent incidence angle θ _fixfixing, depend on frequencies omega _{n ω}velocity coefficient; A _α(θ _fix, ω _{n ω}) represent incidence angle θ _fixfixing, depend on frequencies omega _{n ω}decay factor coefficient.

Described 3rd step is achieved in that

Seismologic record and elastic parameter meet joint distribution:

$\left[\begin{array}{c}m\\ d_{\mathrm{obs}}\end{array}\right]~N_{n_m+n_d}(\left[\begin{array}{c}{\mathrm{\μ}}_m\\ {\mathrm{\μ}}_{d_{\mathrm{obs}}}\end{array}\right],\left[\begin{array}{cc}{\mathrm{\Σ}}_m& {\mathrm{\Σ}}_{m,d_{\mathrm{obs}}}\\ {\mathrm{\Σ}}_{d_{\mathrm{obs}},m}& {\mathrm{\Σ}}_{d_{\mathrm{obs}}}\end{array}\right])---\left(20\right)$

Wherein

${\mathrm{\Σ}}_{d_{\mathrm{obs}},m}=\mathrm{Cov}\{d_{\mathrm{obs}},m\}=\mathrm{SA}{\mathrm{\Σ}}_m^{\′}---\left(21\right)$

At given d _obswhen m Posterior probability distribution be:

$m|d_{\mathrm{obs}}~N_{n_m}({\mathrm{\μ}}_{m|d_{\mathrm{obs}}},{\mathrm{\Σ}}_{m|d_{\mathrm{obs}}})---\left(22\right)$

Posterior error and variance are respectively:

${\mathrm{\μ}}_{m|d_{\mathrm{obs}}}={\mathrm{\μ}}_m+{\left(\mathrm{SA}{\mathrm{\Σ}}_m^{\′}\right)}^T{\mathrm{\Σ}}_{d_{\mathrm{obs}}}^{-1}(d_{\mathrm{obs}}-{\mathrm{\μ}}_{d_{\mathrm{obs}}}),$

${\mathrm{\Σ}}_{m|d_{\mathrm{obs}}}={\mathrm{\Σ}}_m-{\left(\mathrm{SA}{\mathrm{\Σ}}_m^{\′}\right)}^T{\mathrm{\Σ}}_{d_{\mathrm{obs}}}^{-1}\mathrm{SA}{\mathrm{\Σ}}_m^{\′}---\left(23\right)$

The maximum a posteriori solution (MAP) of m just equals posterior error value covariance matrix is evaluated in order to the uncertainty final to inversion result.

Formula (23) is expectation and the variance of m, and namely that m expression is velocities Vp and quality factor q p, and namely the expectation therefore obtaining m obtains the expectation of velocities Vp and quality factor q p, namely maximum probability solution; Variance is then in order to assess the uncertainty of these two parameters.

Compared with prior art, the invention has the beneficial effects as follows: relative to existing technology, invention introduces geological data frequency-domain information, under the guidance of bayesian theory, build the likelihood function of prior imformation needed for inverting and frequency dependence, inversion result not only can obtain the speed of underground medium but also can obtain the decay factor change of medium; The result provided with the form of probability is that follow-up uncertainty analysis provides possibility, also evaluates more comprehensively for reservoir prediction provides simultaneously.

Accompanying drawing explanation

Fig. 1 gas-bearing sandstone reservoir model schematic.

Interface, Fig. 2 reservoir top accurate reflection coefficient is with the change of incident angle and frequency.

Interface, Fig. 3 reservoir top is similar to the change of reflection coefficient with incident angle and frequency.

The interface reflection coefficients error analysis of Fig. 4 reservoir top.

Fig. 5-1 simulated seismogram is with the change (angle-frequency field reflection record data volume) of incident angle and frequency.

Fig. 5-2 simulated seismogram is with the change (being 10 ° of angles incidence sections and 20hz frequency slice) of incident angle and frequency.

The sticky acoustic medium Bayes AVA inversion result of Fig. 6-1.

The sticky acoustic medium Bayes AVF inversion result of Fig. 6-2.

Fig. 7 is the step block diagram of the inventive method.

Embodiment

Below in conjunction with accompanying drawing, the present invention is described in further detail:

The approximate expression of sticky acoustic medium AVA and AVF and bayesian theory combine by the present invention, not only utilize the information that amplitude incident angle converts, and take full advantage of the information converting of amplitude frequency, carry out the linear AVA/AVF inverting of Bayes by the expectation under structure probability meaning and covariance matrix, obtain speed and the decay factor of zone of interest.

The inventive method specifically comprises:

(1) derivation and the application of acoustic medium AVA/AVF approximate expression is glued

For sticky acoustic medium, phase velocity formula can be labeled as:

$\frac{1}{c\left(\mathrm{\ω}\right)}=\frac{1}{c}H\left(\mathrm{\ω}\right),$

H(ω)＝1+Q ^-1F(ω)，

$F\left(\mathrm{\ω}\right)=\frac{i}{2}-\frac{1}{\mathrm{\π}}\log \left(\frac{\mathrm{\ω}}{{\mathrm{\ω}}_r}\right)---\left(1\right)$

Wherein c (ω) is phase velocity, and c is the speed of reference frequency.For normal density medium, by the ess-strain condition of continuity of reflecting interface, reflection coefficient can be written as:

$R(\mathrm{\ω},\mathrm{\θ})=\frac{c_2{H}_1\left(\mathrm{\ω}\right)\cos {\mathrm{\θ}}_1-c_1{H}_2\left(\mathrm{\ω}\right)\cos {\mathrm{\θ}}_2}{c_2{H}_1\left(\mathrm{\ω}\right)\cos {\mathrm{\θ}}_1+c_1{H}_2\left(\mathrm{\ω}\right)\cos {\mathrm{\θ}}_2},---\left(2\right)$

Linearization is carried out to acoustic medium reflection coefficient:

$\frac{\∂R}{\∂\left(\frac{c_2}{c_1}\right)}=\frac{2\cos \mathrm{\θ}}{\sqrt{1-{\left(\frac{c_2}{c_1}\right)}^2{\sin }^2\mathrm{\θ}}*(\frac{c_2}{c_1}\cos \mathrm{\θ}+\sqrt{1-{\left(\frac{c_2}{c_1}\right)}^2{\sin }^2\mathrm{\θ}})},---\left(3\right)$

? place carries out Taylor expansion, and retains single order item (weak velocity contrast is similar to):

$R\left(\mathrm{\θ}\right)=R{|}_{\frac{c_2}{c_1}=1}+\frac{\∂R}{\∂\left(\frac{c_2}{c_1}\right)}{|}_{\frac{c_2}{c_1}=1}(\frac{c_2}{c_1}-1)=\frac{1}{2{\cos }^2\mathrm{\θ}}(\frac{c_2}{c_1}-1)=(1+{\tan }^2\mathrm{\θ})\frac{\mathrm{\Δc}}{{2c}_1}---\left(4\right)$

Phase velocity formula is substituted into, obtains:

$R(\mathrm{\θ},\mathrm{\ω})=(1+{\tan }^2\mathrm{\θ})\frac{\mathrm{\Δc}\left(\mathrm{\ω}\right)}{{2c}_1\left(\mathrm{\ω}\right)}=\frac{1}{2}(1+{\tan }^2\mathrm{\θ})\left(\frac{\frac{c_2}{c_1}-\frac{H_2\left(\mathrm{\ω}\right)}{H_1\left(\mathrm{\ω}\right)}}{\frac{H_2\left(\mathrm{\ω}\right)}{H_1\left(\mathrm{\ω}\right)}}\right),---\left(5\right)$

? place carries out Talor expansion, and retains single order item:

$R(\mathrm{\θ},\mathrm{\ω})=\frac{1}{2}(1+{\tan }^2\mathrm{\θ})(\frac{\mathrm{\Δc}}{c_1}-\frac{\mathrm{\ΔH}\left(\mathrm{\ω}\right)}{H_1\left(\mathrm{\ω}\right)}),---\left(6\right)$

Wherein, c is the speed of reference frequency, and θ, ω are respectively angle and frequency, and H is the intermediate variable with frequency dependence, specifically sees formula (1).

Formula (6) is sticky acoustic medium Bayes AVA/AVF inverting approximate expression used.

(2) prior imformation of Bayes's inverting and likelihood function are set up;

1. prior imformation is set up:

Bayes in Bayesian frame, prior model definition be the statistical models of elastic parameter prior imformation, expressed by the form of probability density function.Meanwhile, prior imformation independent of geological data, can only must be obtained by other channel (as well logging information and geologic knowledge).Acoustic medium speed c and attenuation factor=1/Q is glued to describe underground medium for Chang Midu, and supposes that parameter { ln c (t), α (t) } meets Gaussian distribution.Adopt this hypothesis to be on the one hand because it compares to meet the fact, a large amount of well-log informations shows that the logarithm of speed and decay factor are all close to Gaussian distribution; On the other hand, the hypothesis of Gaussian distribution can bring great convenience to calculating.

First a continuous Gaussian vector field be made up of elastic parameter is defined:

m(t)＝[ln c(t)，α(t)] ^T(7)

Being contemplated to be of it:

E[m(t)]＝μ(t)＝[μ _c，μ _α] ^T(8)

Lnc (t), α (t) in the variance of time sampling point t and s are:

Cov[m(t)，m(s)]＝∑(t，s)＝∑ ₀v _t(τ) (9)

Wherein v _t(τ) be a time correlation function, that τ represents is time delay τ=t-s, and ∑ ₀represent be one time constant covariance matrix:

${\mathrm{\Σ}}_0=\left[\begin{array}{cc}{\mathrm{\σ}}_c^2& {\mathrm{\σ}}_c{\mathrm{\σ}}_{\mathrm{\α}}{v}_{\mathrm{c\α}}\\ {\mathrm{\σ}}_c{\mathrm{\σ}}_{\mathrm{\α}}{v}_{\mathrm{c\α}}& {\mathrm{\σ}}_{\mathrm{\α}}^2\end{array}\right]---\left(10\right)$

In this matrix, diagonal entry represents the variance of wave velocity and decay factor respectively, v _{c α}the related coefficient of representation speed and density.Time correlation function v _t(τ) must be a positive definite function, value be in [-1,1], and v _t(0)=1.Such as bi-exponential function can be expressed as:

$v_t\left(\mathrm{\τ}\right)=\exp [-{\left(\frac{\mathrm{\τ}}{d}\right)}^2]---\left(11\right)$

Wherein d is the parameter of portraying temporal correlation.Thus, discrete elastic parameter prior imformation can be write as:

$m={[\ln c,\mathrm{\α},]}^T~N_{n_m}({\mathrm{\μ}}_m,{\mathrm{\Σ}}_m),---\left(12\right)$

Wherein, m is the vector of elastic parameter composition, and lnc represents respectively and takes the logarithm to speed, and α represents decay factor, represent n the sampling point Normal Distribution about m, μ _m, ∑ _mrepresent the expectation and variance of m respectively.

2. likelihood function is set up:

Based on sticky acoustic medium AVA/AVF approximate expression, the equation both sides of formula (6) are obtained to time t differentiate the situation that this equation is extended to interface continuous time:

$R(t,\mathrm{\θ},\mathrm{\ω})=\frac{1}{2}(1+{\tan }^2\mathrm{\θ})[\frac{\∂}{\∂t}\ln c\left(t\right)-(\frac{i}{2}-\frac{1}{\mathrm{\π}}\log \frac{\mathrm{\ω}}{{\mathrm{\ω}}_r})\frac{\∂}{\∂t}\mathrm{\α}\left(t\right)],---\left(13\right)$

In Bayes AVA/AVF inverting, likelihood function is defined as and obtains seismic observation data d when setting models parameter m _obsprobability, can be write as p (d _obs| m).It is described that to what extent these model parameters can obtain seismic observation data.Be written as with a matrix type:

R＝Am′ (14)

Wherein m ' is for m is to the derivative of time, and A is the sparse matrix be made up of coefficient in equation,

For AVA inverting:

$A=\left[\begin{array}{cc}{A}_c({\mathrm{\θ}}_1,{\mathrm{\ω}}_{\mathrm{fix}})& A_{\mathrm{\α}}({\mathrm{\θ}}_1,{\mathrm{\ω}}_{\mathrm{fix}})\\ ......& ......\\ A_c({\mathrm{\θ}}_{\mathrm{n\θ}},{\mathrm{\ω}}_{\mathrm{fix}})& A_{\mathrm{\α}}({\mathrm{\θ}}_{\mathrm{n\θ}},{\mathrm{\ω}}_{\mathrm{fix}})\end{array}\right],---\left(15a\right)$

For AVF inverting:

$A=\left[\begin{array}{cc}{A}_c({\mathrm{\θ}}_{\mathrm{fix}},{\mathrm{\ω}}_1)& A_{\mathrm{\α}}({\mathrm{\θ}}_{\mathrm{fix}},{\mathrm{\ω}}_1)\\ ......& ......\\ A_c({\mathrm{\θ}}_{\mathrm{fix}},{\mathrm{\ω}}_{\mathrm{n\ω}})& A_{\mathrm{\α}}({\mathrm{\θ}}_{\mathrm{fix}},{\mathrm{\ω}}_{\mathrm{n\ω}})\end{array}\right],---\left(15b\right)$

Just drilling the seismologic record obtained to be expressed as:

d _obs＝SR+e＝SAm′+e (16)

Wherein e is the noise in seismologic record, and S is:

Can be write as each S:

Assuming that it is 0 that noise e meets the expectation, variance is ∑ _egaussian distribution: such observation data also meets Gaussian distribution, and likelihood function is written as:

$p\left(d_{\mathrm{obs}}\right|m)=N_{n_d}({\mathrm{\μ}}_{d_{\mathrm{obs}}},{\mathrm{\Σ}}_{d_{\mathrm{obs}}})---\left(18\right)$

Formula (18) is exactly the likelihood function used by AVA and AVF, wherein, and d _obsrepresent observation geological data, m represents elastic parameter, represent that observation geological data meets Gaussian distribution, represent the expectation of geological data, represent the variance of geological data.So-called likelihood function is when known underground parameter m, obtains observation geological data d _obsprobability have much.Owing to meeting Gaussian distribution, therefore likelihood function here can be expressed with expectation and variance, and expectation and variance meets respectively:

${\mathrm{\μ}}_{d_{\mathrm{obs}}}=\mathrm{SA}{\mathrm{\μ}}_m^{\′},$

${\mathrm{\Σ}}_{d_{\mathrm{obs}}}=\mathrm{SA}{\mathrm{\Σ}}_m^{\′\′}{A}^T{S}^T+{\mathrm{\Σ}}_e---\left(19\right)$

(3) for the linear AVA/AVF inverting of Bayes of speed and decay;

Seismologic record and elastic parameter meet joint distribution:

$\left[\begin{array}{c}m\\ d_{\mathrm{obs}}\end{array}\right]~N_{n_m+n_d}(\left[\begin{array}{c}{\mathrm{\μ}}_m\\ {\mathrm{\μ}}_{d_{\mathrm{obs}}}\end{array}\right],\left[\begin{array}{cc}{\mathrm{\Σ}}_m& {\mathrm{\Σ}}_{m,d_{\mathrm{obs}}}\\ {\mathrm{\Σ}}_{d_{\mathrm{obs}},m}& {\mathrm{\Σ}}_{d_{\mathrm{obs}}}\end{array}\right])---\left(20\right)$

Wherein

${\mathrm{\Σ}}_{d_{\mathrm{obs}},m}=\mathrm{Cov}\{d_{\mathrm{obs}},m\}=\mathrm{SA}{\mathrm{\Σ}}_m^{\′}---\left(21\right)$

At given d _obswhen m Posterior probability distribution be:

$m|d_{\mathrm{obs}}~N_{n_m}({\mathrm{\μ}}_{m|d_{\mathrm{obs}}},{\mathrm{\Σ}}_{m|d_{\mathrm{obs}}})---\left(22\right)$

Posterior error and variance are respectively:

${\mathrm{\μ}}_{m|d_{\mathrm{obs}}}={\mathrm{\μ}}_m+{\left(\mathrm{SA}{\mathrm{\Σ}}_m^{\′}\right)}^T{\mathrm{\Σ}}_{d_{\mathrm{obs}}}^{-1}(d_{\mathrm{obs}}-{\mathrm{\μ}}_{d_{\mathrm{obs}}}),$

${\mathrm{\Σ}}_{m|d_{\mathrm{obs}}}={\mathrm{\Σ}}_m-{\left(\mathrm{SA}{\mathrm{\Σ}}_m^{\′}\right)}^T{\mathrm{\Σ}}_{d_{\mathrm{obs}}}^{-1}\mathrm{SA}{\mathrm{\Σ}}_m^{\′}---\left(23\right)$

The maximum a posteriori solution (MAP) of m just should equal posterior error value covariance matrix is evaluated in order to the uncertainty final to inversion result.

As shown in Figure 7, the inventive method comprises:

The first step, input angle territory geological data, frequency field geological data and log data; The geological data of angle domain geological data and frequency field is all expressed as d _obs, these data are the 3-D data volume of time, angle and frequency, and user can extract corresponding data out when carrying out AVA and AVF inverting, d _obsspecifically angle domain geological data or frequency field geological data, depends on user and uses what inversion method.Log data is expressed as: m=[lnc, α ,] ^t, m is the vector of elastic parameter composition, and lnc represents the logarithm of speed respectively, and α represents decay factor, and the two all obtains from well-log information;

Second step, calculates the prior imformation of log data;

3rd step, utilizes prior imformation and likelihood function, carries out linear AVA and the AVF inverting of Bayes, obtains speed and quality factor.

Below by a synthesis road collection, effect of the present invention is described, algorithm C language is write, and picture Matlab makes.Model is accompany sandstone reservoir (as shown in Figure 1) in the middle of shale layer, and the parameter of three bed interfaces is set to respectively: Vp1=300m/s, Qp1=100; Vp2=4000, Qp2=10; Vp3=3500, Qp3=80.Wavelet is ricker wavelet, dominant frequency 35hz; Time sampling interval is: 2ms; Angular range is from 0 °-45 ° changes, and frequency range is: 2hz-80hz.

First the comparative analysis error (as Suo Shi Fig. 2, Fig. 3 and Fig. 4) of sticky acoustic medium AVA/AVF approximate expression and accurate reflection coefficient, result is presented at that the upper and lower velocity contrast of reflecting interface is little, quality factor poor little when, degree of approximation is very high.And these 2 approximate conditions are all easier to meet, the sticky acoustic medium AVA/AVF approximate expression of therefore deriving has very high precision and using value.Then, the record (as shown in Fig. 5-1 and Fig. 5-2) of seismic amplitude with incident angle and frequency change is obtained by convolution model.Next amplitude is utilized to carry out the linear AVA/AVF inverting of Bayes at incident angle domain information and amplitude in frequency-domain information respectively, obtain speed and the decay factor change (as shown in Fig. 6-1 and Fig. 6-2) of underground medium, the value of initial model is the average of medium velocity.Be not difficult to find out, the sticky linear AVA inverting of acoustic medium Bayes can be finally inversed by the conversion of medium velocity accurately, but limited for the inversion accuracy of decay factor; Bayes linear AVF inverting then point-devicely can be finally inversed by speed and the decay factor of underground medium.

Along with the aggravation of oil-gas exploration difficulty, people have to sight to turn to more hidden lithologic deposit from structural deposit.Therefore, traditional structure imaging has been difficult to the demand of current oil-gas exploration.And the wide-azimuth acquisition technique developed on this basis and relative amplitude preserved processing technology all achieve significant progress, also played a great role in reservoir prediction by the prestack inversion comprising AVO technology simultaneously and provided guarantee.But traditional AVO analyzing total is hypothesis underground medium is perfectly elastic.Decay and velocity dispersion phenomenon can be there is in the Petrophysical measurement in VSP data, well-log information and laboratory all explicitly seismic wave in actual propagation process.Especially for the region containing hydrocarbon, decay clearly.Ignore seismic wave attenuation and can bring huge risk to AVO analysis and reservoir prediction.

The attenuation by absorption of seismic event is brought into whole inverting framework and is got off by the present invention, make use of the information of seismic reflection data angle domain and frequency field simultaneously, it is also combined with Bayes's inversion method and builds new prior imformation and likelihood function by the Reflection Efficient Approximation of frequency of having derived angle domain, inversion result not only can obtain the change of sticky acoustic medium medium velocity, can obtain the change of underground medium decay factor simultaneously.This invention is not only outstanding to seism processing work meaning, more finds subterranean oil gas reservoir and provides important instruction.

Technique scheme is one embodiment of the present invention, for those skilled in the art, on the basis that the invention discloses application process and principle, be easy to make various types of improvement or distortion, and the method be not limited only to described by the above-mentioned embodiment of the present invention, therefore previously described mode is just preferred, and does not have restrictive meaning.

Claims (4)

1. linear AVA and the AVF inversion method of sticky acoustic medium Bayes, is characterized in that: described method comprises:

The first step, input angle territory geological data, frequency field geological data and log data

Second step, sets up prior imformation and the likelihood function of log data;

3rd step, utilizes described prior imformation and likelihood function, carries out linear AVA and the AVF inverting of Bayes, obtains speed and quality factor.

2. linear AVA and the AVF inversion method of sticky acoustic medium Bayes according to claim 1, is characterized in that: in the described first step, the geological data of angle domain geological data and frequency field is all expressed as d _obs, these data are the 3-D data volume of time, angle and frequency; Log data is expressed as: m=[lnc, α ,] ^t, wherein, m is the vector of elastic parameter composition, and lnc represents the logarithm of speed respectively, and α represents decay factor, and the two all obtains from well-log information.

3. linear AVA and the AVF inversion method of sticky acoustic medium Bayes according to claim 2, is characterized in that: described second step is achieved in that

The prior imformation setting up log data is as follows:

$m={[\ln c,\mathrm{\α}]}^T~N_{n_m}({\mathrm{\μ}}_m,{\mathrm{\Σ}}_m)---\left(12\right)$

Wherein, represent n the sampling point Normal Distribution about m, μ _m, ∑ _mrepresent the expectation and variance of m respectively, by what obtain the statistics of well logging sampling point;

Set up likelihood function as follows:

$p\left(d_{\mathrm{obs}}\right|m)=N_{n_d}({\mathrm{\μ}}_{d_{\mathrm{obs}}},{\mathrm{\Σ}}_{d_{\mathrm{obs}}})---\left(18\right)$

Wherein, represent that observation geological data meets Gaussian distribution, represent the expectation of geological data, represent the variance of geological data;

Expectation and variance meets respectively:

${\mathrm{\μ}}_{d_{\mathrm{obs}}}=\mathrm{SA}{\mathrm{\μ}}_m^{\′},$

${\mathrm{\Σ}}_{d_{\mathrm{obs}}}=\mathrm{SA}{\mathrm{\Σ}}_m^{\′\′}{A}^T{S}^T+{\mathrm{\Σ}}_e---\left(19\right)$

∑ " _mrepresenting asks second order to lead to the statistical variance of elastic parameter, ∑ _erepresent the variance of noise;

Wherein, S is:

Can be write as each S:

For AVA inverting, adopt:

$A=\left[\begin{array}{cc}{A}_c({\mathrm{\θ}}_1,{\mathrm{\ω}}_{\mathrm{fix}})& A_{\mathrm{\α}}({\mathrm{\θ}}_1,{\mathrm{\ω}}_{\mathrm{fix}})\\ ......& ......\\ A_c({\mathrm{\θ}}_{\mathrm{n\θ}},{\mathrm{\ω}}_{\mathrm{fix}})& A_{\mathrm{\α}}({\mathrm{\θ}}_{\mathrm{n\θ}},{\mathrm{\ω}}_{\mathrm{fix}})\end{array}\right],---\left(15a\right)$

For AVF inverting, adopt:

$A=\left[\begin{array}{cc}{A}_c({\mathrm{\θ}}_{\mathrm{fix}},{\mathrm{\ω}}_1)& A_{\mathrm{\α}}({\mathrm{\θ}}_{\mathrm{fix}},{\mathrm{\ω}}_1)\\ ......& ......\\ A_c({\mathrm{\θ}}_{\mathrm{fix}},{\mathrm{\ω}}_{\mathrm{n\ω}})& A_{\mathrm{\α}}({\mathrm{\θ}}_{\mathrm{fix}},{\mathrm{\ω}}_{\mathrm{n\ω}})\end{array}\right],---\left(15b\right)$

Wherein, s ₁(θ _i, ω _i) expression incident angle is θ _i, dominant frequency is ω _iwavelet; Subscript 1,2 until nwave represents the time delay of wavelet; A _c(θ _{n θ}, ω _fix) represent frequencies omega _fixfixing, depend on incidence angle θ _{n θ}velocity coefficient; A _α(θ _{n θ}, ω _fix) represent frequencies omega _fixfixing, depend on incidence angle θ _{n θ}decay factor coefficient; A _c(θ _fix, ω _{n ω}) represent incidence angle θ _fixfixing, depend on frequencies omega _{n ω}velocity coefficient; A _α(θ _fix, ω _{n ω}) represent incidence angle θ _fixfixing, depend on frequencies omega _{n ω}decay factor coefficient.

4. linear AVA and the AVF inversion method of sticky acoustic medium Bayes according to claim 3, is characterized in that: described 3rd step is achieved in that

Seismologic record and elastic parameter meet joint distribution:

$\left[\begin{array}{c}m\\ d_{\mathrm{obs}}\end{array}\right]~N_{n_m+n_d}(\left[\begin{array}{c}{\mathrm{\μ}}_m\\ {\mathrm{\μ}}_{d_{\mathrm{obs}}}\end{array}\right],\left[\begin{array}{cc}{\mathrm{\Σ}}_m& {\mathrm{\Σ}}_{m,d_{\mathrm{obs}}}\\ {\mathrm{\Σ}}_{d_{\mathrm{obs}},m}& {\mathrm{\Σ}}_{d_{\mathrm{obs}}}\end{array}\right])---\left(20\right)$

Wherein

${\mathrm{\Σ}}_{d_{\mathrm{obs}},m}=\mathrm{Cov}\{d_{\mathrm{obs}},m\}=\mathrm{SA}{\mathrm{\Σ}}_m^{\′}---\left(21\right)$

At given d _obswhen m Posterior probability distribution be:

$m|d_{\mathrm{obs}}~N_{n_m}({\mathrm{\μ}}_{m|d_{\mathrm{obs}}},{\mathrm{\Σ}}_{m|d_{\mathrm{obs}}})---\left(22\right)$

Posterior error and variance are respectively:

${\mathrm{\μ}}_{m|d_{\mathrm{obs}}}={\mathrm{\μ}}_m+{\left(\mathrm{SA}{\mathrm{\Σ}}_m^{\′}\right)}^T{\mathrm{\Σ}}_{d_{\mathrm{obs}}}^{-1}(d_{\mathrm{obs}}-{\mathrm{\μ}}_{d_{\mathrm{obs}}}),$

${\mathrm{\Σ}}_{m|d_{\mathrm{obs}}}={\mathrm{\Σ}}_m-{\left(\mathrm{SA}{\mathrm{\Σ}}_m^{\′}\right)}^T{\mathrm{\Σ}}_{d_{\mathrm{obs}}}^{-1}\mathrm{SA}{\mathrm{\Σ}}_m^{\′}---\left(23\right)$

The maximum a posteriori solution (MAP) of m just equals posterior error value covariance matrix is evaluated in order to the uncertainty final to inversion result.