CN109521468A - A kind of PP-PS joint inversion system based on Kalman filter - Google Patents
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Abstract
The present invention relates to a kind of gas reservoir prospecting techniques, especially a kind of PP-PS joint inversion system based on Kalman filter, by based on the AVO joint inversion model containing noise, Kalman filter model is added, wherein the AVO joint inversion model containing noise includes the vector m for surveying geological meaning attribute information, the vector m includes velocity of longitudinal wave α, shear wave velocity β, density item ρ, the Kalman filter model includes time update and measurement updaue, the vector m after obtaining maximum likelihood estimation with the measurement updaue is updated by the time to obtain velocity of longitudinal wave α, shear wave velocity β, density item ρ, the vector m after maximum likelihood estimation is higher than conventional without the vector m precision that Kalman filter model is added, the result of exploration also more may be used It leans on, preferably solves the problems, such as that the conventional AVO inverting in the presence of the prior art is lower based on density caused by the progress of longitudinal wave reflection data and S-wave velocity inversion precision.
Description
Technical field
The present invention relates to a kind of gas reservoir prospecting technique, especially a kind of PP-PS joint inversion system based on Kalman filter
System.
Background technique
Seismic prospecting target has turned to lithologic deposit via structure type oil-gas reservoir, and this requires us from seismic data
It is middle to obtain attribute information more reliable and with clear geological meaning.AVO inversion technique can be from amplitude with the change of geophone offset
The elastic parameters such as velocity of longitudinal wave, shear wave velocity and density information is extracted in change directly to estimate the property of subsurface rock and fluid
Matter.Due to the multi-solution of error and underground medium on seismic acquisition data, AVO inverting has ill-posedness.For inverting
Ill-posedness, Conventional solutions are as follows: 1. due to merely using longitudinal wave reflection data carry out inverting can not obtain it is credible
As a result, lack accurate shear wave velocity and density information will lead to the misinterpretation of reservoir, converted shear wave seismic data can be with
More accurately shear wave velocity and density estimation are provided.With longitudinal wave excitation, the development of three-component reception technique, benefit is greatly reduced
With the cost of conversion transversal wave exploration, the development of PP-PS joint inversion (i.e. PP wave and the joint inversion of PS wave) is also promoted.Joint
Inverting can improve inversion accuracy compared with simple PP inversion method to a certain extent；2. another method is to establish
Three parametric inversion of maximum a posteriori probability under Bayesian frame merges a variety of prior informations and goes to seek velocity of longitudinal wave, shear wave speed
The Posterior distrbutionp of degree and density；Wherein, although the AVO that AVO and the joint inversion of PP wave-PS wave can be more traditional in the prior art
Inverting improves a degree of inversion accuracy, but in order to preferably survey geological property, it is also necessary to join in AVO and PP wave-PS wave
It closes and continues to improve inversion accuracy on inverse model.
Summary of the invention
It is an object of the invention to overcome the conventional AVO inverting in the presence of the prior art be based on longitudinal wave reflection data into
Density caused by row and S-wave velocity inversion precision are lower, and error is larger in fluid identification, provides a kind of by Kalman filtering
(Kalman filtering) introduces the joint inversion model of existing AVO and PP-PS wave, utilizes linear system state equation pair
System mode carries out the joint inversion system of novel AVO and the PP-PS of optimal estimation.
In order to achieve the above-mentioned object of the invention, the present invention provides following technical schemes:
A kind of PP-PS joint inversion system based on Kalman filter, including the AVO joint inversion model containing noise and
Kalman filter model, the AVO joint inversion model containing noise include for survey geological meaning attribute information to
M is measured, the Kalman filter model includes time update and measurement updaue, updates by the time and the measurement updaue obtains
The vector m after maximum likelihood estimation out, the vector m include velocity of longitudinal wave α, shear wave velocity β, density item ρ.
Wherein AVO joint inversion model, that is, prior art AVO and PP-PS joint inversion containing noise.
The present invention is by being added Kalman filter model, wherein containing based on the AVO joint inversion model containing noise
The AVO joint inversion model for having noise includes the vector m for surveying geological meaning attribute information, and the vector m includes longitudinal wave
Speed alpha, shear wave velocity β, density item ρ, the Kalman filter model include time update and measurement updaue, pass through the time
It updates and the measurement updaue obtains the vector m after maximum likelihood estimation to obtain velocity of longitudinal wave α, shear wave velocity β, density item ρ,
The vector m after maximum likelihood estimation is higher than conventional without the vector m precision that Kalman filter model is added, exploration
As a result also relatively reliable, preferably solve the conventional AVO inverting in the presence of the prior art be based on longitudinal wave reflection data into
Density caused by row and the lower problem of S-wave velocity inversion precision.
Preferably, the AVO joint inversion model containing noise includes seismic convolution model, the seismic convolution model
Are as follows:
dobs=WR+e；(1)
Wherein R is about RPP(θi) and RPS(θi) matrix, RPP(θi) and RPS(θi) be respectively incidence angle be θiWhen longitudinal wave,
The reflection coefficient of converted shear wave is formed by the Stolt-Weglein Time Continuous equation inference in PP-PS forward modeling, this is existing
There is technology；
Wherein W is the diagonal sparse matrix of different firing angles；
Wherein e is the noise that seismic data includes.
Final R and RPP(θi) and RPS(θi) relational expression are as follows:
W is the diagonal sparse matrix of different firing angles:
Wherein WPP(θk) are as follows:
S1(θk)…Sns(θk) it is incidence angle θkWavelet sampling；Similarly, WPS(θk) matrix form having the same.
Preferably, the AVO joint inversion model containing noise are as follows:
Wherein, dobsIt for measured value, is measured by wave detector, dPP(θk) and dPS(θk) it be incidence angle is θkWhen, longitudinal wave and conversion
The data matrix that shear wave measurement obtains.
Wherein, G=WAD, G are the matrix comprising W and A, and W is the rarefaction of the convolution matrix of different incidence angles, and A is corresponding
The coefficient matrix of parameter, D are differential operator, this part is the prior art；
α is velocity of longitudinal wave, and β is shear wave velocity, and ρ is density item；Vector m is about longitudinal wave, the matrix of shear wave and density item
Transposition.
E is the noise that seismic data includes, i.e. measurement noise, indicates the system noise and amount of Gaussian distributed with q, p
Noise is surveyed, covariance is respectively Q and R.
Systematic procedure noise: the mainly error of state transfer generation.The determination of the covariance Q of process noise is usually to compare
More difficult, because we cannot be directly observed the process signal m to be estimatedk, then can establish a relatively simple mould
Type is to generate good result.
Measure noise: the measurement as caused by influencing wave detector, environment and human factor is inaccurate, cannot accurately see
Measured value.
Preferably, the AVO inverse model by described containing noise regards a discrete control process as, and considers to use
Angle updates replaces the time to update, by the AVO joint inversion model containing noise substitute into time update after obtain
Model are as follows:
Wherein, mkSystem mode when for k-th of incidence angle, the system mode include longitudinal wave, shear wave velocity and close
Parameter is spent, Φ is state-transition matrix, this Inversion System Φ takes unit matrix I, qk-1System mistake when for -1 incidence angle of kth
Journey noise, pkMeasurement noise when for k-th of incidence angle, dkD when for k-th of incidence angleobs, GkWhen for k-th of incidence angle
Calculation matrix.
Time, which updates, estimates to front projection and state error covariance, to next step time or angle
Prior estimate sought.
Preferably, new observation data are added in prior estimate and are acquired improved Posterior estimator, it is available
The time of Posterior estimator updates are as follows:
Wherein,For k-th of state (angle) m gone out by preceding k-1 status predicationkEstimated value,It is logical
Cross the posteriority state estimation at -1 moment of kth that preceding k-1 state (angle) obtains.Pk|k-1ForThe error covariance of estimation,
Pk-1|k-1ForPosterior estimator error covariance.
Preferably, the AVO joint inversion model by described containing noise substitutes into the measurement updaue, by new observation data
It is added in prior estimate and acquires improved Posterior estimator, the measurement updaue of available Posterior estimator are as follows:
Kk=Pk|k-1Gk T(GkPk|k-1Gk T+Rk)-1
Pk|k=(I-KkGk)Pk|k-1； (6)
Wherein, KkFor kalman gain, Pk|kForPosterior estimator error covariance；
For the transposition of the calculation matrix of k-th of incidence angle；
GkFor the calculation matrix of k-th of incidence angle；
RkThe covariance of noise, R are measured for the k momentPPFor longitudinal wave reflection coefficient, RPSFor transverse wave reflection coefficient；
It is for the posteriority state estimation obtained by the corresponding observation data of angle before k angle and k, i.e., optimal to estimate
The vector m after calculation.
The effect of measurement updaue equation is to be fed back, and exactly new observation data are added in prior estimate and are acquired
Improved Posterior estimator, Kalman filter are exactly to find in status predication and amendment in such a way that this iteration updates
Optimal balance point is optimal estimation.
Compared with prior art, beneficial effects of the present invention:
The present invention is by being added Kalman filter model, wherein containing based on the AVO joint inversion model containing noise
The AVO joint inversion model for having noise includes the vector m for surveying geological meaning attribute information, and the vector m includes longitudinal wave
Speed alpha, shear wave velocity β, density item ρ, the Kalman filter model include time update and measurement updaue, pass through the time
It updates and the measurement updaue obtains the vector m after maximum likelihood estimation to obtain velocity of longitudinal wave α, shear wave velocity β, density item ρ,
The vector m after maximum likelihood estimation is higher than conventional without the vector m precision that Kalman filter model is added, exploration
As a result also relatively reliable, preferably solve the conventional AVO inverting in the presence of the prior art be based on longitudinal wave reflection data into
Density caused by row and the lower problem of S-wave velocity inversion precision.
Detailed description of the invention:
Fig. 1 is the flow chart that the present invention works.
Marked in the figure: the 1- time updates, 2- measurement updaue.
Specific embodiment
Below with reference to test example and specific embodiment, the present invention is described in further detail.But this should not be understood
It is all that this is belonged to based on the technology that the content of present invention is realized for the scope of the above subject matter of the present invention is limited to the following embodiments
The range of invention.
Specific embodiment is as follows, as shown in Figure 1, the earthquake that is, existing instrument detects is believed by original state parameter
Cease dobs, the prediction of formula 5-1 state variable is substituted into, error covariance is calculated forward by 5-2, this is based on Kalman filter
Time in PP-PS joint inversion system updates 1, then updates error covariance by measurement updaue 2, i.e., calculates first
Kalman gain, further according to formula 6-2 observation dkMore new estimation, the error covariance in final updating formula 6-3, obtains most
Vector m, the Lai Tigao velocity of longitudinal wave of excellent estimation, shear wave velocity, the precision of density item, so as to improve detection accuracy.
Wherein formula 6 is the measurement updaue 2 in the PP-PS joint inversion system based on Kalman filter, and formula 6 includes 6-
1,6-2 and 6-3, as follows:
Kk=Pk|k-1Gk T(GkPk|k-1Gk T+Rk)-1
Pk|k=(I-KkGk)Pk|k-1； (6)
Formula 6, i.e., the AVO joint inversion model by described containing noise substitutes into the measurement updaue 2, by new observation number
According to being added in prior estimate and acquiring improved Posterior estimator, the measurement updaue 2 i.e. formula 6 of Posterior estimator is obtained.
Wherein, KkFor kalman gain, Pk|kForPosterior estimator error covariance；
For the transposition of the calculation matrix of k-th of incidence angle；
GkFor the calculation matrix of k-th of incidence angle；
RkThe covariance of noise, R are measured for the k momentPPFor longitudinal wave reflection coefficient, RPSFor transverse wave reflection coefficient；
It is for the posteriority state estimation obtained by the corresponding observation data of angle before k angle and k, i.e., optimal to estimate
The vector m after calculation.
The effect of 2 equation of measurement updaue is to be fed back, and exactly new observation data are added in prior estimate and are asked
Improved Posterior estimator is obtained, Kalman filter is exactly to seek in status predication and amendment in such a way that this iteration updates
Optimal balance point is looked for be optimal estimation.
Wherein formula 5 is the time in the PP-PS joint inversion system based on Kalman filter to update 1, and formula 5 includes 5-
1,5-2, as follows:
Wherein,For k-th of the state or angle m gone out by preceding k-1 status predicationkEstimated value,It is logical
Cross the posteriority state estimation at -1 moment of kth that preceding k-1 state or angle obtain.Pk|k-1ForThe error covariance of estimation,
Pk-1|k-1ForPosterior estimator error covariance, QkFor qkCovariance.
Formula 5 is that formula 4 derives, i.e., the time update 1 is added in the AVO joint inversion final form containing noise
It derives, formula 4 are as follows:
Wherein, mkSystem mode when for k-th of incidence angle, the system mode include longitudinal wave, shear wave velocity and close
Parameter is spent, Φ is state-transition matrix, this Inversion System Φ takes unit matrix I, qk-1System mistake when for -1 incidence angle of kth
Journey noise, pkMeasurement noise when for k-th of incidence angle, dkD when for k-th of incidence angleobs, GkWhen for k-th of incidence angle
Calculation matrix.
Q, p respectively indicate the system noise of Gaussian distributed and measure noise, and covariance is respectively Q and P.
Systematic procedure noise: the mainly error of state transfer generation.The determination of the covariance Q of process noise is usually to compare
More difficult, because we cannot be directly observed the process signal m to be estimatedk, then can establish a relatively simple mould
Type is to generate good result.
Measure noise: the measurement as caused by influencing wave detector, environment and human factor is inaccurate, cannot accurately see
Measured value.
Formula 4 is by prior art formula 3, i.e., the AVO joint inversion formal grammar containing noise forms:
Wherein, dobsIt for measured value, is measured by wave detector, dPP(θk) and dPS(θk) it be incidence angle is θkWhen, longitudinal wave and conversion
The data matrix that shear wave measurement obtains.
Wherein, G=WAD, G are the matrix comprising W and A, and W is the rarefaction of the convolution matrix of different incidence angles, and A is corresponding
The coefficient matrix of parameter, D are differential operator, this part is the prior art；
α is velocity of longitudinal wave, and β is shear wave velocity, and ρ is density item；Vector m is about longitudinal wave, the matrix of shear wave and density item
Transposition.
E is the noise that seismic data includes, i.e. measurement noise, indicates the system noise and amount of Gaussian distributed with q, p
Noise is surveyed, covariance is respectively Q and R.
It will introduce formula 1 to 3 below, the derivation process of formula 7 to 16, the i.e. derivation process of PP-PS forward modeling part,
Middle formula 3 is formed by the convolution formal grammar of reflection coefficient and seismic wavelet:
dobs=WR+e； (1)
Wherein dobsFor about dPP(θi) and dPS(θi) matrix:
Wherein W is the diagonal sparse matrix of different firing angles:
S1(θk)…Sns(θk) it is incidence angle θkWavelet sampling；Similarly, WPS(θk) matrix form having the same.
Eventually by seismic convolution model, AVO joint inversion form, that is, formula 3 containing noise can be obtained.
Wherein R are as follows:
R=ADm； (10)
ap(θi), aS(θi),aρ(θi),bS(θi), bρ(θi) it be incidence angle is θiWhen, the corresponding n of longitudinal wave, converted shear wave multiplied by
The diagonal coefficient matrix of n.RPP(θi) and RPS(θi) be respectively incidence angle be θiWhen longitudinal wave, converted shear wave reflection coefficient.When n is
Between number of samples, dtFor time-derivative operator, expression formula are as follows:
The prototype of formula 11 is formula 7, it may be assumed that
In a time interval, it is assumed that have m incidence angle.Then formula 7 can be formed by formula 15 is discrete, associated to push away
Formula is led there are also formula 13, formula 14 and formula 16, as follows:
The derivation of formula 13 is using Stolt-Weglein Time Continuous equation (Stoltand Weglein, 1985), the party
Journey is the popularization of Aki-Richards linear equation.
Aki-Richards approximate equation is as follows:
Wherein, the coefficient expressions of relevant parameter are as follows:
WithThe respectively average value of upper and lower level velocity of longitudinal wave, shear wave velocity and density；ΔVP, Δ VSWith Δ ρ
For the difference of upper and lower level medium；θ is the average angle of incidence of upper and lower medium longitudinal wave；For the average incident of upper and lower medium converted shear wave
Angle.γ isRatio.
Stolt and Weglein (1985) is pushed away from the Aki-Richards approximate formula for being suitable for single uniform interface
It is derived Time Continuous equation:
Wherein, ap(t, θ), aS(t, θ), aρ(t,θ),bS(t,θ),bρ(t, θ) is the summary table that formula 2 changes over time
It reaches.Assuming thatIt is represented by constant or slowly varying background model, thenThen it is considered as one
V in window when aP(t), Vs(t) average or sliding average.
There are following hypothesis passes between Stolt and Weglein continuous time equation and Aki-Richards approximation relation
System:
As can be seen that incidence angle θ is the independent variable of reflection coefficient from formula above.However, seismic data is practical
On be function about offset distance, from when m- offset distance domain then m- angle domain conversion depend on velocity function, Ke Yitong
It crosses angle offset, the methods of ray tracing altogether and carries out conversion between not same area.
Above formula 1-3 and formula 7 to 16 are the derivation process of AVO and PP-PS forward modeling part, i.e., as existing skill
Art.
Formula 4 arrives the core that formula 6 is the PP-PS joint inversion system based on Kalman filter, that is, when passing through described
Between update 1 and the measurement updaue 2 obtain the vector m after maximum likelihood estimation, obtained by the vector m after maximum likelihood estimation
The higher density item of precision, shear wave velocity and velocity of longitudinal wave, to improve exploration precision.
Claims (6)
1. a kind of PP-PS joint inversion system based on Kalman filter, which is characterized in that including the AVO joint containing noise
Inverse model and Kalman filter model, the AVO joint inversion model containing noise includes for surveying geological meaning category
Property information vector m, the Kalman filter model include the time update and measurement updaue, by the time update and it is described
Measurement updaue show that the vector m after maximum likelihood estimation, the vector m include velocity of longitudinal wave α, shear wave velocity β, density item ρ.
2. a kind of PP-PS joint inversion system based on Kalman filter according to claim 1, which is characterized in that institute
Stating the AVO joint inversion model containing noise includes seismic convolution model, the seismic convolution model are as follows:
dobs=WR+e； (1)
Wherein R is about RPP(θi) and RPS(θi) matrix, RPP(θi) and RPS(θi) be respectively incidence angle be θiWhen longitudinal wave, conversion
The reflection coefficient of shear wave is formed by the Stolt-Weglein Time Continuous equation inference in PP-PS forward modeling；
Wherein W is the diagonal sparse matrix of different firing angles；
Wherein e is the noise that seismic data includes.
3. a kind of PP-PS joint inversion system based on Kalman filter according to claim 1, which is characterized in that institute
State the AVO joint inversion model containing noise are as follows:
dobs=Gm+e
M=[ln α ln β ln ρ]T； (3)
Wherein, dobsFor measured value, the seismic response obtained by geophone in field inspection, wherein l is the discrete of incidence angle
Number, kalman filtering in k value range be [1, l]；
G is the matrix comprising W, A and D, and W is the rarefaction of the convolution matrix of different incidence angles, and A is the coefficient matrix of relevant parameter
Forward operator, D is differential operator.
4. a kind of PP-PS joint inversion system based on Kalman filter according to claim 1, which is characterized in that will
The AVO inverse model containing noise regards a discrete control process as, and consideration is updated with angle and replaces the time
It updates, the AVO joint inversion model containing noise is substituted into the model obtained after the time update are as follows:
Wherein, mkSystem mode when for k-th of incidence angle, the system mode include longitudinal wave, shear wave velocity and density ginseng
Number, Φ is state-transition matrix, this Inversion System Φ takes unit matrix I, qk-1Systematic procedure when for -1 incidence angle of kth is made an uproar
Sound, measurement noise when pk is k-th of incidence angle, dkD when for k-th of incidence angleobs, GkMeasurement when for k-th of incidence angle
Matrix.
5. a kind of PP-PS joint inversion system based on Kalman filter according to claim 1, which is characterized in that will
New observation data are added in prior estimate and acquire improved Posterior estimator, and the time of available Posterior estimator updates
Are as follows:
Wherein,For k-th of the state or angle m gone out by preceding k-1 status predicationkEstimated value,To pass through preceding k-
The posteriority state estimation at -1 moment of kth that 1 state or angle obtain.Pk|k-1ForThe error covariance of estimation, Pk-1|k-1
ForPosterior estimator error covariance.
6. a kind of PP-PS joint inversion system based on Kalman filter according to claim 1, which is characterized in that will
The AVO joint inversion model containing noise substitutes into the measurement updaue, and new observation data are added in prior estimate
And improved Posterior estimator is acquired, the measurement updaue of available Posterior estimator are as follows:
Kk=Pk|k-1Gk T(GkPk|k-1Gk T+Rk)-1
Pk|k=(I-KkGk)Pk|k-1； (6)
Wherein, KkFor kalman gain, Pk|kForPosterior estimator error covariance；
For the transposition of the calculation matrix of k-th of incidence angle；
GkFor the calculation matrix of k-th of incidence angle；
RkThe covariance of noise, R are measured for the k momentPPFor longitudinal wave reflection coefficient, RPSFor transverse wave reflection coefficient；
For by angle before k angle and k it is corresponding observation data obtain posteriority state estimation, i.e., after maximum likelihood estimation
The vector m.
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| CN115210609A (en) * | 2020-02-21 | 2022-10-18 | 株式会社东京测振 | Estimation device, vibration sensor system, method executed by estimation device, and program |
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Cited By (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN111025388A (en) * | 2019-12-19 | 2020-04-17 | 河海大学 | Multi-wave combined prestack waveform inversion method |
| CN115210609A (en) * | 2020-02-21 | 2022-10-18 | 株式会社东京测振 | Estimation device, vibration sensor system, method executed by estimation device, and program |
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