CN106324674B - A kind of shale gas TOC pre-stack seismic inversion Forecasting Methodologies - Google Patents
A kind of shale gas TOC pre-stack seismic inversion Forecasting Methodologies Download PDFInfo
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Abstract
The present invention relates to unconventionaloil pool field of seismic exploration, specifically disclose a kind of shale gas TOC pre-stack seismic inversion Forecasting Methodologies, and this method includes the following steps：Step 1 establishes shale reservoir TOC inversion objective functions；Step 2, the shale TOC prestack inversions based on elastic impedance：The prior distribution of the reservoir TOC is established according to the statistical analysis to log data, random sampling is done to established prior distribution by Monte Carlo simulation analogue technique respectively, the final random sample spatial distribution for obtaining reservoir TOC, estimate the maximum value of reservoir TOC posterior probability, the corresponding TOC values in position place where this maximum value are exactly the final result of inverting.Integrated application of the present invention bayesian theory, statistics petrophysical model, Monte Carlo random sampling technology scheduling theory, it being capable of several physical parameters of Simultaneous Inversion, it is influenced when eliminating independent inverting a certain kind parameter by what other parameter was limited, and then enhances the confidence level of inverting.
Description
Technical field
The present invention relates to unconventionaloil pool field of seismic exploration, more particularly to shale gas TOC pre-stack seismic inversions prediction side
Method.
Background technology
Shale gas is a kind of very important unconventional petroleum resources, and resource potential is huge, and reservoir study and evaluation are pages
The Main Task at rock gas exploration initial stage, fluid identification of reservoir refer to know reservoir containing characteristic of fluid using seismic data
It not and describes, pre-stack seismic inversion is fluid identification of reservoir and the effective way of evaluation, to accurately finding Favorable Areas with important
Realistic meaning.The principal element of Shale Gas Accumulation includes demonstration mineralogical composition, adsorbed gas content, total content of organic carbon, gassiness
Amount, permeability, maturity of organic matter, buried depth, effective thickness, porosity, strata pressure, temperature etc..Wherein total organic carbon
Content (TOC) is directly proportional to shale Gas content, directly affects the size of shale Gas content, is ground to north America region shale gas reservoir
After studying carefully, it is believed that the TOC contents the high more is conducive to the enrichment of shale gas, and commercially valuable shale gas gas reservoir should generally have
TOC is more than 2.0%, therefore the accurate calculating of TOC is particularly important for improving shale gas reservoir gas-bearing amount precision of prediction.
Seismic inversion is the effective way for obtaining underground medium elastic parameter.According to different, the seismic inversion using seismic data
Post-stack inversion and prestack inversion can be divided into.Post-stack inversion utilizes poststack seismic data, main inverting stratum longitudinal wave information；Prestack
Shake inverting utilizes the abundant information that Prestack seismic data is included, and in addition to inverting longitudinal wave information, can also estimate formation shear, rock
Stone modulus, fluid sensitive parameter, physical parameter, anisotropic parameters, even absorption parameter, the information such as density.In pre-stack seismic
It is different according to the earthquake direct problem analytical expression of use in inverting, the prestack inversion based on wave equation can be divided into, based on earthquake
Wave accurate reflection coefficient equation and its approximate prestack inversion and seismic scattering inverting based on Seismic Wave Scattering coefficient equation etc.,
Wherein, the prestack seismic inversion method based on wave equation is limited by computational efficiency and stability, it is difficult in actual seismic data
Middle inverting obtains legitimate result, and practicability is smaller；According to refutation strategy difference, based on seismic reflection coefficient equation and its approximately
Prestack inversion method can be divided into AVO invertings, AVA invertings and elastic impedance inverting again.According to underground medium equivalent model difference, can divide
For uniform, non-uniform dielectric, isotropism, anisotropic medium, elasticity, viscoelastic media and mutual group between them
Close medium pre-stack seismic inversion etc..
Existing method is the equation of the relationship of the two to be established by being obtained with density fitting, and then TOC is calculated, and is somebody's turn to do
Prestack inversion method comprehensively utilizes seismic data and log data and carries out inverting, the TOC obtained by inverting to shale reservoir TOC
Relationship between numerical values recited and reservoir density can obtain the oily situation of shale formation, so as to fulfill shale oil-gas possibility
Evaluation.
The existing method by being fitted with density calculates TOC, is only merely good linear between Application density and TOC
Relationship, the unstability without considering inversion of Density, simply by building, linear approximate relationship can not between density and TOC
Veritably realize shale evaluation of oil and gas bearing property.
Invention content
The present invention is under the guidance of bayesian theory frame, and using elastic impedance inversion prediction shale reservoir TOC, this method exists
Under the premise of the stability for taking full advantage of elastic impedance inverting, use in conjunction bayesian theory, Monte Carlo random sampling skill
Art counts petrophysical model, expectation-maximization algorithm theories and methods, the final prediction for realizing shale reservoir TOC.It proposes
A kind of more stable and accurate shale reservoir TOC inversion methods so that inversion result has stronger confidence level, finally realizes page
Rock evaluation of oil and gas bearing property.
In order to solve the above technical problems, the technical solution adopted by the present invention is：A kind of shale gas TOC pre-stack seismic inversions are pre-
Survey method, includes the following steps：
Step 1 establishes shale reservoir TOC inversion objective functions：
Bayesian formula is expressed as：
In formula (1-1), A represents observation sample information, and B then represents parameter to be estimated, and p (B) represents the elder generation of parameter B to be estimated
Testing distribution, P (B | A) represents the Posterior distrbutionp of parameter B to be estimated, P (A | B) it is the likelihood for contacting chance event A and chance event B
Function, ∫ P (B) P (A | B) dB are the full probabilities of observation sample, if ∫ P (B) P (A | B) dB is a constant, are denoted asFormula (1-1) is derived by applied to object function in reservoir TOC refutation processes：
P([φ,Vsh,T]|[EI1,EI2,EI3])=α × P ([φ, Vsh,T])P([EI1,EI2,EI3]|[φ,Vsh, T]) (1-4),
In formula (1-4), φ, Vsh, T represents porosity, shale content and TOC, EI successively1,EI2,EI3Three are represented respectively
The elastic impedance of a different angle, P () represent probability density function,
Decorrelative transformation is done to the elastic impedance of three different angles, make it is mutual indepedent between three, to formula (1-4)
It does deformation and obtains following formula：
P([EI1,EI2,EI3]|[φ,Vsh,T])
=P (EI1|[φ,Vsh,T])P(EI2|[φ,Vsh,T])P(EI3|[φ,Vsh, T]) (1-5),
In formula (1-5), EI1, EI2, EI3Elastic impedance parameter respectively after decorrelative transformation,
The position of maximum a posteriori probability in Posterior distrbutionp is found, the parameter value corresponding to the position is reservoir TOC
Final inversion result：
[φ,Vsh, T] and=argMaxP ([φ, Vsh,T]|[EI1,EI2,EI3]) (1-6),
Formula (1-4) and formula (1-5) are substituted into formula (1-6), gives up constant α, establishes the object function of final inverting, i.e.,：
In formula (1-7), P ([φ, Vsh, T]) be reservoir TOC prior distribution, P (EI1|[φ,Vsh,T])P(EI2|[φ,
Vsh,T])P(EI3|[φ,Vsh, T]) it is the likelihood function for contacting prior distribution and Posterior probability distribution；
Step 2, the shale TOC prestack inversions based on elastic impedance：
The prior distribution of the reservoir TOC is established according to the statistical analysis to log data：It is assumed that institute in well-log information
Each reservoir physical parameter provided obeys Gaussian mixtures, and each Gaussian mixtures are by N number of Gaussian component
It is made up of weighted average, every statistical parameter in each Gaussian component is obtained in Gaussian mixtures using EM algorithms：
Then mean value, variance and weight establish N number of Gaussian Profile, and according to their own weight respectively according to every statistical parameter
The Gaussian mixtures for averagely, finally obtaining reservoir TOC are weighted, expression formula is as follows：
In formula (2-1), T represents reservoir TOC, N and represents the number of Gaussian component, αkThe weight of k-th of Gaussian component is represented,
MeetThe mean value of Gaussian component is represented,Represent the variance of Gaussian component；
Random sampling is done to established prior distribution respectively by Monte Carlo simulation analogue technique, finally obtains reservoir
The random sample spatial distribution of TOC；
Structure statistics petrophysical model, the statistics petrophysical model expression formula are as follows：
EI=f (T, φ, Vsh)+ε (3-1),
In formula (3-1), f () representative function, EI is elastic impedance variable, and ε is stochastic error variable；
For each sampling point in the random sample spatial distribution of reservoir TOC, all asked by counting petrophysical model
Going out the value of corresponding elastic impedance, all elastic impedance values just together constitute the random sample spatial distribution of elastic impedance,
The two is combined, their Joint Distribution can be obtained, three components in Joint Distribution are obtained respectively using expectation-maximization algorithm
Statistical parameter；
The maximum value of reservoir TOC posterior probability is estimated according to formula (1-7), the position place where this maximum value is corresponding
TOC values are exactly the final result of inverting.
Shale gas TOC pre-stack seismic inversion Forecasting Methodologies proposed by the present invention, it is contemplated that shale reservoir is as unconventional oil
The particularity of gas reservoir carrys out inverting reservoir physical parameter using elastic impedance data instead of elastic parameter, anti-this makes it possible to avoid
The situation of inverting accuracy reduction is caused during drilling due to the participation of inaccurate density information, opposite improves inverting
Accuracy, in addition, in refutation process, integrated application bayesian theory, statistics petrophysical model, Monte Carlo are random
Sampling techniques scheduling theory, can several physical parameters of Simultaneous Inversion, by other ginsengs when eliminating independent inverting a certain kind parameter
The influence of number limitation, and then the confidence level of inverting is enhanced, there is directive significance to the exploration and development of shale oil and gas reservoir.
Description of the drawings
The key step schematic diagram of Fig. 1 shale gas TOC pre-stack seismic inversion Forecasting Methodologies of the present invention.
Fig. 2 is original log and the log curve correlation figure after Backus is average.
Fig. 3 is certainty petrophysical model proof diagram.
Fig. 4 is the TOC values that inverting obtains and the comparison diagram of TOC values obtained using well material computation.
Fig. 5 A are elastic impedance schematic diagram data.
Fig. 5 B are TOC inversion result schematic diagrames.
Specific embodiment
A kind of key step of shale gas TOC pre-stack seismic inversion Forecasting Methodologies proposed by the present invention, as shown in Figure 1.
The first step establishes shale reservoir TOC inversion objective functions：
Bayes' theorem is proposed by the famous scholar Thomas Bayes of Britain, also commonly known as Bayesian inference, is
One of most important theories in probability theory.Bayes' theorem is related to three basic conceptions：Prior distribution, Posterior distrbutionp and contact
The likelihood function of the two.
Bayesian formula can be expressed as：
Wherein, A represents observation sample information, and B then represents parameter to be estimated, and p (B) represents the priori point of parameter B to be estimated
Cloth, P (B | A) represent the Posterior distrbutionp of parameter B to be estimated.In general, in the case where having prior information, according to existing
Prior information is parameter B to be estimated certain cognition summary and induction etc., and makes suitable vacation using the summary and induction of front
If carrying out the probability distribution situation of summary parameters totality, i.e. prior distribution p (B)；In the case of no any prior information, we
A certain prior distribution can also be assumed by subjective consciousness, makes the probability distribution situation of its summary parameters totality, to connect
Posterior probability of getting off is asked for.P (A | B) is the likelihood function of contact event A and event B, usually can be according to the relationship of A and B
To obtain.∫ P (B) P (A | B) dB is the full probability of observation sample, and bayesian theory is thought, after being asked for by Bayesian formula
During testing probability, and ∫ P (B) P (A | B) dB functions only as Posterior distrbutionp the effect of regularization factors, therefore can see it
It is a constant to do, and is denoted asSo above formula is represented by：
P (B | A)=α * p (B) P (A | B) (1-2)
α is constant in formula, by above-mentioned bayesian theory and its formula expression, it will be seen that bayesian theory
Indeed through the prior probability to certain object, the process of its posterior probability is calculated using Bayesian formula, i.e., this waits to estimate
Meter object is to belong to certain a kind of probability, selects class of the class with maximum a posteriori probability belonging to as the object.
By the discussion of bayesian theory and its formula, object function in reservoir TOC refutation processes can be applied to
Derivation, herein we assume that the object function of inverting is treated in A representatives, represented with R；Assuming that B represents observation data (known), use
M is represented, is connected the two using Bayesian formula, expression formula is as follows：
In above formula, R=[φ, Vsh, T], φ, Vsh, T represents porosity, shale content and TOC successively；M represents elasticity
Impedance, i.e. m=[EI1,EI2,EI3], EI1,EI2,EI3The elastic impedance of three different angles is represented respectively；P () represents probability
Density function.
In above formula, ∫ P (R) P (m | R) dR represents the full probability of elastic impedance parameter, to posterior probability P (R |m) ask for only
Play the role of regularization factors, therefore be assumed to a constant, be denoted as α, i.e.,：
P([φ,Vsh,T]|[EI1,EI2,EI3])=α × P ([φ, Vsh,T])P([EI1,EI2,EI3]|[φ,Vsh,T]) (1-4)
φ represents porosity, V in formulashShale content is represented, T represents TOC.Under normal circumstances, the bullet of three different angles
Property impedance between there are certain correlation, and the difference between three angles is smaller, and correlation is higher, inverting it is steady
It is qualitative poorer；Conversely, the difference between three angles is bigger, correlation is lower, and the stability of inverting is higher.Therefore,
In the reasonable scope, the angle difference for choosing elastic impedance parameter is as larger as possible, and the elastic impedance of three angles is gone
Relevant treatment, makes mutual indepedent between three, in this context, can do deformation to formula and obtain following formula：
P([EI1,EI2,EI3]|[φ,Vsh,T])
=P (EI1|[φ,Vsh,T])P(EI2|[φ,Vsh,T])P(EI3|[φ,Vsh,T]) (1-5)
In above formula, EI1, EI2, EI3Elastic impedance parameter respectively after decorrelative transformation.
The position of maximum a posteriori probability in Posterior distrbutionp is found, the parameter value corresponding to the position is reservoir TOC
Final inversion result：
[φ,Vsh, T] and=argMaxP ([φ, Vsh,T]|[EI1,EI2,EI3]) (1-6)
Formula (1-4) and formula (1-5) are substituted into formula (1-6), since constant α does not act on final inversion result, therefore
Given up, obtain the object function of final inverting, i.e.,：
In above formula, P ([φ, Vsh, T]) prior distribution that is reservoir TOC, the general statistical analysis according to log data and
It establishes.P(EI1|[φ,Vsh,T])P(EI2|[φ,Vsh,T])P(EI3|[φ,Vsh, T]) to contact prior distribution and posterior probability
The likelihood function of distribution can be realized by counting petrophysical model and Monte Carlo random sampling technical tie-up.
Second step：Shale TOC prestack inversions based on elastic impedance
Bayesian theory is related to three basic conceptions, one of them is exactly prior distribution.Prior distribution is Bayes
The basic viewpoint of group.Bayesian schools think, before observation sample is obtained by observation, to have to parameter to be estimated and certain recognize
Know, this cognition can be according to objective basis or according to subjective consciousness.
It is preliminary to understand in well-log information generally by for statistical analysis to well-log information during reservoir TOC predictions
Then the specific distribution situation of the TOC provided is recognized as basis using the priori to reservoir TOC, establishes prior distribution.
The present invention uses Gaussian mixtures.The method for establishing Gaussian mixtures is as follows：Here it is assumed that in well-log information
Each reservoir physical parameter provided obeys Gaussian mixtures, and each Gaussian mixtures are by N number of Gauss point
Amount is made up of weighted average, and every statistics ginseng in each Gaussian component is obtained in Gaussian mixtures using EM algorithms
Number：Then mean value, variance and weight establish N number of Gaussian Profile, and according to their own power respectively according to every statistical parameter
It is weighted the Gaussian mixtures for averagely, finally obtaining reservoir TOC again, expression formula is as follows：
In above formula, T represents reservoir TOC, N and represents the number of Gaussian component, αkThe weight of k-th of Gaussian component is represented, it is full
FootThe mean value of Gaussian component is represented,Represent the variance of Gaussian component.
Expectation-maximization algorithm can be considered as two processes, and first process is to calculate desired value (i.e. E steps), second
Process is to ask for the maximum value of previous step expected value (i.e. M steps), and the expectation maximum value found in M-step is for next
The calculating of E-step, by the alternately calculating of above-mentioned two step, until finally obtaining the result of the condition of satisfaction, because
This, expectation-maximization algorithm is also referred to as EM algorithms.EM algorithms are versatile the biggest advantage is to easy to operate, stability
Height can be widely applied in the research calculating of every field.
It is past due to the limitation factor of the restriction of physical condition, such as observation procedure in practical seismic prospecting
Toward so that we can not obtain completely observing data set, then expectation-maximization algorithm can be introduced for this incomplete
Observe the correlation computations of data set.
When using elastic impedance predicting reservoir TOC, it is first for calculating TOC and physical parameter to introduce expectation-maximization algorithm
Test the parameters in distribution and the parameters in the Joint Distribution of physical parameter and elastic impedance.
Rock physics theory has erected bridge between seismic elastic parameter and reservoir physical parameter, and there are many research
Person proposes some classical petrophysical models.Since subsurface reservoir condition is ever-changing, simple certainty rock physics
The relationship between elastic impedance parameter and reservoir TOC can not be accurately depicted in model, therefore introduces random error, structure
Into statistical petrophysical model, expression formula is as follows：
M=fRPM(T)+ε (2-2)
In above formula, m represents elastic impedance, and T represents TOC, fRPMRepresent a certain rock object between elastic impedance and TOC
Reason relationship, ε represent stochastic error, for weakening influence of the underground complicated geological structure to the relationship of the two；In general, it utilizes
Relative different between certainty petrophysical model and real logging data calculates random error, and usually to choose mean value be zero
Gauss truncated error.
Monte Carlo random sampling technology is a kind of very important number of one kind using Probability Statistics Theory as guiding theory
According to computational methods.Random sampling technical basis in Monte Carlo is in law of great number, basic thought：By treating Solve problems
Feature carries out analysis understanding, establishes the probabilistic model therewith with certain same characteristic features, and it is (i.e. random that repetition test is carried out to it
Sampling), statistical nature parameter is then carried out to result of the test by statistical theory and is asked for.
During reservoir TOC predictions, the superiority of Monte Carlo simulation analogue technique is fully applied：1) it is special using covering
Carlow simulation technology carries out random sampling to the prior distribution of TOC, obtains the random sample spatial distribution of TOC；2) in addition
It is additionally operable to do random sampling to TOC and elastic impedance Joint Distribution and obtains its random sample space, be final TOC posterior probability
Ask for lay the foundation.
Foregoing describes the substantially processes using elastic impedance predicting reservoir TOC, in refutation process, the system of foundation
Meter petrophysical model is closely connected elastic impedance and TOC, and in fact, elastic impedance parameter is obtained by seismic data inversion
It arrives, belongs to time-domain, and reservoir TOC is according to obtained from well-log information, belongs to Depth Domain, it is seen that the domain of the two is not
Together, resolution ratio is also different, and the resolution ratio of log data is higher than the resolution ratio of seismic data.It is different based on above analysis
Information source, valid data scale is also different, if directly applied, can be affected to subsequent inversion problem, therefore, right
Seismic data and well-log information do scale matching.During scale matching treatment, usually emphasis is needed there are two problem
Consider：(1) in the case of different scale, the calculating of equal value between physical quantity；(2) when doing scale matching treatment, error turns
Shifting problem.
Two problems set forth above are directed to, we are averagely added respectively using Backus with the method for conditional probability successively
To solve.
First against in the different scale the problem of, it is averaged using Backus, i.e.,：
Backus, which is put down, is all based on effective media theory, and assumed condition is：(1) All Media is linear elasticity
's；(2) as friction or liquid viscosity and caused by internal energy loss be not present；(3) thickness on stratum is much small
In the wavelength of earthquake.Based on above 3 points it is assumed that the accurate solution of layered medium effective elasticity parameter can be derived.
In Method in Transverse Isotropic Medium, the direction of symmetry axis and x3Direction overlap, elastic stiffness tensor can
To be represented with following matrix, i.e.,：
In above formula, a, b, c, d, f, m are independent elastic constant, and Backus was proposed in 1962 years, in long wave limit item
Under part, if a layered medium is made of multilayer transverse isotropy material, (direction where i.e. each layer of symmetry axis is
Perpendicular to level), then the layered medium is equivalent anisotropic, and equivalent stiffness can be expressed as：
Wherein：
A=<a-f2c-1>+<c-1>-1<fc-1>2；
B=<b-f2c-1>+<c-1>-1<fc-1>2；
C=<c-1>-1；D=<d-1>-1；F=<c-1>-1<fc-1>；M=<m> (2-5)
A, B, C, D, F, M are independent elastic constant, bracket in above formula<·>Represent each variable in bracket according to it
Volume fraction be weighted average, here it is be averaged for the matched Backus of scale.
The problem of being directed to error transfer, using conditional probability estimation P (mf|mc)。
For conditional probability method of estimation, we use mfRepresent the elastic impedance parameter under well-log information scale, mcRepresent ground
Elastic impedance parameter under shake data scale, we can estimate according to conditional probability, utilize mfAsk for mc。
Since seismic data from well-log information is belonging respectively to different domains, and resolution ratio also differs greatly, use thus
Backus averagely does consistency treatment, to weaken because different scale data is to the influence caused by follow-up reservoir TOC invertings.For
Well in practical work area by carrying out spectrum analysis to seismic data, chooses Backus of the suitable frequency as well-log information
Average frequency, and then realize seismic data and consistency of the well-log information on scale.Fig. 2 is original log with passing through
Log curve correlation figure after Backus is average.In Fig. 2, solid line represents original log, and dotted line representative is put down by Backus
Log after by comparison, is averaged, the resolution ratio of curve is declined, compared with primitive curve, no by Backus
The detail section of curve can be shown well.
By for statistical analysis to the parameter curve provided on well, it is assumed that three-component Gaussian mixtures are obeyed,
The statistical nature (mean value, standard deviation and weight) of each single item Gaussian component is obtained by expectation-maximization algorithm, establishes TOC elder generations
Test distribution, and random sampling done to established prior distribution respectively using Monte Carlo simulation analogue technique, set herein with
Machine frequency in sampling is 3000 times, the final random sample spatial distribution for obtaining reservoir TOC.
It is for statistical analysis by the log (elastic parameter and physical parameter curve) to being provided, judge elastic ginseng
Existing relationship between number and TOC, and can be retouched using method and Connolly elastic impedances the equation structure of multiple regression
State elastic impedance and the certainty petrophysical model of TOC, and the elastic impedance value estimated according to certainty petrophysical model
Deviation between practical impedance value is added random error for certainty petrophysical model, is weakened with this in modeling process
It is middle because of the influence to modeling such as approximate operation and other geologic(al) factors (temperature, pressure etc.), be finally completed statistics rock
The structure of physical model, expression formula are as follows：
EI=f (T, φ, Vsh)+ε (3-1)
In above formula, f () representative function, EI is elastic impedance variable, and ε is stochastic error variable.
Fig. 3 is certainty petrophysical model proof diagram, and solid line represents the elastic impedance value of reality in Fig. 3, is denoted as calculating
Value；Dotted line represents the elastic impedance value obtained using constructed statistics petrophysical model, is denoted as match value；From from figure
It is found that the goodness of fit of practical calculated value and match value is higher.Random error is added for it, is finally completed statistical rock physics mould
The foundation of type.
Each sampling point in the random sample spatial distribution of reservoir TOC can be asked by counting petrophysical model
Go out the value of corresponding elastic impedance, according to this method, the elasticity corresponding to each sampling point in TOC random sample spatial distributions is obtained
Impedance value, all elastic impedance values just together constitute the random sample spatial distribution of elastic impedance, the two are combined, can obtain
Their Joint Distribution is obtained, the statistical parameter of three components in Joint Distribution is obtained respectively using expectation-maximization algorithm, according to
Bayesian formula be finally obtained TOC posteriority conditional probability P (T | [EI1,EI2,EI3]), in formula, T represents reservoir TOC parameters.That
Namely show under the premise of the elastic impedance of known three angles, can to obtain the conditional probability distribution situation of T, then
The maximum value of reservoir TOC posterior probability is estimated according to formula, the corresponding TOC values in position place where this maximum value are exactly inverting
Final result.
Fig. 4 is the TOC values that inverting obtains and the comparison of TOC values obtained using well material computation, it can be seen that in target
Interval, the two situation of coincideing is preferable, shows that the inversion method has certain confidence level, can be used for the prediction of reservoir TOC.
Before profile inversion is done, physical parameter prior distribution, statistics rock are completed using the log data provided on well
Stone physical model and physical parameter and the foundation of elastic impedance data aggregate distribution；However it is provided using seismic data folded
Preceding seismic data is extracted by pre-processing of the information, angle gathers, part angle gathers are superimposed to complete large, medium and small angle elastic impedance
Inverting.
It is elastic impedance data in Fig. 5 A, Fig. 5 B are TOC inversion results, it may be verified that it is corresponding with elastic impedance data preferable,
Wherein bright colored portion is corresponded in reservoir at oil-containing high level in figure, and with color gradually from light to dark, the oil-containing category in reservoir
Property is lower and lower, and dark color is represented at aqueous high level.
Claims (1)
1. a kind of shale gas TOC pre-stack seismic inversion Forecasting Methodologies, which is characterized in that it includes the following steps：
Step 1 establishes shale reservoir TOC inversion objective functions：
Bayesian formula is expressed as：
In formula (1-1), A represents observation sample information, and B then represents parameter to be estimated, and p (B) represents the priori point of parameter B to be estimated
Cloth, P (B | A) represent the Posterior distrbutionp of parameter B to be estimated, and P (A | B) it is the likelihood letter for contacting chance event A and chance event B
Number, ∫ P (B) P (A | B) dB are the full probabilities of observation sample, if ∫ P (B) P (A | B) dB is a constant, are denoted asFormula (1-1) is derived by applied to object function in reservoir TOC refutation processes：
P([φ,Vsh,T]|[EI1,EI2,EI3])=α × P ([φ, Vsh,T])P([EI1,EI2,EI3]|[φ,Vsh,
T]) (1-4),
In formula (1-4), φ, Vsh, T represents porosity, shale content and TOC, EI successively1,EI2,EI3Three are represented respectively not
With the elastic impedance of angle, P () represents probability density function,
Decorrelative transformation is done to the elastic impedance of three different angles, makes mutual indepedent between three, formula (1-4) is done and is become
Shape obtains following formula：
P([EI1,EI2,EI3]|[φ,Vsh,T])
=P (EI1|[φ,Vsh,T])P(EI2|[φ,Vsh,T])P(EI3|[φ,Vsh, T]) (1-5),
In formula (1-5), EI1, EI2, EI3Elastic impedance parameter respectively after decorrelative transformation,
Find Posterior distrbutionp in maximum a posteriori probability position, the parameter value corresponding to the position be reservoir TOC most
Whole inversion result：
[φ,Vsh, T] and=arg MaxP ([φ, Vsh,T]|[EI1,EI2,EI3]) (1-6),
Formula (1-4) and formula (1-5) are substituted into formula (1-6), gives up constant α, establishes the object function of final inverting, i.e.,：
In formula (1-7), P ([φ, Vsh, T]) be reservoir TOC prior distribution, P (EI1|[φ,Vsh,T])P(EI2|[φ,Vsh,
T])P(EI3|[φ,Vsh, T]) it is the likelihood function for contacting prior distribution and Posterior probability distribution；
Step 2, the shale TOC prestack inversions based on elastic impedance：
The prior distribution of the reservoir TOC is established according to the statistical analysis to log data：It is assumed that provided in well-log information
Each reservoir physical parameter obey Gaussian mixtures, and each Gaussian mixtures are passed through by N number of Gaussian component
Weighted average is formed, and every statistical parameter in each Gaussian component is obtained in Gaussian mixtures using EM algorithms：Mean value,
Then variance and weight establish N number of Gaussian Profile, and added according to their own weight respectively according to every statistical parameter
Weight average, finally obtains the Gaussian mixtures of reservoir TOC, and expression formula is as follows：
In formula (2-1), T represents reservoir TOC, N and represents the number of Gaussian component, αkThe weight of k-th of Gaussian component is represented, is met The mean value of Gaussian component is represented,Represent the variance of Gaussian component；
Random sampling is done to established prior distribution by Monte Carlo simulation analogue technique respectively, it is final to obtain reservoir TOC
Random sample spatial distribution；
Structure statistics petrophysical model, the statistics petrophysical model expression formula are as follows：
EI=f (T, φ, Vsh)+ε (3-1),
In formula (3-1), f () representative function, EI is elastic impedance variable, and ε is stochastic error variable；
For each sampling point in the random sample spatial distribution of reservoir TOC, all it is obtained pair by counting petrophysical model
The value for the elastic impedance answered, all elastic impedance values just together constitute the random sample spatial distribution of elastic impedance, by two
Person combines, and can obtain their Joint Distribution, the system of three components in Joint Distribution is obtained respectively using expectation-maximization algorithm
Count parameter；
The maximum value of reservoir TOC posterior probability, the corresponding TOC values in position place where this maximum value are estimated according to formula (1-7)
It is exactly the final result of inverting.
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| CN113311483B (en) * | 2020-02-27 | 2024-04-30 | 中国石油天然气集团有限公司 | Pre-stack elastic parameter combination inversion method and system based on shale oil |
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