CN106556867B - Phase-controlled porosity inversion method based on Bayesian classification - Google Patents
Phase-controlled porosity inversion method based on Bayesian classification Download PDFInfo
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Abstract
The invention discloses a phase-controlled porosity inversion method based on Bayesian classification, and belongs to the technical field of petroleum geological exploration. The phase-controlled inversion method comprises the following steps of (1) carrying out intersection analysis on a logging curve of rock porosity and logging curves of various rock elasticity parameters obtained through laboratory tests to obtain at least one rock elasticity parameter data sensitive to the rock porosity; (2) obtaining the porosity after screening and the elasticity parameter data after screening; (3) establishing a well-seismic initial model and simultaneously obtaining prior probability distribution of the porosity after screening; (4) obtaining the resampling porosity and simultaneously obtaining fitting screening elastic parameter data and fitting resampling elastic parameter data; (5) obtaining a resampling error; (6) acquiring reconstructed elastic parameter data; (7) obtaining a prior sample sequence and carrying out Bayesian classification to obtain prior probability and posterior probability distribution; (8) the known elastic parameter data volume is converted into a porosity data volume by bayesian inversion.
Description
Technical Field
The invention relates to the technical field of petroleum geological exploration, in particular to a phase-controlled porosity inversion method based on Bayesian classification.
Background
Porosity is one of the important parameters characterizing hydrocarbon reservoirs. The porosity of the reservoir is a key parameter in oil and gas exploration and development, and plays a key role in reservoir prediction structure interpretation. The seismic porosity can be used for transverse prediction of a reservoir layer in a seismic exploration stage; at the time of development, the reservoir can be described by calibrating the porosity by logging, and the porosity is also an important reference for reservoir estimation.
At present, seismic porosity inversion methods mainly have two types. Firstly, the porosity is solved by utilizing the velocity according to the relationship between the porosity and the seismic wave propagation velocity. For example, Wylie (1956) proposes an experimental formula describing the time-averaged equation of wave velocity versus porosity. The time-averaging equation is widely applied to calculating the porosity of a rock stratum in acoustic logging, but people quickly find the defects of the equation, particularly the equation overestimates the speed of waves in clay-containing sandstone, and the formation porosity and the longitudinal wave time difference have linearity under certain conditions.
Raymer (1980) developed a nonlinear empirical formula for describing porosity versus wave velocity that was applicable to a wider range of porosities, including unconsolidated sediments with high porosity, but this formula also ignored the effect of other parameters, and calculated porosities that were close to the measured core porosity for formations with porosities less than 37%, and the method was not applicable when porosity exceeded 37%. Domenico (1984) then changed the time-averaged equation to a purely empirical formula for describing the relationship between velocity and rock porosity, which simplifies the relationship between velocity and rock properties, especially neglecting the effect of clay content on sandstone shear velocity.
The second method is a porosity calculation method based on the Biot-Gassmann equation, and the comparison is typically the method proposed by Zhang waves (1994). The method has the disadvantages that a plurality of parameters need to be provided in advance, besides 4 parameters except the porosity in the Gassmann equation, stress, pore pressure, fluid viscosity coefficient, seismic wave attenuation coefficient and the like need to be provided, and the wide application of the method is limited by too many input parameters.
In a word, to obtain a good porosity prediction effect, a large amount of geological, well logging, petrophysical and seismic multi-attribute parameter data are needed, the porosity has no definite theoretical relationship with other parameters, and the porosity is very sensitive to seismic facies. In order to enhance the applicability of the porosity calculation method, the dependence on empirical formulas must be reduced; to reduce the complexity of the porosity calculation method, a large number of input parameters must be avoided; in order to improve the prediction accuracy of the porosity, it is necessary to process specific phases of a specific reservoir separately.
Disclosure of Invention
To address at least one of the above-identified problems and deficiencies in the prior art, the present invention provides a phase-controlled porosity inversion method based on bayesian classification. The technical scheme is as follows:
the invention aims to provide a phase-controlled porosity inversion method based on Bayesian classification.
According to an aspect of the present invention, there is provided a phase-controlled porosity inversion method based on bayesian classification, the phase-controlled inversion method comprising the steps of:
(1) carrying out intersection analysis on a logging curve of rock porosity obtained by actually measuring a target reservoir region and logging curves of various rock elasticity parameters obtained by laboratory tests so as to obtain at least one rock elasticity parameter data sensitive to the rock porosity;
(2) screening the rock porosity and the rock elasticity parameter data under constraint conditions to obtain screened porosity and screened elasticity parameter data;
(3) establishing a well-seismic initial model based on the screened porosity and well side channel elastic parameter data in the screened elastic parameter data, and simultaneously obtaining prior probability distribution of the screened porosity;
(4) obtaining resampling porosity based on the prior probability distribution of the screened porosity, and simultaneously enabling the screened porosity and the resampling porosity to respectively obtain corresponding fitting screening elastic parameter data and fitting resampling elastic parameter data through the well-seismic initial model;
(5) performing error statistical analysis on the well side channel elastic parameter data and the fitting screening elastic parameter data to obtain a resampling error;
(6) resampling elastic parameter data and the resampling error based on the fit to obtain reconstructed elastic parameter data;
(7) obtaining a prior sample sequence based on the reconstructed elastic parameter data and the resampling porosity, and carrying out Bayesian classification on the prior sample sequence to obtain prior probability and posterior probability distribution of each type of the resampling porosity;
(8) and converting the known elastic parameter data volume into the porosity data volume by Bayesian inversion based on the prior probability and posterior probability distribution of the resampled porosity various types.
Specifically, in step (1), the rock elasticity parameter data is all elasticity parameter data corresponding to an elasticity parameter curve having a linear or non-linear relationship through intersection analysis of the well log of the rock porosity and the well logs of the multiple rock elasticity parameters.
Specifically, in step (2), the constraint condition is a physical property threshold range of the target reservoir region determined under the constraint of a seismic physical phase, and the porosity after screening and the well side channel elasticity parameter data both meet the physical phase condition of the target reservoir region.
Further, in the step (3), the initial well-seismic model is a fitting relation between the porosity after screening and the well side channel elastic parameter data.
Specifically, in step (3), the prior probability distribution is obtained by multivariate gaussian distribution fitting based on the filtered porosity.
Specifically, in step (4), a monte carlo simulation is performed based on the prior probability distribution of the filtered porosity to obtain the resampled porosity.
Further, in step (5), an error probability distribution is obtained in the error statistical analysis, and the error probability distribution is assumed to obey a gaussian distribution, and then truncated gaussian sampling is performed on the error probability distribution to obtain the resampling error.
Further, the a priori sample sequence is a data pair of a one-to-many mapping of the resampled porosity and the reconstructed elasticity parameter data.
Further, the data pair of the one-to-many mapping relationship is a data pair formed by a plurality of reconstructed elastic parameter data corresponding to a resampling porosity in the prior sample sequence.
Specifically, in step (7), the bayesian classification of the prior sample sequence comprises the following steps:
a1 classifying the resampled porosity in the prior sample sequence to obtain prior probabilities of the resampled porosity classes;
a2, counting the corresponding reconstruction elastic parameter data of the resampling porosity classes to obtain the posterior probability distribution of the resampling porosity classes.
Further, the known elastic parameter data volume is a data volume obtained by pre-stack elastic parameter inversion.
Further, the at least one rock elasticity parameter data sensitive to the rock porosity is one of poisson's ratio data, wave impedance data, longitudinal and transverse wave velocity data and density data or any combination thereof.
Further, the seismic object is a classified data volume divided according to the rock microstructure, depositional cause, compaction and diagenetic cause or identifiability of seismic elastic parameters.
Further, the expression of the multivariate gaussian distribution fitting is as follows:
where Ρ (φ) is the porosity prior probability distribution after the screening, akFor each element of Gaussian distribution weight, mukIs the k-th mean value of the porosity after screeningkIs the k-th covariance of the porosity after screening.
Further, in step (7), in the process of obtaining the prior probability and posterior probability distribution of the resampled porosity classes through the bayesian classifier, the resampled porosity in the prior sample sequence is classified through a discriminant function, where an expression of the discriminant function is:
wherein beta is elastic parameter data corresponding to the i-th class of the resampled porosity in the prior sample sequence;
μithe elastic parameter data mean value corresponding to the i-th type of resampling porosity is obtained;
Σithe elastic parameter data covariance corresponding to the i-th type of the resampling porosity is obtained;
ωithe porosity is resampled for category i.
Further, in step (8), the known elastic parameter data volume implements the bayesian inversion by using a bayesian equation, where the expression of the bayesian equation is:
wherein,is the porosity data obtained by the Bayesian inversion;
j is the category number of the physical property parameters of the target storage layer;
class j porosity data obtained for the bayesian classification;
the probability distribution of longitudinal wave velocity in the corresponding elastic parameters under the condition of knowing the j-th porosity data is obtained;
the probability distribution of the transverse wave velocity in the corresponding elastic parameter under the condition of knowing the j-th porosity data is obtained;
the probability distribution of the density in the corresponding elastic parameter under the condition that the porosity data of the j type are known;
is the probability distribution of the porosity data of the j-th class.
The technical scheme provided by the invention has the beneficial effects that:
1. the well seismic initial model of the phase-controlled porosity inversion method based on Bayesian classification can be obtained without strictly depending on an empirical formula, and can be adjusted according to conditions;
2. the phase control porosity inversion method based on Bayesian classification reduces inversion multi-solution through phase control constraint and improves inversion accuracy;
3. the phase-controlled porosity inversion method based on Bayesian classification can avoid directly establishing complex relations between porosity and various parameters according to the independence assumption condition under the Bayesian inversion thought, and only needs to respectively establish the relations;
4. the phase-controlled porosity inversion method based on Bayesian classification provided by the invention considers the scatter distribution characteristics of porosity and other parameters, namely, error factors, and the inversion result can reflect the actual rule better.
Drawings
FIG. 1 is a flow diagram of a Bayesian classification based phased porosity inversion method according to an embodiment of the present invention;
FIG. 2 is a seismic profile of a target reservoir region of a Bayesian classification based phased porosity inversion method in accordance with embodiments of the present invention;
FIG. 3 is a plot of a junction analysis of a log of rock porosity and logs of various rock elasticity parameters for a Bayesian classification based phased porosity inversion method in accordance with an embodiment of the present invention;
FIG. 4 is a view of elastic parameter data volume obtained from pre-stack elastic parameter inversion of a Bayesian classification based phased porosity inversion method in accordance with an embodiment of the present invention;
FIG. 5 is a lithology volume view in a seismic object based on a Bayesian classification-based phased porosity inversion method according to an embodiment of the present invention;
FIG. 6 is a prior probability distribution plot of filtered porosity for a Bayesian classification based phased porosity inversion method in accordance with embodiments of the present invention;
FIG. 7a is a plot of a convergence analysis of porosity and elastic parameters in an initial model of well seismic based on a Bayesian classification phase-controlled porosity inversion method in accordance with an embodiment of the present invention;
FIG. 7b is an error profile of well side-channel elastic parameter data and fitting screen elastic parameter data of a Bayesian classification-based phased porosity inversion method in accordance with an embodiment of the present invention;
FIG. 8 is a comparison view of the well-logging rock porosity and the porosity obtained through Bayesian inversion of a Bayesian classification-based phased porosity inversion method according to an embodiment of the present invention;
FIG. 9 is a cross-sectional effect view of a porosity data volume obtained from Bayesian classification-based phased porosity inversion in accordance with a Bayesian classification-based phased porosity inversion method according to an embodiment of the present invention;
fig. 10 is a cross-sectional effect view of a porosity body obtained by an empirical formula conversion method in comparison with the effect view shown in fig. 9.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, embodiments of the present invention will be described in detail with reference to the accompanying drawings.
Referring to FIG. 1, a flow diagram of a Bayesian classification based phased porosity inversion method in accordance with one embodiment of the present invention is shown. The phase control porosity inversion method based on Bayesian classification comprises the following steps:
(1) carrying out intersection analysis on a logging curve of rock porosity obtained by carrying out actual measurement on a target reservoir region and logging curves of various rock elastic parameters obtained by laboratory tests so as to obtain at least one rock elastic parameter data sensitive to the rock porosity;
(2) screening the rock porosity and rock elasticity parameter data under the constraint condition to obtain the screened porosity and screened elasticity parameter data;
(3) establishing a well-seismic initial model based on the screened porosity and well side channel elastic parameter data in the screened elastic parameter data, and simultaneously obtaining prior probability distribution of the screened porosity;
(4) obtaining resampling porosity based on prior probability distribution of the screened porosity, and simultaneously enabling the screened porosity and the resampling porosity to respectively obtain corresponding fitting screening elastic parameter data and fitting resampling elastic parameter data through a well-seismic initial model;
(5) performing error statistical analysis on the well side channel elastic parameter data and the fitting screening elastic parameter data to obtain a resampling error;
(6) resampling elastic parameter data and resampling errors based on the fit to obtain reconstructed elastic parameter data;
(7) obtaining a prior sample sequence based on the reconstructed elastic parameter data and the resampling porosity, and carrying out Bayesian classification on the prior sample sequence to obtain prior probability and posterior probability distribution of each type of the resampling porosity;
(8) and converting the known elastic parameter data volume into the porosity data volume by Bayesian inversion based on the prior probability and posterior probability distribution of various types of the resampled porosity.
Specifically, in step (1), a target horizon and a well position need to be determined, intersection analysis is performed on a well logging curve of rock porosity obtained by actually measuring a target reservoir region and well logging curves of various rock elasticity parameters obtained through laboratory tests, for example, intersection analysis is performed on a well logging curve of poisson ratio, a well logging curve of wave impedance, and a well logging curve of density, and all elasticity parameter data corresponding to an elasticity parameter curve having a relatively obvious linear or nonlinear relationship with the well logging curve of rock porosity are used as prediction parameters, that is, rock elasticity parameter data. The rock elasticity parameter data may be one or any combination of poisson's ratio data, wave impedance data, longitudinal and transverse wave velocity data and density data. For example, the rock elasticity parameter data may be poisson ratio data and wave impedance data, the rock elasticity parameter data may also be wave impedance data, longitudinal and transverse wave velocity data and density data, and the poisson ratio data, the wave impedance data, the longitudinal and transverse wave velocity data and the density data, which are only one illustrative example, and therefore are not listed here, and those skilled in the art can make corresponding selection or combination according to needs.
In the step (2), the constraint condition is a physical property threshold range of the target storage layer area determined under the constraint of the seismic object, and the porosity and the well side channel elastic parameter data after screening both accord with the object condition of the target storage layer area.
Specifically, the seismic facies mainly comprise seismic rock facies, seismic object facies and seismic sedimentary facies, and the phased seismic inversion technology is used for depicting the reservoir stratum by using a targeted method from the perspective of geological causes, so that the technology is suitable for detailed depiction of reservoir stratum development with certain overall characteristic distribution. The technology emphasizes the combination of geology and geophysical prospecting, and the synthesis of the results of seismic phase bodies and seismic attribute bodies, and the key of successful prediction is the understanding and the grasp of the overall characteristics of reservoir development. The seismic lithofacies body, the seismic object facies body and the seismic sedimentary facies body are used as constraint conditions to control seismic reservoir porosity inversion, the multi-solution of porosity prediction is reduced from the angle of geological causes, and the porosity prediction precision is improved. Wherein, the lithofacies body controls the effectiveness of the inversion data, the facies body is further controlled on the basis of the lithofacies, and the sedimentary facies body mainly controls the inversion target area.
Specifically, the seismic object phase refers to a seismic physical phase, namely a seismic elastic parameter-distinguishable attribute class related to reservoir physical properties, and is a classified data body divided according to the microstructure of rock, comprehensive lithology (sedimentary origin), physical properties (compaction and diagenetic origin) or identifiability of seismic elastic parameters. The research scale of the seismic object is established on the basis of seismic resolution, and the thickness of the category is determined by taking seismic elasticity parameter discrimination as a principle.
Seismic lithofacies refer to a seismic distinguishable dimension of a depositional unit described by lithology (sand, silt and clay), stratigraphic structure (large-scale interbedded or disordered), rock classification (particle size, clay position and cementation) and seismic characteristics (longitudinal wave velocity, transverse wave velocity and density). The seismic facies is an extension of the traditional facies concept, and the scheme for dividing the seismic facies and the seismic object facies has two key points: first, the analytical scale of the lithofacies volume is macroscopic, seismic resolvable; second, the idea of correlating the litho-facies body with the seismic elastic parameters is considered, so that it can be identified and predicted by the seismic elastic parameters.
In the step (3), the well-seismic initial model is a fitting relation of the porosity after screening and the well side channel elastic parameter data. The well seismic initial model can be set as one of the following mathematical models as required:
first order linear model:
second degree polynomial model:
cubic polynomial model:
power model:
an index model:
logarithmic model:
inverse proportion model:
wherein, PElasticIn order to be the elastic parameter data,porosity data, a and b are model parameters; the above models are all empirical formulas that support linearity and nonlinearity. It can be seen that with the well-seismic initial model, when the independent variable is set to the porosity after screening, the method can be used for screening the porosityScreening elastic parameter data by taking the obtained dependent variable as fitting; when the independent variable is set to the resampled porosity, the dependent variable can be obtained as fitted resampled elastic parameter data.
And while establishing a borehole seismic initial model, adopting multivariate Gaussian fitting to the porosity after screening under the control constraint of the seismic object, and then counting the rule of prior probability distribution of the porosity after screening. The expression of multivariate gaussian distribution fitting is:
where p (φ) is the porosity prior probability distribution after screening, akFor each element of Gaussian distribution weight, mukIs the k-th mean of porosity after screeningkIs the k-th covariance of the porosity after screening.
In one example of the invention, the prior probability distribution of the filtered porosity is obtained by using a monte carlo simulation. Specifically, the monte carlo simulation has the characteristics that: the Monte Carlo (Monte Carlo) method (i.e., MCM), also known as statistical test method. The method is a method for solving problems approximately by using a series of random numbers, and is a means for processing mathematical problems by searching a probability statistical similarity and obtaining an approximate solution of the similarity by an experimental sampling process. The solution of the problem obtained by using the approximation method is closer to the result of physical experiments, but not the result of classical numerical calculation. In this example, the application of Monte Carlo simulation to porosity inversion based on bayesian classification can effectively ensure the effectiveness of the inversion solution under the condition of ensuring the well logging porosity distribution rule under phase control.
In the step (5), after the error statistical analysis is carried out on the well side channel elastic parameter data and the fitting screening elastic parameter data to obtain error probability distribution, the error probability distribution is assumed to obey Gaussian distribution, and then the error probability distribution is subjected to truncation Gaussian sampling to obtain resampling errors. Specifically, the truncated gaussian resampling is characterized by: the truncated gaussian distribution is similar to the gaussian distribution, except that the minimum value and the maximum value of the gaussian distribution are infinite, and the truncated gaussian distribution specifies the minimum value and the maximum value of the sample, so that the result of error resampling can be effectively controlled without exceeding the value of an effective data range.
And after the resampling error is obtained, adding the resampling error and the well side channel elastic parameter data to obtain reconstructed elastic parameter data. The reconstructed elastic parameter data and the resampling porosity form a prior sample sequence, and in the prior sample sequence, one resampling porosity corresponds to a plurality of reconstructed elastic parameter data, so that a data pair with one-to-many mapping relation is formed. All mapping data pairs are saved after obtaining the mapping data pairs of the reconstructed elastic parameter data and the resampled porosity.
Inversion of longitudinal wave impedance I by seismicseisAnd porosity phi of the logwellCalculating an earthquake porosity body phi as an example, acquiring an empirical relation between the well earthquake porosity and the longitudinal wave impedance suitable for the area through well earthquake intersection, wherein epsilon is used for describing the error between the longitudinal wave impedance calculated according to the empirical relation and the actual earthquake longitudinal wave group impedance, and the expression of a gold earthquake initial model (namely the empirical relation between the well earthquake porosity and the longitudinal wave impedance) is as follows:
wherein the error distribution epsilon is subjected to truncated Gaussian sampling to obtain epsiloni,i＝1,…,neAnd utilizing Monte Carlo (Monte-Carlo) simulation to make porosity resampling so as to obtain resampling porosity conforming to original porosity sampling distributionThus, a joint sampling space of porosity and longitudinal wave impedance, namely a priori sample sequence is obtained, and the expression of the prior sample sequence is as follows:
in step (7), the bayesian classification of the prior sample sequence comprises the following steps:
a1 classifying the resampling porosities in the prior sample sequence to obtain prior probabilities of the resampling porosities, wherein the resampling porosities in the prior sample sequence can be classified through a discriminant function in the step;
a2, counting the corresponding reconstructed elastic parameter data of each resampled porosity class to obtain the posterior probability distribution of each resampled porosity class.
Specifically, a Bayesian classifier is designed according to Bayesian decision theory based on a minimum error rate.
The probability density function of a multivariate gaussian distribution is defined by:
from the minimum error probability decision rule, the following function can be used as the discriminant function:
gi(x)＝p(X|ωi)P(ωi),i＝1,2,…,N
here, P (ω)i) Is of the class omegaiA priori probability of occurrence, p (X | ω |)i) Is of the class omegaiAnd N is the number of classes.
Let class ωiClass-conditional probability density function p (X | ω) of 1,2, … …, Ni) I 1,2, … …, N obeys a normal distribution, i.e. there is p (X | ω)i)～N(μi,Σi) Then the above equation can be written as:
because the logarithmic function is a monotonous changing function, the new discriminant function g obtained by taking logarithm at the right end of the formula is used for replacing the original discriminant function gi(X) does not change the performance of the corresponding classifier. Thus, it is preferable
Obviously, the second term in the above formula is independent of the class to which the sample belongs, and is eliminated from the discriminant function, so that the classification result is not changed. Thus, the discriminant function giThe expression of (X) is:
the discrimination boundaries between classes are:
gi(X)-gj(X)＝0，i＝1,2,…,N，j＝1,2,…,N
wherein beta is elastic parameter data corresponding to the i-th class of the resampled porosity in the prior sample sequence;
μithe elastic parameter data mean value corresponding to the i-th type of resampling porosity is obtained;
Σithe elastic parameter data covariance corresponding to the i-th type of the resampling porosity is obtained;
ωithe porosity is resampled for category i.
In step (8), the Bayesian inversion is implemented by a Bayesian equation for the known elastic parameter data volume, wherein the known elastic parameter data volume is obtained by pre-stack elastic parameter inversion. Specifically, the porosity prediction by the Bayesian inversion idea is realized by the following steps:
the inversion objective function is the maximum posterior probability distribution of the porosity under the condition of known elastic parameters, and can be expressed as:
the significance of the functional is as follows: the posterior probability distribution of porosity is calculated knowing the longitudinal/transverse wave velocity and density. When the posterior probability takes the maximum value, the porosity class is the final inversion result. According to the actual situation, the rock elasticity parameter can also be other elasticity parameters, such as poisson's ratio, ramen and the like. According to bayesian formula, equation (1) can be written as:
due to P ([ v ]p,vs,ρ]) Being constant, equation (2) can also be written as:
according to the class condition independence assumption of the Bayesian classification algorithm, the following can be obtained:
bringing (4) into (3) can result in:
equation (5) is the expression of the final bayesian equation.
Wherein,is the porosity data obtained by the Bayesian inversion;
j is the category number of the physical parameters of the target storage layer;
class j porosity data obtained for bayesian classification;
the probability distribution of longitudinal wave velocity in corresponding elastic parameters under the condition of known j-th porosity data;
the probability distribution of the transverse wave velocity in the corresponding elastic parameters under the condition of known j-th porosity data is obtained;
is the probability distribution of the density in the corresponding elastic parameter under the condition of known j-th porosity data;
is the probability distribution of the porosity data of the j-th class.
The invention aims to provide a phase-control porosity inversion method based on Bayesian classification, which utilizes the Bayesian classification inversion method and comprehensively applies rock physics statistics intersection analysis, Monte Carlo simulation technology and phase-control constraint inversion technology to realize accurate prediction of reservoir porosity. The method starts with the optimization of one or more rock elastic parameters in the intersection relationship between reservoir logging porosity and various reservoir logging rock elastic parameters which are generally distributed in a scattered manner, respectively fits the determined model relationship (including linear and nonlinear relationships) between the reservoir porosity and the rock elastic parameters under the condition of independence assumption, controls the fitting precision by adopting a phase control constraint technology, reduces the multiple solution of porosity prediction, improves the porosity prediction precision, simultaneously carries out random characteristic analysis and Monte Carlo simulation on the logging porosity data to ensure the rationality of an inversion result, then carries out error statistical analysis on the model relationship, adds random errors into the determined model obtained by fitting, further establishes the complete mapping relationship between the porosity and the rock elastic parameters, and can describe all possible porosities which are not reflected on logging information, and finally, calculating the posterior probability distribution of the reservoir porosity by using a Bayesian classification method, and realizing the direct prediction of the reservoir porosity by using one or more rock elasticity parameters.
The specific process of the phase-controlled porosity inversion method based on Bayes classification is further described in detail by taking the prestack data of the area with the west Liu-Zhao Huangzhuang in the Liang Lizhou slope of the Liyang valley as an example.
And step A, performing rock physical intersection statistical analysis on the logging information of the target reservoir region, and preferably selecting sensitive rock elastic parameters capable of predicting the porosity.
A01) Determining a target horizon and a well position, wherein the white horizon is a target storage region within 50ms of upward drift as shown in FIG. 2;
A02) extracting a logging porosity curve and elastic parameter curves such as Poisson's ratio, wave impedance, density and the like;
A03) performing intersection analysis on the logging curve of the rock porosity and logging curves of various rock elastic parameters, and finding that the logging curve of the rock porosity and the logging curve of longitudinal wave impedance in the rock elastic parameters have a good linear relation, as shown in fig. 3, the logging curves basically show the characteristics of low pore resistance and high pore resistance, and the porosity range is about 0-0.15;
A04) the wave impedance data volume is obtained by pre-stack inversion and sparse pulse inversion, as shown in fig. 4.
Step B, screening the screened elastic parameter data which meet the reservoir phase conditions by using the seismic phase as a constraint condition, and screening the well side channel elastic parameters in the screened porosity and the screened elastic parameter data;
B01) setting a data analysis screening threshold according to a physical property threshold range of a target area determined by the seismic object, wherein the lithologic body selected as the phase control constraint in the example is sandstone with a numerical value greater than 12100 as shown in fig. 5;
B02) extraction of valid data pairs (porosity after screening)And well bypass wave impedance Iseis)，
Step C, counting the prior probability distribution rule of the screened porosity under the phase control, meanwhile, performing well seismic intersection on the screened porosity under the phase control and well side channel elastic parameters (namely the well side channel wave impedance), and fitting and establishing a well seismic initial model;
C01) the porosity after screening under phase control is fitted with multivariate Gaussian distribution to obtain distribution parameters (mean, variance, etc.) as shown in FIG. 6, where unitary Gaussian distribution fitting (curve segment) is used according to actual conditions
C02) The intersection plot of the screened porosity and the well bypass wave impedance under phase control is shown as scatter plot in fig. 7 a;
C03) selection fittingBasic theoretical model, here a univariate linear model is chosen
C04) And acquiring initial well-seismic model parameters a and b with the porosity as an independent variable and the elastic parameter as a dependent variable, and displaying the parameters in a converged manner as shown in a graph 7a (curve segment).
D, performing error analysis on the well bypass wave impedance and the wave impedance fitted by the well seismic initial model, and establishing a complete mapping of the resampling porosity and the reconstructed wave impedance according to the resampling porosity and the well seismic initial model;
D01) performing error analysis on the elasticity parameters calculated by the well-seismic initial model of the well-logging porosity under the phase control and the well bypass wave impedance under the phase control to determine an error distribution P (epsilon), as shown in FIG. 7 b;
D02) resampling the screened porosity under phase control by adopting Monte Carlo simulation to obtain resampled porosity,nφis the number of resamples, as shown in FIG. 6;
D03) the error distribution is truncated Gaussian resampled to obtain a resample error, epsiloni,i＝1,…,ne，neIs the number of resamples;
D04) establishing a many-to-one mapping relation between the reconstructed wave impedance and the resampling porosity, calculating and storing all mapping data pairs,
step E, classifying all resampling porosity values in the data pair by using a Bayesian classifier, and calculating the posterior probability distribution of the resampling porosity
And F, taking the screened elastic parameter data under the phase control as input, using the obtained prior probability and posterior probability distribution of the porosity, and predicting the porosity data volume under the phase control by adopting a Bayesian inversion idea.
Here, the elastic parameter data of the well side channel can be used as input first and substituted into the inversion objective function
The calculated porosity, in contrast to the known porosity from the log, is displayed as a quality control of the treatment process, as shown in figure 8.
If the inversion effect is accurate, substituting the wave impedance volume into the inversion objective function, and calculating the final porosity volume, as shown in fig. 9. Here, the inversion result is compared with the porosity effect directly converted by the empirical formula, as shown in fig. 10, the porosity value range 0-0.14 calculated by the method is more practical than the porosity value range 0-0.07 directly converted by the empirical formula, and the detail description is clearer.
The technical scheme provided by the invention has the beneficial effects that:
1. the well seismic initial model of the phase-controlled porosity inversion method based on Bayesian classification can be obtained without strictly depending on an empirical formula, and can be adjusted according to conditions;
2. the phase control porosity inversion method based on Bayesian classification reduces inversion multi-solution through phase control constraint and improves inversion accuracy;
3. the phase-controlled porosity inversion method based on Bayesian classification can avoid directly establishing complex relations between porosity and various parameters according to the independence assumption condition under the Bayesian inversion thought, and only needs to respectively establish the relations;
4. the phase-controlled porosity inversion method based on Bayesian classification provided by the invention considers the scatter distribution characteristics of porosity and other parameters, namely, error factors, and the inversion result can reflect the actual rule better.
The above description is only for the purpose of illustrating the preferred embodiments of the present invention and is not to be construed as limiting the invention, and any modifications, equivalents, improvements and the like that fall within the spirit and principle of the present invention are intended to be included therein.
Claims (14)
1. A phase-controlled porosity inversion method based on Bayesian classification comprises the following steps:
(1) carrying out intersection analysis on a logging curve of rock porosity obtained by actually measuring a target reservoir region and logging curves of various rock elasticity parameters obtained by laboratory tests so as to obtain at least one rock elasticity parameter data sensitive to the rock porosity;
(2) screening the rock porosity and the rock elasticity parameter data under constraint conditions to obtain screened porosity and screened elasticity parameter data;
(3) establishing a well-seismic initial model based on the screened porosity and well side channel elastic parameter data in the screened elastic parameter data, and simultaneously obtaining prior probability distribution of the screened porosity;
(4) obtaining resampling porosity based on the prior probability distribution of the screened porosity, and simultaneously enabling the screened porosity and the resampling porosity to respectively obtain corresponding fitting screening elastic parameter data and fitting resampling elastic parameter data through the well-seismic initial model;
(5) performing error statistical analysis on the well side channel elastic parameter data and the fitting screening elastic parameter data to obtain a resampling error;
(6) resampling elastic parameter data and the resampling error based on the fit to obtain reconstructed elastic parameter data;
(7) obtaining a prior sample sequence based on the reconstructed elastic parameter data and the resampling porosity, and carrying out Bayesian classification on the prior sample sequence to obtain prior probability and posterior probability distribution of each type of the resampling porosity;
(8) converting the known elastic parameter data volume into a porosity data volume through Bayesian inversion based on the prior probability and posterior probability distribution of the resampled porosity various types;
in the step (1), the rock elasticity parameter data is all elasticity parameter data corresponding to an elasticity parameter curve with linear or nonlinear relation analyzed through intersection of the logging curve of the rock porosity and the logging curves of the multiple rock elasticity parameters;
in the step (2), the constraint condition is a physical property threshold range of the target storage layer area determined under the constraint of a seismic object, and the porosity and the well side channel elastic parameter data after screening both accord with the object condition of the target storage layer area.
2. The Bayesian classification-based phased porosity inversion method according to claim 1,
in the step (3), the well-seismic initial model is a fitting relation between the screened porosity and the well side channel elastic parameter data.
3. The Bayesian classification-based phased porosity inversion method according to claim 2,
in step (3), the prior probability distribution is obtained by multivariate gaussian distribution fitting based on the filtered porosity.
4. The Bayesian classification-based phased porosity inversion method according to claim 3,
in step (4), performing Monte Carlo simulation based on the prior probability distribution of the screened porosity to obtain the resampled porosity.
5. The Bayesian classification-based phased porosity inversion method according to claim 4,
in step (5), an error probability distribution is obtained in the error statistical analysis, and the error probability distribution is assumed to obey a gaussian distribution, and then truncated gaussian sampling is performed on the error probability distribution to obtain the resampling error.
6. The Bayesian classification-based phased porosity inversion method according to claim 5,
the a priori sample sequence is a data pair of a one-to-many mapping of the resampled porosity and the reconstructed elastic parameter data.
7. The Bayesian classification-based phased porosity inversion method according to claim 6,
the data pair of the one-to-many mapping relation is formed by a plurality of reconstructed elastic parameter data corresponding to one resampling porosity in the prior sample sequence.
8. The Bayesian classification-based phased porosity inversion method according to any one of claims 3-7,
in step (7), the bayesian classification of the sequence of prior samples comprises the steps of:
a1 classifying the resampled porosity in the prior sample sequence to obtain prior probabilities of the resampled porosity classes;
a2, counting the corresponding reconstruction elastic parameter data of the resampling porosity classes to obtain the posterior probability distribution of the resampling porosity classes.
9. The Bayesian classification-based phased porosity inversion method according to claim 8,
the known elastic parameter data volume is obtained by pre-stack elastic parameter inversion.
10. The Bayesian classification-based phased porosity inversion method according to claim 9,
the at least one rock elasticity parameter data sensitive to the rock porosity is one of a poisson's ratio data volume, wave impedance data, longitudinal and transverse wave velocity data and density data or any combination thereof.
11. The Bayesian classification-based phased porosity inversion method according to claim 10,
the seismic object is a classified data body divided according to the rock microstructure, the sedimentary origin, the compaction and the identifiability of the diagenesis or the seismic elasticity parameters.
12. The Bayesian classification-based phased porosity inversion method according to claim 11,
the expression of the multivariate Gaussian distribution fitting is as follows:
wherein,the filtered porosity prior probability distribution, akFor each element of Gaussian distribution weight, mukIs the k-th means, Σ, of the porosity after screeningkAnd the k-th element covariance of the porosity after screening, phi is porosity data, N is the category number, and N is a Gaussian distribution function.
13. The Bayesian classification-based phased porosity inversion method according to claim 12,
in step (7), in the process of obtaining the prior probability and the posterior probability distribution of the resampled porosity classes through the bayesian classifier, classifying the resampled porosity in the prior sample sequence through a discriminant function, wherein an expression of the discriminant function is as follows:
wherein X is elastic parameter data corresponding to the ith type of resampling porosity in the prior sample sequence;
μithe elastic parameter data mean value corresponding to the i-th type of resampling porosity is obtained;
Σi -1transpose of the elastic parameter data covariance matrix corresponding to the i-th type of resampling porosity;
ωithe resampling porosity is of type i;
P(ωi) Is of the class omegaiA priori probability of occurrence.
14. The Bayesian classification-based phased porosity inversion method according to claim 13,
in step (8), the known elastic parameter data volume implements the bayesian inversion through a bayesian equation, where the expression of the bayesian equation is:
wherein,is the porosity data obtained by the Bayesian inversion;
j is the category number of the physical property parameters of the target storage layer;
class j porosity data obtained for the bayesian classification;
the probability distribution of longitudinal wave velocity in the corresponding elastic parameters under the condition of knowing the j-th porosity data is obtained;
the probability distribution of the transverse wave velocity in the corresponding elastic parameter under the condition of knowing the j-th porosity data is obtained;
the probability distribution of the density in the corresponding elastic parameter under the condition that the porosity data of the j type are known;
is the probability distribution of the porosity data of the j-th class.
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