CN112147682B - AVO inversion method and system based on Bayes and series inversion theory - Google Patents
AVO inversion method and system based on Bayes and series inversion theory Download PDFInfo
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Abstract
An AVO inversion method and system based on Bayes and series inversion theory are disclosed. The method can comprise the following steps: obtaining a fluid term high-order AVO expression based on incidence angle approximation according to a Zoeppritz equation and a Gassmann theory; calculating parameters of a fluid item high-order AVO expression according to a series theory to obtain a fluid item high-order AVO formula; obtaining an inversion target function according to Bayes theory; and constructing a prestack longitudinal wave high-order AVO inversion formula according to the fluid item high-order AVO formula and the inversion target function. The method is based on the Zoeppritz equation and the Gassmann theory, combines the Bayes theory and the series inversion theory, constructs the prestack longitudinal wave high-order AVO inversion formula, can realize the actual reservoir fluid identification of the working area with high precision, high stability, high noise immunity and high efficiency, and has extremely high industrial practical value and popularization and application prospect.
Description
Technical Field
The invention relates to the technical field of oil reservoir geophysics, in particular to an AVO inversion method and system based on Bayes and series inversion theory.
Background
The identification technology of the pore fluid of the underground reservoir taking seismic data as a main body is one of the key technologies described in the reservoir at the present stage. On the premise of ensuring the quality of seismic data, the fluid indicator factor is an important parameter for determining the identification accuracy of reservoir fluid. The definition of the fluid indicator originates from the field of reflection coefficients, generally expressed in the form of intercepts and gradients. Identification technology along with reservoir fluidThe definition of the fluid indicator factor has evolved from the reflectance domain to the impedance domain. At this stage, the Lame parameter attribute becomes the most commonly used fluid indicator, and when the rock skeleton parameters of the underground reservoir are not changed, the Lame parameter has good pore fluid identification capability, but when the rock skeleton parameters of the reservoir are changed, the identification capability of the Lame parameter attribute on the pore fluid is weakened. To address this problem, Russell et al (2003) derived a new fluid indicator factor Russell fluid factor F ═ ρ F based on the Biot-Gassmann theory, where ρ is the density and F is the fluid term. However, the Russell fluid factor is affected by both pore fluid and the rock skeleton, and certain errors exist. Russell et al (2006) propose direct characterization of fluid indicators with Gassmann fluid item f, which is greatly reduced in impact by the rock framework compared to previous fluid indicators, and therefore can more accurately identify reservoir pore fluids. Yinxiao (2014) and the like are based on the Biot-Gasssmann theory and directly extract the bulk modulus K of the fluid f As a fluid indicator, the influence of a rock skeleton is further eliminated, and the fluid has better recognition capability on pore fluid, but the expression form is too complex, so that the fluid is difficult to be directly applied to actual production. Thus, the Gassmann fluid term f remains, to date, one of the most widely used fluid indicator factors in reservoir pore fluid identification.
The expression form of the Zoeppritz equation is complex, so that the Zoeppritz equation is difficult to apply to actual production. Therefore, many AVO approximation formulas have been derived, assuming certain specific conditions. The AVO approximation formula based on Gassmann fluid term f is generally linear with high accuracy at small angles, but at high angles of incidence, the accuracy is difficult to meet our needs. A few higher order AVO approximation formulas are also derived based on the mean angle assumption, i.e., the angle in the formula is the mean angle of the incident and transmission angles. However, when the actual seismic data is inverted, the transmission angles of all interfaces are difficult to obtain, the average angle is often approximated by the incident angle, and the accuracy is slightly lost.
Prestack AVO inversion is one of the important means for obtaining fluid indicative factors from seismic data. The AVO technique is a geophysical technique for predicting the lithology and pore fluid of underground reservoirs by using the relation between the amplitude of seismic waves and offset. The Zoeppritz equation is the core principle of the AVO technology, and because the Zoeppritz equation is complex, the traditional AVO inversion method mostly operates based on a linear AVO approximate formula and belongs to a linear inversion method. With the progress of the computer level, many nonlinear methods have been developed in recent years, but due to the nonlinear characteristics of the algorithm, the calculation amount is very large and time is very long. Therefore, it is necessary to develop an AVO inversion method and system based on bayesian and series inversion theories.
The information disclosed in this background section is only for enhancement of understanding of the general background of the invention and should not be taken as an acknowledgement or any form of suggestion that this information forms the prior art already known to a person skilled in the art.
Disclosure of Invention
The invention provides an AVO inversion method and system based on Bayes and series inversion theory, which are based on a Zoeppritz equation and a Gassmann theory and combined with the Bayes theory and the series inversion theory to construct a prestack longitudinal wave high-order AVO inversion formula, can realize the actual reservoir fluid identification of a work area with high precision, high stability, high noise immunity and high efficiency, and have extremely high industrial practical value and popularization and application prospects.
According to one aspect of the invention, an AVO inversion method based on Bayesian and series inversion theories is provided. The method may include: obtaining a fluid term high-order AVO expression based on incidence angle approximation according to a Zoeppritz equation and a Gassmann theory; calculating parameters of the fluid item high-order AVO expression according to a series theory to obtain a fluid item high-order AVO formula; obtaining an inversion target function according to Bayes theory; and constructing a prestack longitudinal wave high-order AVO inversion formula according to the fluid item high-order AVO formula and the inversion target function.
Preferably, the fluid term higher order AVO expression is:
wherein,
wherein,
when in use
Then, the AVO expression is a first-order linear AVO expression; when in use
Then, the AVO expression is a second-order nonlinear AVO expression; when in use
And the expression is a third-order nonlinear AVO expression.
Preferably, the calculating parameters of the fluid item high-order AVO expression according to a series theory to obtain the fluid item high-order AVO formula includes: obtaining first-order, second-order and third-order expansion of the reflection coefficient of the longitudinal wave; calculating a first-order parameter according to the actual seismic record and the first-order expansion; calculating a second order parameter according to the first order parameter and the second order expansion; calculating a third order parameter according to the second order parameter and the third order expansion; calculating parameters of the fluid item high-order AVO expression according to the first-order parameter, the second-order parameter and the third-order parameter; and substituting the parameters of the fluid item high-order AVO expression into the fluid item high-order AVO expression to obtain the fluid item high-order AVO formula.
Preferably, the first order expansion is:
preferably, the second order expansion is:
preferably, the third order expansion is:
preferably, the parameters of the fluid item higher order AVO expression are:
preferably, the inversion objective function is:
where m is the inversion objective function, d is the observation data, G is the mapping operator between the observation data and the model data, G T A transposed matrix of G, C d For the noise covariance matrix, α is the weight coefficient and Q is the regularization term that depends on the type of prior distribution chosen.
According to another aspect of the present invention, an AVO inversion system based on bayesian and series inversion theory is provided, wherein the system comprises: a memory storing computer-executable instructions; a processor executing computer executable instructions in the memory to perform the steps of: obtaining a fluid term high-order AVO expression based on incidence angle approximation according to a Zoeppritz equation and a Gassmann theory; calculating parameters of the fluid item high-order AVO expression according to a series theory to obtain a fluid item high-order AVO formula; obtaining an inversion target function according to Bayes theory; and constructing a prestack longitudinal wave high-order AVO inversion formula according to the fluid item high-order AVO formula and the inversion target function.
Preferably, the fluid term higher order AVO expression is:
wherein,
wherein,
when in use
Then, the AVO expression is a first-order linear AVO expression; when in use
Then, the AVO expression is a second-order nonlinear AVO expression; when in use
And the expression is a third-order nonlinear AVO expression.
Preferably, the calculating parameters of the fluid item high-order AVO expression according to a series theory to obtain the fluid item high-order AVO formula includes: obtaining first-order, second-order and third-order expansion of the reflection coefficient of the longitudinal wave; calculating a first-order parameter according to the actual seismic record and the first-order expansion; calculating a second order parameter according to the first order parameter and the second order expansion; calculating a third order parameter according to the second order parameter and the third order expansion; calculating parameters of the fluid item high-order AVO expression according to the first-order parameter, the second-order parameter and the third-order parameter; and substituting the parameters of the fluid item high-order AVO expression into the fluid item high-order AVO expression to obtain the fluid item high-order AVO formula.
Preferably, the first order expansion is:
preferably, the second order expansion is:
preferably, the third order expansion is:
preferably, the parameters of the fluid item higher order AVO expression are:
preferably, the inversion objective function is:
where m is the inversion objective function, d is the observation data, G is the mapping operator between the observation data and the model data, G T A transposed matrix of G, C d For the noise covariance matrix, α is the weight coefficient and Q is the regularization term that depends on the type of prior distribution chosen.
The beneficial effects are that:
(1) the derived Gassmann fluid term high-order AVO approximate formula based on the incidence angle approximation has higher precision;
(2) the prestack AVO inversion method constructed based on the Bayesian theory and the series inversion theory has higher noise immunity, stability and efficiency;
(3) compared with the conventional prestack linear AVO inversion method, the prestack nonlinear AVO inversion method based on the Gassmann fluid term third-order AVO approximate formula has higher inversion accuracy.
The method and apparatus of the present invention have other features and advantages which will be apparent from or are set forth in detail in the accompanying drawings and the following detailed description, which are incorporated herein, and which together serve to explain certain principles of the invention.
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The above and other objects, features and advantages of the present invention will become more apparent by describing in more detail exemplary embodiments thereof with reference to the attached drawings, in which like reference numerals generally represent like parts.
FIG. 1 shows a flow chart of the steps of an AVO inversion method based on Bayesian and series inversion theory according to the present invention.
FIG. 2 shows a schematic diagram of an accuracy analysis of AVO expression based on incident angle approximation according to one embodiment of the present invention.
FIGS. 3a and 3b show schematic views of a log model synthetic noiseless angle gather and a log model synthetic 50% noise angle gather, respectively, according to an embodiment of the invention.
4a, 4b, and 4c show schematic representations of Gassmann fluid terms, shear modulus, density based on a first order AVO approximation formula and a third order AVO approximation formula, respectively, in accordance with well log data and an embodiment of the present invention.
Fig. 5a, 5b, and 5c show schematic diagrams of Gassmann fluid term error, shear modulus error, density error based on a third order AVO approximation formula and inversion results, respectively, and a first order AVO approximation formula, according to an embodiment of the invention.
FIGS. 6a, 6b, and 6c show graphs of Gassmann fluid terms, shear modulus, density, respectively, from well log data corresponding to different objective functions of a third order AVO approximation formula based on one embodiment of the present invention.
Fig. 7a, 7b and 7c are schematic diagrams illustrating a bayesian theory based on a third order AVO approximation formula and a Gassmann fluid term error, a shear modulus error and a density error based on a least squares theory, respectively, according to an embodiment of the present invention.
FIG. 8 shows a schematic diagram of an actual seismic section of an X-site according to one embodiment of the invention.
Fig. 9a and 9b show schematic diagrams of a Gassmann fluid entry inversion profile and a density inversion profile, respectively, according to one embodiment of the invention.
Detailed Description
The invention will be described in more detail below with reference to the accompanying drawings. While the preferred embodiments of the present invention are shown in the drawings, it should be understood that the present invention may be embodied in various forms and should not be limited to the embodiments set forth herein. Rather, these embodiments are provided so that this disclosure will be thorough and complete, and will fully convey the scope of the invention to those skilled in the art.
FIG. 1 shows a flow chart of the steps of an AVO inversion method based on Bayesian and series inversion theory according to the present invention.
In this embodiment, the AVO inversion method based on bayesian and series inversion theories according to the present invention may include: step 101, obtaining a fluid item high-order AVO expression based on incidence angle approximation according to a Zoeppritz equation and a Gassmann theory; 102, calculating parameters of a fluid item high-order AVO expression according to a series theory to obtain a fluid item high-order AVO formula; 103, acquiring an inversion target function according to a Bayes theory; and 104, constructing a prestack longitudinal wave high-order AVO inversion formula according to the fluid item high-order AVO formula and the inversion target function.
In one example, the fluid term higher order AVO expression is:
wherein,
wherein,
when in use
Then, the AVO expression is a first-order linear AVO expression; when in use
Then, the AVO expression is a second-order nonlinear AVO expression; when in use
And the expression is a third-order nonlinear AVO expression.
In one example, calculating parameters of a fluid item high order AVO expression according to a series theory, obtaining the fluid item high order AVO expression includes: obtaining first-order, second-order and third-order expansion of the reflection coefficient of the longitudinal wave; calculating a first-order parameter according to the actual seismic record and the first-order expansion; calculating a second-order parameter according to the first-order parameter and the second-order expansion; calculating a third order parameter according to the second order parameter and the third order expansion; calculating parameters of a high-order AVO expression of the fluid item according to the first-order parameter, the second-order parameter and the third-order parameter; and substituting the parameters of the fluid item high-order AVO expression into the fluid item high-order AVO expression to obtain a fluid item high-order AVO formula.
In one example, the first order expansion is:
in one example, the second order expansion is:
in one example, the third order expansion is:
in one example, the parameters of the fluid term higher order AVO expression are:
in one example, the inverse objective function is:
where m is the inversion objective function, d is the observation data, G is the mapping operator between the observation data and the model data, G T A transposed matrix of G, C d For the noise covariance matrix, α is the weight coefficient and Q is the regularization term that depends on the type of prior distribution chosen.
Specifically, the AVO inversion method based on bayesian and series inversion theories according to the present invention may include:
with the progress of seismic exploration technology and the development of computer technology, the linear AVO approximate formula cannot completely meet the requirements of people on precision. Based on the Zoeppritz equation, which can be converted to:
where X is sin θ, θ represents an incident angle, and a is ρ 2 /ρ 1 ，B＝β 1 /α 1 ，C＝α 2 /α 1 ，D＝β 2 /α 1 。
For incident longitudinal waves, the conversion relationship between velocity, density change rate and fluid factor, shear modulus change rate can be expressed as:
wherein, s ═ K +4 mu/3, f 1 、μ 1 And K 1 Respectively representing the Gassmann fluid term, shear modulus and bulk modulus of the upper layer, f 2 、μ 2 And K 2 Respectively representing the lower Gassmann fluid term, shear modulus and bulk modulus.
Substituting the formula (7) to the formula (10) into the formula (6), and using Maple software to match the formula (6)
And
performing Taylor expansion to obtain a high-order AVO expression of the fluid term based on the incidence angle approximation as formula (1), when
Then, the AVO expression is a first-order linear AVO expression; when in use
Then, the AVO expression is a second-order nonlinear AVO expression; when in use
And the expression is a third-order nonlinear AVO expression. Here, only the prestack nonlinear AVO inversion method based on the third order AVO approximation formula is studied.
The series method is a method for converting a nonlinear relation, any equation can be expanded through series, the idea is introduced into nonlinear AVO inversion, series expansion is respectively carried out on f, mu and rho, and parameters of a fluid term high-order AVO expression are obtained and are expressed as a formula (5).
Coefficient of longitudinal wave reflection R PP Can be unfolded as follows:
R PP ＝R 1 +R 2 +R 3 +...(11)，
substituting the formula (5) into the formula (7) to the formula (10), and combining with the formula (11) to obtain first, second and third expansion of the longitudinal wave reflection coefficient, which are respectively formula (2) to formula (4), R 1 、R 2 And R 3 Can be represented by R PP Calculating to obtain; calculating a first order parameter f from the actual seismic record and the first order expansion (1) 、μ (1) And ρ (1) (ii) a Calculating a second order parameter f according to the first order parameter and the second order expansion (2) 、μ (2) And ρ (2) (ii) a Calculating a third order parameter f according to the second order parameter and the third order expansion (3) 、μ (3) And ρ (3) (ii) a Substituting the first-order parameter, the second-order parameter and the third-order parameter into the formula (5) to calculate the parameter of the fluid item high-order AVO expression; and substituting the parameters of the fluid item high-order AVO expression into the fluid item high-order AVO expression to obtain a fluid item high-order AVO formula.
103, acquiring an inversion target function according to a Bayes theory; and each step of the series inversion needs to use a linear AVO inversion method based on Bayesian theory. The likelihood function is modeled by a multivariate gaussian distribution function, and can be expressed as:
the prior information distribution is simulated by adopting the three-variable Cauchy distribution, and can be expressed as follows:
wherein, P om ＝1/π 2N |Ψ N/2 ，Φ＝(D i ) T Ψ -1 D i 。
The posterior probability distribution can be expressed as:
the maximum derivation of the posterior probability P (m | d) with respect to the objective function m is obtained, and the resulting inversion equation can be expressed as formula (6). Wherein,
q is a 3N × 3N off-diagonal matrix, and the elements in Q can be represented as:
and constructing a prestack longitudinal wave high-order AVO inversion formula according to the fluid item high-order AVO formula and the inversion target function.
The method is based on the Zoeppritz equation and the Gassmann theory, and combines the Bayes theory and the series inversion theory to construct the prestack longitudinal wave high-order AVO inversion formula, so that the method can realize the actual reservoir fluid identification of the working area with high precision, high stability, high noise immunity and high efficiency, and has extremely high industrial practical value and popularization and application prospects.
Application example
To facilitate understanding of the solution of the embodiments of the present invention and the effects thereof, a specific application example is given below. It will be understood by those skilled in the art that this example is merely for the purpose of facilitating an understanding of the present invention, and that any particular details thereof are not intended to limit the invention by any formula.
FIG. 2 shows a schematic diagram of an accuracy analysis of an AVO expression based on an incidence angle approximation according to one embodiment of the present invention.
FIGS. 3a and 3b show schematic views of a log model synthetic noiseless angle gather and a log model synthetic 50% noise angle gather, respectively, according to an embodiment of the invention. And establishing a longitudinal wave synthetic angle gather according to actual logging data. Calculating the reflection coefficient of the longitudinal wave from 1 degree to 40 degrees, and performing convolution with 25Hz Richer wavelet to obtain a synthetic angle gather of the longitudinal wave, as shown in figure 3a, and adding random noise into the seismic gather to synthesize the angle gather, as shown in figure 3 b.
Fig. 4a, 4b, and 4c show schematic diagrams of Gassmann fluid terms, shear modulus, density based on a first order AVO approximation formula and a third order AVO approximation formula, respectively, with dashed, solid, and dotted lines representing model data, inversion results based on a third order AVO approximation formula, and inversion results based on a first order AVO approximation formula, respectively, in accordance with well log data and an embodiment of the present invention.
Fig. 5a, 5b and 5c respectively show schematic diagrams of Gassmann fluid term error, shear modulus error and density error based on a third-order AVO approximation formula and an inversion result and a first-order AVO approximation formula according to an embodiment of the present invention, where the solid line is an error between an inversion result of the third-order approximation formula and model data, and the dotted line is an error between an inversion result of the first-order approximation formula and model data.
As can be seen from the figure, the trend of the inversion result curve based on the AVO approximate formula is consistent with that of the model data curve, the error of the inversion result based on the third-order AVO approximate formula is smaller, and the curve is closer to the model data curve.
Fig. 6a, 6b and 6c respectively show schematic diagrams of Gassmann fluid terms, shear modulus and density corresponding to different objective functions based on a third-order AVO approximation formula according to an embodiment of the present invention, where a dotted line is model data, a solid line is an inversion result based on bayesian theory, and a dotted line is an inversion result based on least squares theory.
Fig. 7a, 7b, and 7c respectively show schematic diagrams of Gassmann fluid term error, shear modulus error, and density error based on bayesian theory and least square theory based on third-order AVO approximation formula according to an embodiment of the present invention, where the solid line is an error between an inversion result and model data based on bayesian theory, and the dotted line is an error between an inversion result and model data based on least square theory.
As can be seen from the figure, the inversion result curve and the model data curve tend to be consistent; when random noise exists in seismic records, the inversion result based on the least square method shakes, and the inversion result based on the Bayesian theory is more stable.
FIG. 8 shows a schematic diagram of an actual seismic profile of an X-site with a destination interval of 1690ms to 1720ms (PP time) with a gas formation as a result of well log interpretation, according to one embodiment of the present invention.
Fig. 9a and 9b respectively show schematic diagrams of a Gassmann fluid item inversion profile and a density inversion profile according to an embodiment of the present invention, where the logging curves shown in fig. 9a to 9b are longitudinal wave velocities, the gas layer of the logging interpretation is between 1700ms and 1710ms, the inversion results obtained by the inversion basically correspond to the logging interpretation results, the fluid characteristics of the work area can be well indicated, and the effectiveness and the practicability of the novel combined inversion algorithm are further verified.
In conclusion, the prestack longitudinal wave high-order AVO inversion formula is constructed on the basis of the Zoeppritz equation and the Gassmann theory and in combination with the Bayesian theory and the series inversion theory, the high-order AVO inversion formula can realize the actual reservoir fluid identification of the work area with high precision, high stability, high noise immunity and high efficiency, and has extremely high industrial practical value and popularization and application prospects.
It will be appreciated by persons skilled in the art that the above description of embodiments of the invention is intended only to illustrate the benefits of embodiments of the invention and is not intended to limit embodiments of the invention to any examples given.
According to an embodiment of the present invention, an AVO inversion system based on bayesian and series inversion theory is provided, wherein the system comprises: a memory storing computer-executable instructions; a processor executing computer executable instructions in the memory to perform the steps of: obtaining a fluid term high-order AVO expression based on incidence angle approximation according to a Zoeppritz equation and a Gassmann theory; calculating parameters of a fluid item high-order AVO expression according to a series theory to obtain a fluid item high-order AVO formula; obtaining an inversion target function according to Bayes theory; and constructing a prestack longitudinal wave high-order AVO inversion formula according to the fluid item high-order AVO formula and the inversion target function.
In one example, the fluid term higher order AVO expression is:
wherein,
wherein,
when in use
Then, it is a first-order linear AVO expression; when the temperature is higher than the set temperature
Then, the AVO expression is a second-order nonlinear AVO expression; when in use
And the expression is a third-order nonlinear AVO expression.
In one example, calculating parameters of a fluid item high order AVO expression according to a series theory, obtaining the fluid item high order AVO expression includes: obtaining first-order, second-order and third-order expansion of the reflection coefficient of the longitudinal wave; calculating a first-order parameter according to the actual seismic record and the first-order expansion; calculating a second-order parameter according to the first-order parameter and the second-order expansion; calculating a third order parameter according to the second order parameter and the third order expansion; calculating parameters of a high-order AVO expression of the fluid item according to the first-order parameter, the second-order parameter and the third-order parameter; and substituting the parameters of the fluid item high-order AVO expression into the fluid item high-order AVO expression to obtain a fluid item high-order AVO formula.
In one example, the first order expansion is:
in one example, the second order expansion is:
in one example, the third order expansion is:
in one example, the parameters of the fluid term higher order AVO expression are:
in one example, the inverse objective function is:
where m is the inversion objective function, d is the observation data, G is the mapping operator between the observation data and the model data, G T A transposed matrix of G, C d For the noise covariance matrix, α is the weight coefficient and Q is the regularization term that depends on the type of prior distribution chosen.
The system is based on a Zoeppritz equation and a Gassmann theory, combines a Bayesian theory and a series inversion theory, constructs a prestack longitudinal wave high-order AVO inversion formula, can realize the actual reservoir fluid identification of a work area with high precision, high stability, high noise immunity and high efficiency, and has extremely high industrial practical value and popularization and application prospects.
It will be appreciated by persons skilled in the art that the above description of embodiments of the invention is intended only to illustrate the benefits of embodiments of the invention and is not intended to limit embodiments of the invention to any examples given.
Having described embodiments of the present invention, the foregoing description is intended to be exemplary, not exhaustive, and not limited to the embodiments disclosed. Many modifications and variations will be apparent to those of ordinary skill in the art without departing from the scope and spirit of the described embodiments.
Claims (7)
1. An AVO inversion method based on Bayes and series inversion theory is characterized by comprising the following steps:
obtaining a fluid term high-order AVO expression based on incidence angle approximation according to a Zoeppritz equation and a Gassmann theory;
calculating parameters of the fluid item high-order AVO expression according to a series theory to obtain a fluid item high-order AVO formula;
obtaining an inversion target function according to Bayes theory;
constructing a prestack longitudinal wave high-order AVO inversion formula according to the fluid item high-order AVO formula and the inversion target function;
wherein the fluid term higher order AVO expression is:
wherein,
wherein,
when in use
Then, the AVO expression is a first-order linear AVO expression; when in use
Then, the AVO expression is a second-order nonlinear AVO expression; when in use
Then, the expression is a three-order nonlinear AVO expression;
wherein, the calculating the parameters of the fluid item high-order AVO expression according to the series theory to obtain the fluid item high-order AVO formula comprises:
obtaining first-order, second-order and third-order expansion of the reflection coefficient of the longitudinal wave;
calculating a first-order parameter according to the actual seismic record and the first-order expansion;
calculating a second order parameter according to the first order parameter and the second order expansion;
calculating a third order parameter according to the second order parameter and the third order expansion;
calculating parameters of the fluid item high-order AVO expression according to the first-order parameter, the second-order parameter and the third-order parameter;
and substituting the parameters of the fluid item high-order AVO expression into the fluid item high-order AVO expression to obtain the fluid item high-order AVO formula.
2. The AVO inversion method based on bayesian and series inversion theory of claim 1, wherein the first order expansion is:
3. the AVO inversion method based on Bayesian and series inversion theory of claim 1, wherein the second order expansion is:
4. the AVO inversion method based on Bayesian and series inversion theory of claim 1, wherein the third order expansion is:
5. the AVO inversion method based on Bayesian and series inversion theory of claim 1, wherein the parameters of the fluid term higher order AVO expression are:
6. the AVO inversion method based on Bayesian and series inversion theory of claim 1, wherein the inversion objective function is:
where m is the inversion objective function, d is the observation data, G is the mapping operator between the observation data and the model data, G T A transposed matrix of G, C d For a noise covariance matrix, α is the weight coefficient and Q is the regularization term that depends on the type of prior distribution selected.
7. An AVO inversion system based on Bayesian and series inversion theory, the system comprising:
a memory storing computer-executable instructions;
a processor executing computer executable instructions in the memory to perform the steps of:
obtaining a fluid term high-order AVO expression based on incidence angle approximation according to a Zoeppritz equation and a Gassmann theory;
calculating parameters of the fluid item high-order AVO expression according to a series theory to obtain a fluid item high-order AVO formula;
obtaining an inversion target function according to Bayes theory;
constructing a prestack longitudinal wave high-order AVO inversion formula according to the fluid item high-order AVO formula and the inversion target function;
wherein the fluid term higher order AVO expression is:
wherein,
wherein,
when in use
Then, the AVO expression is a first-order linear AVO expression; when in use
Then, the AVO expression is a second-order nonlinear AVO expression; when in use
Then, the expression is a three-order nonlinear AVO expression;
wherein, the calculating the parameters of the fluid item high-order AVO expression according to the series theory to obtain the fluid item high-order AVO formula comprises:
obtaining first-order, second-order and third-order expansion of the reflection coefficient of the longitudinal wave;
calculating a first-order parameter according to the actual seismic record and the first-order expansion;
calculating a second order parameter according to the first order parameter and the second order expansion;
calculating a third order parameter according to the second order parameter and the third order expansion;
calculating parameters of the fluid item high-order AVO expression according to the first-order parameter, the second-order parameter and the third-order parameter;
and substituting the parameters of the fluid item high-order AVO expression into the fluid item high-order AVO expression to obtain the fluid item high-order AVO formula.
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