CN113985480A - AVO inversion method and device based on angle correction - Google Patents
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Abstract
The invention discloses an AVO inversion method and device based on angle correction, wherein the method comprises the following steps: performing edge detection on the two-dimensional seismic record or attribute data after the offset after the stacking based on a gradient structure tensor algorithm to obtain a local dip angle; according to the local inclination angle, angle correction is carried out on an Aki-Richards approximation formula to obtain an improved AVO expression; and obtaining an AVO three-parameter inversion result by adopting an AVO inversion method based on Bayes according to the improved AVO expression. According to the invention, heterogeneous body scattering of carbonate rock media is considered, deviation exists between a ray incidence angle and a traditional assumed horizontal layered uniform medium incidence angle, two-dimensional seismic records or attribute data are regarded as two-dimensional images, a gradient structure tensor algorithm is adopted to obtain a local dip angle, and then angle correction is carried out on a traditional AVO approximate formula according to the obtained local dip angle, so that the improved AVO expression better conforms to the heterogeneous characteristic of the carbonate rock, and the AVO inversion precision is improved.
Description
Technical Field
The invention relates to the field of oil and gas geophysical exploration, in particular to an AVO inversion method and device based on angle correction.
Background
The reservoir prediction technology of carbonate rock is similar to that of clastic rock, and the lithofacies, lithological properties and fluid-containing properties of the reservoir are described mainly through information such as earthquake, geology and well logging, but the reservoir description of the carbonate rock has the difficulty that the carbonate rock is heterogeneous, the difference of longitudinal and transverse properties of the rock is large, the carbonate rock reservoir is difficult to be drawn through summarizing the spatial law, and great challenges are brought to the oil-gas exploration of the carbonate rock. The avo (amplitude verse issues) technology is one of the conventional and mainstream reservoir prediction methods. The AVO reverse modeling technology has a good application effect in clastic rock reservoirs such as sandstone reservoirs, but the method has an unsatisfactory effect in inverting carbonate reservoirs. On one hand, due to the complex carbonate reservoir formation reason, the diversity of seismic reflection characteristics and seismic angle gather change characteristics exists (application of AVO technology in carbonate fracture-cave reservoir prediction, Chenjun and the like, 2014), and on the other hand, due to the fact that AVO inversion is based on a convolution model, the medium is generally assumed to be layered, uniform and isotropic, and the method is not suitable for complex carbonate reservoir inversion.
Disclosure of Invention
In order to overcome the defects and shortcomings in the prior art, the invention provides an AVO inversion method and device based on angle correction, wherein the method and device consider non-homogeneous body scattering, and the ray incidence angle has deviation from the incidence angle of a traditional assumed horizontal laminar homogeneous medium, and correct the angle.
In order to solve the problems in the prior art, the invention is realized by the following technical scheme:
an AVO inversion method based on angle correction comprises the following steps:
s1, performing edge detection on the two-dimensional seismic record or attribute data after the offset of the stack based on a gradient structure tensor algorithm to obtain a local dip angle;
s2, according to the local inclination angle, carrying out angle correction on a Aki-Richards approximation formula to obtain an improved AVO expression;
and S3, obtaining an AVO three-parameter inversion result by adopting an AVO inversion method based on Bayes according to the improved AVO expression.
Further, step S1 specifically includes:
s11, regarding the two-dimensional seismic record or instantaneous phase of the post-stack migration with different signal-to-noise ratios as a two-dimensional image, and calculating the horizontal gradient g for any point on the imagexAnd a vertical gradient gyThen the gradient squared tensor matrix is:
s12, performing eigen decomposition on the gradient square tensor matrix to obtain:
wherein λ is1，λ2Is a characteristic value, v1，v2Is a feature vector;
s13, when the tilt-up angle is negative and the tilt-down angle is positive, the local tilt angle of the two-dimensional structure is:
further, in step S2: the correction angle is:
the improved AVO expression is as follows:
wherein,
in addition to this, the present invention is,
and
respectively are the average values of longitudinal wave velocity, transverse wave velocity and density of the upper and lower layers; Δ VP,ΔVSAnd Δ ρ is the difference between the longitudinal wave velocity, the transverse wave velocity and the density of the upper and lower layer media; theta is the average incident angle of longitudinal waves of the upper medium and the lower medium,
further, in step S3, the prior probability distribution function in the bayesian-based AVO inversion method is:
wherein M is seismic inversion parameter, I is prior geological information, const is constant, and C is a multi-dimensional parameter model with M variablesmA parameter covariance matrix of M x M, diagonal elements representing the variance of the model parameters, and off-diagonal elements representing the cross-correlation between the parameters; mu.smRepresenting the most possible model in the prior information for the prior model parameter; obtaining parameter C from velocity and density log datamAnd mum。
Further, assume data dobsObeys a gaussian distribution, the likelihood function is as follows:
wherein d isobsFor observation data, G is the known mapping of model space to data space, i.e. the forward operator of the modified AVO expression.
Further, the final posterior probability density function is:
further, the AVO three-parameter inversion result is:
m＝(GTCn -1G+Cm -1)-1(GTCn -1dobs+Cm -1um)，
the covariance expression of the posterior distribution is:
C＝(GTCn -1G+Cm -1)-1。
in another aspect, the present invention provides an apparatus for an AVO inversion method based on angle correction, including:
the local dip angle calculation module is used for carrying out edge detection on the two-dimensional seismic record or attribute data after the offset after the stacking based on a gradient structure tensor algorithm to obtain a local dip angle;
the AVO angle correction module is used for carrying out angle correction on the Aki-Richards approximation formula according to the local inclination angle to obtain an improved AVO expression;
and the three-parameter inversion module is used for acquiring an AVO three-parameter inversion result by adopting an AVO inversion method based on Bayes according to the improved AVO expression.
The specific functions of each module are realized by adopting the steps of the AVO inversion method based on angle correction.
The invention also provides a computer device, which comprises a memory, a processor and a computer program stored on the memory and capable of running on the processor, wherein the processor executes the computer program to execute the steps of the AVO inversion method based on angle correction.
The present invention also provides a computer readable storage medium having stored thereon a computer program which, when executed by a processor, performs the steps of the above-described method for AVO inversion based on angle correction.
Compared with the prior art, the beneficial technical effects brought by the invention are as follows:
according to the invention, heterogeneous body scattering of the carbonate rock medium is fully considered, deviation exists between a ray incidence angle and a traditional assumed horizontal layered uniform medium incidence angle, two-dimensional seismic records or attribute data are regarded as two-dimensional images, a gradient structure tensor algorithm is adopted to obtain a local inclination angle, and then angle correction is carried out on a traditional AVO approximate formula according to the obtained local inclination angle, so that the improved AVO expression better conforms to the heterogeneous characteristic of the carbonate rock, and the AVO inversion precision is improved.
According to the improved AVO expression, the three-parameter fast inversion is realized by adopting an AVO inversion method based on a Bayesian framework.
Drawings
FIG. 1 is a flowchart of an AVO inversion method based on angle correction according to embodiment 1 of the present invention;
fig. 2 is a schematic diagram of two-dimensional reflection profile tilt angle symbol definition in embodiment 1 of the present invention.
Detailed Description
The technical scheme of the invention is further elaborated in the following by combining the drawings in the specification.
The present embodiment provides an AVO inversion method based on angle correction, as shown in fig. 1, including:
s1, performing edge detection on the two-dimensional seismic record or attribute data after the offset of the stack based on a gradient structure tensor algorithm to obtain a local dip angle;
s2, according to the local inclination angle, carrying out angle correction on a Aki-Richards approximation formula to obtain an improved AVO expression;
and S3, obtaining an AVO three-parameter inversion result by adopting an AVO inversion method based on Bayes according to the improved AVO expression.
Step S1 specifically includes:
s11, regarding the two-dimensional seismic record or instantaneous phase of the post-stack migration with different signal-to-noise ratios as a two-dimensional image, and calculating the horizontal gradient g for any point on the imagexAnd a vertical gradient gyThen the gradient squared tensor matrix is:
s12, performing eigen decomposition on the gradient square tensor matrix to obtain:
wherein λ is1，λ2Is a characteristic value, v1，v2Is a feature vector;
s13, defining the tilt-up angle as negative and the tilt-down angle as positive, the local tilt angle of the two-dimensional structure is as follows as shown in FIG. 2:
in step S2: the correction angle is:
the improved AVO expression is as follows:
wherein,
in addition to this, the present invention is,
and
respectively are the average values of longitudinal wave velocity, transverse wave velocity and density of the upper and lower layers; Δ VP,ΔVSAnd Δ ρ is the difference between the longitudinal wave velocity, the transverse wave velocity and the density of the upper and lower layer media; theta is the average incident angle of longitudinal waves of the upper medium and the lower medium,
step S3 uses an inversion method based on a bayesian framework.
Bayesian theory expresses posterior probability density distribution of model parameters through prior distribution and likelihood function, and combines known prior information and observation data to obtain the best fitting solution of the model parameters, and simultaneously uses probability distribution to describe inversion result of credibility, so as to better know inversion multi-solution.
Suppose the seismic model parameters are m, d is the observed data, and G is the known mapping of model space to data space. The improved AVO expression (5) is written in matrix form:
order to
Can be abbreviated as: d ═ Gm.
As mentioned above, the statistical inversion based on bayesian theory is to regard the inversion parameter m as a random variable obeying a certain probability distribution p (m) and obtain a corresponding solution by maximizing the posterior probability density function p (m | d). Wherein, p (m) is called prior probability, and the prior probability of the model parameters is obtained by logging or geologic statistics and other methods, which is equivalent to introducing additional constraint information in inversion, playing a role of regularization term, and reducing the multiple solution of inversion. Meanwhile, p (d | m) is called a likelihood function, describing a conditional probability density of observed data d given a model parameter m, which represents the degree of approximation between a model value calculated by forward modeling and a true value given the model parameter m. According to the bayesian formula (equation 8) in probability statistics, under the condition of known observation data and prior distribution, the conjecture posterior probability p (m | d) and the distribution parameters thereof can be obtained:
where p (d) is a constant, which can be used as a normalization constant, and is generally negligible, so the above equation can be written as:
p(m|d)＝p(m)p(d|m) (9)
the posterior probability distribution of the parameters is estimated by a Bayesian method, which can be regarded as the process of obtaining the posterior probability distribution by the prior probability distribution function through the action with the likelihood function. In geophysical inversion, the posterior probability of a model parameter m given measured data d is typically:
p(m|d,I)∝p(m|I)p(d|m,I) (10)
wherein I is geological information, and after the prior distribution P (m | I) and the conditional probability distribution P (d | m, I) of the model observation data are given, we can obtain the final posterior probability density function. The prior distribution of the model can effectively reduce the inversion unsuitability. In geophysical inversion, the prior distribution of model parameters may be subject to different statistical distributions, depending on different inversion requirements and actual geological conditions: such as gaussian distribution, cauchy distribution, long tail distribution, etc. Based on the assumption that parameters obey long-tail distribution, sparse pulse inversion results with higher resolution can be obtained; by introducing a correlation matrix, a sparse solution of the inversion can be obtained, based on the assumption that the parameters obey the Cauchy distribution. Taking the gaussian distribution as an example, a solution under a bayesian framework is solved.
By assuming that each variable in the prior information obeys Gaussian distribution, the model parameters obey M-dimensional Gaussian distribution, and the prior probability distribution function is:
wherein for a multidimensional parametric model with M variables, CmA parameter covariance matrix, M x M, with diagonal elements representing the variance of the model parameters and off-diagonal elements representing the cross-correlation between the parameters. Mu.smIs a prior model parameter and represents the most probable model in prior information. In AVO inversion, parameter C can be obtained from velocity and density log datamAnd mum。
Suppose data dobsObeys a gaussian distribution, the likelihood function is as follows:
according to the Bayesian formula, the posterior probability density function can be expressed as:
wherein, CnAs a co-ordination of dataAnd (4) a variance matrix. The subsurface elastic parameters are solved based on linear approximation equations, whose positive operator G has the following form:
Fforward＝Gm (14)
the final a posteriori probability density function can be obtained as:
when solving the maximum posterior probability of the model parameters, it is equivalent to solving the minimum value of f (m). Order to
The value of the parameter m can be solved. Due to the linear relationship between the observation data and the model parameters, the AVO three-parameter inversion result can be finally displayed and expressed:
m＝(GTCn -1G+Cm -1)-1(GTCn -1dobs+Cm -1um) (17)
the covariance expression of the posterior distribution is given at the same time:
C＝(GTCn -1G+Cm -1)-1 (18)
the embodiment also provides a device of an AVO inversion method based on angle correction, which includes:
the local dip angle calculation module is used for carrying out edge detection on the two-dimensional seismic record or attribute data after the offset after the stacking based on a gradient structure tensor algorithm to obtain a local dip angle;
the AVO angle correction module is used for carrying out angle correction on the Aki-Richards approximation formula according to the local inclination angle to obtain an improved AVO expression;
and the three-parameter inversion module is used for acquiring an AVO three-parameter inversion result by adopting an AVO inversion method based on Bayes according to the improved AVO expression.
The present embodiment also provides a computer device, which includes a memory, a processor, and a computer program stored in the memory and executable on the processor, and when the processor executes the computer program, the processor executes the steps of the above-mentioned AVO inversion method based on angle correction.
The present embodiment also provides a computer-readable storage medium having stored thereon a computer program which, when executed by a processor, implements the steps of the above-described AVO inversion method based on angle correction.
As will be appreciated by one skilled in the art, embodiments of the present invention may be provided as a method, system, or computer program product. Accordingly, the present invention may take the form of an entirely hardware embodiment, an entirely software embodiment or an embodiment combining software and hardware aspects. Furthermore, the present invention may take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, and the like) having computer-usable program code embodied therein.
The present invention is described with reference to flowchart illustrations and/or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each flow and/or block of the flow diagrams and/or block diagrams, and combinations of flows and/or blocks in the flow diagrams and/or block diagrams, can be implemented by computer program instructions. These computer program instructions may be provided to a processor of a general purpose computer, special purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be stored in a computer-readable memory that can direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer-readable memory produce an article of manufacture including instruction means which implement the function specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
The above-mentioned embodiments are intended to illustrate the objects, technical solutions and advantages of the present invention, and it should be understood that the above-mentioned embodiments are only exemplary embodiments of the present invention, and are not intended to limit the scope of the present invention, and any modifications, equivalent substitutions, improvements and the like made within the spirit and principle of the present invention should be included in the scope of the present invention.
Claims (10)
1. An AVO inversion method based on angle correction is characterized by comprising the following steps:
s1, performing edge detection on the two-dimensional seismic record or attribute data after the offset after the stacking based on a gradient structure tensor algorithm, and solving a local inclination angle;
s2, according to the local inclination angle, carrying out angle correction on a Aki-Richards approximation formula to obtain an improved AVO expression;
and S3, obtaining an AVO three-parameter inversion result by adopting an AVO inversion method based on Bayes according to the improved AVO expression.
2. The AVO inversion method of claim 1, wherein step S1 specifically includes:
s11, two-dimensional seismic recording of post-stack migration with different signal-to-noise ratiosOr the instantaneous phase is regarded as a two-dimensional image, and the horizontal gradient is calculated for any point on the image
And vertical gradient
Then the gradient squared tensor matrix is:
s12, performing eigen decomposition on the gradient square tensor matrix to obtain:
wherein λ is1，λ2Is a characteristic value, v1，v2Is a feature vector;
s13, when the tilt-up angle is negative and the tilt-down angle is positive, the local tilt angle of the two-dimensional structure is:
3. the AVO inversion method of claim 2, wherein in step S2: the correction angle is:
(ii) a The improved AVO expression is as follows:
wherein,
，
in addition to this, the present invention is,
, 
and
respectively are the average values of longitudinal wave velocity, transverse wave velocity and density of the upper and lower layers;
, 
and
the difference between the longitudinal wave velocity, the transverse wave velocity and the density of the upper and lower layers of medium; theta is the average incidence angle of longitudinal waves of the upper medium and the lower medium,
。
4. the AVO inversion method of any of claims 1-3, wherein in step S3, the prior probability distribution function in the Bayesian-based AVO inversion method is:
wherein m is a seismic inversion parameter,Ifor prior geological information, const is a constant, for a multidimensional parametric model with M variables, CmA parameter covariance matrix of M x M, diagonal elements representing the variance of the model parameters, and off-diagonal elements representing the cross-correlation between the parameters; mu.smIs a priori modelA type parameter representing a most likely model in the prior information; obtaining parameter C from velocity and density log datamAnd mum。
5. The AVO inversion method of claim 4, wherein: suppose data dobsObeys a gaussian distribution, the likelihood function is as follows:
wherein d isobsFor observation data, G is the known mapping of model space to data space, i.e. the forward operator of the modified AVO expression.
6. The AVO inversion method of claim 5, wherein: the final a posteriori probability density function is:
7. the AVO inversion method of claim 5, wherein: the AVO three-parameter inversion result is:
the covariance expression of the posterior distribution is:
8. an AVO inversion apparatus based on angle correction, comprising:
the local dip angle calculation module is used for carrying out edge detection on the two-dimensional seismic record or attribute data after the offset after the stacking based on a gradient structure tensor algorithm to obtain a local dip angle;
the AVO angle correction module is used for carrying out angle correction on the Aki-Richards approximation formula according to the local inclination angle to obtain an improved AVO expression;
and the three-parameter inversion module is used for acquiring an AVO three-parameter inversion result by adopting an AVO inversion method based on Bayes according to the improved AVO expression.
9. A computer device comprising a memory, a processor and a computer program stored on the memory and executable on the processor, the processor performing the steps of the method of any of the preceding claims 1-7 when executing the computer program.
10. A computer-readable storage medium, on which a computer program is stored which, when being executed by a processor, carries out the steps of the method of any one of the preceding claims 1 to 7.
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