New AVO formula elastic parameter automatic differentiation inversion method based on deep learning framework

Abstract

The present invention is applicable to the technical field of oil and gas geophysical exploration, and provides a new AVO formula elastic parameter automatic differential inversion method based on a deep learning framework, which proposes a seismic elastic AVO expression containing only bulk modulus κ, shear modulus μ and density ρ. The new AVO formula is multi-parameter inverted using an automatic differential algorithm based on a deep learning framework. This method effectively eliminates the negative impact of traditional methods on the accuracy of reservoir inversion. In addition, this method significantly reduces the computational cost of inverting complex seismic models, and achieves more efficient and economical AVO analysis. This method has excellent performance and can accurately simulate the changes in elastic parameters of different formations with changes in the incident angle. This not only improves the accuracy of AVO inversion, but also greatly improves the reliability of reservoir identification and evaluation. This improvement in accuracy is of great significance for improving the overall effect of seismic exploration and its practical application in the fields of oil and gas resource development.

Description

Technical Field

[0001] The present invention belongs to the technical field of oil and gas geophysical exploration, and in particular relates to a new AVO formula elastic parameter automatic differential inversion method based on a deep learning framework. Background Art

[0002] AVO technology is a method for identifying reservoir structural characteristics by observing the change in the amplitude of seismic waves with the offset, which has important research significance in oil and gas exploration and development. Since different types of fluids have different reflection characteristics for seismic waves, AVO theory can accurately analyze and distinguish different types of fluids, thereby improving the accuracy of oil and gas reservoir identification. The research and application of AVO theory provides important technical support for the sustainable development of the oil and gas industry.

[0003] AVO inversion can predict the physical properties of underground formations and is crucial for reservoir evaluation and development of oil and gas reservoirs. When longitudinal waves propagate in isotropic media, reflection waves and transmission waves are generated at the reflection interface. For this, the Zoeppritz equation can be used to analyze the changes in the reflection coefficient and the elastic parameters on both sides of the medium interface with the change of the incident angle, so as to identify the reservoir. Although the Zoeppritz equation can accurately calculate the reflection coefficient under different incident angles, its direct application in inversion has certain limitations due to the cumbersome calculation. For this reason, in actual inversion, approximate formulas are often used for inversion. In practical applications, the appropriate approximate formula should be selected according to the target to be inverted. At the same time, different parameters have different sensitivities to amplitude changes. In practical applications, the sensitivity of these parameters should be comprehensively considered to select the appropriate approximate formula for inversion.

[0004] At present, the least squares method is the most commonly used inversion algorithm in AVO inversion. AVO inversion is a complex nonlinear ill-posed inverse problem with multiple solutions. Using the least squares method to approximate the solution will lead to inaccurate solutions, especially when the inversion model is significantly different from the actual geological conditions. At the same time, this method is highly dependent on the initial model. If the selected initial model is significantly different from the actual situation, the inversion result is very likely to fall into the local optimal solution rather than the global minimum, which ultimately leads to low solution accuracy. In terms of computational efficiency, when processing large-scale seismic data, the computational complexity and memory requirements of the least squares method are high, and high-performance computing resources are required to support large-scale inversion. In addition, this method is easily affected by noise. When there is a high noise level in the seismic data, the inversion results will be affected, reducing the inversion accuracy. Therefore, it is crucial to develop a new generation of AVO inversion methods. Summary of the invention

[0005] The purpose of the embodiments of the present invention is to provide a new AVO formula elastic parameter automatic differentiation inversion method based on a deep learning framework, aiming to solve the problems raised in the above background technology.

[0006] The embodiment of the present invention is implemented as follows: a new AVO formula elastic parameter automatic differentiation inversion method based on a deep learning framework includes the following specific steps:

[0007] Step 1: Input pre-stack seismic angle gathers at different incident angles.

[0008] Step 2: Establish the initial model of each elastic parameter to be inverted;

[0009] Step 3: Use the proposed seismic elastic AVO formula to perform forward calculations on the parameter initial model to obtain synthetic seismic records at different incident angles;

[0010] Step 4: Use the automatic differentiation method based on the deep learning framework to perform inversion prediction on the three parameters to be inverted;

[0011] Step 5: Construct a loss function with L1 regularization and TV regularization constraints;

[0012] Step 6: Iterate the inversion until the termination condition is reached;

[0013] Step 7: Use the elastic parameters obtained by inversion to predict the reservoir.

[0014] A further technical solution is that in step 3, the seismic elastic AVO expression is derived as follows: the relationship between the bulk modulus, shear modulus, and longitudinal and transverse wave velocities and density is expressed as:

[0015]

[0016]

[0017] Among them, v p is the longitudinal wave velocity, v s is the shear wave velocity, κ is the bulk modulus, μ is the shear modulus, and ρ is the density;

[0018] The AVO approximation proposed by Gary is as follows:

[0019]

[0020] Where R(θ) is the reflection coefficient corresponding to the incident angle, Δκ=κ 2 -κ 1 , Δμ-μ 2 -μ 1 , Δρ=ρ 2 -ρ 1 , κ 1 , μ1 , 1 、v p1 、v s1 ,θ 1 Respectively represent the bulk modulus, shear modulus, density, longitudinal wave velocity, shear wave velocity and incident angle of the upper medium; κ 2 , μ 2 , 2 、v p2 、v s2 ,θ 2 represent the bulk modulus, shear modulus, density, longitudinal wave velocity, shear wave velocity and incident angle of the underlying medium respectively;

[0021] Substituting the above formula into the equation, we get the seismic elastic AVO approximation:

[0022]

[0023] The synthetic seismic record is calculated by convolution of reflection coefficient and seismic wavelet, namely:

[0024] S=W*R(θ)

[0025] Among them, S represents the seismic record, W is the seismic wavelet, R(θ) is the reflection coefficient, and * is the convolution calculation.

[0026] According to a further technical solution, step 4 comprises the following specific steps:

[0027] Using the Adam optimization algorithm, first, initialize the parameters: set the time step t, initialize the first-order momentum estimation variable m 0 and the second-order momentum estimation variable v 0 , the initial values ​​of the three are all 0; set the learning rate α to 0.01, the decay rate of the first-order momentum β 1 =0.9, the decay rate of the second-order momentum β 2 = 0.999 and a very small constant ∈ to prevent division by zero; in each iteration, the gradient g is calculated t , and update the first-order momentum estimate and the second-order momentum estimate respectively, as follows:

[0028] m t =β 1 m t-1 +(1-β 1 ) t

[0029]

[0030] Among them, m t is the first-order momentum estimate for the t-th iteration, v t is the second-order momentum estimate for the t-th iteration;

[0031] The bias-corrected momentum estimate is:

[0032]

[0033] in, is the bias-corrected first-order momentum estimate, is the bias-corrected second-order momentum estimate;

[0034] Therefore, the three parameters to be inverted can be iteratively updated:

[0035]

[0036] in, are the first-order momentum estimates of the parameters bulk modulus κ, shear modulus μ, and density ρ, respectively. They are the second-order momentum estimates of the parameters bulk modulus κ, shear modulus μ, and density ρ, respectively.

[0037] A further technical solution is that in step 5, the constructed loss function consists of the following three parts:

[0038] The first part measures the error by calculating the square difference between the predicted value and the true value, that is, constructing the loss function through the L2 norm, as follows:

[0039]

[0040] Among them, R is the reflection coefficient obtained by forward calculation of the three parameters obtained by inversion, W is the seismic wavelet, S′ is the prestack seismic angle gather input in step 1, ||·|| 2 is the L2 norm;

[0041] Since the reflection coefficient is sparse, the L1 norm is used for regularization constraint to effectively select relevant features and improve the accuracy of inversion;

[0042] The second part of the loss function is as follows:

[0043] J 2 =λ 1 ||R|| 1

[0044] Among them, ||·|| 1 is the L1 norm, λ 1 is the regularization parameter;

[0045] TV regularization is further used for constraints to improve the inversion accuracy while maintaining edge features by minimizing the total change in gradients. For a two-dimensional matrix u, its TV regularization is defined as follows:

[0046]

[0047] in, and are the gradients of u in the x and y directions respectively;

[0048] The third part of the loss function is as follows:

[0049] J 3 =λ 2 ||κ|| TV +λ 2 ||μ|| TV +λ 2 ||ρ|| TV

[0050] Among them, ||·|| TV is the TV regularization term, λ 2 is the regularization parameter.

[0051] The constructed loss function is as follows:

[0052] J=J 1 +J 2 +J 3

[0053] The embodiment of the present invention provides a new AVO formula elastic parameter automatic differential inversion method based on a deep learning framework, which proposes a seismic elastic AVO expression containing only bulk modulus κ, shear modulus μ and density ρ. The new AVO formula is inverted with multiple parameters using an automatic differential algorithm based on a deep learning framework. Compared with the traditional inversion method least squares method, this method is more sensitive to changes in elastic parameters bulk modulus κ, shear modulus μ and density ρ, has high inversion accuracy, and can effectively and accurately identify reservoirs. The negative impact of traditional methods on reservoir inversion accuracy is effectively eliminated. In addition, this method significantly reduces the computational cost of inverting complex seismic models and achieves more efficient and economical AVO analysis. In the test of typical geological models, this method demonstrates its excellent performance. It can accurately simulate the changes in elastic parameters of different formations. This not only improves the accuracy of AVO inversion, but also greatly improves the reliability of reservoir identification and evaluation. This improvement in accuracy is of great significance for improving the overall effect of seismic exploration and its practical application in fields such as oil and gas resource development. BRIEF DESCRIPTION OF THE DRAWINGS

[0054] Figure 1 A flowchart of a new AVO formula elastic parameter automatic differentiation inversion method based on a deep learning framework provided in an embodiment of the present invention;

[0055] Figure 2 are the bulk modulus, shear modulus, and density of the geological model;

[0056] Figure 3 is the initial model for bulk modulus, shear modulus, and density;

[0057] Figure 4 are the inversion results of bulk modulus, shear modulus and density obtained using this method;

[0058] Figure 5 Inversion results of bulk modulus, shear modulus and density obtained using the least squares inversion method. DETAILED DESCRIPTION

[0059] In order to make the purpose, technical solution and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention.

[0060] The specific implementation of the present invention is described in detail below in conjunction with specific embodiments.

[0061] like Figure 1 As shown, a new AVO formula elastic parameter automatic differentiation inversion method based on a deep learning framework is provided as an embodiment of the present invention. By combining the relationship between seismic wave longitudinal and shear wave velocities, density, shear modulus and bulk modulus with the AVO approximation proposed by Gray, a new seismic elastic AVO approximate expression is derived, which can be used to directly predict elastic parameters characterizing reservoir characteristics, such as bulk modulus κ, shear modulus μ and density ρ. On this basis, the new AVO formula is inverted for multi-parameters using an automatic differentiation algorithm based on a deep learning framework. The inversion method can automatically derive and gradient update the target equation, and obtain the inversion results of bulk modulus κ, shear modulus μ and density ρ by inputting pre-stack angle gathers with different incident angles. When constructing the loss function, the reflection coefficient characteristics are considered, and the L1 norm regularization constraint and TV regularization constraint are used.

[0062] The specific steps include:

[0063] Step 1: Input pre-stack seismic angle gathers at different incident angles.

[0064] Step 2: Establish the initial model of each elastic parameter to be inverted;

[0065] Step 3: Forward model the parameter initial model using the proposed seismic elastic AVO formula to obtain synthetic seismic records at different incident angles. The derivation process of the seismic elastic AVO expression is as follows: The relationship between the bulk modulus, shear modulus, and longitudinal and shear wave velocities and density can be expressed as:

[0066]

[0067] Among them, v p is the longitudinal wave velocity, v s is the shear wave velocity, κ is the bulk modulus, μ is the shear modulus, and ρ is the density.

[0068] The AVO approximation proposed by Gary is as follows:

[0069]

[0070] Where R(θ) is the reflection coefficient corresponding to the incident angle, Δκ=κ 2 -κ 1 , Δμ=μ 2 -μ 1 , Δρ=ρ 2 -ρ 1 , κ 1 , μ 1 , 1 、v p1 、v s1 ,θ 1 Respectively represent the bulk modulus, shear modulus, density, longitudinal wave velocity, shear wave velocity and incident angle of the upper medium; κ 2 , μ 2 , 2 、v p2 、v s2 ,θ 2 They represent the bulk modulus, shear modulus, density, longitudinal wave velocity, shear wave velocity and incident angle of the underlying medium respectively.

[0071] Substituting the above formula into the formula, we can get the seismic elastic AVO approximation proposed by this method:

[0072]

[0073] The synthetic seismic record can be obtained by convolution of reflection coefficient and seismic wavelet, namely:

[0074] S=W*R(θ)

[0075] Among them, S represents the seismic record, W is the seismic wavelet, R(θ) is the reflection coefficient, and * is the convolution calculation.

[0076] Step 4: Use the automatic differentiation method based on the deep learning framework to invert and predict the three parameters to be inverted. The specific inversion method principle is as follows: The automatic differentiation method based on the deep learning framework calculates the gradient of the objective function relative to the parameter to be inverted, continuously updates the model, optimizes the parameters, and reduces the error. This example uses the Adam optimization algorithm. First, initialize the parameters: set the time step t, initialize the first-order momentum estimation variable m 0 and the second-order momentum estimation variable v 0 , the initial values ​​of the three are all 0. Set the learning rate α to 0.01, the decay rate of the first-order momentum β 1 =0.9, the decay rate of the second-order momentum β 2 = 0.999 and a very small constant ∈ to prevent division by zero. In each iteration, the gradient g is calculated t , and update the first-order momentum estimate and the second-order momentum estimate respectively, as follows:

[0077] m t =β 1 m t-1 +(1-β 1 ) t

[0078]

[0079] Among them, m t is the first-order momentum estimate for the t-th iteration, v t is the second-order momentum estimate for the t-th iteration.

[0080] The bias-corrected momentum estimate is:

[0081]

[0082]

[0083] in, is the bias-corrected first-order momentum estimate, is the bias-corrected second-order momentum estimate.

[0084] Thus, the three parameters to be inverted can be iteratively updated.

[0085]

[0086] in, are the first-order momentum estimates of the parameters bulk modulus κ, shear modulus μ, and density ρ, respectively. They are the second-order momentum estimates of the parameters bulk modulus κ, shear modulus μ, and density ρ, respectively.

[0087] Step 5: Construct a loss function with L1 regularization and TV regularization constraints. The loss function consists of the following three parts. The first part measures the error by calculating the square difference between the predicted value and the true value, that is, constructing the loss function through the L2 norm, as shown below:

[0088]

[0089] Among them, R is the reflection coefficient obtained by forward calculation of the three parameters obtained by inversion, W is the seismic wavelet, S′ is the prestack seismic angle gather input in step 1, ||·|| 2 is the L2 norm.

[0090] Since the reflection coefficient is sparse, the L1 norm is used for regularization constraints to effectively select relevant features and improve the accuracy of inversion. The second part of the loss function is as follows:

[0091] J 2 =λ 1 ||R|| 1

[0092] Among them, ||·|| 1 is the L1 norm, λ 1 is the regularization parameter.

[0093] To further improve the inversion accuracy, TV regularization is used for constraints, which improves the inversion accuracy while maintaining the edge features by minimizing the total change of the gradient. For a two-dimensional matrix u, its TV regularization is defined as follows:

[0094]

[0095] in, and are the gradients of u in the x and y directions respectively.

[0096] The third part of the loss function is as follows:

[0097] J 3 =λ 2 ||κ|| TV +λ 2 ||μ|| TV +λ 2 ||ρ|| TV

[0098] Among them, ||·|| TV is the TV regularization term, λ 2 is the regularization parameter.

[0099] The constructed loss function is as follows:

[0100] J=J 1 +J2 +J 3

[0101] Step 6: Iterate the inversion until the termination condition is reached.

[0102] Step 7: Use the elastic parameters obtained by inversion to predict the reservoir.

[0103] As a preferred embodiment of the present invention, the method is applied to the following geological model: This model contains 426 seismic traces with a depth of 131 m. Figure 2 a, b, c are the bulk modulus, shear modulus and density of the geological model respectively. Under the same initial model, the traditional least square method and the new method proposed in the present invention are used for inversion respectively, and the inversion results are compared.

[0104] Figure 3 a, b, and c in are the initial models of bulk modulus, shear modulus, and density, respectively. Figure 4 and Figure 5 As shown in the figure, a, b, and c in each figure are the inversion results of bulk modulus, shear modulus, and density, respectively. Compared with conventional P-wave velocity and S-wave velocity attributes, bulk modulus, shear modulus, and density are more sensitive to reservoir changes, which improves the accuracy of reservoir identification. By comparing the inversion results obtained by the two methods, it can be seen that the new inversion method proposed in the present invention effectively improves the inversion effect of elastic parameters, and the inversion accuracy of density terms is particularly significantly improved.

[0105] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions and improvements made within the spirit and principles of the present invention should be included in the protection scope of the present invention.

Claims

1. A new AVO formula elastic parameter automatic differentiation inversion method based on deep learning framework, characterized by: The specific steps include: Step 1: Input pre-stack seismic angle gathers with different incidence angles; Step 2: Establish the initial model of each elastic parameter to be inverted; Step 3: Use the proposed seismic elastic AVO formula to perform forward calculations on the parameter initial model to obtain synthetic seismic records at different incident angles; Step 4: Use the automatic differentiation method based on the deep learning framework to perform inversion prediction on the three parameters to be inverted; Step 5: Construct a loss function with L1 regularization and TV regularization constraints; Step 6: Iterate the inversion until the termination condition is reached; Step 7: Use the elastic parameters obtained by inversion to predict reservoirs; In step 3, the derivation process of the seismic elastic AVO expression is as follows: The relationship between bulk modulus, shear modulus, longitudinal and transverse wave velocity and density is expressed as: ； ； in, is the longitudinal wave velocity, is the shear wave velocity, is the bulk modulus, is the shear modulus, is the density; The AVO approximation proposed by Gary is as follows: ； in, is the reflection coefficient corresponding to the incident angle, , , , , , , , , ; represent the bulk modulus, shear modulus, density, longitudinal wave velocity, shear wave velocity and incident angle of the upper medium respectively; represent the bulk modulus, shear modulus, density, longitudinal wave velocity, shear wave velocity and incident angle of the underlying medium respectively; Substituting the above formula into the equation, we get the seismic elastic AVO approximation: ； The synthetic seismic record is calculated by convolution of reflection coefficient and seismic wavelet, namely: ； in, Represents earthquake records, is the seismic wavelet, is the reflection coefficient, Calculates convolution.

2. The new AVO formula elastic parameter automatic differentiation inversion method based on deep learning framework according to claim 1 is characterized in that: The step 4 comprises the following specific steps: Using the Adam optimization algorithm, first, initialize the parameters: set the time step t, initialize the first-order momentum estimation variable and the second-order momentum estimation variable , the initial values ​​of the three are all 0; set the learning rate is 0.01, the decay rate of the first-order momentum , the decay rate of the second-order momentum and a very small constant to prevent division by zero ; In each iteration, the gradient is calculated , and update the first-order momentum estimate and the second-order momentum estimate respectively, as follows: ； ； in, is the first-order momentum estimate for the t-th iteration, is the second-order momentum estimate for the t-th iteration; The bias-corrected momentum estimate is: ； ； in, is the bias-corrected first-order momentum estimate, is the bias-corrected second-order momentum estimate; Therefore, the three parameters to be inverted can be iteratively updated: ； ； ； in, The parameters are bulk modulus , shear modulus ,density The first-order momentum estimate of The parameters are bulk modulus , shear modulus ,density The second-order momentum estimate of .

3. The new AVO formula elastic parameter automatic differentiation inversion method based on deep learning framework according to claim 2 is characterized in that: In step 5, the constructed loss function consists of the following three parts: The first part measures the error by calculating the square difference between the predicted value and the true value, that is, constructing the loss function through the L2 norm, as follows: ； in, is the reflection coefficient obtained by forward calculation of the three parameters obtained by inversion, is the seismic wavelet, is the pre-stack seismic angle gather input in step 1, is the L2 norm; Since the reflection coefficient is sparse, the L1 norm is used for regularization constraint to effectively select relevant features and improve the accuracy of inversion; The second part of the loss function is as follows: ； in, is the L1 norm, is the regularization parameter; Then TV regularization is used for constraints to improve the inversion accuracy while maintaining edge features by minimizing the total change in gradients. For a two-dimensional matrix u, its TV regularization is defined as follows: ； in, and are the gradients of u in the x and y directions respectively; The third part of the loss function is as follows: ； in, is the TV regularization term, is the regularization parameter; The constructed loss function is as follows: 。

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