VTI medium least square reverse time migration method and system suitable for Adam gradient optimization algorithm

Abstract

The invention relates to a VTI medium least square reverse time migration method and system suitable for an Adam gradient optimization algorithm, and belongs to the field of seismic migration imaging, and the method specifically comprises the following steps: carrying out the subtraction of conventional approximate longitudinal and transverse wave reflectivity models C33 and C55 with the background speed of the conventional approximate longitudinal and transverse wave reflectivity models C33 and C55, carrying out the division, carrying out the normalization processing, and constructing a real longitudinal and transverse wave reflection coefficient model. And linear forward modeling is carried out on the basis of a VTI medium first-order stress velocity elastic wave equation. And expressing the linearized forward modeling in a deep learning framework in an RNN convolution form to obtain a simulated seismic record of the linearized forward modeling. And making a difference between the simulated seismic record and the actual seismic record, and establishing a target function. And optimizing the gradient by using an Adam gradient optimization algorithm in deep learning, and updating the longitudinal and transverse wave reflection coefficient model by using the optimized gradient until the precision requirement is met. According to the method, the precision of gradient optimization is improved, the problem of extremely slow convergence is solved, and finally a more accurate least square reverse time migration result is obtained.

Description

TECHNICAL FIELD

[0001] The present application belongs to the field of seismic migration imaging, and particularly relates to a VTI medium least square reverse-time migration method and system suitable for Adam gradient optimization algorithm. BACKGROUND

[0002] The least square reverse-time migration can solve the imaging problem of the reverse-time migration as a least square inversion problem, and solves an imaging result best matched with observed seismic data through an iterative algorithm, and has the advantages of suppressing migration noise, improving deep imaging, improving continuity and uniformity of the same phase axis, and improving amplitude fidelity, so the least square reverse-time migration has great application potential in future practical production. However, the conventional least square reverse-time migration method is mostly based on inversion of isotropic medium, and the real underground medium often has anisotropic characteristics, so the least square reverse-time migration under the assumption of isotropic medium does not conform to the actual situation. Therefore, the least square reverse-time migration based on VTI medium anisotropic parameters which is more in line with the actual geological conditions has become a research hotspot in the field of geophysics.

[0003] In the VTI medium least square reverse-time migration imaging, the conventional migration imaging target is often replaced by C 33 and C 55 , which is not a real P-S reflection coefficient model, and because C 33 and C 55 are of the order of magnitude, the convergence is extremely slow, the migration imaging result is poor, and it is often difficult to meet the requirements of the industry on imaging accuracy. Therefore, it is extremely important to reconstruct a suitable P-S reflection coefficient model and select a suitable acceleration optimization algorithm. SUMMARY

[0004] The present application provides a VTI medium least square reverse-time migration method suitable for Adam gradient optimization algorithm, which theoretically constructs a real P-S reflection coefficient model, and expresses the least square reverse-time migration in RNN convolution and automatic differentiation in deep learning to solve, and then updates the gradient by using the Adam gradient optimization algorithm in deep learning to solve the problem of slow convergence, and finally obtains a more accurate least square reverse-time migration result.

[0005] The present application is realized by the following technical solutions: A VTI medium least square reverse-time migration method suitable for Adam gradient optimization algorithm, the method specifically includes the following steps: Firstly, a real P-S reflection coefficient model is constructed, and the conventional approximate P-S reflectivity modelC 33 and C 55 After being divided by the difference between itself and the background velocity, the normalized true P-S wave reflection coefficient model is obtained; Secondly, the linearized forward of the true P-S wave reflection coefficient model in the first step is carried out based on the first-order stress velocity elastic wave equation of VTI medium; Thirdly, the linearized forward is expressed in the form of RNN convolution in the deep learning framework, and the simulated seismic record of the linearized forward is obtained; Fourthly, the simulated seismic record obtained in the third step is subtracted from the actual seismic record to establish the objective function; the objective function is expressed in the automatic differentiation technology framework in deep learning, and the gradient of the P-S wave reflection coefficient model is obtained by solving the objective function using the automatic differentiation technology; Fifthly, the gradient obtained in the fourth step is optimized using the Adam gradient optimization algorithm in deep learning, and the true P-S wave reflection coefficient model in the first step is updated using the optimized gradient until the accuracy requirement is met (generally, 20 iterations are enough).

[0006] Further, the formula used in the first step is: (1), I pp and I ps respectively represent the true P-S wave reflection coefficient model, C0 33 and C 0 55 are the background velocities, which are C 33 and C 55 The results after Gaussian smoothing.

[0007] Further, in the second step, the Thomson parameter model C 11 ( x , z )、 C 13 ( x , z )、 C 33 ( x , z ) and C 55 ( x , z ) and the true P-S wave reflection coefficient model I pp and I psBased on the first-order stress-velocity elastic wave formula (2) of VTI medium, linear forward modeling is carried out, and the reflection coefficient model is solved in the first iteration I pp And I ps The initial value is 0, wherein represents the density of the medium, u x , u z respectively represent x , z the velocity component of the direction, , respectively represent x , z the normal stress component of the direction, represents the shear stress component, f x And f z is the source, and the formula (2) is: .

[0008] Further, in the third step, the forward modeling calculation is equivalent to the operation of the convolution kernel in the RNN neural network, and the linear forward modeling is expressed in the form of RNN convolution in the deep learning framework by using formula (3), to obtain the simulated seismic record of linear forward modeling d sny , wherein, t represents the time, and B represents u x , u z , , , , f represents f x And f z The formula (3) is: ; Further, in the fourth step, the simulated seismic record d sny is subtracted from the actual seismic record d obs to establish the objective function, and the formula (4) is: , wherein the actual seismic record d obs is obtained by field observation, g represents the gradient of the P-wave and S-wave reflection coefficient model g pp And g ps , backwardderivative function representing automatic differentiation; Further, the fifth step, using the Adam optimization algorithm formula (5) in deep learning, respectively, the gradient of the P-wave and S-wave reflection coefficient model is optimized to obtain the optimized gradient, formula (5) g k The gradient before processing g pp And g ps , G k The gradient after processing G pp And G ps , And Respectively represent the average exponential decay rate of the control gradient term and the gradient square term, the value is , , s 0=0, r 0=0, Indicates that the corresponding elements are multiplied, is a very small constant, the value is 1x10 -10 , the formula (5) is: ; Using formula (6), update the P-wave and S-wave reflection coefficient model, and then repeat the above steps until the result reaches the accuracy requirement (generally 20 iterations), obtain the final migration imaging result as shown in Figures 10A-10B , I Represent I pp And I ps , α The model update amount is 0.25, and the formula (6) is: .

[0009] A VTI medium least square reverse time migration system suitable for Adam gradient optimization algorithm, the system comprises a real P-wave and S-wave reflection coefficient model construction module, a linearized forward module, a simulated seismic record obtaining module, a P-wave and S-wave reflection coefficient model gradient solving module and an accuracy checking and iteration instruction issuing module; The real P-wave and S-wave reflection coefficient model construction module runs the first step of the VTI medium least square reverse time migration method suitable for Adam gradient optimization algorithm; The linearized forward module runs the second step of the VTI medium least square reverse time migration method suitable for Adam gradient optimization algorithm; The obtaining analog seismic record module runs the third step in the VTI medium least square reverse time migration method suitable for the Adam gradient optimization algorithm; The gradient solving module of the P-S wave reflection coefficient model runs the fourth step in the VTI medium least square reverse time migration method suitable for the Adam gradient optimization algorithm; The precision checking and iteration instruction issuing module runs the fifth step in the VTI medium least square reverse time migration method suitable for the Adam gradient optimization algorithm.

[0010] Compared with the prior art, the method constructs a real P-S wave reflection coefficient model in theory, expresses the least square reverse time migration in RNN convolution and automatic differentiation in deep learning, and then updates the gradient by using the Adam gradient optimization algorithm in deep learning, so that the precision of gradient optimization is improved, the convergence speed of inversion is accelerated, time is saved, and the precision of least square reverse time migration imaging is finally significantly improved. BRIEF DESCRIPTION OF DRAWINGS

[0011] Figure 1 It is a conventional VTI medium least square reverse time migration method flowchart; Figure 2 It is a VTI medium least square reverse time migration method flowchart suitable for the Adam gradient optimization algorithm; Figure 3A It is a BP model diagram of Vp Figure 3B It is a BP model diagram of Vs Figure 3C It is a BP model diagram of Figure 3D It is a BP model diagram of Figure 3E It is a BP model diagram of Figure 4A It is a real reflection coefficient model diagram of Ipp; Figure 4B It is a real reflection coefficient model diagram of Ips; Figure 5 It is a simulated seismic record diagram; Figure 6 It is a real seismic record diagram; Figure 7A It is a conventional VTI medium least square reverse time migration gradient profile diagram of Ipp; Figure 7B It is a conventional VTI medium least square reverse time migration gradient profile diagram of Ips; Figure 8A ​​VTI medium least square reverse time migration gradient profile for Ipp suitable for Adam gradient optimization algorithm; Figure 8B VTI medium least square reverse time migration gradient profile for Ips suitable for Adam gradient optimization algorithm; Figure 9A Conventional VTI medium least square reverse time migration result map for Ipp; Figure 9B Conventional VTI medium least square reverse time migration result map for Ips; Figure 10A VTI medium least square reverse time migration result map for Ipp suitable for Adam gradient optimization algorithm; Figure 10B VTI medium least square reverse time migration result map for Ips suitable for Adam gradient optimization algorithm. DETAILED DESCRIPTION

[0012] The technical solutions of the present application are further explained below by examples in conjunction with the drawings, but the protection scope of the present application is not limited in any form by the examples.

[0013] The present application improves the conventional VTI medium least square reverse time migration imaging algorithm, theoretically constructs a real P-S wave reflection coefficient model, and solves the least square reverse time migration in RNN convolution and automatic differentiation in deep learning, and then updates the gradient by using the Adam gradient optimization algorithm in deep learning. Experiments prove that the present application solves the problem of slow gradient convergence, improves the precision of gradient optimization, saves time, and finally obtains more accurate least square reverse time migration results.

[0014] Example 1 The present application is described by taking a BP model (as shown in Figures 3A-3E ) as an example, the lateral length of the model is 6300m, the longitudinal depth is 1800m, and the grid step of the model x , z is 10m.

[0015] Based on the model, a total of 630 shots are performed, the shot points are uniformly distributed above the model with an interval of 10m, 630 geophones are set, and the geophones are also uniformly distributed above the model with an interval of 10m, and the depth of the shot points and the geophones is 0m.

[0016] The specific embodiment of the present application is described in detail below, and the flow is as shown in Figure 2 , and the specific steps are as follows: Firstly, a BP model with a lateral length of 6300m and a longitudinal depth of 1800m is obtained Vp ,x , z ), Vs ( x , z ), p ( x , z and anisotropy parameters e ( x , z )and d ( x , z )(like Figures 3A-3E (As shown) Meshization, Model x , z The grid step size is 10m in all directions. Based on the given BP model, the Thomson parameter model can be easily calculated using empirical algorithms. C 11 ( x , z ), C 13 ( x , z ), C 33 ( x , z )and C 55 ( x , z ),in x , z Represents spatial location coordinates, ( x =1, 2, 3, … , 630 , z =1, 2, 3, … , 180 , ) C 33 ( x , z )and C 55 ( x , z It is usually defined as a conventional approximate P-wave and S-wave reflection coefficient model; using equation (1) to... C 33 ( x , z )and C 55 ( x , z The model was modified to obtain the true P-wave and S-wave reflection coefficient model, as shown below. Figures 4A-4B As shown, where, I pp and I psThese represent the actual P-wave and S-wave reflection coefficient models, respectively. C 0 33 and C 0 and 55 represent the background speed, which are respectively C 33 and C 55 After Gaussian smoothing, the formula (1) is: ; Step 2: Utilizing the Thomson parameter model C 11 ( x , z ), C 13 ( x , z ), C 33 ( x , z )and C 55 ( x , z ) and P-wave and S-wave reflection coefficient models I pp and I ps Based on the first-order stress-velocity elastic wave formula (2) for VTI medium, a linearized forward model is performed. In the first iteration, the reflection coefficient model is used. I pp and I ps The initial values ​​are all set to 0, where Indicates the density of the medium. u x , u z They represent x , z The velocity component in the direction; , They represent x , z Normal stress components in the direction, Represents the shear stress components. f x and f z As the earthquake source, formula (2) is: ; The third step, forward modeling, can be equivalent to the operation of convolution kernels in an RNN neural network. Using formula (3), the linearized forward modeling is expressed in the form of RNN convolution in a deep learning framework to obtain the simulated seismic record of the linearized forward modeling. d sny Take a record of an earthquake as follows:Figure 5 As shown, where, t B represents the moment. u x , u z , , , , f represent f x and f z The formula (3) is: ; Step 4: Use formula (4) to process the simulated earthquake records. d sny Compared with actual earthquake records d obs (Take an actual earthquake record from one shot, such as...) Figure 6 (As shown) A target function is established by subtraction, and the target function is expressed in the framework of automatic differentiation in deep learning. The gradient of the P-wave and S-wave reflection coefficient model is obtained by solving the target function using automatic differentiation. The actual seismic records... d obs Obtained from field observations, g Gradient of the model representing the longitudinal and transverse wave reflection coefficients g pp and g ps ,like Figures 7A-7B As shown, backward The formula (4) represents the automatic differentiation function, and is: ; Step 5: Using the Adam optimization algorithm formula (5) in deep learning, optimize the gradients of the P-wave and S-wave reflection coefficient models respectively, and obtain the optimized gradients as follows: Figures 8A-8B As shown, in formula (5) g k Gradient before processing g pp and g ps , G k Represents the gradient after optimization. G pp and G ps , and These represent the hyperparameters that control the average exponential decay rate of the gradient term and the squared gradient term, respectively, and are typically set to values ​​of [value missing]. , , s 0=0, r 0=0, This indicates element-wise multiplication. It is an extremely small constant, typically taking the value 1 × 10⁻⁶. -10 The formula (5) is: ; Using formula (6), update the P-wave and S-wave reflection coefficient models, and then repeat the above steps until the results meet the accuracy requirements (generally 20 iterations are sufficient), to obtain the final migration imaging results as shown in the figure. Figures 10A-10B As shown, I represent I pp and I ps , α The model update amount is set to 0.25 here, and the formula (6) is: .

[0017] To demonstrate the beneficial effects of the method described in this invention, it is compared here with the conventional VTI medium least squares reverse time migration method (process as follows). Figure 1 Compare the offset results obtained (as shown in the figure). Figures 9A-9B The results are from the least-squares reverse-time migration of a conventional VTI medium. Figures 10A-10B Comparing the two figures, we can see that the least squares reverse time migration (LSTM) results for VTI media obtained by the proposed method have a clearer structure and stronger continuity of the phase axis, resulting in a significant improvement in the overall accuracy of the imaging results. This demonstrates that the proposed method provides a better solution for least squares reverse time migration of VTI media.

[0018] Example 2 This embodiment provides a system for running the method described in Embodiment 1. The system includes a module for constructing a real P-wave and S-wave reflection coefficient model, a linearization forward modeling module, a module for obtaining simulated seismic records, a gradient solution module for the P-wave and S-wave reflection coefficient model, and a gradient optimization and update module. The module for constructing the real P-wave and S-wave reflection coefficient model runs the first step of the VTI medium least squares reverse time migration method applicable to the Adam gradient optimization algorithm. The linearized forward modeling module described above performs the second step of the VTI medium least squares inverse time migration method applicable to the Adam gradient optimization algorithm; The module for obtaining simulated seismic records performs the third step of the VTI medium least squares reverse time migration method applicable to the Adam gradient optimization algorithm. The gradient solution module of the P-wave and S-wave reflection coefficient model runs the fourth step of the VTI medium least squares reverse time migration method applicable to the Adam gradient optimization algorithm; The gradient optimization update module performs step 5 of the VTI medium least squares reverse time migration method applicable to the Adam gradient optimization algorithm.

Claims

1. A least-squares reverse-time migration method for VTI media suitable for the Adam gradient optimization algorithm, characterized in that, The method is as follows: The first step is to construct a realistic P-wave and S-wave reflection coefficient model, replacing the conventional approximate P-wave and S-wave reflectivity model. C 33 and C 55 The true P-wave and S-wave reflection coefficient model is obtained by subtracting each coefficient from its own background velocity and then dividing the result by normalization. The second step is to perform a linearized forward modeling of the real longitudinal and transverse wave reflection coefficients from the first step, based on the first-order stress-velocity elastic wave equation of the VTI medium. The third step is to express the linearized forward modeling in the form of RNN convolution in a deep learning framework to obtain the simulated seismic record of the linearized forward modeling. The fourth step is to subtract the simulated seismic records obtained in the third step from the actual seismic records to establish the objective function; then, express the objective function in the framework of automatic differentiation in deep learning, and use automatic differentiation to solve the objective function to obtain the gradient of the P-wave and S-wave reflection coefficient model. The fifth step involves using the Adam gradient optimization algorithm in deep learning to optimize the gradient obtained in the fourth step, and then using the optimized gradient to update the true P-wave and S-wave reflection coefficient model from the first step until the accuracy requirements are met.

2. The VTI medium least squares reverse time migration method applicable to the Adam gradient optimization algorithm according to claim 1, characterized in that, The formula used in the first step is: (1), I pp and I ps These represent the actual P-wave and S-wave reflection coefficient models, respectively. C0 33 and C 0 and 55 represent the background speed, which are respectively C 33 and C 55 The result after Gaussian smoothing.

3. The VTI medium least-squares reverse time migration method applicable to the Adam gradient optimization algorithm according to claim 2, characterized in that, The second step involves using the Thomson parameter model. C 11 ( x , z ), C 13 ( x , z ), C 33 ( x , z )and C 55 ( x , z ) and the actual P-wave and S-wave reflection coefficient model I pp and I ps Based on the first-order stress-velocity elastic wave formula (2) for VTI medium, a linearized forward model is performed. In the first iteration, the reflection coefficient model is used. I pp and I ps The initial values ​​are all set to 0, where Indicates the density of the medium. u x , u z They represent x , z The velocity component in the direction, , They represent x , z Normal stress components in the direction, Represents the shear stress components. f x and f z As the earthquake source, formula (2) is: .

4. The VTI medium least squares reverse time migration method applicable to the Adam gradient optimization algorithm according to claim 3, characterized in that, In the third step, the forward modeling calculation is equivalent to the operation of the convolution kernel in an RNN neural network. Using formula (3), the linearized forward modeling is expressed in the form of RNN convolution in a deep learning framework to obtain the simulated seismic record of the linearized forward modeling. d sny ,in, t B represents the moment. u x , u z , , , f represents f x and f z The formula (3) is: .

5. The VTI medium least squares reverse time migration method applicable to the Adam gradient optimization algorithm according to claim 4, characterized in that, The fourth step involves using formula (4) to process the simulated earthquake records. d sny Compared with actual earthquake records d obs The objective function is established by taking the difference, and formula (4) is as follows: Among them, actual earthquake records d obs Obtained from field observations, g Gradient of the model representing the longitudinal and transverse wave reflection coefficients g pp and g ps , backward This indicates the function of automatic differentiation.

6. The VTI medium least-squares reverse time migration method applicable to the Adam gradient optimization algorithm according to claim 5, characterized in that, The fifth step involves using the Adam optimization algorithm formula (5) in deep learning to optimize the gradients of the P-wave and S-wave reflection coefficient models, respectively, to obtain the optimized gradients. In formula (5) g k Gradient before processing g pp and g ps , G k Represents the processed gradient G pp and G ps , and These represent the hyperparameters controlling the average exponential decay rate of the gradient term and the squared gradient term, respectively, and their values ​​are [values ​​to be filled in]. , , s 0=0, r 0=0, This indicates element-wise multiplication. It is an extremely small constant, with a value of 1 × 10⁻⁶. -10 Formula (5) is: ; Using formula (6), update the P-wave and S-wave reflection coefficient models, and then repeat the above steps until the results meet the accuracy requirements to obtain the final migration imaging results. I represent I pp and I ps , α The model update amount is set to 0.25 here, and the formula (6) is: .

7. A VTI medium least-squares reverse time migration system suitable for the Adam gradient optimization algorithm, characterized in that, The system includes a module for constructing a real P-wave and S-wave reflection coefficient model, a linearization forward modeling module, a module for obtaining simulated seismic records, a gradient solution module for the P-wave and S-wave reflection coefficient model, and a module for verifying accuracy and issuing iteration commands. The module for constructing a real P-wave and S-wave reflection coefficient model performs the first step of the VTI medium least squares reverse time migration method applicable to the Adam gradient optimization algorithm as described in any one of claims 1-6; The linearized forward modeling module performs the second step of the VTI medium least squares reverse time migration method applicable to the Adam gradient optimization algorithm as described in any one of claims 1-6; The module for obtaining simulated seismic records performs the third step of the VTI medium least squares reverse time migration method applicable to the Adam gradient optimization algorithm as described in any one of claims 1-6; The gradient solution module of the P-wave and S-wave reflection coefficient model performs the fourth step of the VTI medium least squares reverse time migration method applicable to Adam gradient optimization algorithm as described in any one of claims 1-6; The verification accuracy and the iteration instruction module execute the fifth step of the VTI medium least squares reverse time migration method applicable to Adam gradient optimization algorithm as described in any one of claims 1-6.

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