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

Abstract

The application 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. C 33 And C 55 After being subtracted from and divided by the background velocity respectively, normalization processing is performed to construct a real P-S wave reflectivity model. Linearization forward modeling is performed on the basis of a first-order stress velocity elastic wave equation of a VTI medium. The linearization forward modeling is expressed in the form of RNN convolution in a deep learning framework to obtain simulated seismic records of the linearization forward modeling. A target function is established by subtracting the simulated seismic records from actual seismic records. An Adam gradient optimization algorithm in deep learning is used to optimize the gradient, and the P-S wave reflectivity model is updated by using the optimized gradient until the accuracy requirement is met. The application improves the accuracy of gradient optimization, solves the problem of extremely slow convergence, and finally obtains more accurate least square reverse time migration results.

Description

Technical Field

[0001] This invention belongs to the field of seismic migration imaging, specifically relating to a VTI medium least squares reverse time migration method and system suitable for the Adam gradient optimization algorithm. Background Technology

[0002] Least squares reverse time migration (LSTM) can solve the imaging problem of reverse time migration as a least squares inversion problem. It uses an iterative algorithm to find an imaging result that best matches the observed seismic data. It has advantages such as suppressing migration noise, improving deep imaging, enhancing the continuity and uniformity of phase axes, and improving amplitude fidelity. Therefore, LSTM has great potential for future practical applications. However, most conventional LSTM methods are based on isotropic media for inversion, while real subsurface media often exhibit anisotropic characteristics. LSTM based on the isotropic media assumption does not reflect reality. Therefore, LSTM based on the anisotropic parameters of VTI media, which better reflects actual geological conditions, has become a research hotspot in the field of geophysics.

[0003] In VTI medium least-squares reverse time migration imaging, the conventional migration imaging target is often composed of... C 33 and C 55 An approximation, it is not a true model of the P-wave and S-wave reflection coefficients, and because... C 33 and C 55 The magnitude of these reflections is extremely large, and their convergence is very slow, resulting in poor migration imaging results that often fail to meet the imaging accuracy requirements of industry. Therefore, it is extremely important to reconstruct suitable P-wave and S-wave reflection coefficient models and select appropriate acceleration and optimization algorithms. Summary of the Invention

[0004] This invention addresses the aforementioned technical problems by providing a least-squares reverse-time migration method for VTI media suitable for the Adam gradient optimization algorithm. The method theoretically constructs a model of the true P-wave and S-wave reflection coefficients and solves the least-squares reverse-time migration expression in RNN convolution and automatic differentiation in deep learning. Then, the gradient is updated using the Adam gradient optimization algorithm in deep learning, which solves the problem of slow convergence and finally obtains more accurate least-squares reverse-time migration results.

[0005] This invention is achieved through the following technical solution:

[0006] A least-squares reverse-time migration method for VTI media suitable for the Adam gradient optimization algorithm is described below:

[0007] 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.

[0008] 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.

[0009] 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.

[0010] 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.

[0011] The fifth step is to optimize the gradient obtained in the fourth step using the Adam gradient optimization algorithm in deep learning, and then use the optimized gradient to update the true P-wave and S-wave reflection coefficient model in the first step until the accuracy requirements are met (generally, 20 iterations are sufficient).

[0012] Furthermore, 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.

[0013] Furthermore, in the second step, the Thomson parameter model is used. 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: .

[0014] Furthermore, 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: ;

[0015] Furthermore, in the fourth step, the simulated earthquake record is processed using formula (4). 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, gGradient of the model representing the longitudinal and transverse wave reflection coefficients g pp and g ps , backward This indicates the function of automatic differentiation;

[0016] Furthermore, in the fifth step, the gradients of the P-wave and S-wave reflection coefficient models are optimized using the Adam optimization algorithm formula (5) in deep learning 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 The formula (5) is: ;

[0017] 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: .

[0018] A VTI medium least squares reverse time migration system suitable for Adam gradient optimization algorithm, 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.

[0019] The module for constructing a 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.

[0020] 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;

[0021] 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.

[0022] 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;

[0023] The verification accuracy and the execution of the iteration command module are described in the fifth step of the VTI medium least squares reverse time migration method applicable to the Adam gradient optimization algorithm.

[0024] The beneficial effects of this invention compared with the prior art are as follows: The method of this invention theoretically constructs a true P-wave and S-wave reflection coefficient model, and solves the least squares reverse time migration expression in RNN convolution and automatic differentiation in deep learning. Then, the gradient is updated using the Adam gradient optimization algorithm in deep learning, which improves the accuracy of gradient optimization, speeds up the inversion convergence speed, saves time, and ultimately significantly improves the accuracy of least squares reverse time migration imaging. Attached Figure Description

[0025] Figure 1 The flowchart is for the least squares reverse time migration method for conventional VTI media.

[0026] Figure 2 The flowchart shows the VTI medium least squares reverse time migration method applicable to the Adam gradient optimization algorithm;

[0027] Figure 3A for Vp BP model diagram;

[0028] Figure 3B for Vs BP model diagram;

[0029] Figure 3C The BP model diagram for ρ;

[0030] Figure 3D The BP model diagram for ε;

[0031] Figure 3E The BP model diagram for δ;

[0032] Figure 4AThis is a diagram of the true reflection coefficient model for Ipp;

[0033] Figure 4B This is a diagram of the true reflection coefficient model of Ips;

[0034] Figure 5 To simulate earthquake record diagrams;

[0035] Figure 6 This is a map showing actual earthquake records;

[0036] Figure 7A Least-square reverse-time migration gradient profile for conventional VTI media of Ipp;

[0037] Figure 7B Least-square inverse time migration gradient profile of conventional VTI medium for Ips;

[0038] Figure 8A A VTI medium least-squares reverse-time migration gradient profile for Ipp suitable for Adam gradient optimization algorithm;

[0039] Figure 8B VTI medium least-squares inverse time-shifted gradient profile for Ips applicable to Adam gradient optimization algorithm;

[0040] Figure 9A The results of least-squares reverse time migration for Ipp in conventional VTI media are shown in the figure.

[0041] Figure 9B The least-squares reverse time migration results for Ips in conventional VTI media are shown in the figure.

[0042] Figure 10A The least-squares reverse time migration result for VTI medium suitable for Adam gradient optimization algorithm for Ipp;

[0043] Figure 10B The image shows the VTI medium least-squares reverse time migration results for Ips, applicable to the Adam gradient optimization algorithm. Detailed Implementation

[0044] The technical solution of the present invention will be further explained below with reference to the embodiments and accompanying drawings, but the scope of protection of the present invention is not limited in any way by the embodiments.

[0045] This invention improves the conventional least-squares reverse-time migration imaging algorithm for VTI media. It theoretically constructs a model of the true P-wave and S-wave reflection coefficients and solves the least-squares reverse-time migration expression in RNN convolution and automatic differentiation in deep learning. Then, it uses the Adam gradient optimization algorithm in deep learning to update the gradient. Experiments show that this method solves the problem of slow gradient convergence, improves the accuracy of gradient optimization, saves time, and finally obtains more accurate least-squares reverse-time migration results.

[0046] Example 1

[0047] This invention takes the BP model as an example (e.g.) Figures 3A-3E As shown in the figure, the model has a horizontal length of 6300m and a vertical depth of 1800m. x , z The grid step size for each direction is 10m.

[0048] Based on this model, a total of 630 shots were fired. The shot points were evenly distributed above the model at 10m intervals. 630 receiver points were also evenly distributed above the model at 10m intervals. The depth of both shot points and receiver points was 0m.

[0049] The specific embodiments of the present invention are described in detail below, and the process is as follows: Figure 2 As shown, the specific steps are as follows:

[0050] The first step is to construct a BP model with a horizontal length of 6300m and a vertical depth of 1800m. Vp ( x , z ), Vs ( x , z ), ρ ( x , z and anisotropy parameters ε ( x , z )and δ ( 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 ), C33 ( 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 ps These 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: ;

[0051] 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 modelsI 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: ;

[0052] 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: ;

[0053] 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 as follows) 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: ;

[0054] 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: ;

[0055] 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: .

[0056] 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.

[0057] Example 2

[0058] 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.

[0059] 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;

[0060] 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.

[0061] 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;

[0062] 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 convolutions within a deep learning framework to obtain the simulated seismic records of the linearized forward modeling. The forward modeling simulation 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 convolutions within a deep learning framework to obtain the simulated seismic records 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: ; The fourth step involves subtracting the simulated seismic records obtained in the third step from the actual seismic records to establish an objective function. This objective function is then expressed within the framework of automatic differentiation techniques in deep learning. The gradient of the P-wave and S-wave reflection coefficient model is obtained by solving the objective function using automatic differentiation techniques. Finally, formula (4) is used to convert the simulated seismic 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; 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. and For the background velocity, they 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, 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 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 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: .

5. 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 1-4; 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 1-4; 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 1-4; 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 1-4. 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 1-4.

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