A full waveform inversion method optimized by multi-scale deep learning

Abstract

This invention discloses a multi-scale deep learning-optimized full waveform inversion method. It utilizes a deep neural network to represent the parameters to be inverted and employs a traditional high-performance computing scheme for full waveform inversion based on a convolutional objective function to calculate the gradient. The gradient of the inversion parameters is then input into the deep convolutional neural network model to achieve multi-scale inversion. Simultaneously, a deep learning optimization method is used to represent the inversion parameters at different scales, effectively ensuring that the deep convolutional neural network model simultaneously represents inversion parameter information at multiple scales. Furthermore, this invention introduces a first-order variable-density velocity-stress equation as the forward propagation wavefield. This equation not only possesses high simulation accuracy but also adaptively considers density variations in the subsurface medium, providing direct physical information on velocity and density. This achieves simultaneous modeling of velocity and density, ultimately improving the efficiency, accuracy, and stability of the entire full waveform inversion.

Description

Technical Field

[0001] This invention relates to a method for imaging rock physical parameters of underground media, specifically a multi-scale deep learning optimized full waveform inversion method, which belongs to the interdisciplinary field of deep learning and seismic exploration velocity modeling technology. Background Technology

[0002] Full waveform inversion is a hot topic in seismic exploration, playing a crucial role in high-precision oil and gas resource exploration. Over the past few decades, full waveform inversion techniques based on classical numerical solutions have matured, achieving significant progress in both computational efficiency and accuracy. In recent years, with the rapid development of artificial intelligence, the cross-integration of deep learning and full waveform inversion techniques has become a growing trend.

[0003] Currently, the application of deep learning technology in full waveform inversion mainly falls into three categories: 1. Data-driven full waveform inversion methods, which require training with large sample data; 2. Deep learning-optimized full waveform inversion, which uses deep learning optimization and network automatic differentiation techniques to solve the accurate wave equation inversion problem; 3. Physical information full waveform inversion, which mainly uses the wave equation as a constraint term and trains the network using spatially discrete wave field values ​​to achieve the simulation and inversion of the equation. Among these research directions, the second point has the potential to introduce classical full waveform inversion techniques and optimize them within a deep learning framework to achieve high-precision inversion.

[0004] Effectively utilizing appropriate network architectures to represent inversion parameter models in deep learning optimization is a key approach to achieving high-precision inversion. Since full waveform inversion is a wide-wavenumber reconstruction process, the aforementioned deep learning optimization strategies cannot address the lack of rich low-to-medium wavenumber information in the initial model, leading to poor inversion quality and insufficient resolution. Even though classic full waveform inversion incorporates multi-scale inversion strategies, it is difficult to effectively integrate multi-scale objective functions, rendering these strategies unusable directly. Furthermore, when using deep networks to represent inversion parameter models, how to enable the network to effectively represent inversion parameter information at multiple scales simultaneously is a problem worthy of in-depth consideration. Additionally, current deep learning-based full waveform inversion cannot simultaneously model velocity and rock density, complicating the inversion process. Velocity inversion also requires extensive network parameter storage, ultimately hindering improvements in the overall efficiency and stability of full waveform inversion. Summary of the Invention

[0005] To address the problems of the existing technologies, this invention provides a multi-scale deep learning-optimized full waveform inversion method. It utilizes a deep neural network to represent the parameters to be inverted and employs a traditional high-performance computing scheme for full waveform inversion based on a convolutional objective function to calculate the gradients. The gradients of the inversion parameters are then input into the deeply trained network to achieve multi-scale inversion. Simultaneously, a deep neural network-based segmented inversion parameter representation method is adopted, effectively ensuring that the deep network simultaneously represents inversion parameter information at multiple scales. Furthermore, by introducing a first-order variable-density velocity-stress equation, simultaneous modeling of velocity and density is achieved, thereby simplifying the inversion process and improving the efficiency and stability of the entire full waveform inversion.

[0006] To achieve the above objectives, the technical solution adopted by this invention is: a multi-scale deep learning optimized full waveform inversion method, the specific steps of which are as follows:

[0007] A. First, determine the area to be inverted, and then use the observation system to obtain observation data;

[0008] B. Construct the forward propagation wave field equation, which is a two-dimensional first-order variable density acoustic wave equation.

[0009] C. Construct a convolution objective function, which has good robustness;

[0010] D. Based on the forward propagation wavefield equation in step B and the convolution objective function in step C, determine the inverse propagation wavefield equation of the convolution objective function based on adjoint theory.

[0011] E. Construct the gradient of the model parameters in the convolution objective function using the forward propagation wave field from step B and the reverse propagation wave field from step D. The gradient consists of the gradient of velocity and the gradient of density.

[0012] F. Establish a deep convolutional neural network model, which includes velocity model parameters and density model parameters. The deep convolutional neural network model is used for mapping from random feature variables to multiple physical parameters.

[0013] G. Input the gradient of the model parameters in step E into the gradient of the last layer in the deep convolutional neural network model in step F;

[0014] H. The deep convolutional neural network model in step G is optimized using deep learning optimization methods. The gradient of the model parameters is backpropagated to the correction amount of the network parameters by training the deep convolutional neural network model to achieve full waveform inversion. Finally, the inverted velocity inversion result and density inversion result are obtained.

[0015] I. Set multiple master frequency parameters. Within the frequency band of each master frequency parameter, use a convolutional objective function to obtain the gradient corresponding to the current master frequency parameter. Repeat steps E to H for the gradients corresponding to each master frequency parameter to achieve full waveform inversion of features at different scales.

[0016] Furthermore, the two-dimensional first-order variable-density acoustic wave equation in step B is specifically as follows:

[0017]

[0018] Where, ψ=[σ,v] T These are the variables of the propagating wave field, σ is the particle vibration stress corresponding to the propagating wave field, and v = [v x ,v z [] represents the vibrational velocity of a particle along the x and z directions, and s is the source term. This represents the partial derivative with respect to time t, where T denotes the transpose of the matrix, and the linking matrix... ρ represents the density of the medium, and v represents the velocity of the medium. and This indicates taking the partial derivatives with respect to x and z.

[0019] Furthermore, the convolution objective function in step C is specifically:

[0020]

[0021] Where d is the observed data, v is the synthetic wavefield data, and x is the synthetic wavefield data. r and x ref These represent the positions of the detector point and the reference trace, respectively, with spatial coordinates x = [x, z] and model parameters m = [v, ρ]. T .

[0022] Furthermore, the backpropagation wavefield equation in step D is specifically as follows:

[0023]

[0024] Among them, the reverse propagation wave field in It is the particle vibration stress corresponding to the reverse propagating wave field. and This represents the vibrational velocity of a particle along the x and z directions. It is the reverse source term, and * indicates the convolution operation. This indicates a cross-correlation operation.

[0025] Furthermore, the gradient of the model parameters in step E is specifically as follows:

[0026]

[0027] in It is the gradient of velocity. It is the density gradient.

[0028] Furthermore, the deep convolutional neural network model in step F is specifically as follows:

[0029]

[0030] Where, the model parameter γ = v or ρ, The deep convolutional neural network model is used to represent the model parameters γ, where θ represents the network parameters, L represents the total number of layers in the neural network, and W represents the network parameters. l and b l λ represents the weights and biases of a convolutional or fully connected layer, where the subscripts l∈[1,L], l∈Z, and λ represents the random feature vector of the network input.

[0031] Furthermore, step G specifically involves: first assigning the gradient of the model parameters from step E to the gradient of the network parameters of the last layer, and specifying the initial velocity, density values, and gradient, using the following formula:

[0032]

[0033] Among them, v ini and ρ ini These represent the initial velocity and density, respectively.

[0034] Furthermore, the specific process of training the deep convolutional neural network model to achieve full waveform inversion in step H is as follows: First, the observed data is used as a random feature variable λ, the deep convolutional neural network model is used to represent the model parameters γ, and the external model parameter gradient is input. Optimization iterations are performed using deep learning optimization methods to modify the parameters θ of the deep convolutional neural network model. γ This allows us to represent the updated model parameters γ, and obtain the gradients of the model parameters through high-performance computing. Further optimization and correction of the deep convolutional network model parameters θ γ The process continues until the set number of iterations is reached or the objective function value meets the accuracy requirements. The output of the deep convolutional network model is then used as the final inverted model parameter γ.

[0035] Compared with the prior art, the present invention has the following advantages:

[0036] (1) This invention uses a deep neural network to represent the parameters to be inverted, and uses a traditional full-waveform inversion high-performance computing scheme based on a convolutional objective function to calculate the gradient. The gradient of the inversion parameters is then input into the deep convolutional neural network model to achieve multi-scale inversion. At the same time, a deep learning optimization method is adopted to represent the inversion parameters at different scales, which effectively ensures that the deep convolutional neural network model represents the inversion parameter information at multiple scales at the same time, thus realizing the multi-scale inversion function. This can overcome or alleviate the fundamental low-frequency dependence problem in full-waveform inversion and significantly improve the accuracy of parameter modeling.

[0037] (2) In the process of inversion at different scales, the present invention performs independent representation of the changes in model parameters within the frequency band corresponding to each scale, avoiding the problem that the features of certain scales are difficult to obtain accurately when learning multiple frequency bands continuously, thereby ensuring multi-scale feature learning under deep learning optimization and effectively improving the inversion accuracy.

[0038] (3) This invention uses the first-order variable density velocity-stress equation as the forward propagation wave field, then constructs a convolutional objective function and determines the corresponding reverse propagation wave field. Finally, deep learning optimization is used to realize the full waveform inversion based on the convolutional objective function, and multi-scale inversion is performed under the first-order variable density velocity-stress equation, realizing simultaneous modeling of velocity and density. Since this invention directly adopts the first-order variable density velocity-stress equation, this equation not only has high simulation accuracy, but also can adaptively consider the density changes in the underground medium, and can provide direct physical information on velocity and density for the underground medium, thereby simplifying the inversion process and improving the efficiency and stability of the entire full waveform inversion. Attached Figure Description

[0039] Figure 1 This is a schematic diagram of the deep learning optimized network architecture of the present invention;

[0040] Figure 2 This is a flowchart illustrating the deep learning optimization inversion algorithm of this invention;

[0041] Figure 3 These are the actual model parameters in this invention;

[0042] Where (a) and (b) are the actual velocity and density, respectively;

[0043] Figure 4 These are the initial model parameters in this invention;

[0044] Where (a) and (b) are the initial velocity and density, respectively;

[0045] Figure 5 This is the single-scale inversion result optimized by deep learning in this invention;

[0046] Where (a) and (b) are the single-scale velocity and density inversion results optimized by deep learning, respectively;

[0047] Figure 6 This is the multi-scale inversion result optimized by deep learning in this invention;

[0048] Where (a) and (b) are the multi-scale speed and density inversion results optimized by deep learning, respectively;

[0049] Figure 7 This is the inversion result of the multi-scale deep learning optimization in this invention;

[0050] (a) and (b) are the speed and density inversion results of multi-scale deep learning optimization, respectively. Detailed Implementation

[0051] The present invention will be further described below.

[0052] like Figure 1 and 2 As shown, the specific steps of this invention are as follows:

[0053] A. First, determine the area to be inverted, and then use the observation system to obtain observation data;

[0054] B. Construct the forward propagation wavefield equation, which is a two-dimensional first-order variable-density acoustic wave equation, and the specific formula is as follows:

[0055]

[0056] Where, ψ=[σ,v] T These are the variables of the propagating wave field, σ is the particle vibration stress corresponding to the propagating wave field, and v = [v x ,v z [] represents the vibrational velocity of a particle along the x and z directions, and s is the source term. This represents the partial derivative with respect to time t, where T denotes the transpose of the matrix, and the linking matrix... ρ represents the density of the medium, and v represents the velocity of the medium. and This indicates taking the partial derivatives with respect to x and z;

[0057] C. Construct a convolution objective function, which has good robustness; the specific convolution objective function is as follows:

[0058]

[0059] Where d is the observed data, v is the synthetic wavefield data, and x is the synthetic wavefield data. r and x refThese represent the positions of the detector point and the reference trace, respectively, with spatial coordinates x = [x, z] and model parameters m = [v, ρ]. T ;

[0060] D. Based on the forward propagation wavefield equation from step B and the convolution objective function from step C, determine the inverse propagation wavefield equation of the convolution objective function using adjoint theory. The specific formula is as follows:

[0061]

[0062] Among them, the reverse propagation wave field in It is the particle vibration stress corresponding to the reverse propagating wave field. and This represents the vibrational velocity of a particle along the x and z directions. It is the reverse source term, and * indicates the convolution operation. Indicates cross-correlation operation;

[0063] E. Construct the gradients of the model parameters in the convolution objective function using the forward propagation wavefield from step B and the reverse propagation wavefield from step D. These gradients consist of the velocity gradient and the density gradient, specifically:

[0064]

[0065] in It is the gradient of velocity. It is the density gradient;

[0066] F. Establish a deep convolutional neural network model, which includes velocity model parameters and density model parameters. The deep convolutional neural network model is used for mapping from random feature variables to multiple physical parameters; specifically:

[0067]

[0068] Wherein, the model parameter γ = v or ρ, The deep convolutional neural network model is used to represent the model parameters γ, where θ represents the network parameters, L represents the total number of layers in the neural network, and W represents the network parameters. l and b l λ represents the weights and biases of a convolutional or fully connected layer, where the subscript l∈[1,L],l∈Z, and λ represents the random feature vector of the network input.

[0069] G. First, assign the gradient of the model parameters from step E to the gradient of the network parameters of the last layer, and specify the initial velocity, density values, and gradient. The specific formula is as follows:

[0070]

[0071] Among them, v ini and ρ ini These represent the initial velocity and density, respectively.

[0072] H. Optimize the model parameters of the deep convolutional neural network model from step G using a deep learning optimization method. The deep learning optimization method is one of RMSprop, Adagrad, ASGD, or Adam. The gradient of the model parameters is backpropagated to the correction amount of the network parameters by training the deep convolutional neural network model, achieving full waveform inversion. Specifically: First, the observed data is used as a random feature variable λ, and the deep convolutional neural network model is used to represent the model parameters γ, with the external model parameter gradient being passed in. Optimization iterations are performed using deep learning optimization methods to modify the parameters θ of the deep convolutional neural network model. γ This allows us to represent the updated model parameters γ, and obtain the gradients of the model parameters through high-performance computing. Further optimization and correction of the deep convolutional network model parameters θ γ The process continues until the set number of iterations is reached or the objective function value meets the accuracy requirements. The output is the representation result of the deep convolutional network model, which is the final inverted model parameter γ (i.e., the inversion result, including the inversion of velocity and density).

[0073] I. Different scales correspond to different principal frequencies. Therefore, multiple principal frequency parameters are set, and the features at different scales are the gradients corresponding to different principal frequency parameters. Thus, within the frequency band of each principal frequency parameter, a convolutional objective function is used to obtain the gradient corresponding to the current principal frequency parameter. Steps E to H are repeated for each principal frequency parameter's gradient, thereby achieving full waveform inversion of features at different scales. Simultaneously, to ensure the effectiveness of network learning, independent representation of model parameter changes is performed within each frequency band, thus avoiding the problem of inaccurate acquisition of features at certain scales when learning across multiple frequency bands continuously.

[0074] Experiments have shown that:

[0075] Numerical methods were used to test the inversion performance under deep learning optimization in single-scale and multi-scale modes, as well as the inversion performance under multi-scale deep learning optimization.

[0076] The method of the present invention employs, as follows Figure 1 The network architecture shown is in accordance with Figure 2Design an inversion framework. The deep convolutional neural network model of this invention represents the mapping from random variables to model parameters. The network output is directly added to the initial model to output the model parameters. Utilizing external high-performance gradient calculation, multi-scale and network parameterized deep learning optimization inversion is achieved based on a convolutional objective function. This scheme mainly compares and tests the inversion effects of single-scale and multi-scale deep learning optimization, as well as the inversion effects of multi-scale deep learning optimization. The actual speed and density models tested are as follows: Figure 3 As shown in (a) and 3(b), the velocity and density of the initial model used for inversion are as follows: Figure 4 As shown in (a) and 4(b).

[0077] In the deep learning-optimized single-scale inversion, the dominant frequency is set to 10Hz, with 300 iterations. The other two inversion strategies employ the same multi-scale inversion strategy, which divides the inversion into three frequency bands with dominant frequencies of 8, 10, and 12Hz, and each band iterates 100 times. The multi-scale inversion is implemented by selecting several wavelets with increasing dominant frequencies and performing adaptive filtering based on a convolutional objective function. Figure 5 (a) and 5(b) represent the speed and density results of single-scale inversion optimized by deep learning. Figure 6 (a) and 6(b) represent the speed and density results of multi-scale inversion under deep learning optimization. Figure 7 (a) and 7(b) represent the inversion results of the multi-scale deep learning optimization of the present invention.

[0078] A comparison of the inversion results from the three methods clearly shows that the resolution of the single-scale inversion results under deep learning optimization is insufficient. The multi-scale inversion process under deep learning optimization introduces traditional multi-scale inversion strategies used to improve inversion accuracy into the deep learning-optimized inversion, but the multi-scale inversion results of this method are poor and do not significantly improve inversion accuracy. In contrast, this invention presents a multi-scale deep learning optimization inversion method based on a convolutional objective function and a two-dimensional first-order variable-density acoustic wave equation, which can significantly improve the resolution of the inversion results. Specifically, the inversion results using this method show a more uniform velocity distribution, a more pronounced low-velocity layer, a stronger three-dimensional structure of the density model, and richer wavenumber information. Conversely, the inversion results of the other two methods have larger inversion errors at deeper layers, and some interface structures lack low wavenumber information. The inversion results demonstrate that the inversion method proposed in this invention can effectively recover reliable and high-resolution model parameters from the background model. This also illustrates the advantages of the inversion results of this invention.

[0079] The above description is only a preferred embodiment of the present invention. It should be noted that for those skilled in the art, several improvements and modifications can be made without departing from the principle of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A multi-scale deep learning-optimized full waveform inversion method, characterized in that, The specific steps are as follows: A. First, determine the area to be inverted, and then use the observation system to obtain observation data; B. Construct the forward propagation wavefield equation, which is a two-dimensional first-order variable-density acoustic wave equation, specifically: Where, ψ=[σ,v] T These are the variables of the propagating wave field, σ is the particle vibration stress corresponding to the propagating wave field, and v = [v x ,v z [] represents the vibrational velocity of a particle along the x and z directions, and s is the source term. This represents the partial derivative with respect to time t, where T denotes the transpose of the matrix, and the linking matrix... ρ represents the density of the medium, and v represents the velocity of the medium. and This indicates taking the partial derivatives with respect to x and z; C. Construct a convolution objective function, which has good robustness; D. Based on the forward propagation wavefield equation in step B and the convolution objective function in step C, determine the inverse propagation wavefield equation of the convolution objective function based on adjoint theory. E. Construct the gradient of the model parameters in the convolution objective function using the forward propagation wave field from step B and the reverse propagation wave field from step D. The gradient consists of the gradient of velocity and the gradient of density. F. Establish a deep convolutional neural network model, which includes velocity model parameters and density model parameters. The deep convolutional neural network model is used for mapping from random feature variables to multiple physical parameters. G. First, assign the gradient of the model parameters from step E to the gradient of the network parameters of the last layer in the deep convolutional neural network model from step F, and specify the initial velocity, density values, and gradient. The specific formula is as follows: Where θ represents the network parameters; v ini and ρ ini These represent the initial velocity and density, respectively; ▽χ v It is the gradient of velocity, ▽χ ρ It is the density gradient; H. The deep convolutional neural network model in step G is optimized using deep learning optimization methods. The gradient of the model parameters is backpropagated to the correction amount of the network parameters by training the deep convolutional neural network model to achieve full waveform inversion. Finally, the inverted velocity inversion result and density inversion result are obtained. I. Set multiple master frequency parameters. Within the frequency band of each master frequency parameter, use a convolutional objective function to obtain the gradient corresponding to the current master frequency parameter. Repeat steps E to H for the gradients corresponding to each master frequency parameter to achieve full waveform inversion of features at different scales.

2. The multi-scale deep learning optimized full waveform inversion method according to claim 1, characterized in that, The specific convolution objective function in step C is: Where d is the observed data, v is the synthetic wavefield data, and x is the synthetic wavefield data. r and x ref These represent the positions of the detector point and the reference trace, respectively, with spatial coordinates x = [x, z] and model parameters m = [v, ρ]. T .

3. The multi-scale deep learning optimized full waveform inversion method according to claim 2, characterized in that, The backpropagation wavefield equation in step D is specifically as follows: Among them, the reverse propagation wave field in It is the particle vibration stress corresponding to the reverse propagating wave field. and This represents the vibrational velocity of a particle along the x and z directions. It is the reverse source term, and * indicates the convolution operation. This indicates a cross-correlation operation.

4. The multi-scale deep learning optimized full waveform inversion method according to claim 3, characterized in that, The gradient of the model parameters in step E is specifically as follows: Among them, ▽χ v It is the gradient of velocity, ▽χ ρ It is the density gradient.

5. The multi-scale deep learning optimized full waveform inversion method according to claim 4, characterized in that, The deep convolutional neural network model in step F is specifically as follows: Wherein, the model parameter γ = v or ρ, The deep convolutional neural network model is used to represent the model parameters γ, where θ represents the network parameters, L represents the total number of layers in the neural network, and W represents the network parameters. l and b l λ represents the weights and biases of a convolutional or fully connected layer, where the subscripts l∈[1,L], l∈Z, and λ represents the random feature vector of the network input.

6. The multi-scale deep learning optimized full waveform inversion method according to claim 3, characterized in that, The specific process of training the deep convolutional neural network model to achieve full waveform inversion in step H is as follows: First, the observed data is used as a random feature variable λ, and the deep convolutional neural network model is used to represent the model parameters γ. The external model parameter gradient ▽χ is then passed in. γ The deep convolutional neural network model parameters θ are modified through iterative optimization using deep learning optimization methods. γ This allows us to represent the updated model parameters γ, and obtain the gradient ▽χ of the model parameters through high-performance computing. γ Further optimization and correction of the deep convolutional network model parameters θ γ The process continues until the set number of iterations is reached or the objective function value meets the accuracy requirements. The output of the deep convolutional network model is then used as the final inverted model parameter γ.

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