Elastic wave field forward modeling acceleration method and system based on parallel one-dimensional transverse convolution

Abstract

The invention discloses an elastic wave field forward modeling acceleration method and system based on parallel one-dimensional transverse convolution. The method comprises the following steps: S1, constructing a one-dimensional transverse convolution kernel according to a finite difference coefficient; s2, on the basis of the one-dimensional transverse convolution kernel, executing one-dimensional transverse convolution operation on the input matrix, and calculating to obtain a partial derivative in the x direction; s3, through matrix transposition processing, data arrangement in the z direction is converted into continuous data in the row direction, one-dimensional transverse convolution operation is executed based on the transposed input matrix, and a partial derivative in the z direction is obtained through calculation; and S4, on the basis of the calculated partial derivatives in the x direction and the z direction, elastic wave field forward modeling is executed. According to the technical scheme, high arithmetic strength and high calculation efficiency of convolution in the GPU are fully utilized, and the problem that the GPU reads data slowly according to columns is solved by using a matrix transposition technology.

Description

Technical Field

[0001] This invention relates to the interdisciplinary field of earth science and computer technology, specifically to an accelerated method and system for forward modeling of elastic wave fields based on parallel one-dimensional transverse convolution. Background Technology

[0002] In the field of oil and gas exploration and development, forward numerical modeling is an important tool for understanding the wave propagation process in subsurface media, providing a scientific theoretical basis for finding underground oil and gas reservoirs. The Finite-Difference Time-Domain (FDTD) method is theoretically simple and provides accurate simulations, making it widely used in forward numerical modeling. In two-dimensional forward numerical modeling, the FDTD method typically discretizes the continuous space into numerous uniform and fine grid points, updating the wavefield for all grid points at each time step. This time-stepping iterative process of wavefield evolution requires a significant amount of computation time. Especially when the sampling time span is long, the number of time iterations required increases accordingly, leading to a corresponding increase in computation time. Furthermore, as the model size expands and the finite-difference order increases, the number of grid points needs to be increased to ensure imaging quality, further increasing computation time. The long computation time significantly impacts the real-time performance of forward modeling and hinders subsequent work. Therefore, researching ways to accelerate the computation speed of the FDTD method is of great significance.

[0003] Currently, there are three main methods to accelerate FDTD computation speed. (1) FDTD computation speed improvement method based on different grid partitioning schemes. Since time-iterative computation of wavefield is an inherent characteristic of the FDTD method, it is unavoidable. Domestic and foreign scholars use different grid partitioning schemes to reduce the number of grid points and reduce the amount of computation. The reduction of the number of grid points means that the FDTD computation accuracy will decrease. If you still want to maintain high-precision computation results, you often need to use a higher-order FDTD method or introduce other methods to improve accuracy. (2) FDTD computation speed improvement method based on parallelism. This method divides the computation domain into multiple subdomains by designing parallel algorithms or calling existing parallel computing libraries and assigns them to different processors (CPU or GPU) for processing to accelerate the computation speed of each time step in the FDTD method. However, this method requires complex boundary processing methods to avoid boundary errors between subdomains. (3) FDTD computation speed improvement method based on deep learning. This method uses deep learning methods to build a model and learns the simulated wavefield or seismic data generated by the FDTD method. The trained model can achieve rapid prediction of wavefield or seismic data without time-iterative computation. Deep learning relies on data to implicitly learn physical laws, but the network structure often lacks explicit modeling of physical constraints such as wave equations, which makes deep learning generally weaker than FDTD methods in wave field imaging accuracy.

[0004] Based on the above analysis, the main challenge of current elastic wave forward modeling is that while improving computational efficiency, it is impossible to guarantee the accuracy of numerical simulation.

[0005] Therefore, it is essential to design and develop a forward modeling method and system for elastic waves that achieves the same accuracy in numerical simulation as the traditional finite difference method, but with faster computation speed. Summary of the Invention

[0006] To address the technical problems mentioned above, the purpose of this invention is to provide an accelerated method and system for forward modeling of elastic wave fields based on parallel one-dimensional transverse convolution. The main contributions include: (1) Based on finite difference theory and convolution principles, the finite difference coefficients are used as the kernel weights of the one-dimensional transverse convolution operator, and the derivative calculation of the x-direction partial derivative in the first-order velocity-stress formula is achieved using the one-dimensional transverse convolution operator. (2) By analyzing the GPU data reading principle and convolution calculation logic, the matrix transpose technique is used to swap the rows and columns of the physical quantity storage matrix, improving data reading efficiency, and the one-dimensional transverse convolution operator is used to calculate the z-direction derivative. (3) The sliding calculation method of the one-dimensional transverse convolution operator is transformed into a parallel matrix multiplication, further improving the calculation speed.

[0007] To achieve the above objectives, this invention provides an accelerated method for elastic wavefield forward modeling based on parallel one-dimensional transverse convolution, comprising the following steps:

[0008] S1. Construct a one-dimensional transverse convolution kernel based on the finite difference coefficients;

[0009] S2. Based on the one-dimensional horizontal convolution kernel, perform a one-dimensional horizontal convolution operation on the input matrix to calculate the partial derivative in the x-direction;

[0010] S3. By transposing the matrix, the data arrangement in the z-direction is converted into continuous data in the row direction, and a one-dimensional horizontal convolution operation is performed based on the transposed input matrix to calculate the partial derivative in the z-direction.

[0011] S4. Based on the calculated partial derivatives in the x and z directions, perform forward modeling of the elastic wave field.

[0012] Preferably, S1 includes:

[0013] Dividing the finite difference coefficients by the spatial step size Δx yields the weights of the one-dimensional transverse convolution kernel;

[0014] Based on the finite difference order n, the convolution kernel size is set to 1×n;

[0015] The weights of the one-dimensional horizontal convolution kernel are difference coefficients.

[0016] Preferably, S2 includes:

[0017] A one-dimensional horizontal convolution kernel is used as a sliding window, which slides row by row and column by column starting from the top left corner of the input matrix.

[0018] During each sliding process, the region covered by the convolution kernel is multiplied element-wise with the kernel weights and then summed.

[0019] The result of each calculation is used as the corresponding element of the partial derivative matrix to obtain the first-order partial derivative in the x-direction.

[0020] Preferably, S3 includes:

[0021] Perform a matrix transpose operation on the input matrix to convert the data in the column direction into a continuous row direction;

[0022] Perform a one-dimensional horizontal convolution operation on the transposed matrix to obtain an intermediate result;

[0023] Perform a matrix transpose operation on the intermediate result again to obtain the partial derivative in the z-direction.

[0024] Preferably, the method further includes: converting the sliding calculation method of the one-dimensional horizontal convolution into parallel matrix multiplication to accelerate the convolution calculation process.

[0025] Preferably, the step of converting the sliding computation method of the one-dimensional lateral convolution into parallel matrix multiplication includes:

[0026] Set the one-dimensional horizontal convolution kernel as a row vector;

[0027] Extract the region covered by each sliding step of the convolution in the input matrix into a column vector;

[0028] The row vector is multiplied by multiple column vectors in parallel to obtain the convolution result matrix.

[0029] The present invention also provides an elastic wave field forward modeling acceleration system based on parallel one-dimensional transverse convolution. The system is used to implement the above method and includes: a construction module, a first calculation module, a second calculation module, and a forward modeling module.

[0030] The construction module is used to construct a one-dimensional transverse convolution kernel based on finite difference coefficients;

[0031] The first calculation module is used to perform a one-dimensional horizontal convolution operation on the input matrix based on the one-dimensional horizontal convolution kernel, and calculate the partial derivative in the x-direction;

[0032] The second calculation module is used to convert the data arrangement in the z direction into continuous data in the row direction through matrix transpose processing, and to perform a one-dimensional horizontal convolution operation based on the transposed input matrix to calculate the partial derivative in the z direction.

[0033] The forward modeling module is used to perform forward modeling simulations of elastic wave fields based on the calculated partial derivatives in the x and z directions.

[0034] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0035] This invention fully leverages the high arithmetic strength and computational efficiency of convolution in GPUs, and uses matrix transpose technology to solve the problem of slow column-wise data reading in GPUs. The original process of calculating x-direction partial derivatives by reading data row-wise and z-direction partial derivatives by reading data column-wise is unified into calculating x and z-direction partial derivatives by reading data row-wise. This ensures a sufficient supply of data during convolution calculations, greatly maximizing the computational efficiency of one-dimensional lateral convolution, and a parallel matrix multiplication method is designed to further improve the speed of convolution calculations. This invention demonstrates high computational efficiency while maintaining numerical simulation accuracy consistent with traditional methods, providing reliable and efficient forward modeling technology support for subsequent full-waveform inversion. Attached Figure Description

[0036] To more clearly illustrate the technical solution of the present invention, the drawings used in the embodiments are briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0037] Figure 1 This is a schematic diagram of the method flow according to an embodiment of the present invention;

[0038] Figure 2 This is a schematic diagram illustrating the principle of calculating the partial derivative of one-dimensional lateral convolution in an embodiment of the present invention.

[0039] Figure 3 This is a schematic diagram illustrating the parallel computation principle of the general matrix multiplication implementation in this invention.

[0040] Figure 4 These are simple and complex elastic wave velocity models from embodiments of the present invention. Figure 4 In the diagram, (a) represents the simple velocity model; (b) represents the original size Marmousi model.

[0041] Figure 5 This is a comparison of the numerical simulation accuracy of the embodiments of the present invention with that of traditional finite difference methods; Figure 5 In the figure, (a) represents the comparison of numerical simulation results of the Vz component wave field with the traditional method; (b) represents the comparison of numerical simulation results of the Vx component wave field with the traditional method.

[0042] Figure 6 This invention demonstrates the computational efficiency of different sampling times in a simple elastic wave velocity model. Figure 6In the figure, (a) represents the average time consumption of the convolution method and the FDTD method under different numerical simulation accuracies; (b) represents the average time saving and time efficiency improvement of the convolution method under different numerical simulation accuracies.

[0043] Figure 7 This invention demonstrates the computational efficiency of different differential accuracies in a simple elastic wave velocity model. Figure 7 In the table, (a) represents the average time consumption of the convolution method and the traditional method at different sampling times; (b) represents the average time saving and time efficiency improvement of the convolution method at different sampling times.

[0044] Figure 8 This invention demonstrates the computational efficiency of various complex elastic wave velocity models. Figure 8 In the table, (a) represents the time consumption comparison between the convolution method and the traditional method on different sizes of marmousi models; (b) represents the average time saving and time efficiency improvement of the convolution method on different sizes of marmousi models. Detailed Implementation

[0045] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0046] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0047] Example 1

[0048] Reference Figure 1 , Figure 2 and Figure 3 An accelerated method for elastic wavefield forward modeling based on parallel one-dimensional transverse convolution includes the following steps:

[0049] S1. Construct a one-dimensional transverse convolution kernel based on finite difference coefficients.

[0050] A simple elastic wave velocity model is adopted, which uses a horizontal layered velocity model with a grid size of 200×200 to quickly verify the computational speed of the one-dimensional lateral convolution method in high-order numerical simulations and long sampling time simulations.

[0051] The Marmousi model was used to model complex elastic wave velocities. By setting the downsampling factor down_sample to 0.9, 0.7, 0.5, 0.2 and 0, the model was scaled down to 10%, 30%, 50%, 80% of the original size and the original size, respectively, to verify the computational speed and numerical simulation effect of the proposed method on velocity models of different scales.

[0052] S2. Based on a one-dimensional horizontal convolution kernel, perform a one-dimensional horizontal convolution operation on the input matrix to calculate the partial derivative in the x-direction.

[0053] Convolution kernel settings:

[0054] The finite difference coefficients divided by the spatial stride Δx are used as the kernel weights of the one-dimensional horizontal convolution. The convolution size is set to 1×n according to the finite difference order n. The formula for one-dimensional horizontal convolution and the definition of the convolution kernel are as follows:

[0055]

[0056] In the formula, m and n represent the position indices of the input and output matrices in the row and column directions, respectively; R is the convolution kernel length (finite difference order); i represents the position index of the one-dimensional horizontal convolution kernel and the input matrix in the row direction; S represents the output matrix; The output matrix represents the output matrix in Value at position; K x I represents a one-dimensional horizontal convolution kernel; I represents the input matrix. These are the difference coefficients.

[0057] The principle of finding the partial derivative in the x-direction of convolution:

[0058] Convolution is viewed as a "sliding window." The convolution kernel starts from the top left corner of the input matrix and slides row by row and column by column with a set stride, covering an area of ​​the same size as the convolution kernel each time. During this process, the area covered by each slide is multiplied element-wise by the convolution kernel weights and summed. The result of each step is used as each element of the partial derivative matrix, thus using one-dimensional horizontal convolution to calculate the first-order partial derivative in the x-direction.

[0059] S3. By transposing the matrix, the data arrangement in the z-direction is converted into continuous data in the row direction, and a one-dimensional horizontal convolution operation is performed based on the transposed input matrix to calculate the partial derivative in the z-direction.

[0060] Matrix transpose principle:

[0061] To address the issue of slow z-direction partial derivative calculation due to the low efficiency of GPUs reading non-contiguous data column-wise, matrix transpose is used to transform the originally non-contiguous data in the column direction into contiguous data in the row direction. This method does not change the actual storage location of the data, but improves data reading efficiency by changing the data reading index. Matrix transpose is defined as:

[0062]

[0063] In the formula, a pq This represents the value in the p-th row and q-th column of the matrix, where p = 1, 2, 3, ..., m; q = 1, 2, 3, ..., n.

[0064] Design for accelerated calculation of z-direction partial derivatives:

[0065] After matrix transposition, the data originally arranged in the column direction is rearranged in the row direction, which is more suitable for the GPU's characteristic of efficiently loading data row by row and the sliding calculation method of the one-dimensional horizontal convolution operator. Therefore, a one-dimensional horizontal convolution operator is used to slide and calculate in the transposed matrix from left to right and from top to bottom, and the final calculation result is transposed again, thus achieving fast calculation of the z-direction partial derivative. The z-direction partial derivative result obtained by this method is consistent with the z-direction partial derivative result calculated by directly reading data column by column.

[0066] S4. Based on the calculated partial derivatives in the x and z directions, perform forward modeling of the elastic wave field.

[0067] To further improve the speed of convolution calculation, parallel matrix multiplication is designed to replace the stepwise sliding calculation of convolution. The convolution kernel K... x By setting the matrix multiplication as row vectors and defining the region covered by each sliding step of the convolution in the input matrix I as a column vector, the sequential sliding calculation of the convolution is transformed into the calculation of row and column vectors. The GPU is then used to achieve parallel computation of multiple row and column vectors. The principle of parallel matrix multiplication is as follows:

[0068]

[0069] Where N represents half of the finite difference order.

[0070] A 100-layer PML layer was wrapped around a simple velocity model and complex velocity models of different scales. A 40Hz Ricker wavelet excitation field was injected at (200, 200) in the simple velocity model and (680, 20) in the complex velocity models. The computational efficiency was compared with the traditional elastic wave forward modeling method for different difference orders and sampling durations on the simple velocity model; the computational efficiency and numerical simulation accuracy were also compared with the traditional elastic wave forward modeling method for complex velocity models of different scales.

[0071] Example 2

[0072] The following will describe in detail, with reference to this embodiment, how the present invention solves the technical problems in practical work.

[0073] Reference Figure 4 , Figure 5 , Figure 6 This invention mainly comprises three parts: one-dimensional lateral convolution for partial derivative calculation, storage mode optimization, and convolution calculation optimization. First, the finite difference coefficients are divided by the spatial stride. The values ​​are used as kernel weights, and the x-direction partial derivatives in the first-order velocity-stress formula are calculated by sliding the convolution from left to right and from top to bottom. Secondly, matrix transposition is used to convert column-direction matrix data reading into row-direction data reading, taking advantage of the GPU's fast row-direction data reading capability in two-dimensional matrices. Thirdly, one-dimensional lateral convolution is used to perform sliding window calculations on the transposed matrix, and the result is then transposed again to obtain results with the same mathematical logic as directly reading the two-dimensional matrix data column-by-column for z-direction partial derivative calculation. Then, a matrix parallel computation method is designed to further improve the convolution calculation speed. Finally, the computational efficiency is verified on a simple elastic wave velocity model under different finite difference orders and sampling times, and the numerical simulation accuracy and computational efficiency are verified on marmousi models of different scales.

[0074] The experimental platform configuration in this embodiment is as follows: Intel(R) Core(TM) CPU i5-13490F, 32 GB RAM, NVIDIA GeForce GTX 3060 Ti-GDDR6X, Windows 11 operating system, CUDA 11.8 acceleration, Python 3.9, and PyTorch 2.0.1 deep learning framework. The specific implementation process is as follows:

[0075] 1. Preparation of Marmousi Models of Different Sizes

[0076] By reading the marmousi.mat file into the system, the system detects the marmousi model, corrects positive and negative values, and converts the velocity unit from km / s to m / s in the original marmousi model by expanding the overall value by 1000. Next, downsampling is performed according to the set down_sample value to proportionally reduce the velocity model. Finally, the reduced marmousi model result is saved. The specific code is shown below:

[0077] # 1. Load the input .mat file input_data = loadmat(input_path) # Marmousi original size model velocity_field = input_data['Data'] # 2. Data preprocessing (outlier correction) v_min, v_max = velocity_field.min(), velocity_field.max() data_norm = (velocity_field- v_min) / (v_max - v_min) data_norm = np.maximum(data_norm, 0.0) # Correct negative values ​​# 3. Data processing (Lanczos3 interpolation scaling) resized_norm = zoom(data_norm, scale_factor, down_sample=0.3) resized_data = resized_norm * (v_max - v_min) + v_min resized_data = np.where(resized_data < 1, 0, resized_data) # Enlarge the value by 1000 times # resized_data *= 1000 ## 4. Save the output .mat file: output_dict = { 'Data': resized_data.astype(np.float32), 'original_min': v_min, 'original_max': v_max}savemat(output_path, output_dict, do_compression=True)

[0078] 2. One-dimensional transverse convolution to realize the forward modeling process of elastic waves:

[0079] This embodiment combines one-dimensional lateral convolution computation, storage optimization, and convolution computation optimization to propose an accelerated method and system for elastic wave field forward modeling based on parallel one-dimensional lateral convolution, which improves the forward modeling speed of elastic waves while ensuring the accuracy of numerical simulation.

[0080] 2.1 Setting the One-Dimensional Lateral Convolution Kernel

[0081] Divide the 6th, 8th, and 10th order finite difference coefficients by the space step size. The values ​​after the first step are used as kernel weights for one-dimensional horizontal convolution. Taking the 6th-order finite difference coefficients as kernel weights as an example, the convolution kernel is:

[0082]

[0083] The code for the convolution kernel is as follows:

[0084] kernel_x = torch.tensor([[[[-0.0046875, 0.065104166666667, -1.171875,1.171875, -0.065104166666667, 0.0046875]]]],

[0085] dtype=torch.float32)

[0086] 2.2 Principle of finding partial derivatives in the x-direction through convolution:

[0087] Convolution is viewed as a "sliding window." The convolution kernel starts from the top left corner of the input matrix and slides row by row and column by column with a set stride, covering an area of ​​the same size as the convolution kernel each time. During this process, the area covered by each slide is multiplied element-wise by the convolution kernel weights and summed. The result of each step is used as each element of the partial derivative matrix, thus using one-dimensional horizontal convolution to calculate the first-order partial derivative in the x-direction.

[0088] 3. Design for accelerated calculation of partial derivatives in the z-direction:

[0089] 3.1 Principle of Matrix Transpose:

[0090] To address the issue of slow z-direction partial derivative calculation due to the low efficiency of GPUs reading non-contiguous data column-wise, matrix transpose is used to transform the originally non-contiguous data in the column direction into contiguous data in the row direction. This method does not change the actual storage location of the data, but improves data reading efficiency by changing the data reading index. Matrix transpose is defined as:

[0091] .

[0092] 3.2 Design for accelerated calculation of partial derivatives in the z-direction:

[0093] After matrix transposition, the data originally arranged in the column direction is rearranged in the row direction, which is more suitable for the GPU's characteristic of efficiently loading data row by row. To this end, a one-dimensional lateral convolution operator is used to perform calculations in the transposed matrix from left to right and from top to bottom, and the final calculation result is transposed again, thus achieving fast calculation of the z-direction partial derivative. The z-direction partial derivative result obtained in this way is consistent with the z-direction partial derivative result calculated by directly reading the data column by column.

[0094] 4. Parallel matrix multiplication design

[0095] To further improve the speed of convolution calculation, parallel matrix multiplication is designed to replace the step-by-step sliding calculation of convolution. The convolution kernel Kx is set as a row vector, and the region covered by each sliding step in the input matrix I is set as a column vector. This transforms the sequential sliding calculation of convolution into the calculation of row and column vectors, and the GPU is used to implement parallel calculation of multiple row and column vectors. The principle of parallel matrix multiplication is as follows:

[0096] .

[0097] 5. Accuracy and velocity testing of forward numerical simulation of elastic waves

[0098] A 100-layer PML layer was wrapped around a simple velocity model and complex velocity models of different scales. A 40 Hz Ricker wavelet excitation field was injected at (200, 200) in the simple velocity model and at (680, 20) in the complex velocity models. The computational efficiency was compared with the traditional elastic wave forward modeling method for different difference orders and sampling durations on the simple velocity model; the computational efficiency and numerical simulation accuracy were also compared with the traditional elastic wave forward modeling method for complex velocity models of different scales.

[0099] Implementation results:

[0100] Select Figure 4 (a) uses a simple velocity model with the seismic source located at (200, 200), injecting a 40 Hz Ricker wavelet, and sampling for 2000 ms. The computational speed (computation time) is compared between the traditional finite difference method and the convolution method of this invention at different difference orders. Figure 5 As shown in (b), the method of the present invention improves the computation time by 57.87%, 62.44%, and 68.16% for 6th, 8th, and 10th order difference orders, respectively. Figure 5 As shown in (a), the time efficiency improvement rate increases with the increase of the finite difference order. This phenomenon occurs because, as the finite difference order increases, traditional methods require loading more submatrices to complete the calculation of higher-order finite differences in a single partial derivative operation. This significantly increases the number of cross-row accesses and the amount of data loaded, leading to a significant increase in data access overhead and thus increasing the overall computation time. In contrast, the method of this invention only requires loading one computational region matrix for a single partial derivative calculation in finite difference operations of any order, and thanks to its efficient data reading mode, the data loading overhead remains relatively stable. Therefore, even under high-order precision computation conditions, the method of this invention can still maintain high computational efficiency.

[0101] Select Figure 4(a) uses a simple velocity model where the seismic source is located at (200, 200), a 40 Hz Ricker wavelet is injected, the finite difference order is 6, the sampling time is 10000 ms, and the average time is recorded every 500 ms starting from 2000 ms. The computational speed of the traditional finite difference method and the convolution method of this invention are compared under different sampling times. Figure 6 As shown in (b), the overall computational efficiency of the method of the present invention is improved by 54.37%-64.36%. Figure 6 As shown in (a), the difference in computation time between the two methods gradually increases with the continuous increase of sampling time. The linear relationship between the computation time and sampling time of this invention indicates that the method of this invention has excellent applicability and stability on GPU architecture.

[0102] Select 10%, 30%, 50%, 80% and the original size Figure 4 (b) Model: The seismic source is set at (680, 20), a 40 Hz Ricker wavelet is injected, the sampling time is 4000 ms, and the finite difference order is 6. The computational speed of the traditional finite difference method and the convolution method of this invention is compared under different sampling times, such as... Figure 8 As shown, the time efficiency improvement of the method of the present invention is between 42.02% and 45.60% in different scales of Marmousi models.

[0103] like Figure 7 As shown, the average computation time difference gradually increases with the increase in model size. Both methods exhibit a non-linear growth trend in computation time. This phenomenon mainly stems from the non-linear increase in data access overhead with model size. Traditional methods require loading multiple sub-matrices during computation, and the size of these sub-matrices increases with the number of rows and columns in the model, resulting in a quadratic increase in data loading and a significant increase in the number of cross-row accesses, thus causing a faster non-linear increase in data loading overhead. In contrast, the method of this invention also exhibits a quadratic increase in data loading during computation, but due to the characteristic that the one-dimensional transverse convolution operator only needs to load one computational region matrix in a single partial derivative calculation, and the efficient data reading mode, the non-linear increase in data loading overhead is relatively slower.

[0104] Example 3

[0105] This embodiment also provides an elastic wave field forward modeling acceleration system based on parallel one-dimensional transverse convolution, including: a construction module, a first calculation module, a second calculation module, and a forward modeling module; the construction module is used to construct a one-dimensional transverse convolution kernel based on finite difference coefficients; the first calculation module is used to perform a one-dimensional transverse convolution operation on the input matrix based on the one-dimensional transverse convolution kernel to calculate the partial derivative in the x-direction; the second calculation module is used to convert the data arrangement in the z-direction into continuous data in the row direction through matrix transposition processing, and perform a one-dimensional transverse convolution operation based on the transposed input matrix to calculate the partial derivative in the z-direction; the forward modeling module is used to perform elastic wave field forward modeling simulation based on the calculated partial derivatives in the x-direction and z-direction.

[0106] The embodiments described above are merely preferred embodiments of the present invention and are not intended to limit the scope of the present invention. Various modifications and improvements made to the technical solutions of the present invention by those skilled in the art without departing from the spirit of the present invention should fall within the protection scope defined by the claims of the present invention.

Claims

1. An accelerated method for forward modeling of elastic wave fields based on parallel one-dimensional transverse convolution, characterized in that, Includes the following steps: S1. Construct a one-dimensional transverse convolution kernel based on the finite difference coefficients; S2. Based on the one-dimensional horizontal convolution kernel, perform a one-dimensional horizontal convolution operation on the input matrix to calculate the partial derivative in the x-direction; S3. By transposing the matrix, the data arrangement in the z-direction is converted into continuous data in the row direction, and a one-dimensional horizontal convolution operation is performed based on the transposed input matrix to calculate the partial derivative in the z-direction. S4. Based on the calculated partial derivatives in the x and z directions, perform forward modeling of the elastic wave field.

2. The method for accelerating the forward modeling of elastic wave fields based on parallel one-dimensional transverse convolution as described in claim 1, characterized in that, S1 includes: Dividing the finite difference coefficients by the spatial step size Δx yields the weights of the one-dimensional transverse convolution kernel; Based on the finite difference order n, the convolution kernel size is set to 1×n; The weights of the one-dimensional horizontal convolution kernel are difference coefficients.

3. The method for accelerating the forward modeling of elastic wave fields based on parallel one-dimensional transverse convolution as described in claim 1, characterized in that, S2 includes: A one-dimensional horizontal convolution kernel is used as a sliding window, which slides row by row and column by column starting from the top left corner of the input matrix. During each sliding process, the region covered by the convolution kernel is multiplied element-wise with the kernel weights and then summed. The result of each calculation is used as the corresponding element of the partial derivative matrix to obtain the first-order partial derivative in the x-direction.

4. The method for accelerating the forward modeling of elastic wave fields based on parallel one-dimensional transverse convolution as described in claim 1, characterized in that, S3 includes: Perform a matrix transpose operation on the input matrix to convert the data in the column direction into a continuous row direction; Perform a one-dimensional horizontal convolution operation on the transposed matrix to obtain an intermediate result; Perform a matrix transpose operation on the intermediate result again to obtain the partial derivative in the z-direction.

5. The method for accelerating the forward modeling of elastic wave fields based on parallel one-dimensional transverse convolution according to claim 1, characterized in that, The method also includes converting the sliding calculation method of the one-dimensional horizontal convolution into parallel matrix multiplication to accelerate the convolution calculation process.

6. The accelerated method for elastic wave field forward modeling based on parallel one-dimensional transverse convolution according to claim 5, characterized in that, The steps to convert the sliding computation method of the one-dimensional lateral convolution into parallel matrix multiplication include: Set the one-dimensional horizontal convolution kernel as a row vector; Extract the region covered by each sliding step of the convolution in the input matrix into a column vector; The row vector is multiplied by multiple column vectors in parallel to obtain the convolution result matrix.

7. An elastic wavefield forward modeling acceleration system based on parallel one-dimensional transverse convolution, said system being used to implement the method according to any one of claims 1-6, characterized in that, include: The module consists of a construction module, a first computation module, a second computation module, and a forward modeling module. The construction module is used to construct a one-dimensional transverse convolution kernel based on finite difference coefficients; The first calculation module is used to perform a one-dimensional horizontal convolution operation on the input matrix based on the one-dimensional horizontal convolution kernel, and calculate the partial derivative in the x-direction; The second calculation module is used to convert the data arrangement in the z direction into continuous data in the row direction through matrix transpose processing, and to perform a one-dimensional horizontal convolution operation based on the transposed input matrix to calculate the partial derivative in the z direction. The forward modeling module is used to perform forward modeling simulations of elastic wave fields based on the calculated partial derivatives in the x and z directions.

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