A low-memory inversion imaging method for ground penetrating radar based on super-resolution technology

Abstract

The present invention discloses a low-memory inversion imaging method for ground penetrating radar (GPR) based on super-resolution technology, comprising the following steps: constructing an initial GPR inversion imaging model as a current model; constructing an initial gradient recovery model based on a super-resolution network; acquiring historical GPR model image data and gradient data, training the initial gradient recovery model, and obtaining a gradient recovery model; performing a forward modeling process, compressing the time dimension wavefield based on the Nyquist sampling theorem to obtain a compressed wavefield; spatially downsampling the compressed wavefield to obtain and store a downsampled forward modeled wavefield; calculating fuzzy gradient information based on the downsampled forward modeled wavefield using the accompanying wavefield as a temporary variable; obtaining gradient information based on the fuzzy gradient information and the gradient recovery model; selecting a step size based on the Wolfe criterion, and then updating the current model in combination with the gradient information to determine whether the current model meets the iteration termination condition. If so, outputting the inversion result; otherwise, repeating steps S4 to S8. The method of the present invention can significantly improve memory usage and computational efficiency while ensuring a certain imaging accuracy, fully exploring the application potential of full waveform inversion in engineering practice.

Description

Technical Field

[0001] The present invention belongs to the field of geophysical exploration, and in particular relates to a low-memory inversion imaging method of a ground penetrating radar based on super-resolution technology. Background Art

[0002] Ground Penetrating Radar (GPR) is a high-frequency electromagnetic detection technology that nondestructively locates underground structures, electrical anomalies, or hidden anomalies within objects. As an emerging shallow geophysical survey method, GPR can accurately obtain information about targets in unknown underground areas without destroying surface structures. It features fast detection speed, high accuracy, strong anti-interference capabilities, nondestructive testing, safe detection, low cost, and clear and easy-to-understand results. In recent years, it has developed into an important shallow surface geophysical exploration method in fields such as tunnel engineering, municipal construction, underground pipeline layout, archaeology, military operations, and road defect detection.

[0003] In practical engineering exploration, a simple GPR B-scan profile can provide approximate information on the location and size of underground targets. However, with the continued expansion of GPR exploration, the increasing complexity of detection environments, and the demand for higher precision and resolution of underground targets, it is necessary to obtain more accurate and specific quantitative indicators such as target material, size, and shape. To this end, the observed data can be fitted to obtain appropriate physical parameters through an inversion process. Full waveform inversion utilizes all information, including dynamics and kinematics, to reconstruct the characteristics of the subsurface medium and accurately characterize the subsurface structure, significantly improving the accuracy of GPR data interpretation. However, to date, the widespread application of traditional full waveform inversion is primarily due to its significant computational time and memory usage, which generally cannot meet the real-time requirements of engineering exploration. This is because the solution of traditional full waveform inversion is based on a least-squares calculation of the objective function. Among them, the most commonly used local search methods, such as the steepest descent method and the Newton method, require solving the derivative of the objective function with respect to the model parameters, namely the gradient, to update the search direction. In order to solve the gradient in the process of continuous iteration, the storage of the forward wave field and the accompanying wave field is necessary. This largely leads to the emergence of the above-mentioned problems of full waveform inversion and is also the biggest constraint that makes full waveform inversion difficult to apply in actual engineering. Summary of the Invention

[0004] The object of the present invention is to provide a low-memory inversion imaging method for ground penetrating radar based on super-resolution technology, which can improve the full waveform inversion efficiency of ground penetrating radar, reduce memory requirements and ensure the inversion imaging accuracy.

[0005] The present invention provides a low-memory inversion imaging method for ground penetrating radar based on super-resolution technology, comprising the following steps:

[0006] S1. Construct an initial GPR inversion imaging model as the current model;

[0007] S2. Build an initial gradient recovery model based on the super-resolution network;

[0008] S3 obtains historical ground penetrating radar model image data and gradient data, and trains the initial gradient recovery model obtained in step S2 to obtain a gradient recovery model;

[0009] S4. Perform a forward modeling process and compress the time dimension wavefield based on the Nyquist sampling theorem to obtain a compressed wavefield;

[0010] S5. spatially downsample the compressed wavefield obtained in step S4 to obtain and store the downsampled forward wavefield;

[0011] S6. Based on the downsampled forward wavefield obtained in step S5, the accompanying wavefield is used as a temporary variable to calculate the fuzzy gradient information;

[0012] S7. Obtain gradient information based on the fuzzy gradient information obtained in step S6 and the gradient recovery model obtained in step S3;

[0013] S8. Select the step size based on the Wolfe criterion, and then update the current model based on the gradient information obtained in step S7 to determine whether the current model meets the preset iteration termination condition or the number of iterations reaches the preset value. If so, output the inversion result; otherwise, repeat steps S4 to S8.

[0014] Step S1 specifically includes: constructing an initial GPR inversion imaging model. The model uses all the information of the observation data to reconstruct the underground medium parameters by minimizing the objective function, thereby obtaining the inversion result. The objective function is expressed as follows:

[0015]

[0016] Among them, N s is the number of sources; N g The number of receivers corresponding to each source; r g is the receiver space coordinate vector; d obs (r g ,ts) is the source excitation at r g Observation data received at d cal (m,r g ,ts) is the simulated data of the source pair prediction model forward calculation; T is the observation time; m is the vector of the model medium parameter with respect to the spatial position, which is expressed by the following formula:

[0017] m=ε(r)

[0018] Where ε(r) is the spatial distribution of the model medium parameters;

[0019] The initial gradient recovery model in step S2 includes a bicubic interpolation module, 19 convolutional layer-ReLu layer modules, and a convolutional layer module connected in series; the convolutional layer-ReLu layer module includes a convolutional layer and a ReLu layer connected in series, and the convolution kernel size of the convolution layer is 3×3×64; the convolutional layer module includes a convolution layer, and the convolution kernel size is 3×3×64;

[0020] The input fuzzy gradient information is first processed by the bicubic interpolation module to obtain fuzzy gradient information of a preset dimension size, then processed in sequence by 19 convolutional layer-ReLu layer modules, and finally reconstructed by the convolutional layer module. Zero padding is performed before each convolution to make all feature maps of the same size. The result obtained by the convolutional layer module is added to the input fuzzy gradient information to obtain the gradient information as the output of the model.

[0021] Step S4 is specifically as follows:

[0022] For ground penetrating radar electromagnetic signals, the sampling frequency is calculated based on the Nyquist sampling theorem, and then the maximum sampling interval is calculated using the following formula:

[0023]

[0024] Among them, sampt is the sampling interval; f s is the sampling frequency; f max It is the highest frequency of the electromagnetic signal of the ground penetrating radar;

[0025] In the time dimension, the electromagnetic signal of the ground penetrating radar is composed of discrete time steps. According to the maximum sampling interval time, the maximum sampling interval time step is calculated using the following formula:

[0026] nt=sampt / dt

[0027] Among them, nt is the maximum sampling interval time step; dt is the interval time between each time step of the ground penetrating radar electromagnetic signal;

[0028] The forward wavefield is downsampled with nt as the downsampling interval to obtain the compressed wavefield.

[0029] Step S5 specifically comprises: down-sampling the compressed wavefield obtained in step S4, setting a sampling interval nk, selecting one wavefield data for every nk spatial steps, saving the electromagnetic field value, and obtaining and storing the down-sampled forward wavefield.

[0030] Step S6 is specifically as follows:

[0031] According to the down-sampled forward wave field, the corresponding companion wave field is calculated;

[0032] Based on the obtained downsampled forward wavefield and the corresponding companion wavefield, the fuzzy gradient information of the current model objective function with respect to the model parameters is calculated using the following formula:

[0033]

[0034] in, is the forward modeled wavefield after downsampling; is the corresponding companion wave field; is the fuzzy gradient information of the current model objective function with respect to the model parameters; T is the observation time;

[0035] Step S7 specifically includes: using the gradient recovery model obtained in step S3 to reconstruct the fuzzy gradient information obtained in step S6 to obtain gradient information, which is expressed using the following formula:

[0036]

[0037] Among them, Φ VDSR is the super-resolution operator; It is the gradient information of the current model objective function with respect to the model parameters.

[0038] The present invention discloses a low-memory inversion imaging method for ground-penetrating radar based on super-resolution technology, which can significantly improve the memory usage and computing efficiency while ensuring a certain imaging accuracy, and fully explores the application potential of full waveform inversion in engineering practice. BRIEF DESCRIPTION OF THE DRAWINGS

[0039] Figure 1 Schematic diagram of the process of the present invention;

[0040] Figure 2 is the training set in the gradient recovery model training process of the embodiment of the present invention; Figure 2 a is a random layered model; Figure 2 b is the image data;

[0041] Figure 3 Schematic diagram of the model used in the experiment to verify the effectiveness of the algorithm according to the embodiment of the present invention; Figure 3 a is a schematic diagram of the real model; Figure 3 b is a schematic diagram of the initial model;

[0042] Figure 4 Schematic diagram of the inversion results in the experiment for verifying the effectiveness of the algorithm according to the embodiment of the present invention; Figure 4 a is the result of traditional full waveform inversion (T-FWI); Figure 4b is the full waveform inversion result of the wavefield storage strategy (S-FWI); Figure 4 c is the full waveform inversion result of Nyquist sampling and wavefield storage strategy (NS-FWI); Figure 4 d is the full waveform inversion result optimized by super-resolution technology (V-FWI);

[0043] Figure 5 This is a comparison diagram of the input and output of the gradient recovery model in the effectiveness verification experiment of the algorithm embodiment of the present invention; Figure 5 a is the downsampled fuzzy gradient of the 15th iteration in the inversion; Figure 5 b is the gradient after the gradient recovery model is restored;

[0044] Figure 6 A schematic diagram of a model in a complex model data experiment according to an embodiment of the present invention; Figure 6 a is a schematic diagram of the real model; Figure 6 b is a schematic diagram of the initial model;

[0045] Figure 7 Schematic diagram of inversion results in a complex model data experiment according to an embodiment of the present invention; Figure 7 a is the T-FWI inversion result; Figure 7 b is the inversion result of V-FWI (nt=2); Figure 7 c is the inversion result of V-FWI (nt=3); Figure 7 d is the comparison diagram of the convergence curves of each inversion result; Figure 7 e is the inversion result of V-FWI (nt=4); Figure 7 f is the V-FWI (nt = 5) inversion result;

[0046] Figure 8 This is a schematic diagram of a model used in a real hydrological model data experiment according to an embodiment of the present invention; Figure 8 a is a schematic diagram of the real hydrological model; Figure 8 b is a schematic diagram of the initial model;

[0047] Figure 9 1 is a comparison chart of the inversion results of the method of the present invention and the traditional method in the real hydrological model data experiment of the embodiment of the present invention; Figure 9 a is the T-FWI inversion result; Figure 9 b is the inversion result of V-FWI (nt=2); Figure 9 c is the comparison diagram of the convergence curves of each inversion result; Figure 9 d is the V-FWI (nt=3) inversion result. DETAILED DESCRIPTION

[0048] The present invention provides a low-memory inversion imaging method for ground penetrating radar based on super-resolution technology, the flow chart of which is as follows: Figure 1 As shown, the following steps are included:

[0049] S1. Construct an initial GPR inversion imaging model as the current model, specifically:

[0050] An initial GPR inversion imaging model is constructed. The model uses all the information of the observation data to reconstruct the underground medium parameters by minimizing the objective function, thereby obtaining the inversion result. The objective function is expressed as follows:

[0051]

[0052] Among them, N s is the number of sources; N g The number of receivers corresponding to each source; r g is the receiver space coordinate vector; d obs (r g ,ts) is the source excitation at r g Observation data received at d cal (m,r g ,ts) is the simulated data of the source pair prediction model forward calculation; T is the observation time; m is the vector of the model medium parameter with respect to the spatial position, which is expressed by the following formula:

[0053] m=ε(r)

[0054] Where ε(r) is the spatial distribution of the model medium parameters;

[0055] S2. Build an initial gradient recovery model based on the super-resolution network;

[0056] The initial gradient recovery model includes a bicubic interpolation module, 19 convolutional layer-ReLu layer modules and a convolutional layer module connected in series; the convolutional layer-ReLu layer module includes a convolutional layer and a ReLu layer connected in series, and the convolution kernel size of the convolution layer is 3×3×64; the convolutional layer module includes a convolution layer, and the convolution kernel size is 3×3×64;

[0057] The input fuzzy gradient information is first processed by the bicubic interpolation module to obtain fuzzy gradient information of a preset dimension size, then processed in sequence by 19 convolutional layer-ReLu layer modules, and finally reconstructed by the convolutional layer module. Zero padding is performed before each convolution to make all feature maps of the same size. The result obtained by the convolutional layer module is added to the input fuzzy gradient information to obtain the gradient information as the output of the model.

[0058] In super-resolution methods, it is necessary to use surrounding pixels to infer the center pixel because the pixels in the surrounding area provide certain constraints on the center pixel. Obviously, the same relationship cannot be applied to pixels at the image boundary. Therefore, many super-resolution methods crop the resulting image. However, if the required surrounding area is very large, it is impossible to provide an effective constraint on the center pixel. The final image obtained after cropping is too small to meet practical requirements. At the same time, this continuous convolution method will cause the dimension of the output image to continue to decrease. To solve this problem, we pad with zeros before each convolution to keep all feature maps (including the output image) the same size. It turns out that the zero-padding method works surprisingly well. Therefore, this method is different from most other methods in that pixels near the image boundary can also achieve good prediction results.

[0059] S3 obtains historical ground penetrating radar model image data and gradient data, and trains the initial gradient recovery model obtained in step S2 to obtain a gradient recovery model;

[0060] S4. Perform forward modeling and compress the time dimension wavefield based on the Nyquist sampling theorem to obtain the compressed wavefield, specifically:

[0061] For ground penetrating radar electromagnetic signals, the sampling frequency is calculated based on the Nyquist sampling theorem, and then the maximum sampling interval is calculated using the following formula:

[0062]

[0063] Among them, sampt is the sampling interval; f s is the sampling frequency; f max It is the highest frequency of the electromagnetic signal of the ground penetrating radar;

[0064] In the time dimension, the electromagnetic signal of the ground penetrating radar is composed of discrete time steps. According to the maximum sampling interval time, the maximum sampling interval time step is calculated using the following formula:

[0065] nt=sampt / dt

[0066] Among them, nt is the maximum sampling interval time step; dt is the interval time between each time step of the ground penetrating radar electromagnetic signal;

[0067] The forward wavefield is downsampled with nt as the downsampling interval to obtain the compressed wavefield.

[0068] S5. Perform spatial downsampling on the compressed wavefield obtained in step S4 to obtain and store the downsampled forward wavefield, specifically:

[0069] The compressed wave field obtained in step S4 is downsampled, a sampling interval nk is set, one wave field data is selected every nk spatial steps, the electromagnetic field value is saved, and the downsampled forward wave field is obtained and stored.

[0070] S6. Based on the downsampled forward wavefield obtained in step S5, the accompanying wavefield is used as a temporary variable to calculate the fuzzy gradient information, specifically:

[0071] According to the down-sampled forward wave field, the corresponding companion wave field is calculated;

[0072] Based on the obtained downsampled forward wavefield and the corresponding companion wavefield, the fuzzy gradient information of the current model objective function with respect to the model parameters is calculated using the following formula:

[0073]

[0074] in, is the forward modeled wavefield after downsampling; is the corresponding companion wave field; is the fuzzy gradient information of the current model objective function with respect to the model parameters; T is the observation time;

[0075] S7. According to the fuzzy gradient information obtained in step S6 and the gradient recovery model obtained in step S3, the gradient information is obtained, specifically:

[0076] Using the gradient recovery model obtained in step S3, the fuzzy gradient information obtained in step S6 is reconstructed to obtain gradient information, which is expressed using the following formula:

[0077]

[0078] Among them, Φ VDSR is the super-resolution operator; It is the gradient information of the current model objective function with respect to the model parameters.

[0079] S8. Select the step size based on the Wolfe criterion, and then update the current model based on the gradient information obtained in step S7 to determine whether the current model meets the preset iteration termination condition or the number of iterations reaches the preset value. If so, output the inversion result; otherwise, repeat steps S4 to S8.

[0080] The problem of minimizing the objective function S is a nonlinear least squares problem. Whether it is the commonly used steepest descent method, Newton's method, or the L-BFGS method used in this invention, it is necessary to obtain the gradient of the objective function S with respect to the model parameter m in each iteration to complete the model update. The gradient calculation formula is:

[0081]

[0082] The gradient needs to be continuously updated during the iteration process, so the forward model and the adjoint wave field need to be explicitly stored for calculation, which will result in huge memory usage.

[0083] The method of the present invention is further described below with reference to several embodiments:

[0084] Gradient recovery model training process

[0085] Twenty random layered models were constructed, such as Figure 2 As shown in Figure (a), the model size is 100 × 200, with a dielectric constant of 3 for the first layer, 4 for the second layer, 5 for the third layer, and 6 for the fourth layer. The spatial step size ds = 0.02 m, the time step size dt = 0.045 ns, and a total of 1000 time steps are used. A 0.1 m air layer is set above the surface, with 20 excitation sources and receivers evenly distributed within the air layer. Full waveform inversion is performed on these models, and the gradient information is recorded. These gradients are normalized (the amplitude is normalized to 0-1), resulting in a total of 500 gradient files.

[0086] At the same time, in order to expand the dataset, we added a total of 616 image data to the dataset, such as Figure 2 As shown in Figure 2, image data is more complex than normal gradient data. The inclusion of this data will enhance the network's ability to recover gradients. For image data, we first convert the image to the YCbCr color space and select the luminance Y channel for training.

[0087] First, we select nk = 2 to conduct the experiment. That is, we select a point every 2 spatial steps to obtain downsampled data, resize it to the original size through cubic spline interpolation, and calculate the difference between the original data and the resized data to obtain the residual. The residual and the interpolated data are used to train the network.

[0088] Suppose a dataset consists of X representing a low-resolution image and Y representing a high-resolution image. Our goal is to use a network to predict the high-resolution image. The gradient recovery model uses residual learning, where the residual can be expressed as r = YX, which defines the loss function. Before training, we use data augmentation techniques to modify the training data and further increase the amount of training data. Here, we use random rotations and random flips in the x-direction, and simultaneously train on patches of the data. We crop 64 patches from each data point, further increasing the amount of training data. The super-resolution network has 20 convolutional layers, and the convolution kernel size is 3×3×64, resulting in a receptive field size of 41×41. The patch size is chosen to be 41×41. We train the network using the SGDM method, with an initial learning rate of 0.1, which is reduced by one-tenth every 10 epochs for a total of 50 epochs. Gradient clipping is used to clamp the gradient to the range [-0.01, 0.01], and regularization is applied using the L2 norm with a regularization factor of 0.01.

[0089] Algorithm effectiveness verification experiment

[0090] In order to better demonstrate the advantages of the method of the present invention, we proceed from three directions: (1) by storing only the forward wave field and calculating the wave field and gradient data simultaneously, we reduce the memory usage during operation; (2) by using the Nyquist sampling theorem to implement wave field downsampling in the time dimension, so as to further reduce memory usage and improve computational efficiency; (3) finally, by combining the gradient recovery model based on super-resolution technology, we can greatly improve computational efficiency and save inversion costs without affecting the inversion quality as much as possible. The experiment was conducted on a personal microcomputer. We first verified the advantages of the above strategy through a set of simple model experiments, and compared it with the traditional full waveform inversion. Establish a simple layered model that does not belong to the data set, such as Figure 3 As shown in a, the number of grids in the simulation area is 100×200, the spatial step size ds = 0.02m, the time step size dt = 0.045ns, a total of 1200 time steps are recorded, the time window length is 54ns, and the Ricker wavelet with a center frequency of 200MHz is used to simulate the excitation source. The initial inversion model is as follows Figure 3 As shown in b, the true model is smoothed by Gaussian filter with a filtering factor of 20.

[0091] A 0.1m air layer is set above the model surface, with 40 sources and 100 receivers in the air layer, and a multi-offset data acquisition method is adopted. 40 sources and 100 receivers are set, and a multi-offset data acquisition method is adopted. Two inversion strategies are set: traditional full waveform inversion (T-FWI), wavefield storage strategy full waveform inversion (S-FWI), Nyquist sampling and wavefield storage strategy full waveform inversion (NS-FWI), and finally optimized full waveform inversion (V-FWI) combined with super-resolution technology. The maximum number of iterations in the inversion is controlled to 30. First, the time sampling interval nt and the spatial sampling interval nk are set to 2 to carry out the experiment, and the results can be compared. Figure 4 The inversion effect parameter table obtained by different inversion strategies is shown in Table 1. Figure 5 The downsampled gradients at the 15th iteration in the inversion (5a) and the gradients after restoration by the gradient recovery model (5b) are given. Figure 5 There are obvious "pixel-like blur points" in a, and after being restored by the gradient recovery model Figure 5 There is an obvious smooth trend in b.

[0092] The inversion results show that using the gradient recovery model can reduce computation time and memory usage without significantly affecting inversion accuracy. To quantitatively describe the inversion results, we calculated the model error and tabulated the relevant parameters of the inversion results below. The memory usage section only calculates the memory occupied by the wavefield and gradient.

[0093] Table 1 FWI inversion effect parameters under different optimization strategies

[0094]

[0095] Complex model numerical experiments

[0096] In order to verify the applicability of the method of the present invention to any model, a complex model experiment was established for comparison. The simulation area size was 100×400, the spatial step size ds=0.02m, the time step size dt=0.04ns, and a total of 2200 time steps were recorded. A 0.1m air layer was set above the surface, and a total of 80 sources and 200 receivers were set in the air layer. Multi-offset data acquisition was adopted, and a 400Mhz Ricker wavelet was used to simulate the excitation source. The actual model and the initial model are as follows: Figure 6At the same time, in order to further discuss the impact of the important parameters of the algorithm, spatial downsampling interval nk and temporal downsampling interval nt, on the performance of FWI, three sets of experiments were added compared to the simple model experiment above, with nk = 2 and nt being 3, 4, and 5 respectively. The obtained inversion results, convergence curves, and calculation time and error tables are shown below. It should be noted that when the spatial downsampling interval nk is 2, only 25% of the information in the gradient file is actually retained. When nk is increased to 3, too much effective information is lost, and FWI is prone to problems such as difficulty in convergence or excessive time spent in the online search phase. Therefore, this is not discussed in detail.

[0097] To achieve better imaging results, we adopted a multi-scale strategy, carried out full waveform inversion at two frequency bands, 100Mhz and 400Mhz, and conducted relevant experiments based on a large workstation. The inversion results are as follows: Figure 7 The relevant parameters are summarized in Table 2. While satisfying the Nyquist theorem, selecting the maximum time sampling interval nt can achieve the maximum speedup while minimizing precision loss and further compressing the wavefield storage memory by approximately 4.17%. However, when nt exceeds the maximum sampling interval, precision loss rapidly increases. Furthermore, the loss of effective information in FWI may lead to difficulty in inversion convergence, a reduction in the search step, and difficulty in calculating correct gradient information, resulting in a rapid increase in computation time. Therefore, for the 400 MHz antenna, we selected nt no greater than 3 for the next experiment.

[0098] Table 2 Inversion calculation time and reconstruction error of complex ancient battlefield model

[0099]

[0100]

[0101] Numerical experiments on real hydrological models

[0102] Established a Figure 8 The real hydrological model shown in Figure a has a simulation area of ​​200 × 400, a spatial step size of ds = 0.01 m, a time step size of dt = 0.022 ns, and a total of 2200 time steps. A 0.08 m air layer is placed above the surface, with 80 sources and 200 receivers evenly distributed within the air layer. Multi-offset data acquisition is also used, with a 400 MHz Ricker wavelet as the excitation source. To achieve better imaging, a multiscale strategy is employed, with full-waveform inversion performed at both 100 MHz and 400 MHz. Conventional full-waveform inversion for this model is difficult to perform on a personal computer, so a large workstation was used for the experiments.

[0103] Comparing the traditional full waveform inversion results with the optimized full waveform inversion results Figure 9 The inversion operation time and reconstruction error data are shown in Table 3. As can be seen in the figure, T-FWI effectively inverts complex interface conditions and medium parameters. Due to the complexity of the subsurface medium, some deep information is missing in the inversion results, but this does not affect the geological interpretation. The V-FWI results proposed in this paper are nearly identical to those of T-FWI, and the difference is almost indistinguishable to the naked eye. The reconstruction errors of the two methods relative to the true model are shown in the table. When nt = 2, the V-FWI method achieves a 48.13% speedup compared to T-FWI, reduces memory usage to 6.25% of the original value, and suffers only a 0.56% loss in accuracy. When nt = 3, the V-FWI method achieves a 52.08% speedup compared to T-FWI, reduces memory usage to 4.17% of the original value, and suffers only a 0.98% loss in accuracy. This shows that the V-FWI method is highly conducive to the efficient application of full waveform inversion in practical situations. This optimization method based on the percentage of the original data has unique advantages when dealing with large-scale data and models.

[0104] Table 3 Inversion calculation time and reconstruction error of the real hydrological model

[0105]

Claims

1. A low-memory inversion imaging method for ground penetrating radar based on super-resolution technology, characterized in that: The following steps are involved: S1. Construct an initial GPR inversion imaging model as the current model; S2. Build an initial gradient recovery model based on the super-resolution network; S3 obtains historical ground penetrating radar model image data and gradient data, the initial gradient recovery model obtained in step S2 is trained to obtain a gradient recovery model; S4. Perform forward modeling and compress the time-dimensional wavefield based on the Nyquist sampling theorem to obtain a compressed wavefield. S5. Perform spatial downsampling on the compressed wavefield obtained in step S4 to obtain and store the downsampled forward wavefield; S6. Based on the downsampled forward wavefield obtained in step S5, the accompanying wavefield is used as a temporary variable to calculate the fuzzy gradient information; S7. According to the fuzzy gradient information obtained in step S6 and the gradient recovery model obtained in step S3, the gradient information is obtained; S8. Select a step size based on the Wolfe criterion and, combined with the gradient information obtained in step S7, update the current model to determine whether the current model meets the preset iteration termination condition or the number of iterations reaches the preset value. If so, output the inversion result; otherwise, repeat steps S4-S8. The initial gradient recovery model in step S2 includes a bicubic interpolation module, 19 convolutional layer-ReLu layer modules and a convolutional layer module connected in series. The convolutional layer-ReLu layer module includes a convolutional layer and a ReLu layer connected in series. The convolution kernel size of the convolutional layer is ; The convolution layer module includes a convolution layer with a convolution kernel size of ; The input fuzzy gradient information is first processed by the bicubic interpolation module to obtain fuzzy gradient information of a preset dimension size, then processed in sequence by 19 convolutional layer-ReLu layer modules, and finally reconstructed by the convolutional layer module; zeros are padded before each convolution to make all feature maps of the same size; the result obtained by the convolutional layer module is added to the input fuzzy gradient information to obtain the gradient information as the output of the model.

2. The low-memory inversion imaging method for ground penetrating radar based on super-resolution technology according to claim 1, characterized in that: Step S1 specifically includes: constructing an initial ground penetrating radar inversion imaging model, which utilizes all the information of the observation data to reconstruct the underground medium parameters by minimizing the objective function, thereby obtaining the inversion result.

3. The low-memory inversion imaging method for ground penetrating radar based on super-resolution technology according to claim 2, characterized in that: The objective function is expressed as follows: ;in, is the number of sources; The number of receivers corresponding to each source; is the receiver space coordinate vector; For the source of excitation Observation data received at Simulated data for forward calculation of source pair prediction model; is the observation time; is the vector of the model medium parameter with respect to the spatial position, which is expressed using the following formula; ;in, is the spatial distribution of the model medium parameters.

4. The low-memory inversion imaging method for ground penetrating radar based on super-resolution technology according to claim 1, characterized in that: Step S4 specifically includes the following steps: For ground penetrating radar electromagnetic signals, the sampling frequency is calculated based on the Nyquist sampling theorem, and then the maximum sampling interval is calculated using the following formula: ;in, is the sampling interval; is the sampling frequency; It is the highest frequency of the electromagnetic signal of the ground penetrating radar; In the time dimension, the electromagnetic signal of the ground penetrating radar is composed of discrete time steps. According to the maximum sampling interval time, the maximum sampling interval time step is calculated using the following formula: ;in, is the maximum sampling interval time step; is the interval between each time step of the ground penetrating radar electromagnetic signal; by The forward wavefield is downsampled to obtain the compressed wavefield.

5. The low-memory inversion imaging method for ground penetrating radar based on super-resolution technology according to claim 1, characterized in that: Step S5 is specifically as follows: down-sampling the compressed wave field obtained in step S4, setting the sampling interval , for each wave field data Select one of the spatial steps, save the electromagnetic field value, and obtain and store the down-sampled forward wave field.

6. The low-memory inversion imaging method for ground penetrating radar based on super-resolution technology according to claim 1, characterized in that: Step S6 specifically includes the following steps: According to the down-sampled forward wave field, the corresponding companion wave field is calculated; Based on the obtained downsampled forward wavefield and the corresponding companion wavefield, the fuzzy gradient information of the current model objective function with respect to the model parameters is calculated using the following formula: ;in, is the forward modeled wavefield after downsampling; is the corresponding companion wave field; It is the fuzzy gradient information of the current model objective function with respect to the model parameters; The observation time.

7. The low-memory inversion imaging method for ground penetrating radar based on super-resolution technology according to claim 1, characterized in that: Step S7 specifically includes: using the gradient recovery model obtained in step S3 to reconstruct the fuzzy gradient information obtained in step S6 to obtain gradient information, which is expressed using the following formula: ;in, is the super-resolution operator; It is the gradient information of the current model objective function with respect to the model parameters.

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