Ground penetrating radar low-memory inversion imaging method based on super-resolution technology

Abstract

The invention discloses a ground penetrating radar low-memory inversion imaging method based on a super-resolution technology, and the method comprises the following steps: constructing an initial ground penetrating radar inversion imaging model, and taking the model as a current model; constructing an initial gradient recovery model based on the super-resolution network; acquiring historical ground penetrating radar model image data and gradient data, and training the initial gradient recovery model to obtain a gradient recovery model; performing a forward modeling process, and performing time dimension wave field compression based on the Nyquist sampling law to obtain a compressed wave field; performing space down-sampling on the compressed wave field to obtain and store a down-sampled forward modeling wave field; on the basis of the down-sampled forward modeling wave field, calculating fuzzy gradient information by taking the adjoint wave field as a temporary variable; gradient information is obtained according to the fuzzy gradient information and a gradient recovery model; selecting a step length based on a Wolfe criterion, updating the current model in combination with gradient information, judging whether the current model meets an iteration termination condition, and outputting an inversion result if the current model meets the iteration termination condition; otherwise, repeating the steps S4 to S8. According to the method, while certain imaging precision is ensured, the memory occupation and the calculation efficiency are greatly improved, and the application potential of full waveform inversion in engineering practice is fully explored.

Description

Technical Field

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

[0002] Ground Penetrating Radar (GPR) is a high-frequency electromagnetic detection technology that can non-destructively locate underground structures, electrical anomalies, or hidden anomalies inside objects. As an emerging shallow geophysical survey method, GPR can accurately obtain information about target bodies in unknown underground areas without destroying the surface structure. It has the characteristics of fast detection speed, accurate detection, strong anti-interference ability, non-destructive detection, 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 the fields of tunnel engineering, municipal construction, underground pipeline layout, archaeology, military, road disease detection, etc.

[0003] In actual engineering exploration, the general location and size of underground target bodies can be obtained through simple GPR detection B-scan profiles. However, with the continuous expansion of the GPR detection field, the increasingly complex detection environment, and the requirements for higher precision and higher resolution of underground target bodies, it is necessary to obtain more accurate and specific quantitative indicators such as target material, size, shape, etc. To this end, the observed data can be fitted through the inversion process to obtain appropriate physical parameters. Full waveform inversion utilizes all information including dynamics and kinematics, which can reconstruct the characteristics of underground media and accurately characterize underground structures, greatly improving the interpretation accuracy of GPR data. However, the main reason why traditional full waveform inversion cannot be widely used so far is that it requires a lot of computational time and memory usage, and usually cannot meet the real-time requirements in engineering exploration; this is because the solution process of traditional full waveform inversion is based on the least squares calculation process of the objective function. Among them, the most commonly used local search methods such as the steepest descent method and Newton's method need to solve the derivative of the objective function with respect to the model parameters, that is, 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, which largely leads to the emergence of the above-mentioned problems of full waveform inversion and is also the biggest constraint for the application of full waveform inversion in engineering practice. 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 ground penetrating radar low memory inversion imaging method based on super-resolution technology, comprising the following steps:

[0006] S1. Construct an initial ground penetrating radar inversion imaging model as the current model;

[0007] S2. Based on the super-resolution network, an initial gradient recovery model is constructed;

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

[0009] S4. Perform a forward modeling process, compress the wave field in the time dimension based on the Nyquist sampling law, and obtain a compressed wave field;

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

[0011] S6. Based on the down-sampled 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 according to 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 in combination with 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 is specifically as follows: constructing an initial ground penetrating radar 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 by the following formula:

[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] Among them, 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 convolutional layer is 3×3×64; the convolutional layer module includes a convolutional 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, and then processed by 19 convolutional layer-ReLu layer modules in sequence, and finally reconstructed by the convolutional layer module; zeros are filled 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 the ground penetrating radar electromagnetic signal, 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 time; 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 includes: down-sampling the compressed wave field obtained in step S4, setting a sampling interval nk, selecting one wave field data for every nk spatial steps, saving the electromagnetic field value, and obtaining and storing the down-sampled forward wave field.

[0030] Step S6 is specifically as follows:

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

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

[0033]

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

[0035] Step S7 specifically includes: using the gradient recovery model obtained in step S3, reconstructing 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 performance in terms of 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 It is a schematic diagram of the process of the present invention;

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

[0041] Figure 3 A schematic diagram of a model used in an experiment to verify the effectiveness of an algorithm according to an 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 A schematic diagram of the inversion results in the experiment for verifying the effectiveness of the algorithm of 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 of the 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 It is a schematic diagram of the inversion results in the complex model data experiment of the 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 inversion result of V-FWI (nt=5);

[0046] Figure 8 A schematic diagram of a model 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] Fig. 9 A comparison diagram 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; Fig. 9 a is the T-FWI inversion result; Fig. 9 b is the inversion result of V-FWI (nt = 2); Fig. 9 c is the comparison diagram of the convergence curves of each inversion result; Fig. 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, and its flow chart 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] The 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 to obtain the inversion result. The objective function is expressed by the following formula:

[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] Among them, ε(r) is the spatial distribution of the model medium parameters;

[0055] S2. Based on the super-resolution network, an initial gradient recovery model is constructed;

[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 convolutional layer is 3×3×64; the convolutional layer module includes a convolutional 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, and then processed by 19 convolutional layer-ReLu layer modules in sequence, and finally reconstructed by the convolutional layer module; zeros are filled 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 infer the central pixel with the help of surrounding pixels, because the pixels in the surrounding area provide certain constraints for the central pixel. Obviously, the same relationship cannot be applied to the pixels at the image boundary. Therefore, many super-resolution methods will crop the resulting image. However, if the required surrounding area is very large, it is impossible to provide effective constraints on the central 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 fill zeros before each convolution to keep the size of all feature maps (including the output image) the same. 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. Obtain historical ground penetrating radar model image data and gradient data, train the initial gradient recovery model obtained in step S2 to obtain a gradient recovery model;

[0060] S4. Perform the forward modeling process and compress the time dimension wave field based on the Nyquist sampling law to obtain the compressed wave field, which is specifically:

[0061] For the ground penetrating radar electromagnetic signal, 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 time; 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 wave field obtained in step S4 to obtain and store the downsampled forward wave field, 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 down-sampled forward wavefield obtained in step S5, the fuzzy gradient information is calculated using the adjoint wavefield as a temporary variable, specifically:

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

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

[0073]

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

[0075] S7. Obtain gradient information according to the fuzzy gradient information obtained in step S6 and the gradient recovery model obtained in step S3, 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 in combination with 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] Solving 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 the present invention, it is necessary to obtain the gradient of the objective function S with respect to the model parameter m in each iteration step 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 modeling and adjoint wave fields 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 in conjunction with several embodiments:

[0084] Gradient recovery model training process

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

[0086] At the same time, in order to expand the data set, we added a total of 616 image data to the data set, such as Figure 2 As shown in (b), in fact, image data is more complex than normal gradient data. The addition of this data will enhance the network's recovery effect on gradients. For image data, we first convert the image to the YCbCr color space and select the brightness 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 the downsampled data, adjust it to the original size through cubic spline interpolation, and calculate the difference between the original data and the resized data to get the residual. The residual and the interpolated data are used to train the network.

[0088] Assume that the dataset is a low-resolution image in which X is a low-resolution image and Y is a high-resolution image. Our goal is to predict its high-resolution image through a network. The gradient recovery model uses residual learning, and the residual can be expressed as r = YX, which defines the loss function. Before training, we use data augmentation technology to change the training data and further increase the amount of training data. Here we use random rotation and random flipping in the x direction, and train the data extraction patches at the same time. 64 patches are cropped from a single data, which further increases the amount of training data. The super-resolution network has 20 convolutional layers, and the convolution kernel size is 3×3×64, so the receptive field size is 41×41, and the patch size is selected as 41×41. We use the SGDM method to train the network. The initial learning rate is set to 0.1, and it is reduced by one tenth every 10 rounds, for a total of 50 rounds of training. Using gradient clipping, the gradient is limited to [-0.01, 0.01], and a regularization strategy is used to constrain it. The regularization uses the L2 norm and the regularization factor is selected as 0.01.

[0089] Algorithm effectiveness verification experiment

[0090] In order to better demonstrate the advantages of the method of the present invention, we start from three directions: (1) by storing only the forward wave field, and using the strategy of simultaneously calculating the wave field and gradient data to reduce the memory usage during operation; (2) using the Nyquist sampling theorem to implement wave field downsampling in the time dimension, so as to further reduce memory usage and improve computing efficiency; (3) finally combining the gradient recovery model based on super-resolution technology, the computing efficiency is greatly improved and the inversion cost is saved without affecting the inversion quality as much as possible. The experiment was carried out 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 is ds=0.02m, the time step size is 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 model of the inversion 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, and 40 sources and 100 receivers are set 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), full waveform inversion with wavefield storage strategy (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. In the inversion, the maximum number of iterations is controlled to 30. First, the time sampling interval nt and the space 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] From the inversion results, it can be found that the use of the gradient recovery model for gradient recovery can achieve the purpose of reducing calculation time and memory usage without affecting the inversion accuracy. In order to quantitatively describe the inversion results, we calculate the model error and tabulate the relevant parameters of the above inversion results as follows. The memory usage part only calculates the memory occupied by the wave field 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 was ds=0.02m, the time step size was 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. The multi-offset data acquisition method was adopted, and a 400Mhz Ricker wavelet was used to simulate the excitation source. The real 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, the spatial downsampling interval nk and the temporal downsampling interval nt, on the performance of FWI, three groups of experiments were added when nk = 2 and nt was 3, 4, and 5, respectively, compared with the simple model experiment mentioned above. 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, and when nk increases to 3, too much effective information is lost, and FWI is prone to problems of difficulty in convergence or too long time spent in the online search phase, so it is not discussed in detail.

[0097] In order to achieve better imaging effects, 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 As shown, the relevant parameters are summarized in Table 2. Under the premise of satisfying the Nyquist law, selecting the maximum time sampling interval nt can achieve the maximum speedup ratio while ensuring the degree of precision loss, and can further compress the wave field storage memory, which is about 4.17% of the original; when nt exceeds the limit of the maximum sampling time interval, the precision loss index will rise rapidly, and FWI may cause the inversion to be difficult to converge and the search step size to decrease due to the lack of effective information. At the same time, it is difficult to calculate the correct gradient information, and the calculation time will also rise rapidly; therefore, for the 400Mhz antenna, we select nt not exceeding 3 to carry out the next experiment.

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

[0099]

[0100]

[0101] Numerical experiments with a real hydrological model

[0102] Established a Figure 8 The real hydrological model shown in a has a simulation area size of 200×400, a spatial step size of ds=0.01m, a time step size of dt=0.022ns, and a total of 2200 time steps. A 0.08m air layer is set above the surface, and 80 sources and 200 receivers are evenly set in the air layer. The multi-offset data acquisition method is also adopted, and the excitation source is a 400MHz Ricker wavelet. In order to achieve better imaging effects, a multi-scale strategy is adopted to carry out full waveform inversion on two frequency bands of 100Mhz and 400Mhz. The traditional full waveform inversion for this model is difficult to be performed on a personal microcomputer, so a large workstation is used to carry out related experiments.

[0103] Comparing the traditional full waveform inversion results with the optimized full waveform inversion results Fig. 9 As shown in Table 3, the inversion operation time and reconstruction error data are shown in Table 3. As can be seen from the figure, T-FWI well inverts the complex interface conditions and medium parameters. Due to the complexity of the underground medium, some deep information in the inversion result is missing, but it does not affect the geological interpretation work; the V-FWI results proposed by the present invention are almost consistent with the T-FWI results, and the difference between the two can hardly be judged by the naked eye. The reconstruction errors of the two and the real model are calculated as shown in the table. When nt=2, the acceleration ratio can reach 48.13% relative to T-FWI, and the memory is reduced to the original 6.25%, while the accuracy loss is only 0.56%; when nt=3, the acceleration ratio can reach 52.08% relative to T-FWI, and the memory is reduced to the original 4.17%, while the accuracy loss is only 0.98%. It can be seen that the V-FWI method is very conducive to the efficient application of full waveform inversion in actual situations. This optimization method for the percentage of original data has its unique advantages when facing large-scale data and models.

[0104] Table 3 Inversion operation 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 ground penetrating radar inversion imaging model as the current model; S2. Based on the super-resolution network, an initial gradient recovery model is constructed; S3. Obtain historical ground penetrating radar model image data and gradient data, train the initial gradient recovery model obtained in step S2 to obtain a gradient recovery model; S4. Perform a forward modeling process, compress the wave field in the time dimension based on the Nyquist sampling law, and obtain a compressed wave field; S5. spatially downsample the compressed wave field obtained in step S4 to obtain and store the downsampled forward wave field; S6. Based on the down-sampled forward wavefield obtained in step S5, the accompanying wavefield is used as a temporary variable to calculate the fuzzy gradient information; S7. Obtain gradient information according to the fuzzy gradient information obtained in step S6 and the gradient recovery model obtained in step S3; S8. Select the step size based on the Wolfe criterion, and then update the current model in combination with 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.

2. The low-memory inversion imaging method of 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 underground medium parameters by minimizing the objective function, thereby obtaining an inversion result.

3. The low-memory inversion imaging method of ground penetrating radar based on super-resolution technology according to claim 2 is characterized in that: The objective function is expressed using the following formula: 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; m=ε(r) Where ε(r) is the spatial distribution of the model medium parameters.

4. The low-memory inversion imaging method of ground penetrating radar based on super-resolution technology according to claim 1, characterized in that: 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 convolutional layer is 3×3×64; the convolutional layer module includes a convolutional layer, and the convolution kernel size is 3×3×64; 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 by 19 convolutional layer-ReLu layer modules in sequence, and finally reconstructed by the convolutional layer module; zeros are filled 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.

5. The low-memory inversion imaging method of ground penetrating radar based on super-resolution technology according to claim 1, characterized in that: Step S4 specifically includes the following steps: For the ground penetrating radar electromagnetic signal, the sampling frequency is calculated based on the Nyquist sampling theorem, and then the maximum sampling interval is calculated using the following formula: Among them, sampt is the sampling interval time; f s is the sampling frequency; f max 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: nt=sampt / dt 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; The forward wavefield is downsampled with nt as the downsampling interval to obtain the compressed wavefield.

6. The low-memory inversion imaging method of ground penetrating radar based on super-resolution technology according to claim 1, characterized in that: Step S5 specifically includes: down-sampling the compressed wave field obtained in step S4, setting a sampling interval nk, selecting one wave field data for every nk spatial steps, saving the electromagnetic field value, and obtaining and storing the down-sampled forward wave field.

7. The low-memory inversion imaging method of 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; According to the obtained downsampled forward wavefield and the corresponding companion wavefield, the fuzzy gradient information of the current model objective function about the model parameters is calculated using the following formula: in, is the forward modeled wave field 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.

8. The method for low-memory inversion imaging of 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, reconstructing the fuzzy gradient information obtained in step S6 to obtain gradient information, which is expressed using the following formula: 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.

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