A new method of gravity potential field downward continuation

Abstract

The application discloses a novel gravity potential field downward continuation method, comprising the following steps: S1: establishing a D-Unet network; S2: training the D-Unet network by using high-plane potential field data one and low-plane potential field data one, and obtaining a trained D-Unet network; the low-plane potential field data one is a result obtained by using frequency domain downward continuation on the high-plane potential field data one; S3: obtaining high-plane potential field data two to be downward continued, and obtaining low-plane potential field data two obtained by using frequency domain downward continuation on the high-plane potential field data two; S4: labeling the high-plane potential field data two and the low-plane potential field data two, and inputting the high-plane potential field data two and the low-plane potential field data two into the trained D-Unet network to obtain a final downward continuation result of the high-plane potential field data two. The application has better effectiveness, accuracy and robustness, can more quickly and accurately obtain a gravity potential field downward continuation result, and provides technical support for characteristic analysis and research of a geological body.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of gravity potential field continuation, in particular to a new gravity potential field downward continuation method. BACKGROUND

[0002] The gravity potential field of a geological body is a spatial vector field of the earth's gravity, which is of great significance for the analysis and research of the characteristics of the geological body. The gravity potential field downward continuation is a method of converting high-plane gravity potential field data to low-plane potential field data, restoring the potential field data, especially highlighting high-frequency anomalies in the shallow part, strengthening the characteristics of the underground geological body, and facilitating the interpretation of geological problems. Since the conversion is a mathematical inverse problem, it is unstable. The potential field downward continuation method can be mainly divided into two aspects: spatial domain calculation and frequency domain calculation.

[0003] The spatial domain calculation method has high precision, but due to the complexity of the formula, the process is complicated and the calculation speed is slow, so it is not suitable for large quantity calculation and has poor practicability. In addition, the main method of the spatial domain potential field downward continuation method is the integral iteration method, which has high requirements for the original high-plane potential field data, generally requiring the terrain slope to be less than 15°, so the requirement for the terrain is relatively high, and the scope of application is greatly discounted. Although the integral iteration method has been accelerated compared with the traditional spatial domain equation solving time, the iterative method is still an infinite solution to a large integral equation in nature, so it still needs to occupy a large amount of computing resources and consume a large amount of computing time. In the daily use process, the method is 20 times slower than the frequency domain method, which is very undesirable from the engineering point of view. The frequency domain calculation method has the advantages of high calculation efficiency and is basically not limited by the size of the data, but this method will amplify high-frequency noise during calculation, which limits the precision of the frequency domain calculation method. SUMMARY

[0004] In view of the above problems, the present application aims to provide a new gravity potential field downward continuation method with moderate calculation speed and calculation accuracy.

[0005] The technical scheme of the present application is as follows:

[0006] A new gravity potential field downward continuation method, comprising the following steps:

[0007] S1: establishing a D-Unet network, wherein the D-Unet network is established by using a Densenet network structure instead of the feature extraction part in the Unet network;

[0008] S2: training the D-Unet network by using the high plane potential field data one and the low plane potential field data one, and obtaining the trained D-Unet network; the low plane potential field data one is a result of downward continuation of the high plane potential field data one in frequency domain;

[0009] S3: obtaining high plane potential field data two to be downward continued, and obtaining low plane potential field data two of the high plane potential field data two by downward continuation in frequency domain;

[0010] S4: making the high plane potential field data two and the low plane potential field data two into labels, and inputting them into the trained D-Unet network to obtain a final downward continuation result of the high plane potential field data two.

[0011] Preferably, in step S1, the D-Unet network is composed of a Dense block, a transition layer, a common layer, a convolutional layer, a drop out layer and an up convolutional layer; the activation function of the convolutional layer is a ReLU function, and the convolution kernel is 3*3; the convolution kernel of the up convolutional layer is 2*2;

[0012] The input data of the D-Unet network is 256*256 data;

[0013] After the input data is subjected to one Dense block operation, it is subjected to one 3*3 convolution, and then enters the transition layer; the transition layer performs one 2*2 maximum pooling on the input data, and then the above steps are repeated three times, and finally 32*32*512 data is formed;

[0014] The 32*32*512 data is subjected to two 3*3 convolutions and one drop out layer;

[0015] Then, upward sampling by 2*2 convolution and two 3*3 convolutions are performed, which are repeated three times, and the results of each repetition are concatenated with the transition layer after the Dense block operation, and finally 64*64*16 feature data is formed;

[0016] The 64*64*16 feature data is subjected to one 3*3 convolution, and finally 64*64*1 feature data is formed, forming the output.

[0017] Preferably, the training of the D-Unet network in step S2 specifically comprises the following sub-steps:

[0018] S21: a model space of a sample data set is constructed, the model space is composed of multiple layer sources, each layer source is composed of multiple prisms;

[0019] S22: residual density is assigned to each prism of each layer source, and a hierarchical point casting method is used to randomly select different prisms for differential residual density assignment to obtain an anomaly body distribution result;

[0020] S23: forward operation is performed on the prisms of each layer source to obtain total field data of a low plane;

[0021] S24: the total field data of the low plane is upward continued in the frequency domain to obtain simulated field data of a high plane, i.e., the high plane field data one;

[0022] S25: the simulated field data of the high plane is downward continued in the frequency domain to obtain simulated field data of a low plane, i.e., the low plane field data one;

[0023] S26: the high plane field data one and the low plane field data one are taken as common inputs of the D-Unet network, the model is trained, and a trained D-Unet network is obtained.

[0024] Preferably, in step S22, when residual density is assigned, the assignment range of residual density is [-0.6, 0.6] g / cm 3 .

[0025] Preferably, in step S25, when downward continuation in the frequency domain is performed, the Tikhonov regularization method is used for downward continuation.

[0026] Preferably, when downward continuation is performed, the downward continuation operator is 0.01.

[0027] Preferably, in step S3, when downward continuation in the frequency domain is performed, the Tikhonov regularization method is used for downward continuation.

[0028] Preferably, in step S2, before the high plane field data one and the low plane field data one are input into the D-Unet network for training, 10% of the data in the high plane field data one and the low plane field data one is subjected to noise processing.

[0029] The present application has the following beneficial effects:

[0030] The application can improve the training easiness of the network, make the network more robust, effectively alleviate the gradient vanishing effect, and improve the robustness of the model by replacing the feature extraction part in the Unet network with the Densenet network structure to construct a new D-Unet network. BRIEF DESCRIPTION OF DRAWINGS

[0031] In order to more clearly illustrate the technical solutions in the embodiments of the present application or the prior art, the drawings needed to be used in the embodiments or the prior art description will be briefly introduced. Obviously, the drawings in the following description are only some embodiments of the present application, and other drawings can be obtained by those skilled in the art without creative labor.

[0032] Figure 1 Fig. 1 is a schematic diagram of the D-Unet network model structure of the present application;

[0033] Figure 2 Fig. 2 is a schematic diagram of the structure of the Dense block in the D-Unet network model of the present application;

[0034] Figure 3 Fig. 3 is a model space schematic diagram of a sample data set of a specific embodiment;

[0035] Figure 4 Fig. 4 is a schematic diagram of the downward continuation result of the gravity potential field of a specific embodiment. DETAILED DESCRIPTION

[0036] The present application will be further described below in combination with the drawings and embodiments. It should be noted that the embodiments in the present application and the technical features in the embodiments can be combined with each other without conflict. It should be noted that all technical and scientific terms used in the present application have the same meaning as generally understood by those skilled in the art to which the present application belongs. The present application discloses that the "including" or "containing" and similar words mean that the elements or objects before the words cover the elements or objects listed after the words and their equivalents, and do not exclude other elements or objects.

[0037] The present application provides a new gravity potential field downward continuation method, comprising the following steps:

[0038] S1: establishing a D-Unet network, wherein the D-Unet network is established by using a Densenet network structure to replace the feature extraction part in the Unet network.

[0039] Unet is an improved structure of full convolutional neural network (FCN), which adopts a symmetrical "U" type encoding-decoding structure, extracts sample data features through downsampling and fusion, splices the channel number, and improves the effectiveness and generalization ability of information. However, due to the running mode of Unet, the neighborhood overlapping part will be calculated repeatedly, so that when the network layer is deep, the model occupies a large amount of GPU memory and the operation speed is too slow. If the parameters are not selected correctly, there may also be phenomena such as gradient explosion or gradient disappearance.

[0040] The application replaces the feature extraction part in the Unet network structure with the Densenet network structure to form a new network structure. It can effectively alleviate the gradient disappearance problem of the model by using the Densenet network. At the same time, by using fewer parameters, it can strengthen feature transmission and reduce feature loss through feature reuse. Therefore, it can train with few samples and solve complex problems.

[0041] In one specific embodiment, as shown in Figure 1 The application extracts the main part of the Unet network structure, that is, the "U" type main part of the "U" type encoding-decoding structure, forms a Dense block by processing part of the network structure features in the Densenet, replaces the feature extraction part of the "U" type structure in the Unet network, and forms the final D-Unet network structure. Specifically, the D-Unet network is composed of a Dense block, a transition layer, a common layer, a convolutional layer, a drop out layer, and an up convolutional layer; the activation function of the convolutional layer is ReLU function, and the convolution kernel is 3*3; the convolution kernel of the up convolutional layer is 2*2;

[0042] The input data of the D-Unet network is 256*256 data;

[0043] After the input data is operated by the Dense block once, it is convolved by 3*3, then enters the transition layer, the transition layer performs 2*2 maximum pooling on the input data, and then the above steps are repeated 3 times to finally form 32*32*512 data;

[0044] The 32*32*512 data is convolved twice by 3*3 and undergoes a drop out layer;

[0045] Then, up-sampling is performed by using 2*2 convolution, and 3*3 convolution is performed twice, repeated three times, and the results of each repetition are concatenated with the transition layer after the dense block operation, and finally 64*64*16 feature data is formed.

[0046] The 64*64*16 feature data is convolved once by 3*3, and finally 64*64*1 feature data is formed to form the output.

[0047] In the above embodiment, the convolution layer of the U-shaped main stem of the model is a 3*3 convolution layer, and the activation function is a ReLU function with fast convergence, weak gradient disappearance, and sparse expression. The maximum pooling method is selected for the pooling layer to improve the generalization ability of the model. And add a Dropout layer at the deep part of the model, set the discard probability to reduce the feature reuse rate and improve the generalization ability. The deconvolution method is used as the up-sampling method.

[0048] In the fusion process of the Denseblock, as shown in Figure 2 , the main use is the dense connection mechanism of the Denseblock, which connects all the calculation layers, that is, each layer calculation accepts all the previous layer contents as input. Then, multiple Dense Blocks are connected and combined by using the Transition Layer to form the overall Densenet network architecture. The core is to establish the "short circuit connection" between the front and back layers, which can better propagate the gradient. The Channel-BN-ReLU-Conv module, which is represented as the channel superposition after Batch Normalization, uses ReLU as the activation function, and finally performs 3*3 stride convolution. Through such combination, the training ease of the network is improved, the network is more robust, the gradient vanishing effect is effectively reduced, and the robustness of the model is improved.

[0049] S2: training the D-Unet network by using the high plane potential field data one and the low plane potential field data one to obtain the trained D-Unet network; the low plane potential field data one is a result of downward continuation of the high plane potential field data one in the frequency domain.

[0050] In one specific embodiment, training the D-Unet network specifically includes the following sub-steps:

[0051] S21: constructing a model space of a sample data set, the model space being composed of multiple layer sources, each layer source being composed of multiple prisms.

[0052] In one specific embodiment, as Figure 3As shown, the model space extends the subsurface to a size of 255x255 prisms, each with a length, width and height of 50m, thereby constituting a single-layer depth layer source. The depth of the top surface of all layer sources is selected in the range of 300-800m below the observation surface, the height of the single layer and prism is 50m, and there are 10 layers in total.

[0053] S22: Assign a residual density to each prism of each layer source, and use the layered point casting method to randomly select different prisms for differentiated residual density assignment to obtain an anomaly body distribution result.

[0054] In one specific embodiment, when assigning residual density, the assignment range of residual density is [-0.6, 0.6] g / cm 3 .

[0055] S23: Perform forward calculation on the prisms of each layer source to obtain total field data of the low plane.

[0056] S24: Perform frequency domain upward continuation on the total field data of the low plane to obtain simulated field data of the high plane, i.e., the high plane field data one.

[0057] S25: Perform frequency domain downward continuation on the simulated field data of the high plane to obtain simulated field data of the low plane, i.e., the low plane field data one.

[0058] In one specific embodiment, the Tikhonov regularization method in the frequency domain is used for downward continuation, and the downward continuation operator is 0.01 when performing downward continuation.

[0059] S26: Take the high plane field data one and the low plane field data one as common inputs of the D-Unet network, train the model, and obtain a trained D-Unet network.

[0060] It should be noted that the forward calculation, frequency domain upward continuation, frequency domain downward continuation, Tikhonov regularization method, etc. are all prior art, and the specific steps will not be repeated here.

[0061] In one specific embodiment, before the high plane field data one and the low plane field data one are input into the D-Unet network for training, 10% of the data in the high plane field data one and the low plane field data one are subjected to noise processing, which can improve the convergence ability and robustness of the model.

[0062] S3: Obtain high plane field data two to be downward continued, and use frequency domain downward continuation to obtain low plane field data two after downward continuation of the high plane field data two.

[0063] In a specific embodiment, when frequency domain downward continuation is performed, the Tikhonov regularization method is used for downward continuation.

[0064] S4: The high planar potential field data two and the low planar potential field data two are made into labels and are jointly input into the trained D-Unet network to obtain a final downward continuation result of the high planar potential field data two.

[0065] In a specific embodiment, taking a gravity potential field as an example, the present application is used for downward continuation. In this embodiment, the Tikhonov regularization method is used for downward continuation when frequency domain downward continuation is performed. At the same time, the Tikhonov regularization method is directly used for downward continuation of the gravity potential field, and the accuracy of the present application is compared.

[0066] The computing device CPU used in this embodiment is Intel i9 12900f, the GPU is Nvidia A5000, and the computer system is Windows 10. The results of the gravity potential field downward continuation in this embodiment are shown in FIG. 1, wherein, Figure 4 Figure 4 (a) is a schematic diagram of the gravity potential field to be downward continued (wherein two white lines are the positions of two faults), Figure 4 (b) is a schematic diagram of the result of downward continuation directly using the Tikhonov regularization method, Figure 4 (c) is a schematic diagram of the result of downward continuation using the present application (without adding noise), Figure 4 (d) is a schematic diagram of the result of downward continuation using the present application (adding 10% noise). The error results of each method are shown in Table 1:

[0067] Table 1 Comparison results of different downward continuation methods

[0068] Downward continuation method Tikhonov regularization Invention (no noise added) Invention (10% noise added) Root mean square error 3.8661 3.7403 3.0626 Calculation time 0.2531s 0.1896s 0.1907s

[0069] From Figure 4 and Table 1, it can be seen that the error of the present application is lower than that of the direct use of the Tikhonov regularization method in actual application, and after adding noise, the stability of the model can be improved, and the error is smaller. From the calculation time results, when the present application does not add noise, the calculation time is shortened by 25.09% compared with the direct use of the Tikhonov regularization method, and when the present application adds 10% noise, the calculation time is shortened by 24.65% compared with the direct use of the Tikhonov regularization method. The present application has shorter time consumption and has a great speed advantage over the wave number domain.

[0070] In summary, the present application has improved time consumption and precision compared with the traditional Tikhonov regularization method, and has made significant progress.

[0071] ​The above merely describes preferred embodiments of the present application, and is not intended to limit the present application in any form. Although the present application has been disclosed with the preferred embodiments as above, it is not intended to limit the present application. Any person skilled in the art, without departing from the technical solution of the present application, can make some changes or modifications to the above disclosed technical content to obtain equivalent embodiments with equivalent changes. However, any simple modification, equivalent change and modification made to the above embodiments according to the technical essence of the present application, as long as it does not deviate from the technical solution of the present application, shall still fall within the scope of the technical solution of the present application.

Claims

1. A novel method for downward extension of a gravitational potential field, characterized in that, Includes the following steps: S1: Establish a D-Unet network, which is built by replacing the feature extraction part of the Unet network with a Densenet network structure; The D-Unet network consists of a Dense block, a transition layer, a common layer, a convolutional layer, a drop-out layer, and an up convolutional layer. The activation function of the convolutional layer is the ReLU function, and the convolutional kernel is 3*3. The convolutional kernel of the up convolutional layer is 2*2. The input data for the D-Unet network is 256*256 data; The input data undergoes a Dense block operation, followed by a 3*3 convolution, and then enters the transition layer. The transition layer performs a 2*2 max pooling on the input data. This process is repeated three times to finally form 32*32*512 data. The 32*32*512 data is subjected to two 3*3 convolutions and then goes through a dropout layer. Then, upsampling is performed using 2*2 convolution and two 3*3 convolutions, repeated three times. The result of each repetition is concatenated with the transition layer after the dense block operation, finally forming 64*64*16 feature data. The 64*64*16 feature data is convolved once with a 3*3 convolution to finally form 64*64*1 feature data, which is then output. S2: The D-Unet network is trained using high-plane potential field data one and low-plane potential field data one to obtain a trained D-Unet network; the low-plane potential field data one is the result of the high-plane potential field data one after frequency domain downward extension. S3: Obtain the second high-plane potential field data to be extended downward, and use frequency domain downward extension to obtain the second low-plane potential field data after downward extension of the second high-plane potential field data; S4: The high plane potential field data 2 and the low plane potential field data 2 are made into labels and input together into the trained D-Unet network to obtain the final downward extension result of the high plane potential field data 2.

2. The novel downward extension method of gravitational potential field according to claim 1, characterized in that, Step S2, training the D-Unet network specifically includes the following sub-steps: S21: Construct the model space of the sample dataset, wherein the model space consists of multiple layers of sources, and each layer of sources consists of multiple prisms; S22: Assign residual density values ​​to each prism of each layer source, and use the layered projection method to randomly select different prisms for differentiated residual density assignment to obtain the distribution results of the anomaly. S23: Perform forward modeling on the prisms of each layer source to obtain the overall potential field data of the lower plane; S24: Extend the overall potential field data of the lower plane upward in the frequency domain to obtain the simulated potential field data of the higher plane, namely the first potential field data of the higher plane. S25: The analog potential field data of the high plane is extended downward in the frequency domain to obtain the analog potential field data of the low plane, namely the low plane potential field data one. S26: Use the high plane potential field data 1 and the low plane potential field data 1 as the common input of the D-Unet network to train the model and obtain the trained D-Unet network.

3. The novel downward extension method of gravitational potential field according to claim 2, characterized in that, In step S22, when assigning the residual density value, the range of the residual density value is [-0.6, 0.6] g / cm³. 3 .

4. The novel downward extension method of gravitational potential field according to claim 2, characterized in that, In step S25, when performing downward extension in the frequency domain, the Tikhonov regularization method is used for downward extension.

5. The novel downward extension method of gravitational potential field according to claim 4, characterized in that, When performing downward extension, the downward extension operator is set to 0.

01.

6. The novel downward extension method of gravitational potential field according to claim 4, characterized in that, In step S3, when performing downward extension in the frequency domain, the Tikhonov regularization method is used for downward extension.

7. The novel downward extension method of gravitational potential field according to any one of claims 1-6, characterized in that, In step S2, before the high-plane bit field data one and the low-plane bit field data one are input into the D-Unet network for training, 10% of the data in the high-plane bit field data one and the low-plane bit field data one are subjected to noise processing.

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