CN114048823A

CN114048823A - Resistivity inversion model establishment method based on full convolution network

Info

Publication number: CN114048823A
Application number: CN202111411003.0A
Authority: CN
Inventors: 王绪本; 袁崇鑫; 邓飞; 王堃鹏
Original assignee: Chengdu Univeristy of Technology
Current assignee: Chengdu Univeristy of Technology
Priority date: 2021-11-25
Filing date: 2021-11-25
Publication date: 2022-02-15

Abstract

The invention discloses a resistivity inversion model building method based on a full convolution network, which comprises the following steps: establishing magnetotelluric sounding model sample data sets with different resistivity sizes and shapes, and performing forward transformation by adopting Maxwell equations to obtain apparent resistivity and phase data corresponding to the magnetotelluric sounding model sample data sets; the apparent resistivity and the phase data are used as model input, the magnetotelluric sounding model corresponding to the apparent resistivity and the phase data is used as output, a full convolution neural network U-net network is constructed, learning mapping is carried out, and training and parameter adjustment are carried out on the network, so that an optimal inversion network weight and a hyper-parameter model are obtained; fitting a linear function to a corresponding underground resistivity model by using the trained apparent resistivity and phase data; and inputting the apparent resistivity and the phase data concentrated in the verification into the model to obtain inverted resistivity data.

Description

Resistivity inversion model establishment method based on full convolution network

Technical Field

The invention relates to the technical field of magnetotelluric sounding, in particular to a resistivity inversion model building method based on a full convolution network.

Background

The magnetotelluric sounding has the characteristics of low detection cost, large detection depth, obvious structural reflection and the like, the resistivity is one of the most important parameters in electromagnetic exploration, and an accurate resistivity model is a key premise of magnetotelluric imaging technology. Such resistivity model information is typically obtained by conventional inversion, which is time consuming and labor intensive, because in conventional inversion problems multiple forward modeling problems need to be solved, and the large width and large depth of the measured electromagnetic data greatly increases the computational cost of forward simulation. Accurate simulation of electromagnetic phenomena requires accurate models and leads to millions of unknown forward problems (Shantsev et al, 2017). Magnetotelluric inversion is a typical linear inverse problem, has multiple solutions, and most magnetotelluric inversion methods of the class are based on objective function iterative inversion and obtain better calculation results, such as OCCAM inversion (Constable et al, 1987), fast relaxation inversion (RRI) (Smith J T and book J R, 1991), nonlinear conjugate gradient inversion (Rodi W and Mackie R L, 2001), and improved REBOCC inversion (sirinpumvarporous W and egberg G, 2000), SBI inversion (De Groot-Hedlin C and Constable S, 2004), adaptive regularization inversion (chember et al, 2005), least squares regularization inversion (LEE S K et al, 2009; Oskooi and Darijani, 2014), magnetotelluric gaussian-newton three-dimensional inversion (sasaev, 2004; Avdeev and avdea, 2009), and others. Although these conventional methods have been successful in many applications, they are still limited in some cases due to the problems of strong dependence on initial resistivity models, low computational efficiency, human subjective factors, etc., and influence the accuracy and stability of inversion to some extent.

In recent years, with the rise of big data and artificial intelligence, an inversion method for solving a nonlinear problem based on deep learning has been greatly developed in geophysical data processing. Such as: the xu sea wave and the like (2006) adopt a neural network to realize direct current electrical method two-dimensional resistivity inversion; the WangHe and the like (2018) build a BP neural network model and optimize by using a genetic algorithm, so that magnetotelluric two-dimensional inversion of the genetic neural network is realized; the Qian before wearing et al (2013) combines the BP neural network with the particle swarm optimization, and is applied to the resistivity imaging nonlinear inversion. HINTON and the like (2006) provide a Deep Neural Network (DNN) model, the DNN has obvious advantages in feature extraction and modeling, deeper features can be mined from original input data, and the model has super-strong complex function approximation performance. With the development of a Convolutional Neural Network (CNN) into a type of deep neural network, the characteristics of the CNN can effectively reduce the complexity of the network in the aspects of local connection, weight sharing, pooling operation and the like, and improve the robustness and fault-tolerant capability of a network model (2017).

At present, the application of CNN in the field of geophysical has achieved some research results, such as: puzyrev (2019) utilizes CNN to realize two-dimensional inversion of the electromagnetic data received by the ground and transmitted by the vertical magnetic dipole source in the well; puzyrev and Swidinsky (2020) apply DL to the one-dimensional inversion of marine frequency domain controllable electromagnetic data; noh et al (2020) realize frequency domain aviation electromagnetic data convolution neural network one-dimensional inversion, Yang et al (2019) successfully apply FCN to seismic velocity model inversion, and the research shows that various deep learning network models have good application effects in the field of geophysical. However, in the electromagnetic inversion, the FCN network model is not used in the magnetotelluric inversion.

In the prior art, for example, the patent of the invention in china with the patent application number "202110455258.0" and the name "magnetotelluric inversion method based on full convolution neural network" includes: constructing a multi-dimensional geoelectric model, calculating apparent resistivity of corresponding dimensions by forward modeling, forming a sample set, and dividing the sample set into a plurality of training sets and test sets; constructing a full convolution neural network structure model to obtain initialized full convolution neural network model parameters; training and testing the model based on the training set and the testing set to obtain optimized full convolution neural network structure model parameters; determining whether the training of the full convolution neural network structure model is finished or not according to the fitting error change corresponding to the training set and the test set; and finally, inputting the actually measured apparent resistivity into the trained model for inversion, and further optimizing the model by analyzing the accuracy of an inversion result until an inversion fitting error meets a set error requirement.

In addition, like the magnetotelluric inversion based on the convolutional neural network, the Liaojiong's magnetotelluric inversion based on the convolutional neural network' first, two-dimensional forward modeling is carried out on different models to construct a sample data set, then, apparent resistivity and phase data are used as dual-channel network input, a convolutional neural network framework is built by using geoelectric model parameters corresponding to the apparent resistivity and phase data as output, supervision learning and parameter adjustment are carried out on the network, so that the optimal inversion network arrangement and the hyper-parameters are obtained, and finally, an unknown geoelectric model is inverted by using the trained network.

The above technique has the following disadvantages:

firstly, the feature extraction is insufficient, the sensitivity to the feature details is insufficient, the receptive field is too small, and the global information cannot be acquired. Secondly, it does not consider the relationship between pixels in the classification of the object, neglects the spatial regularization step used in the general segmentation method based on pixel classification, and lacks spatial consistency. Thirdly, the storage overhead is large, if the size of the image block used for each pixel is 15x15, the required storage space is 225 times that of the original image; fourth, computational inefficiency results because the adjacent pixel blocks are duplicated, and the computer needs to do a large number of duplicate calculations. And fifthly, only the condition of single-channel parameters is considered, information extraction is less, precision is low, and errors are larger.

Disclosure of Invention

Aiming at the problems, the invention aims to provide a resistivity inversion model building method based on a full convolution network, and the technical scheme adopted by the invention is as follows:

the resistivity inversion model building method based on the full convolution network comprises the following steps:

establishing a sample data set of magnetotelluric depth measurement models with different resistivity sizes and shapes, and performing forward transformation by adopting Maxwell equations to obtain apparent resistivity and phase data corresponding to the sample data set; dividing a sample data set into a training set and a verification set;

the apparent resistivity and the phase data in the training set are used as model input, the magnetotelluric depth measurement model corresponding to the model input is used as output, a full convolution neural network U-net network is established, learning mapping is carried out, training and parameter adjustment are carried out on the full convolution neural network U-net network, and therefore the optimal inversion network weight and the hyper-parameter model are obtained;

fitting a linear function to a corresponding underground resistivity model by using the trained apparent resistivity and phase data; and inputting the apparent resistivity and the phase data concentrated in the verification into the underground resistivity model to obtain inverted resistivity data.

Further, the U-net network includes a first convolution layer, a first operation layer, a first maximum pooling layer, a second operation layer, a second maximum pooling layer, a third operation layer, a third maximum pooling layer, a fourth operation layer, a fourth maximum pooling layer, a fifth operation layer, a first deconvolution layer, a sixth operation layer, a second deconvolution layer, a seventh operation layer, a third deconvolution layer, an eighth operation layer, a fourth deconvolution layer, a ninth operation layer, and a second convolution layer, which are connected in sequence, a first hopping connection layer disposed between the first operation layer and the ninth operation layer, a second hopping connection layer disposed between the second operation layer and the eighth operation layer, a third hopping connection layer disposed between the third operation layer and the seventh operation layer, and a fourth hopping connection layer disposed between the fourth operation layer and the sixth operation layer.

Further, the first operation layer, the second operation layer, the third operation layer, the fourth operation layer, the fifth operation layer, the sixth operation layer, the seventh operation layer, the eighth operation layer and the ninth operation layer comprise a third convolution layer, a normalization layer and an activation function which are connected in sequence.

Preferably, the apparent resistivity and phase data are used to fit linear functions to the corresponding subsurface resistivity model with a maximum number of iterations of 20.

Further, the first jump connection layer, the second jump connection layer, the third jump connection layer and the fourth jump connection layer combine the local shallow feature mapping, the global feature mapping and the deep feature mapping in a jump layer mode.

Preferably, the receptive field size of the U-net network is set to 64, 128, 256, 512 and 1024 in sequence.

Further, the expression of the fitted linear function is:

wherein the content of the first and second substances,

representing a U-Net based network, and also representing a non-linear mapping of the network,

respectively representing the input and output of the network,

which indicates the set of parameters to be learned,

the convolution weights representing the activation function,

represents the convolution weight of the soft-max function,

representing the deviation of the activation function (prior art),

the deviation of the soft-max function is expressed,

represents the non-linear activation function introduced and,

represents a sub-sampling function (e.g., max pool, average pool),

which represents a convolution operation, is a function of,

representing the soft-max function.

Compared with the prior art, the invention has the following beneficial effects:

(1) the invention skillfully provides an original U-Net in image processing to read an input image in an RGB color channel, wherein the channel represents information in the input image; in addition, the invention adopts Maxwell equation forward transformation to obtain the visual resistivity and phase dual-channel data which are generated at different gather positions, the input gather is the same as the model gather, and all the gather electromagnetic data are sent to the network together to improve the data redundancy.

(2) The invention realizes the projection of the domain by a required network by establishing a resistivity model, namely, truncating a characteristic diagram obtained by the last 3 x 3 convolution into the same size of the resistivity model, and modifying the channel of an output layer into 1. Training the neural network in the contraction and expansion process, and directly mapping the electromagnetic data to an accurate resistivity model;

(3) the present invention is in the maximum pooling layer, i.e. the first half of the network is coding, its function is feature extraction (obtaining local features and making picture-level classification), and the theoretical meaning of this down-sampling is that it can increase the robustness to some small disturbances of the input image, reduce the risk of overfitting, reduce the amount of computation, and increase the size of the receptive field. In addition, the invention is in the deconvolution layer, namely the latter half of the network decodes, namely utilize the abstraction characteristic of the previous code to resume the course of the original picture size, decode when resuming the (deconvolution) data of downsampling, the characteristic size will change, will have the loss of information inevitably, in this time, the effect of jumping the connection layer is highlighted, jump the connection layer and has played the role of supplementary information;

(4) the invention sets a jump connection layer in a U-Net network, which is a structure for realizing feature fusion, and uses overlapping operation, namely copying and shearing, in the U-Net, so that the jump connection layer in the U-Net plays a role of supplementing information, and a model depends on more information;

(5) the invention combines the local shallow feature mapping of the right path with the global and deep feature mapping of the left path in the network structure, thereby improving the problem of insufficient information during up-sampling and further improving the precision;

(6) the four largest pooling layers of the invention are used for reducing dimensionality, and the four deconvolution layers are used for recovering dimensionality; nine third convolutional layers are used for feature extraction, and four jump connection layers are used for feature fusion;

in conclusion, the method can realize accurate positioning and imaging on the geoelectric model, can approach to a real model more accurately, and simultaneously compares the FCN network model with nonlinear conjugate gradient inversion to verify the feasibility, effectiveness and generalization capability of the FCN network model in magnetotelluric inversion.

Drawings

In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings needed to be used in the embodiments will be briefly described below, it should be understood that the following drawings only illustrate some embodiments of the present invention, and therefore should not be considered as limiting the scope of protection, and it is obvious for those skilled in the art that other related drawings can be obtained according to these drawings without inventive efforts.

FIG. 1 is a diagram of a network model architecture of the present invention.

FIG. 2 is a resistivity model (one) in a simulated random training dataset of the present invention.

FIG. 3 is a resistivity model (two) in a simulated random training dataset of the present invention.

FIG. 4 is a resistivity model (III) in a simulated random training dataset of the present invention.

FIG. 5 is a resistivity model (IV) in a simulated random training dataset of the present invention.

FIG. 6 is a plot of the mean variance between the predicted resistivity value and the true resistivity for the present invention.

FIG. 7 is a design stratigraphic model (one) of the present invention.

FIG. 8 is an FCN inversion model (one) of the present invention.

Fig. 9 shows an NLCG inversion model (one) according to the present invention.

FIG. 10 is a design stratigraphic model (two) of the present invention.

FIG. 11 shows the FCN inversion model (two) of the present invention.

Fig. 12 shows an NLCG inversion model (two) according to the present invention.

Figure 13 is a graph (one) of the predicted, NLCG and design model resistivity values in the resistivity and depth profile at 300km for the present invention.

Figure 14 is a graph (one) of the resistivity values predicted, NLCG and design model resistivity values in the 500km resistivity and depth profile of the present invention.

Figure 15 is a graph of predicted, NLCG and design model resistivity values at 300km for the invention in a resistivity and depth profile (two).

Figure 16 is a graph (two) of the resistivity values predicted, NLCG and design model resistivity values in the 500km resistivity and depth profile of the present invention.

FIG. 17 is a prediction chart of the present invention.

FIG. 18 shows the FCN prediction results of the present invention.

Fig. 19 shows the results of NLCG inversion according to the present invention.

Detailed Description

To further clarify the objects, technical solutions and advantages of the present application, the present invention will be further described with reference to the accompanying drawings and examples, and embodiments of the present invention include, but are not limited to, the following examples. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present application.

Examples

As shown in fig. 1 to 19, the present embodiment provides a method for building a resistivity inversion model based on a full convolution network. The U-Net network of the present embodiment is composed of a contracted path (left) for capturing geological features and an expanded path (right) for symmetric shape, thereby achieving accurate positioning. This form of symmetry is an encoder-decoder architecture that employs a companding architecture based on max-pool and transposed convolution. Given a fixed size convolution kernel (3 x 3 in this example), the effective acceptance domain of the net increases as the depth of the input into the net increases. Channels in the left path as the depth of the network increasesThe numbers are 64, 128, 256, 512 and 1024. In this embodiment, a layer jump method is adopted, and local shallow feature mapping of the right path is combined with global and deep feature mapping of the left path. The corresponding operational definitions are given in the table below, in which

And

for the convolution kernel, the mean and standard deviation in the batch normalization were calculated for each dimension of the small batch.

Wherein the content of the first and second substances,

representing a learnable parameter.

As shown in fig. 1, in the present embodiment, first, the original U-Net proposed in the image processing reads an input image in an RGB color channel, which represents information in the input image. In order to process electromagnetic data, the method inputs dual channels of apparent resistivity and phase, the dual channels are generated at different gather positions, the input gather is the same as the model gather, and all gather electromagnetic data are sent to a network together, so that the data redundancy is improved. Secondly, in normal U-Net, the output and input are in the same (image) domain. However, in the establishment of the resistivity model, in order to achieve this goal, the projection of the network implementation domain is required, that is, the feature map obtained by the last 3 × 3 convolution is truncated to be set to the same size as the resistivity model, and the channel of the output layer is modified to be 1. The neural network is enabled to train itself in the contraction and expansion process, and electromagnetic data are directly mapped to an accurate resistivity model.

In this embodiment, the electrical data of Qinghai-Tibet east edge is selected to establish a suitable small-scale training set. In the network model herein, the training output is the model resistivity and the training input is the apparent resistivity and phase from the forward modeling.

As shown in fig. 2 to fig. 5, in this embodiment, the initial model size is set to 600km × 180km, random models with different shapes and different resistivity values are generated, and four models in the simulated random training data set are selected in this embodiment. Secondly, for simplicity, this embodiment assumes 2 to 6 layers of each model as background resistivity, and the resistivity value of each layer varies arbitrarily between 5 Ω to 5000 Ω, and the size of each resistivity model is 60 × 121 grid points, i.e. 5KM apart in the lateral direction and 3KM apart in the longitudinal direction, and the frequency ranges from 0.0001 to 1000.

In order to solve maxwell's equations, the present embodiment employs a finite element format. That is, the maxwell equation is solved by using finite elements for each resistivity model, and the resistivity model has 60 × 121 grid points, that is, the apparent resistivity and the phase have 60 × 121 grid points. The resulting apparent resistivity and phase settings were input to the network model, which, like the resistivity model dataset, had 1000 samples.

In this embodiment, a two-dimensional resistivity model is inverted, and in a training phase, apparent resistivity and a phase value are read and enter 2 channels, the dimension is 60 × 121, and the hyper-parameters are set as follows:

the total number of training rounds is 2000, the mean square error value is rapidly reduced when training is started, after 1000 training rounds, the loss value is basically stable, the mean variance between the predicted resistivity value and the real resistivity is shown in figure 6, and a model with a smaller loss value is selected for testing.

In the present embodiment, the prediction results are as shown in fig. 7 to 12, and the prediction results are substantially matched with the corresponding actual geological structure conditions visually.

Further, the present embodiment compares the apparent resistivity of the test with the conventional NLCG inversion of the phase input channel, and compares the method proposed by the present embodiment with the NLCG. The present embodiment uses the same parameter settings as those used to generate the forward simulation training resistivity model data, with a maximum number of iterations of 20, a minimum fitting accuracy of 0.05, and a smoothing coefficient of 0.1. In this case, the same computer is used to perform numerical experiments, fig. 9 shows NLCG inversion results, comparing the two methods results, the FCN-based inversion method shows better results, and most of the geological structure, especially the deep structural features, are preserved.

For quantitative analysis of prediction accuracy, two horizontal positions, x =300km and x =500km, were selected in this example, and the prediction, NLCG and design model resistivity values were plotted in the resistivity and depth profiles as shown in fig. 13-16. It can be seen from the figure that most of the predicted values and trend trends match well with the true values and trends.

In this example, a test was performed using the Qinghai-Tibet eastern Cantonese bunghur-Hechuan segment. And compared with the numerical results of the NLCG method. The numerical experiment was performed on association T480, CPU: intel (R) core (TM) i5-8250U CPU @ 1.60 GHz; memory: 8 GB; GPU: NVIDIA GeForce MX 150.

In addition, the time required for computing on the CPU by a simulation model through NLCG inversion is 55 minutes and 23 seconds, and after the FCN-based inversion network is trained for 1633 minutes and 20 seconds, even on a lower device, the simulation model of the present embodiment only needs 2 seconds for predicting a new resistivity value each time, which is 1661 times faster than NLCG. This shows that the neural network can effectively approximate the non-linear mapping even with unknown apparent resistivity and phase data input. Compared with the traditional NLCG method, the method does not need iteration to find the optimal solution, and the calculation time is short. The main calculation time mainly occurs in a training stage, and is only executed once in the model building process, so that the FCN training cost can be ignored compared with the time required by performing traditional inversion on a large amount of data. Thus, FCN-based inversion methods result in a total computation time that is only a fraction of the time required for conventional physical inversion.

As shown in fig. 17 to 19, the actual address region experiment provides good evidence for the feasibility of the method for inverting the electromagnetic data from the original input apparent resistivity and phase input deep learning network without the initial resistivity model. This shows that even when unknown real experimental data is input, the neural network can effectively approximate the nonlinear mapping. Compared with the traditional NLCG method, the method does not need iteration to find the optimal solution, and the calculation time is short. The main calculation time mainly occurs in a training stage, and is only executed once in the model building process, so that the FCN training cost can be ignored compared with the time required by performing traditional inversion on a large amount of data. Thus, FCN-based inversion methods result in a total computation time that is only a fraction of that required by conventional physical inversion techniques.

The above-mentioned embodiments are only preferred embodiments of the present invention, and do not limit the scope of the present invention, but all the modifications made by the principles of the present invention and the non-inventive efforts based on the above-mentioned embodiments shall fall within the scope of the present invention.

Claims

1. The resistivity inversion model building method based on the full convolution network is characterized by comprising the following steps of:

2. The full convolution network resistivity-based inversion model building method of claim 1, the U-net network is characterized by comprising a first rolling layer, a first operation layer, a first maximum pooling layer, a second operation layer, a second maximum pooling layer, a third operation layer, a third maximum pooling layer, a fourth operation layer, a fourth maximum pooling layer, a fifth operation layer, a first deconvolution layer, a sixth operation layer, a second deconvolution layer, a seventh operation layer, a third deconvolution layer, an eighth operation layer, a fourth deconvolution layer, a ninth operation layer and a second rolling layer which are connected in sequence, a first jumping connection layer arranged between the first operation layer and the ninth operation layer, a second jumping connection layer arranged between the second operation layer and the eighth operation layer, a third jumping connection layer arranged between the third operation layer and the seventh operation layer, and a fourth jumping connection layer arranged between the fourth operation layer and the sixth operation layer.

3. The method for building the resistivity inversion model based on the full convolution network according to claim 2, wherein the first operation layer, the second operation layer, the third operation layer, the fourth operation layer, the fifth operation layer, the sixth operation layer, the seventh operation layer, the eighth operation layer and the ninth operation layer comprise a third convolution layer, a normalization layer and an activation function layer which are connected in sequence.

4. The full-convolution-network-based resistivity inversion model building method according to claim 1, wherein the first, second, third and fourth hopping connection layers combine local shallow feature mapping, global feature mapping and deep feature mapping in a layer hopping manner.

5. The full convolution network-based resistivity inversion model building method according to claim 1, wherein reception fields of the U-net network are sequentially set to 64, 128, 256, 512 and 1024.

6. The method for building a resistivity inversion model based on a full convolution network according to claim 3, wherein the expression of the fitted linear function is as follows: