Semi-aviation transient electromagnetic data denoising method based on decoupling representation learning

Through the method based on decoupling characterization learning, the problem of complex noise removal in semi-aviation transient electromagnetic data is solved, effective processing and signal separation of large noise data is achieved, and data cleanliness and signal accuracy is improved.

CN119717032AActive Publication Date: 2025-03-28CHENGDU UNIVERSITY OF TECHNOLOGY

Patent Information

Application Number
CN202411876680.3
Authority / Receiving Office
CN · China
Patent Type
Applications(China)
Current Assignee / Owner
Filing Date
2024-12-19
Publication Date
2025-03-28
Estimated Expiration
2044-12-19

AI Technical Summary

Technical Problem

The prior art is difficult to effectively remove complex noise in semi-aviation transient electromagnetic data, especially under high noise conditions, where traditional methods rely on empirical parameter selection and a single representation of deep learning methods is difficult to separate signals and noise.

Method used

Using a method based on decoupled representation learning, a known geophysical constrained electromagnetic resistivity model database is obtained, and the noise addition and segmentation of forward simulation data is carried out, and a decoupled representation learning network is built, and a pair of decoupled representations are outputted by the network to separate signals and noises.

Benefits of technology

It realizes effective denoising of complex field high noise data, improves data cleanliness and signal accuracy, and solves the shortcomings of traditional methods in noise processing.

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Abstract

The invention discloses a semi-aviation transient electromagnetic data denoising method based on decoupling representation learning, and the method comprises the steps: obtaining a known geophysical constraint electromagnetic resistivity model database DL-RMD, and carrying out the forward modeling processing, and obtaining forward modeling data; performing noise addition on the forward modeling data to obtain a plurality of sample pairs, and splitting the sample pairs into a training set, a verification set and a test set; establishing a decoupling representation learning network, and outputting a pair of decoupling analyses by using the decoupling representation learning network; training the decoupling characterization learning network by using the training set, and performing parameter adjustment fitting to obtain a trained decoupling characterization learning network; verifying and testing the trained decoupling representation learning network by using a verification set and a test set respectively; and acquiring actually acquired semi-aviation transient electromagnetic data, and performing de-noising processing by using the trained decoupling representation learning network. Through the scheme, the method has the advantages of simple logic, accuracy, reliability and the like.
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Description

Technical Field

[0001] The invention relates to the technical field of electromagnetic data processing, in particular to a semi-aeronautical transient electromagnetic data denoising method based on decoupled representation learning. Background Art

[0002] Semi-aerial transient electromagnetic method is a geophysical exploration technology developed on the basis of magnetotellurics. It extracts and measures geoelectric structure by observing the received secondary field signals, and by placing the observation system on a flying vehicle, such as a fixed-wing aircraft or helicopter, it can achieve rapid coverage of some large, inaccessible measurement areas. Since the system is observed in motion (fixed-wing aircraft or helicopter flight), it will inevitably introduce a lot of noise, and the noise conditions are complex, which brings great difficulties to the subsequent data processing. In order to ensure the accuracy and reliability of detection, noise removal is required.

[0003] Among them, semi-aeronautical transient electromagnetic data denoising refers to removing noise from noise data collected in the field to obtain clean data after denoising. However, most traditional methods rely on the selection of some empirical parameters, which puts high demands on the experience of denoising personnel, and these methods are more suitable for data with low noise levels, and it is difficult to denoise complex field large noise data. Among them, in the public technology of "publication number CN113655532A, named a method and system for removing motion noise from non-full-time semi-aeronautical transient electromagnetic data", it adopts: obtaining time domain secondary field sample data, and its sampling frequency and sample data period; extending the multiple half-cycle sample data contained in the secondary field sample data to the full time length; performing preliminary fitting on the full-time motion noise baseline, and obtaining the expected frequency through spectrum analysis; according to the expected frequency, using the inverse discrete Fourier transform to invert the full-time time domain motion noise; removing the obtained motion noise from the secondary field sample data. This technology only removes motion noise, and the noise caused by complex terrain cannot be processed.

[0004] Existing deep learning-based methods all output predictions of noise or signals, which is a single learning scheme rather than a decoupled one. This single representation makes it difficult to separate signal from noise, and the representation results often contain both noise and signal, which makes it difficult to effectively separate noise and signal when processing complex real signals, and can only focus on part of the information in the signal.

[0005] Therefore, it is urgent to propose a logically simple, accurate and reliable semi-aeronautical transient electromagnetic data denoising method based on decoupled representation learning. Summary of the invention

[0006] In view of the above problems, the purpose of the present invention is to provide a semi-aeronautical transient electromagnetic data denoising method based on decoupled representation learning. The technical solution adopted by the present invention is as follows:

[0007] The semi-aeronautical transient electromagnetic data denoising method based on decoupled representation learning includes the following steps:

[0008] Obtain the known geophysical constrained electromagnetic resistivity model database DL-RMD, and perform forward modeling to obtain forward simulation data;

[0009] Noise is added to the forward simulation data, and several sample pairs are obtained, which are then split into training set, validation set, and test set;

[0010] Build a decoupled representation learning network and use it to output a pair of decoupled parsing;

[0011] The decoupled representation learning network is trained using the training set, and parameter adjustment and fitting are performed to obtain the trained decoupled representation learning network;

[0012] The trained decoupled representation learning network is verified and tested using the validation set and test set respectively;

[0013] The actual collected semi-aeronautical transient electromagnetic data are obtained and denoised using the trained decoupled representation learning network.

[0014] Furthermore, adding noise to the forward modeling data includes the following steps:

[0015] Dividing the forward simulation data into two parts at a ratio of 1:1 to obtain first forward simulation data and second forward simulation data;

[0016] Gaussian noise is added to the first forward simulation data, and its expression is:

[0017] s n1 =s1+N(0,1)

[0018] Among them, s n1 represents the data after adding Gaussian noise; s1 represents the first forward simulation data; N(0,1) represents Gaussian noise;

[0019] Add mixed noise to the second forward simulation data, and its expression is:

[0020]

[0021] Among them, s n2 represents the data after adding mixed noise; s2 represents the second forward simulation data; STD represents linear noise; n represents the background noise distribution.

[0022] Furthermore, the expression of the background noise distribution n is:

[0023]

[0024] Where b is the noise level at 1 ms and t is the time.

[0025] Further, the decoupled representation learning network includes an encoder and a decoder;

[0026] The encoder comprises a first input layer, a first embedding layer and a first backbone network connected in sequence; the embedding layer performs a convolution operation on the forward simulation data with added noise obtained by the first input layer to obtain an embedded output; the first backbone network encodes the embedded output to obtain encoded data;

[0027] The decoder includes a second backbone network and a first linear layer connected in sequence; the second backbone network decodes the encoded data to obtain decoded data; and the first linear layer decouples and analyzes the decoded data output by the second backbone network.

[0028] Furthermore, the structures of the first backbone network and the second backbone network are the same, and the first backbone network includes a second input layer, a second embedding layer, a mixing layer, a second linear layer and a second output layer connected in sequence; the mixing layer includes a signal mixing layer and a channel mixing layer connected in sequence; the second input layer obtains forward simulation data with added noise; the second embedding layer performs a one-dimensional convolution operation on the data input by the second input layer to obtain embedded data; the signal mixing layer performs signal mixing on the embedded data to obtain first data; the channel mixing layer performs channel mixing on the first data after signal mixing to obtain second data; the second linear layer performs a full connection operation on the second data after channel mixing to obtain third data.

[0029] Furthermore, the signal mixing layer includes a first token transfer layer, a WKV operation layer and a first normalization layer; the first token transfer layer obtains the embedded data output by the second embedding layer, and puts the last data in the embedded data at the front end of the embedded data, and splits it in the channel dimension to obtain the value, key and received value of the embedded data; the WKV operation layer performs a WKV addition attention operation on the value and key of the embedded data to obtain fourth data; the fourth data output by the WKV operation layer is matrix multiplied with the received value of the embedded data, and is sent to the first normalization layer for normalization processing to obtain fifth data.

[0030] Furthermore, the channel mixing layer includes a second token transfer layer and a second normalization layer; the second token transfer layer obtains the fifth data and puts the last data in the fifth data at the front end of the fifth data to obtain the value corresponding to the fifth data and the received value; the value corresponding to the fifth data output by the second token transfer layer and the received value are mixed by matrix multiplication to obtain sixth data; the second normalization layer normalizes the sixth data.

[0031] Furthermore, the training set is used to train the decoupled representation learning network, and parameter adjustment and fitting are performed. The total loss function L is added to the decoupled representation learning network. oss , which is expressed as:

[0032] L oss =L s +L no

[0033] Among them, L s represents the signal loss function; L no represents the noise loss function;

[0034] The signal loss function L s The expression is:

[0035]

[0036] in, represents the data without adding noise to the sample pair; represents the decoupled representation of the signal output by the decoupled representation learning network; n 1 Indicates the total number of signals;

[0037] The noise loss function L no The expression is:

[0038]

[0039] in, Represents the data after adding noise to the sample pair; represents the decoupled representation of the noise output of the decoupled representation learning network; n 2 Indicates the total number of data after adding noise.

[0040] Furthermore, the semi-aeronautical transient electromagnetic data actually collected are obtained, and denoising is performed using the trained decoupled representation learning network, including the following steps:

[0041] Input the actually collected semi-aeronautical transient electromagnetic data into the trained decoupled representation learning network to obtain the dual-channel network output data of the decoupled representation learning network;

[0042] The dual-channel network output data is split by array splitting to obtain the noise prediction value and signal prediction value of the decoupled representation learning network;

[0043] The noise prediction value of the decoupling characterization learning network is subtracted from the actual collected semi-aeronautical transient electromagnetic data to obtain the denoised data.

[0044] Compared with the prior art, the present invention has the following beneficial effects:

[0045] (1) The present invention adopts the known geophysical constrained electromagnetic resistivity model database DL-RMD, adds noise to the forward simulation data, and combines deep learning to perform data denoising, which effectively solves the problem that traditional methods mostly rely on the selection of empirical parameters and are more suitable for data with low noise levels, but it is difficult to denoise complex field data with large noise.

[0046] (2) The present invention combines decoupled representation learning to enable the network to output a pair of decoupled representations of signal and noise, solving the problem that a single representation in existing deep learning is difficult to separate signal and noise, and the representation result often contains both noise and signal. This makes it difficult to effectively separate noise and signal when processing complex actual signals, and only part of the information in the signal can be focused on.

[0047] (3) When obtaining the final denoising result, the present invention uses the noise data minus the network's prediction of the noise. This residual learning method has better performance and better denoising results.

[0048] (4) The present invention sets up a decoupled representation learning network, which has the advantages of improving model interpretability, balancing data representation and decoupling capabilities, being applicable to complex data sets, improving sample diversity, and promoting cross-domain decoupled representation. It can reliably output noise representation and signal representation.

[0049] In summary, the present invention has the advantages of simple logic, accuracy and reliability, and has high practical value and promotion value in the field of electromagnetic data processing technology. BRIEF DESCRIPTION OF THE DRAWINGS

[0050] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings required for use in the embodiments are briefly introduced below. It should be understood that the following drawings only show certain embodiments of the present invention and therefore should not be regarded as limiting the scope of protection. For those skilled in the art, other related drawings can be obtained based on these drawings without creative work.

[0051] Figure 1 It is a logic flow chart of the present invention.

[0052] Figure 2This is a schematic diagram of data noise addition in the present invention.

[0053] Figure 3 Schematic diagram of the structure of the decoupled representation learning network in the present invention.

[0054] Figure 4 This is a diagram of the backbone network structure in the present invention.

[0055] Figure 5 This is a schematic diagram of training loss in the present invention.

[0056] Figure 6 This is the denoising result diagram in the present invention. DETAILED DESCRIPTION

[0057] In order to make the purpose, technical scheme and advantages of this application clearer, the present invention is further described below in conjunction with the accompanying drawings and embodiments, and the embodiments of the present invention include but are not limited to the following embodiments. Based on the embodiments in this application, all other embodiments obtained by ordinary technicians in this field without making creative work are within the scope of protection of this application.

[0058] In this embodiment, the term "and / or" is merely a term used to describe the association relationship of associated objects, indicating that three relationships may exist. For example, A and / or B may represent three situations: A exists alone, A and B exist at the same time, and B exists alone.

[0059] The terms "first" and "second" in the description and claims of this embodiment are used to distinguish different objects rather than to describe a specific order of objects. For example, a first target object and a second target object are used to distinguish different target objects rather than to describe a specific order of target objects.

[0060] In the embodiments of the present application, words such as "exemplary" or "for example" are used to indicate examples, illustrations or descriptions. Any embodiment or design described as "exemplary" or "for example" in the embodiments of the present application should not be interpreted as being more preferred or more advantageous than other embodiments or designs. Specifically, the use of words such as "exemplary" or "for example" is intended to present related concepts in a specific way.

[0061] In the description of the embodiments of the present application, unless otherwise specified, the meaning of "multiple" refers to two or more than two. For example, multiple processing units refer to two or more processing units; multiple systems refer to two or more systems.

[0062] like Figures 1 to 6 As shown, this embodiment provides a semi-aeronautical transient electromagnetic data denoising method based on decoupled representation learning, which includes the following steps:

[0063] The first step is to obtain the known geophysical constrained electromagnetic resistivity model database DL-RMD and perform forward modeling to obtain forward simulation data. Here, 5000 models randomly selected from the geophysical constrained electromagnetic resistivity model database DL-RMD are forward modeled.

[0064] In the second step, noise is added to the forward simulation data to obtain several sample pairs, which are then divided into training set, validation set and test set in a ratio of 7:2:1. Figure 2 As shown, Figure 2 (a) is an example of a model in the DL-RMD model set. Figure 2 (b) is the forward modeling data obtained by the model (a). Figure 2 (c) in FIG. 1 is the result of adding noise to the forward modeling data in (b). Here, the forward modeling data is divided into two parts at a ratio of 1:1 to obtain the first forward modeling data and the second forward modeling data.

[0065] Gaussian noise is added to the first forward simulation data, and its expression is:

[0066] s n1 =s1+N(0,1)

[0067] Among them, s n1 represents the data after adding Gaussian noise; s1 represents the first forward simulation data; N(0,1) represents Gaussian noise with mean 0 and variance 1.

[0068] Add mixed noise to the second forward simulation data, and its expression is:

[0069]

[0070] Among them, s n2 represents the data after adding mixed noise; s2 represents the second forward simulation data; STD represents linear noise; n represents the background noise distribution.

[0071] Among them, the expression of background noise distribution n is:

[0072]

[0073] Where b is the noise level at 1 ms and t is the time.

[0074] The third step is to build a decoupled representation learning network and use it to output a pair of decoupled parsing. Figure 3 to Figure 4As shown, the input of the encoder is single-channel data, and the output is 256-channel data for decoding by the decoder; the input of the decoder is 256 channels, and the output is dual channels, the first channel is the decoder's decoupled representation of noise, and the second channel is the decoder's decoupled representation of the signal. Specifically, the decoupled representation learning network includes an encoder and a decoder. Among them, the encoder includes a first input layer, a first embedding layer, and a first backbone network connected in sequence; the embedding layer performs a convolution operation on the forward simulation data with added noise obtained by the first input layer to obtain an embedded output; the first backbone network encodes the embedded output to obtain encoded data. In addition, the decoder includes a second backbone network and a first linear layer connected in sequence; the second backbone network decodes the encoded data to obtain decoded data; the first linear layer decouples and parses the decoded data output by the second backbone network.

[0075] In this embodiment, the structures of the first backbone network and the second backbone network are the same, and the first backbone network includes a second input layer, a second embedding layer, a mixing layer, a second linear layer and a second output layer connected in sequence; the mixing layer includes a signal mixing layer and a channel mixing layer connected in sequence; the second input layer obtains forward simulation data with added noise; the second embedding layer performs a one-dimensional convolution operation on the data input by the second input layer to obtain embedded data; the signal mixing layer performs signal mixing on the embedded data to obtain first data; the channel mixing layer performs channel mixing on the first data after signal mixing to obtain second data; the second linear layer performs a full connection operation on the second data after channel mixing to obtain third data.

[0076] Among them, the signal mixing layer includes a first token transfer layer, a WKV operation layer and a first normalization layer; the first token transfer layer obtains the embedded data output by the second embedding layer, and puts the last data in the embedded data at the front end of the embedded data, and splits it in the channel dimension to obtain the value, key and received value of the embedded data; the WKV operation layer performs WKV addition attention operation on the value and key of the embedded data to obtain the fourth data; the fourth data output by the WKV operation layer is matrix multiplied with the received value of the embedded data, and is sent to the first normalization layer for normalization processing to obtain the fifth data.

[0077] In addition, the channel mixing layer includes a second token transfer layer and a second normalization layer; the second token transfer layer obtains the fifth data and puts the last data in the fifth data to the front of the fifth data to obtain the value corresponding to the fifth data and the received value; the value corresponding to the fifth data output by the second token transfer layer and the received value are mixed by matrix multiplication to obtain the sixth data; the second normalization layer normalizes the sixth data.

[0078] The fourth step is to train the decoupled representation learning network using the training set and adjust and fit the parameters to obtain the trained decoupled representation learning network. Here, the parameters of the decoupled representation learning network are adjusted to achieve fitting, that is, the test set loss fluctuates within a certain range. Figure 5 It shows the change of loss value during network training, and we can see that the loss gradually converges.

[0079] In this embodiment, a total loss function L is added to the decoupled representation learning network. oss , which is expressed as:

[0080] L oss =L s +L no

[0081] Among them, L s represents the signal loss function; L no represents the noise loss function;

[0082] The signal loss function L s The expression is:

[0083]

[0084] in, represents the data without adding noise to the sample pair; represents the decoupled representation of the signal output by the decoupled representation learning network; n 1 Indicates the total number of signals.

[0085] The noise loss function L no The expression is:

[0086]

[0087] in, Represents the data after adding noise to the sample pair; represents the decoupled representation of the noise output of the decoupled representation learning network; n 2 Indicates the total number of data after adding noise.

[0088] In the fifth step, the validation set and test set are used to verify and test the trained decoupled representation learning network respectively.

[0089] The sixth step is to obtain the actual collected semi-aeronautical transient electromagnetic data and use the trained decoupled representation learning network to perform denoising. Specifically:

[0090] (1) The actual collected semi-aeronautical transient electromagnetic data are input into the trained decoupled representation learning network to obtain the dual-channel network output data of the decoupled representation learning network.

[0091] (2) The dual-channel network output data is split by array splitting to obtain the noise prediction value and signal prediction value of the decoupled representation learning network; here, this is a pair of decoupled representations, the first channel is the representation of the noise, and the second channel is the representation of the signal.

[0092] (3) The noise prediction value of the decoupling characterization learning network is subtracted from the actual collected semi-aeronautical transient electromagnetic data to obtain the denoised data.

[0093] from Figure 6 It can be seen that the actual data Figure 6 (a) The latter part is subject to much noise interference, making it difficult to use information. Figure 6 (b) is the data after processing by the present invention, the data noise is obviously removed, the data trend is smooth, and it conforms to the actual law. It can be seen that the present invention effectively improves the efficiency and accuracy of actual data denoising, and at the same time provides an efficient general framework template for denoising actual noise data of similar geological engineering in the future.

[0094] The above embodiments are only preferred embodiments of the present invention and are not intended to limit the protection scope of the present invention. Any changes that adopt the design principles of the present invention and are made through non-creative labor on this basis should fall within the protection scope of the present invention.

Claims

1. A semi-aeronautical transient electromagnetic data denoising method based on decoupled representation learning, characterized in that: The following steps are involved: Obtain the known geophysical constrained electromagnetic resistivity model database DL-RMD, and perform forward modeling to obtain forward simulation data; Noise is added to the forward simulation data, and several sample pairs are obtained, which are then split into training set, validation set, and test set; Build a decoupled representation learning network and use it to output a pair of decoupled parsing; The decoupled representation learning network is trained using the training set, and parameter adjustment and fitting are performed to obtain the trained decoupled representation learning network; The trained decoupled representation learning network is verified and tested using the validation set and test set respectively; The actual collected semi-aeronautical transient electromagnetic data are obtained and denoised using the trained decoupled representation learning network.

2. The semi-aeronautical transient electromagnetic data denoising method based on decoupled representation learning according to claim 1 is characterized in that: Adding noise to the forward modeling data includes the following steps: Dividing the forward simulation data into two parts at a ratio of 1:1 to obtain first forward simulation data and second forward simulation data; Gaussian noise is added to the first forward simulation data, and its expression is: s n1 =s1+N(0,1) Among them, s n1 represents the data after adding Gaussian noise; s1 represents the first forward simulation data; N(0,1) represents Gaussian noise; Add mixed noise to the second forward simulation data, and its expression is: Among them, s n2 represents the data after adding mixed noise; s2 represents the second forward simulation data; STD represents linear noise; n represents the background noise distribution.

3. The semi-aeronautical transient electromagnetic data denoising method based on decoupled representation learning according to claim 2 is characterized in that: The expression of the background noise distribution n is: Where b is the noise level at 1 ms and t is the time.

4. The semi-aeronautical transient electromagnetic data denoising method based on decoupled representation learning according to claim 1 is characterized in that: The decoupled representation learning network includes an encoder and a decoder; The encoder comprises a first input layer, a first embedding layer and a first backbone network connected in sequence; the embedding layer performs a convolution operation on the forward simulation data with added noise obtained by the first input layer to obtain an embedded output; the first backbone network encodes the embedded output to obtain encoded data; The decoder includes a second backbone network and a first linear layer connected in sequence; the second backbone network decodes the encoded data to obtain decoded data; The first linear layer decouples and analyzes the decoded data output by the second backbone network.

5. The semi-aeronautical transient electromagnetic data denoising method based on decoupled representation learning according to claim 4 is characterized in that: The first backbone network and the second backbone network have the same structure, and the first backbone network includes a second input layer, a second embedding layer, a mixing layer, a second linear layer and a second output layer connected in sequence; the mixing layer includes a signal mixing layer and a channel mixing layer connected in sequence; the second input layer obtains forward simulation data with added noise; the second embedding layer performs a one-dimensional convolution operation on the data input by the second input layer to obtain embedded data; The signal mixing layer performs signal mixing on the embedded data to obtain first data; the channel mixing layer performs channel mixing on the first data after signal mixing to obtain second data; and the second linear layer performs a full connection operation on the second data after channel mixing to obtain third data.

6. The semi-aeronautical transient electromagnetic data denoising method based on decoupled representation learning according to claim 5 is characterized in that: The signal mixing layer includes a first token transfer layer, a WKV operation layer and a first normalization layer; the first token transfer layer obtains the embedded data output by the second embedding layer, and puts the last data in the embedded data at the front end of the embedded data, and splits it in the channel dimension to obtain the value, key and received value of the embedded data; the WKV operation layer performs a WKV addition attention operation on the value and key of the embedded data to obtain the fourth data; the fourth data output by the WKV operation layer is matrix multiplied with the received value of the embedded data, and is sent to the first normalization layer for normalization processing to obtain the fifth data.

7. The semi-aeronautical transient electromagnetic data denoising method based on decoupled representation learning according to claim 6 is characterized in that: The channel mixing layer includes a second token transfer layer and a second normalization layer; the second token transfer layer obtains the fifth data and puts the last data in the fifth data at the front of the fifth data to obtain the value corresponding to the fifth data and the received value; The value corresponding to the fifth data output by the second token transfer layer and the received value are mixed by matrix multiplication to obtain sixth data; The second normalization layer performs normalization processing on the sixth data.

8. The semi-aeronautical transient electromagnetic data denoising method based on decoupled representation learning according to claim 4, 5, 6 or 7, characterized in that: Use the training set to train the decoupled representation learning network, adjust the parameters and fit them, and add the total loss function L to the decoupled representation learning network. oss , which is expressed as: L oss =L s +L no Among them, L s represents the signal loss function; L no represents the noise loss function; The signal loss function L s The expression is: in, represents the data without adding noise to the sample pair; represents the decoupled representation of the signal output by the decoupled representation learning network; n 1 Indicates the total number of signals; The noise loss function L no The expression is: in, Represents the data after adding noise to the sample pair; represents the decoupled representation of the noise output of the decoupled representation learning network; n 2 Indicates the total number of data after adding noise.

9. The semi-aeronautical transient electromagnetic data denoising method based on decoupled representation learning according to claim 8 is characterized in that: The actual collected semi-aeronautical transient electromagnetic data are obtained and denoised using the trained decoupled representation learning network, including the following steps: Input the actually collected semi-aeronautical transient electromagnetic data into the trained decoupled representation learning network to obtain the dual-channel network output data of the decoupled representation learning network; The dual-channel network output data is split by array splitting to obtain the noise prediction value and signal prediction value of the decoupled representation learning network; The noise prediction value of the decoupling characterization learning network is subtracted from the actual collected semi-aeronautical transient electromagnetic data to obtain the denoised data.

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