CN117574062A - Small loop transient electromagnetic signal denoising method based on VMD-DNN model - Google Patents
Small loop transient electromagnetic signal denoising method based on VMD-DNN model Download PDFInfo
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Abstract
The invention belongs to the technical field of transient electromagnetism, and relates to a small loop transient electromagnetic signal denoising method based on a VMD-DNN model, which comprises the steps of performing variation modal decomposition on a noise-containing signal, performing VMD denoising processing to obtain a VMD denoised signal; the scale of the VMD denoised signal is changed, the VMD denoised signal is folded and adjusted to be matrix data of 40 multiplied by 25 multiplied by 1, normalization is carried out, and the data range is changed to 0-1; and carrying out denoising treatment on the normalized signal through a deep neural network model, and outputting a transient electromagnetic signal of 1000 multiplied by 1 to obtain a denoising result of the transient electromagnetic signal. The method solves the problems that the signal-to-noise ratio of the small loop transient electromagnetic signal is low in the late stage, and the noise is difficult to effectively suppress by the traditional denoising method, and the denoised signal is very close to an ideal signal.
Description
Technical Field
The invention belongs to the technical field of transient electromagnetic, and particularly relates to a small loop transient electromagnetic signal denoising method based on a VMD-DNN model.
Background
The transient electromagnetic method is a geophysical prospecting method based on the law of electromagnetic induction, and is widely applied to mineral exploration, groundwater exploration and various engineering geophysical prospecting. In particular, the small loop TEM system has been successfully applied to geological structure investigation in narrow spaces, such as application scenarios of coal mine water burst and tunnel detection. The small loop transient electromagnetic system usually adopts a transmitting coil with the diameter smaller than 3 meters to detect a target body, the device is flexible and small in occupied area, can generate optimal coupling with a shallow layer detection target, and has stronger resolving power on shallow layer abnormal bodies. The transient electromagnetic system comprises a transmitting coil, a receiving coil, a transmitter and a receiver. The transmitter excites square wave current on the transmitting coil to generate a primary field, and the underground medium excites induced eddy current under the action of the primary field, so that the induced eddy current cannot disappear immediately after the current is turned off. The receiving coil receives the secondary field signal caused by the eddy current, the receiver amplifies and samples the weak secondary field signal, and the spatial distribution and physical characteristics of the geological structure can be obtained by processing and analyzing the secondary field signal. Since small loop transient electromagnetic systems employ miniaturized transmit coils, the effective transmit magnetic moment is limited, which results in very weak secondary field signals, which often contain a significant amount of noise components in the actual observed signals. The early signal of the secondary field response of the transient electromagnetic reflects near-surface information, while the late signal contains formation deep information. Because the late signal of the small-loop transient electromagnetic system is very sensitive to noise, noise interference can lead to the late signal being completely submerged, and the small-loop transient electromagnetic instrument cannot effectively detect the deep underground structure, so that the method has great significance in removing noise in the transient electromagnetic signal.
For small loop transient electromagnetic instruments, noise in the signal is mainly derived from electromagnetic interference of the external environment and noise floor of the instrument, and the noise is usually random and unordered, has no fixed characteristics, and is difficult to establish mathematical modeling, so that the traditional denoising method is difficult to work. The denoising method based on the Variational Mode Decomposition (VMD) can realize suppression of random noise in the signal, but each decomposed eigenmode has the problem of spectrum aliasing, and the noise cannot be completely removed under the condition of not losing the signal.
Disclosure of Invention
The invention aims to solve the technical problem of providing a small loop transient electromagnetic signal denoising method based on a VMD-DNN model, so as to solve the problem that the small loop transient electromagnetic signal has low signal-to-noise ratio in the late stage and the noise is difficult to effectively suppress by the traditional denoising method.
The present invention has been achieved in such a way that,
a small loop transient electromagnetic signal denoising method based on a VMD-DNN model, the method comprising:
the noisy signal is decomposed into a variation modeThe sum of all the eigenmode signals is equal to the input noise-containing signal;
VMD denoising: calculating the correlation between each eigenmode signal and the noise-containing signal, setting a correlation threshold, when the correlation is larger than the correlation threshold, considering the eigenmode signal as an effective signal component, otherwise, regarding the eigenmode signal as a noise signal component, adding all the effective signal components for reconstruction, and discarding all the noise signals to obtain a VMD denoised signal;
normalization: the scale of the VMD denoised signal is changed, the VMD denoised signal is folded and adjusted to be matrix data of 40 multiplied by 25 multiplied by 1, normalization is carried out, and the data range is changed to 0-1;
denoising the normalized signal through a deep neural network model, outputting a transient electromagnetic signal of 1000 multiplied by 1, and obtaining a denoising result of the transient electromagnetic signal;
the deep neural network model sequentially comprises an input layer, a first convolution layer, a pooling layer, a second convolution layer, an excitation layer, a flattening layer, a long-short-time memory coding layer, a long-short-time memory decoding layer, a full-connection layer and an output layer according to the sequence of signal processing;
the input layer has an input size of 40 x 25 x 1 and an output size of 40 x 25 x 1, and inputs a signal to the first convolution layer,
the convolution kernel size of the first convolution layer is 2 multiplied by 2, the number of convolution kernels is 128, the steps are 2 multiplied by 2, and the convolution kernels are output to the pooling layer,
the pooling mode of the pooling layer is maximum pooling, the step length is 2 multiplied by 2, the pooling window size is 2 multiplied by 2, and the pooling window size is output to the second convolution layer,
the convolution kernel size of the second convolution layer is 2 multiplied by 2, the number of convolution kernels is 64, the steps are 2 multiplied by 2, and the convolution kernels are output to the excitation layer;
the excitation layer adopts a LeakyReLU function as an activation function, and the formula is as follows:
，
wherein,gradient (S)/(S)>，/>Representing the input signal;
the input size of the flattened layer is 40 multiplied by 25 multiplied by 1, the output size of the flattened layer is 1000 multiplied by 1, and the signals are converted into one dimension from a two-dimension array;
the long-short time memory coding layer is divided into a first long-short time memory layer and a second long-short time memory layer;
the number of hidden units of the first long short time memory layer is 128, and the hidden units are output to the second long short time memory layer,
the number of hidden units of the second long short time memory layer is 64, and the hidden units are output to the long short time memory decoding layer;
the input size of the full connection layer is 1000 multiplied by 1, the output size is 1000 multiplied by 1, and the full connection layer is output to the output layer,
the output layer adopts a regression output mode, and the output size is 1000 multiplied by 1.
Further, the long-short time memory decoding layer is divided into a third long-short time memory layer and a fourth long-short time memory layer,
wherein the number of hidden units in the third long short time memory layer is 128, and the hidden units are output to the fourth long short time memory layer,
the number of hidden units of the fourth long short time memory layer is 64, and the hidden units are output to the full connection layer.
Further, the deep neural network model is trained by obtaining a synthesized noise-containing signal through one-dimensional forward modeling;
the process of obtaining the synthesized noise-containing signal by one-dimensional forward modeling specifically comprises the following steps: in forward modeling, a random method is adopted to model real topography, the number of model layers is 50, the thickness of each layer is 6 meters, the total thickness is 300 meters, the resistivity of each layer is omega.m, random numbers in 1 to 1000 are adopted, the sampling time of forward modeling signals is 1us to 1 ms, the sampling interval is 1us, and 1000 sampling points are added in each group of signals, so that 10000 combined signals are generated by the method; different noises are added to each group of signals to form 50 groups of noise-containing signals with different signal to noise ratios, the signal to noise ratios of the 50 groups of signals are respectively 1,2,3, … and 50, and the signal to noise ratio calculation formula is as follows:
，
wherein the method comprises the steps ofIs a synthetic signal without noise, using the angle mark +.>Distinguishing the synthesized noise-containing signals->，/>Is->The corresponding synthesized noise-containing signal is then processed,/>for the total length of the signal, 500000 groups are obtainedNoise-containing signals with different stratum structures and different signal-to-noise ratios;
to be synthesized into noise-containing signalsPerforming transformation mode decomposition into ++>A bandwidth limited eigenmode signal，/>For the number of bits of the decomposed eigenmode signals, the sum of all eigenmode signals and the input synthesized noise-containing signal +.>The signals are equal;
computing each eigenmode signalAnd the synthesized noise-containing signal->Correlation of->Setting a correlation threshold +.>When the correlation->Greater than the correlation threshold->At the moment, the vision eigenmode signal->As effective signal component, otherwise, as noise signal component, adding all effective signal components to reconstruct, and discarding all noise signalObtaining a VMD denoised signal;
the scale of the signals after the VMD is subjected to noise elimination is changed, the signals are folded and adjusted to matrix data of 40 multiplied by 25 multiplied by 1, normalization is carried out, and the data range is changed to 0-1.
Further, the processes of performing the variational modal decomposition of the noise-containing signal and the synthesized noise-containing signal are the same, and both the processes comprise:
in the process of decomposition of the variation mode, the solving process is carried out through Hilbert transformation, wiener filtering and heterodyne demodulation, and the solving process is expressed as follows in the time domain:
，
where min represents the minimum, t represents time,intrinsic mode signal->Is the pulse center frequency of the eigenmode signal, +.>For the number of intrinsic mode signals, < >>，/>Represents the square of the 2-norm, +.>Representing the partial derivative of t, j representing the imaginary number,/-, and>for dirac distribution, x represents convolution, s.t. represents subject to, i.e. let +.>Sum equal to->Meeting the conditions by->Represented as a noisy signal to be decomposed or a synthesized noisy signal by introducing a quadratic penalty termαAnd Lagrangian multiplier->Converting the decomposition process into an unconstrained variational model:
，
updating eigenmode signals by alternating direction of multipliersPulse center frequency +.>Lagrangian multiplier->，/>And->Representing a concept->Representing the fourier transform from the time domain to the frequency domain;
for the firstIndividual eigenmode functions->After fourier transformation, it is expressed in the frequency domain as:
，
，
，
wherein,indicates the number of decomposition times->、/>、/>Respectively indicate->、/>、/>Is used for the estimation of the (c),、/>、/>are respectively->、/>And->Fourier transform of->Representing the pulse frequency; />Update parameters representing lagrangian multipliers;
the variant modal decomposition stops updating and ends when the following condition is satisfied:
，
wherein the method comprises the steps ofTo stop updating the threshold.
Compared with the prior art, the invention has the beneficial effects that:
(1) According to the invention, transient electromagnetic signals are obtained by forward modeling of models of different stratum structures, and different random noise is added on the basis to construct a data set, so that the problem that actual measurement data are difficult to obtain in a large scale is effectively solved;
(2) According to the invention, the VMD method is adopted to decompose the noise-containing signals, and a cross-correlation function is utilized to judge whether each analyzed intrinsic mode signal is reserved during reconstruction, so that the loss of signal components caused by mode spectrum aliasing is effectively solved;
(3) The method adopts a method combining the variation modal decomposition and the deep neural network to remove noise in the transient electromagnetic signal, effectively solves the problem of low signal-to-noise ratio of the small loop transient electromagnetic signal, has the advantage of high signal-to-noise ratio, and the signal after noise elimination is very close to an ideal signal.
Drawings
FIG. 1 is a flow chart of a method according to an embodiment of the present invention;
FIG. 2 is a waveform diagram of a noise-containing synthesized signal according to an embodiment of the present invention, (a) is a time domain signal under conventional coordinates, and (b) is a logarithmic display;
FIG. 3 is a schematic diagram of a deep neural network model according to an embodiment of the present invention;
FIG. 4 is a waveform diagram of an actual measurement transient electromagnetic signal provided by an embodiment of the present invention, wherein (a) - (e) show that each eigenmode function obtained by decomposing a noisy signal is derived from IMF1-IMF5;
FIG. 5 is a waveform diagram of an eigenmode signal of a noise-containing transient electromagnetic signal decomposed by a VMD according to an embodiment of the present invention;
FIG. 6 is a signal waveform diagram of VMD reconstruction according to an embodiment of the present invention;
FIG. 7 is a waveform diagram of signals after passing through a deep neural network model according to an embodiment of the present invention;
fig. 8 is a comparison result of a signal after VMD noise cancellation and a signal after deep neural network noise cancellation with an ideal signal according to an embodiment of the present invention.
Detailed Description
Referring to fig. 1, a small loop transient electromagnetic signal denoising method based on a VMD-DNN model, the method comprises:
the noisy signal is decomposed into a variation modeKThe sum of all the eigenmode signals is equal to the input noise-containing signal;
VMD denoising: calculating the correlation between each eigenmode signal and the noise-containing signal, setting a correlation threshold, when the correlation is larger than the correlation threshold, considering the eigenmode signal as an effective signal component, otherwise, regarding the eigenmode signal as a noise signal component, adding all the effective signal components for reconstruction, and discarding all the noise signals to obtain a VMD denoised signal;
normalization: the scale of the signals after the VMD noise elimination is changed, the signals are folded and adjusted to matrix data of 40 multiplied by 25 multiplied by 1, normalization is carried out, and the data range is changed to 0-1;
and carrying out denoising treatment on the normalized signal through a deep neural network model, and outputting a transient electromagnetic signal of 1000 multiplied by 1 to obtain a denoising result of the transient electromagnetic signal.
The deep neural network model is shown in fig. 3:
the method comprises the steps of sequentially comprising an input layer, a first convolution layer, a pooling layer, a second convolution layer, an excitation layer, a flattening layer, a long-short-time memory coding layer, a long-short-time memory decoding layer, a full-connection layer and an output layer according to the sequence of signal processing;
the input layer has an input size of 40 x 25 x 1 and an output size of 40 x 25 x 1, and inputs a signal to the first convolution layer,
the convolution kernel size of the first convolution layer is 2 multiplied by 2, the number of convolution kernels is 128, the steps are 2 multiplied by 2, and the convolution kernels are output to the pooling layer,
the pooling mode of the pooling layer is maximum pooling, the step length is 2 multiplied by 2, the pooling window size is 2 multiplied by 2, and the pooling window size is output to the second convolution layer,
the convolution kernel size of the second convolution layer is 2 multiplied by 2, the number of convolution kernels is 64, the steps are 2 multiplied by 2, and the convolution kernels are output to the excitation layer;
the excitation layer adopts a LeakyReLU function as an activation function, and the formula is as follows:
，
wherein,gradient (S)/(S)>，/>Representing the input signal;
the input size of the flattened layer is 40 multiplied by 25 multiplied by 1, the output size of the flattened layer is 1000 multiplied by 1, and the signals are converted into one dimension from a two-dimension array;
the long-short time memory coding layer is divided into a first long-short time memory layer and a second long-short time memory layer;
the number of hidden units of the first long short time memory layer is 128, and the hidden units are output to the second long short time memory layer,
the number of hidden units of the second long short time memory layer is 64, and the hidden units are output to the long short time memory decoding layer;
the input size of the full connection layer is 1000 multiplied by 1, the output size is 1000 multiplied by 1, and the full connection layer is output to the output layer,
the output layer adopts a regression output mode, and the output size is 1000 multiplied by 1.
The long-short time memory decoding layer is divided into a third long-short time memory layer and a fourth long-short time memory layer,
wherein the number of hidden units in the third long short time memory layer is 128, and the hidden units are output to the fourth long short time memory layer,
the number of hidden units of the fourth long short time memory layer is 64, and the hidden units are output to the full connection layer.
The deep neural network model needs to be trained to form a trained deep neural network model, data required by training is subjected to one-dimensional forward modeling to obtain synthesized transient electromagnetic attenuation signals, during forward modeling, a random method is adopted to simulate real terrain, the number of model layers is 50, the thickness of each layer is 6 meters, the total thickness is 300 meters, the resistivity (omega.m) of each layer is a random number within 1 to 1000, the sampling time of the forward modeling signals is 1us to 1 ms, the sampling interval is 1us, and each group of signals is 1000 sampling points in total, so that 10000 combined signals are generated by the method; on the basis, different noises are added to each group of signals to form 50 groups of noise-containing signals with different signal-to-noise ratios, the signal-to-noise ratios of the 50 groups of signals are respectively 1,2,3, … and 50, and the signal-to-noise ratio calculation formula is as follows:
（1），
wherein the method comprises the steps ofIs a synthetic signal without noise, using the angle mark +.>Distinguishing the synthesized noise-containing signals->，/>Is thatThe corresponding synthesized noise-containing signal is then processed,/>obtaining 500000 groups of noisy signals with different stratum structures and different signal to noise ratios for the total length of the signals, and obtaining 500000 groups of noisy synthesized signals with different stratum structures and different signal to noise ratios, which are shown in fig. 2, wherein fig. 2 (a) is a time domain signal under a conventional coordinate, and the log coordinates shown in fig. 2 (b) are adopted for convenience of display due to small amplitude of late signals;
for each combined noisy signalPerforming a Variant Mode Decomposition (VMD) into +.>An eigenmode signal of limited bandwidth +.>These eigenmode signals have a specific sparsity, the sum of all eigenmode signals and the input noise-containing composite signal +.>The signals are equal. In the variant mode decomposition process, it is assumed that each eigenmode signal is close to the pulse center frequency +.>. The solution process is subjected to hilbert transform, wiener filtering and heterodyne demodulation, and the process can be expressed as:
（2），
where min represents the minimum, t represents time,is an intrinsic mode signal>Is the pulse center frequency of the eigenmode signal, +.>For the number of intrinsic mode signals, < >>，/>Represents the square of the 2-norm, +.>Representing the partial derivative of t, j representing the imaginary number,/-, and>for dirac distribution, x represents convolution, s.t. represents subject to, i.e. let +.>Sum equal to->Meeting the conditions by->Represented as a noisy signal to be decomposed or a synthesized noisy signal by introducing a quadratic penalty termαAnd Lagrangian multiplier->Converting the decomposition process into an unconstrained variational model:
（3），
the eigenvalue signals can be updated by the alternating direction method of the multiplierPulse center frequency +.>Lagrangian multiplier->，/>And->Representing a concept->Representing the fourier transform from the time domain to the frequency domain;
（4），
（5），
（6），
wherein,indicates the number of decomposition times->、/>、/>Respectively indicate->、/>、/>Estimated value of ∈10->、/>、/>Are respectively->、/>And->Fourier transform of->Representing the pulse frequency; />Update parameters representing Lagrangian multiplier, when +.>When the value of (2) is 0, ">Can be effectively turned off and the update parameter is selected +.>；
The VMD algorithm stops updating and ends when the following conditions are satisfied:
（7），
wherein the method comprises the steps ofTo stop the updated threshold, it is set by itself. After obtaining the signal components of each eigenmode, calculate the signal of each eigenmode and the noise-containing synthesized signal +.>Is related to (a)Sex->Setting a correlation threshold +.>When the correlation->When the correlation is larger than the correlation, the vision eigenmode signal is +.>Is a valid signal component, otherwise is considered a noise signal component. And adding all the effective signal components to reconstruct, and discarding all noise signals to obtain the VMD denoised signal. The correlation calculation method is as follows:
（8），
wherein the method comprises the steps ofRepresents +.o after VMD decomposition>Intrinsic mode signal->The original signal is represented by a representation of the original signal,COVrepresenting the covariance of the two signals, +.>Representing standard deviation;
then, the size of the VMD denoised signal is changed, the VMD denoised signal is 1000 multiplied by 1 one-dimensional data, the VMD denoised signal is folded and adjusted to 25 multiplied by 40 multiplied by 1 matrix data, the length and width heights of the matrix data are 40, 25 and 1, normalization is carried out, and the data amplitude is adjusted to 0-1;
the reconstruction of 500000 groups of noisy synthesized signals is completed according to the steps,
then, according to the same scale changing method, the synthesized signals corresponding to the 500000 groups of noisy synthesized signals are also adjusted to matrix data of 40 multiplied by 25 multiplied by 1, normalization is carried out, the data range is changed to 0-1, and finally a data set is formed for training of a subsequent deep neural network;
the loss function of the training network is selected as follows:
(9)，
wherein the method comprises the steps ofX out AndXand respectively outputting and inputting data of the deep neural network model.
After the deep neural network model is trained, storing the trained deep neural network model; when in use, small loop transient electromagnetic data (the waveform is shown in figure 2) to be processed is subjected to VMD decomposition through the same processing process as the synthesized noise signals, the eigenmode functions are divided according to the frequency bandwidth, figures 4 (a) - (e) show the eigenmode functions obtained by decomposing the noise-containing signals, and figure 5 shows the frequency bandwidth of each eigenmode function; and reconstructing, wherein fig. 6 shows the signal-to-noise ratio and cross-correlation coefficient of each eigenmode function, selecting eigenmode functions meeting the requirements as effective signals, discarding components which do not meet the residual eigenmode functions to obtain reconstructed signals, fig. 7 shows the noise-containing signals and the VMD denoised signal results, a certain improvement of the signal-to-noise ratio can be seen, the reconstructed signals are input into a trained deep neural network model for denoise processing, the transient electromagnetic signals with 1000 multiplied by 1 are output, the denoising results of the transient electromagnetic signals are finally obtained, and the comparison results of the VMD denoised signals and the deep neural network denoised signals with ideal signals are shown, so that the denoising effect is very good, and the denoised signals are very close to the ideal signals.
The present invention will be described in further detail with reference to the following examples in order to make the objects, technical solutions and advantages of the present invention more apparent. It should be understood that the specific embodiments described herein are for purposes of illustration only and are not intended to limit the scope of the invention.
Claims (4)
1. The small loop transient electromagnetic signal denoising method based on the VMD-DNN model is characterized by comprising the following steps of:
the noisy signal is decomposed into a variation modeThe sum of all the eigenmode signals is equal to the input noise-containing signal;
VMD denoising: calculating the correlation between each eigenmode signal and the noise-containing signal, setting a correlation threshold, when the correlation is larger than the correlation threshold, considering the eigenmode signal as an effective signal component, otherwise, regarding the eigenmode signal as a noise signal component, adding all the effective signal components for reconstruction, and discarding all the noise signals to obtain a VMD denoised signal;
normalization: the scale of the VMD denoised signal is changed, the VMD denoised signal is folded and adjusted to be matrix data of 40 multiplied by 25 multiplied by 1, normalization is carried out, and the data range is changed to 0-1;
denoising the normalized signal through a deep neural network model, outputting a transient electromagnetic signal of 1000 multiplied by 1, and obtaining a denoising result of the transient electromagnetic signal;
the deep neural network model sequentially comprises an input layer, a first convolution layer, a pooling layer, a second convolution layer, an excitation layer, a flattening layer, a long-short-time memory coding layer, a long-short-time memory decoding layer, a full-connection layer and an output layer according to the sequence of signal processing;
the input layer has an input size of 40 x 25 x 1 and an output size of 40 x 25 x 1, and inputs a signal to the first convolution layer,
the convolution kernel size of the first convolution layer is 2 multiplied by 2, the number of convolution kernels is 128, the steps are 2 multiplied by 2, and the convolution kernels are output to the pooling layer,
the pooling mode of the pooling layer is maximum pooling, the step length is 2 multiplied by 2, the pooling window size is 2 multiplied by 2, and the pooling window size is output to the second convolution layer,
the convolution kernel size of the second convolution layer is 2 multiplied by 2, the number of convolution kernels is 64, the steps are 2 multiplied by 2, and the convolution kernels are output to the excitation layer;
the excitation layer adopts a LeakyReLU function as an activation function, and the formula is as follows:
，
wherein,gradient (S)/(S)>， />Representing the input signal;
the input size of the flattened layer is 40 multiplied by 25 multiplied by 1, the output size of the flattened layer is 1000 multiplied by 1, and the signals are converted into one dimension from a two-dimension array;
the long-short time memory coding layer is divided into a first long-short time memory layer and a second long-short time memory layer;
the number of hidden units of the first long short time memory layer is 128, and the hidden units are output to the second long short time memory layer,
the number of hidden units of the second long short time memory layer is 64, and the hidden units are output to the long short time memory decoding layer;
the input size of the full connection layer is 1000 multiplied by 1, the output size is 1000 multiplied by 1, and the full connection layer is output to the output layer,
the output layer adopts a regression output mode, and the output size is 1000 multiplied by 1.
2. The VMD-DNN model-based small loop transient electromagnetic signal denoising method according to claim 1, wherein the long-short-time memory decoding layer is divided into a third long-short-time memory layer and a fourth long-short-time memory layer,
wherein the number of hidden units in the third long short time memory layer is 128, and the hidden units are output to the fourth long short time memory layer,
the number of hidden units of the fourth long short time memory layer is 64, and the hidden units are output to the full connection layer.
3. The small loop transient electromagnetic signal denoising method based on the VMD-DNN model according to claim 1, wherein the deep neural network model is trained by obtaining a synthesized noisy signal through one-dimensional forward modeling;
the process of obtaining the synthesized noise-containing signal by one-dimensional forward modeling specifically comprises the following steps: in forward modeling, a random method is adopted to model real topography, the number of model layers is 50, the thickness of each layer is 6 meters, the total thickness is 300 meters, the resistivity of each layer is omega.m, random numbers in 1 to 1000 are adopted, the sampling time of forward modeling signals is 1us to 1 ms, the sampling interval is 1us, and 1000 sampling points are added in each group of signals, so that 10000 combined signals are generated by the method; different noises are added to each group of signals to form 50 groups of noise-containing signals with different signal to noise ratios, the signal to noise ratios of the 50 groups of signals are respectively 1,2,3, … and 50, and the signal to noise ratio calculation formula is as follows:
，
wherein the method comprises the steps ofIs a synthetic signal without noise, using the angle mark +.>Distinguishing the synthesized noise-containing signals->，/>Is->Corresponding synthesized noisy signal, +.>Obtaining 500000 groups of noise-containing signals with different stratum structures and different signal to noise ratios for the total length of the signals;
to be synthesized into noise-containing signalsPerforming transformation mode decomposition into ++>An eigenmode signal of limited bandwidth +.>，For the number of bits of the decomposed eigenmode signals, the sum of all eigenmode signals is combined with the input noise-containing signalThe signals are equal;
computing each eigenmode signalAnd the synthesized noise-containing signal->Correlation of->Setting a correlation threshold +.>When the correlation->Greater than the correlation threshold->At the moment, the vision eigenmode signal->If the signal is an effective signal component, otherwise, the signal is regarded as a noise signal component, all the effective signal components are added for reconstruction, all noise signals are removed, and a VMD denoised signal is obtained;
the scale of the signals after the VMD is subjected to noise elimination is changed, the signals are folded and adjusted to matrix data of 40 multiplied by 25 multiplied by 1, normalization is carried out, and the data range is changed to 0-1.
4. A method for denoising small loop transient electromagnetic signals based on VMD-DNN model according to claim 3, wherein the process of performing the variational modal decomposition of the noisy signal and the synthesized noisy signal are the same, both comprising:
in the process of decomposition of the variation mode, the solving process is carried out through Hilbert transformation, wiener filtering and heterodyne demodulation, and the solving process is expressed as follows in the time domain:
，
where min represents the minimum, t represents time,is an intrinsic mode signal>Is the pulse center frequency of the eigenmode signal, +.>For the number of intrinsic mode signals, < >>，/>Represents the square of the 2-norm, +.>Representing the partial derivative of t, j representing the imaginary number,/-, and>for dirac distribution, x represents convolution, s.t. represents subject to, i.e. let +.>Sum equal toMeeting the conditions by->Represented as a noisy signal to be decomposed or a synthesized noisy signal by introducing a quadratic penalty termαAnd Lagrangian multiplier->Converting the decomposition process into an unconstrained variational model:
，
updating eigenmode signals by alternating direction of multipliersPulse center frequency +.>Lagrangian multiplier->，And->Representing a concept->Representing the fourier transform from the time domain to the frequency domain;
for the firstIndividual eigenmode functions->After fourier transformation, it is expressed in the frequency domain as:
，
，
，
wherein,indicates the number of decomposition times->、/>、/>Respectively indicate->、/>、/>Is used for the estimation of the (c),、/>、/>are respectively->、/>And->Fourier transform of->Representing the pulse frequency; />Update parameters representing lagrangian multipliers;
the variant modal decomposition stops updating and ends when the following condition is satisfied:wherein->To stop updating the threshold.
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