CN115061196A - Micro-seismic signal identification method based on empirical mode decomposition (IMF) guidance - Google Patents

Micro-seismic signal identification method based on empirical mode decomposition (IMF) guidance Download PDF

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CN115061196A
CN115061196A CN202210985006.3A CN202210985006A CN115061196A CN 115061196 A CN115061196 A CN 115061196A CN 202210985006 A CN202210985006 A CN 202210985006A CN 115061196 A CN115061196 A CN 115061196A
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任晓翠
王艳辉
雷思罗
李力民
马骏
朱君
吴龙
傅海滨
曹洋
苏爽
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Chengdu Chuanyou Ruifei Technology Co ltd
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Abstract

The invention relates to a microseismic signal identification method based on IMF (empirical mode decomposition) guidance, which comprises the steps of dividing processed original microseismic signal data into two paths, directly inputting one path into a U-shaped structure neural network, and obtaining IMF1 components by the other path through the IMF; the input layer of the U-shaped structure neural network receives original microseismic signal data, and simultaneously, IMF1 components obtained by decomposing original microseismic signals by an empirical mode are added in the encoding stage of the U-shaped structure neural network, so that the characteristic extraction is guided and restrained; the IMF1 component is subjected to dimensionality reduction through a pooling layer in an encoding stage, and then decoded through a decoding stage to output a recognition prediction result. According to the method, the feature learning capability of the network model is improved by introducing an EMD method, so that the model utilizes the IMF1 component after EMD decomposition to supplement and constrain the original signal in the feature extraction process to improve the microseismic signal identification rate with low signal-to-noise ratio.

Description

Micro-seismic signal identification method based on empirical mode decomposition (IMF) guidance
Technical Field
The invention relates to the technical field of signal identification, in particular to a microseismic signal identification method based on IMF (empirical mode decomposition) guidance.
Background
The microseism is the micro vibration generated by the rock mass movement under the stratum, and the microseism monitoring technology is to use the microseism signal received by the detector to deduce and analyze the underground lithologic structure. The microseismic signal identification method is an important step of a processing flow and can improve the effectiveness of subsequent signal analysis. In the early development stage of the microseismic monitoring technology, the microseismic signal identification work is mainly carried out manually, but the data volume increases exponentially, so that the method is time-consuming and labor-consuming, and has higher requirements on the professional performance of operators. Later scholars proposed many automatic extraction methods, such as STA/LTA algorithm, AIC algorithm, etc., and such algorithms have been used extensively. However, the above algorithm requires the trigger threshold to be preset empirically, which still requires a high professional literacy for the operator, and the setting of the threshold for different regions and different geological structures also needs to be updated in time. In addition, for microseismic signals with low signal-to-noise ratio and small amplitude, the identification accuracy of the method is low.
In order to realize more automatic microseismic signal identification, the identification and classification of microseismic events by using a neural network becomes a research hotspot. With the improvement of hardware equipment and theoretical technology, various different neural network models gradually make effective progress. The U-type convolutional neural network (U-Net) is developed rapidly in the medical field initially, and achieves good results in a medical image segmentation task, and learners also achieve good results in microseismic signal identification by utilizing the U-Net. The U-Net can automatically extract the waveform characteristics without additional operation, overcomes the limitation of the traditional method, saves a full connection layer compared with the common Convolutional Neural Network (CNN), can realize a small sample training model through data enhancement, and has obvious advantages in processing complex image segmentation tasks with small training sample amount. However, in the case of a microseismic signal with low signal-to-noise ratio and insignificant signal characteristics, the separation of the event part and the noise part by the U-Net is insufficient, and the recognition accuracy is limited. In view of the above problems, some researchers have taken some improvement measures: the time domain signal is decomposed by the wavelet packet, and the decomposed wavelet packet coefficient and the time domain signal are simultaneously input into the CNN for model training, so that the characteristic extraction information of the wavelet domain and the time domain signal can be mutually supplemented, and the learning of a network model is facilitated. However, in this method, only simple information fusion is performed after the wavelet packet coefficient and the time domain signal are respectively subjected to feature extraction, and the feature extraction of the network cannot be substantially affected. In addition, wavelet packet decomposition requires manual selection of wavelet bases, and the effect is not ideal when processing a mutation signal.
Disclosure of Invention
The invention aims to overcome the defects of the prior art, provides a microseismic signal identification method based on IMF (empirical mode decomposition) guidance, and solves the problems of the existing microseismic signal identification method.
The purpose of the invention is realized by the following technical scheme: an IMF-guided microseismic signal identification method based on empirical mode decomposition (EMF), the microseismic signal identification method comprising:
dividing the processed original microseismic signal data into two paths, wherein one path is directly input into a U-shaped structure neural network, and the other path is decomposed by an empirical mode to obtain an IMF1 component;
the input layer of the U-shaped structure neural network receives original microseismic signal data, and simultaneously, IMF1 components obtained by decomposing original microseismic signals by an empirical mode are added in the encoding stage of the U-shaped structure neural network, so that the characteristic extraction is guided and restrained;
and (3) performing dimensionality reduction on the IMF1 component through a pooling layer in the encoding stage to enable the IMF1 component to be matched with the size of the corresponding feature map, and then outputting a recognition prediction result after decoding through the decoding stage.
The microseismic signal identification method further comprises a training step of a U-shaped structure neural network model, before training, a data format needs to be converted into three-dimensional data with the size of NxMxK, wherein N is the number of single-channel seismic waveform sampling points, M is the joint number of multiple channels, K is the number of channels, and 10 cross folding is adopted in the training for strict evaluation.
The training step of the neural network model with the U-shaped structure specifically comprises the following steps:
step 1: inputting microseismic signals according to a format;
step 2: taking 10% as a test set, and dividing 90% of the rest 90% of data into a training set and 10% as a verification set;
and step 3: the amplification of the training set is realized by a random time window moving method with the length of the left and right movement of the time window not exceeding 0.1 of the length of the sample, and zero filling is carried out in the opposite direction of movement;
and 4, step 4: respectively cutting the two ends of all samples to be 0.1 of the length of the sample so as to remove zero padding parts and unify the format;
and 5: performing empirical mode decomposition on the signal sequence obtained in the step to obtain an IMF1 component matched with the size of the signal sequence;
step 6: inputting microseismic signals into a network for training, wherein epoch is set to be 50, batch is set to be 20, and each submodule in an encoding stage is added with a corresponding IMF1 component to constrain a feature diagram, wherein the IMF1 component adopts a maximum pooling idea for dimensionality reduction so as to ensure that the feature diagram size is matched with that of the corresponding submodule;
and 7: and since 10 cross-folding is adopted, the final identification accuracy is averaged for 10 times, and the classification performance of the model is further evaluated by drawing an ROC curve and calculating an AUC value.
The encoding stage and the decoding stage are both composed of four sub-modules; each submodule in the encoding stage comprises a pooling layer and two convolution layers, and each submodule is added with an IFM1 component after empirical mode decomposition, so that feature extraction is restrained; and each module in the decoding stage comprises an anti-convolution layer, two convolution layers and a fusion layer, the characteristics are recovered through the anti-convolution layer, and the output characteristic graph is fused with the output characteristic graph corresponding to the encoding stage through the fusion layer.
The obtaining of the IMF1 component by empirical mode decomposition specifically includes:
a1, finding out local maximum and minimum of original microseismic signal array x (t), utilizing cubic curve interpolation to connect local maximum and minimum to obtain maximum envelope x max (t) and a minima envelope x min (t);
A2, local maximum x for each time max (t) and a minimum value x min (t) averaging to obtain an instantaneous average value m (t);
a3, subtracting the instantaneous average value m (t) from the original microseismic signal array x (t) to obtain a new array h (t) with low frequency removed;
a4, judging whether the new sequence h (t) meets two conditions of the intrinsic mode function IMF, if yes, h (t) is used as an intrinsic mode function, if not, the steps A1-A3 are repeated with h (t) as the original sequence until the two conditions of the intrinsic mode function IMF are met;
a5, obtaining a first inherent mode function c 1 (t) mixing c 1 (t) separating r from the original sequence 1 (t)=x(t)-c 1 (t);
A6, converting remainder c 1 (t) the decomposition process of step A5 is performed as a new sequence until the remaining term r n (t) becomes a monotonic function or constant, ending the decomposition when no IMF is decomposed, resulting in a separation from the original sequence
Figure 150723DEST_PATH_IMAGE001
A component of intrinsic mode function (c) 1 (t),c 2 (t),...,c 1 (t)) and a trend term r n (t)。
The invention has the following advantages: the method for identifying the microseismic signal guided by IMF based on empirical mode decomposition improves the automation degree of microseismic event identification, reduces manual operation, avoids manual subjective intervention, and increases the efficiency of classification processing under the large-era background that the data volume exponentially increases. The method is based on microseismic event classification, and has the advantages that the requirements on the classifier are higher than those of the classifier for classifying natural seismic events due to the characteristics of low signal-to-noise ratio and small amplitude of microseismic signals, and the high recognition rate is ensured. The feature learning capability of the network model is improved by introducing an EMD method, so that the model utilizes an IMF1 component after EMD decomposition to supplement and constrain the original signal in the feature extraction process to improve the microseismic signal identification rate with low signal-to-noise ratio.
Drawings
FIG. 1 is a schematic flow diagram of the present invention;
FIG. 2 is a schematic diagram of a neural network with a U-shaped structure;
FIG. 3 is a plot of microseismic events and noise versus waveforms;
FIG. 3 (a) is a schematic waveform of a microseismic event;
FIG. 3 (b) is a schematic diagram of a waveform of noise;
FIG. 4 is a waveform diagram before and after EMD decomposition;
FIG. 4 (a) is a schematic waveform of an original microseismic signal;
FIG. 4 (b) is a waveform diagram of the IMF1 component;
FIG. 5 is a schematic diagram of the output results of the network model;
FIG. 5 (a) is a schematic waveform of a microseismic event;
FIG. 5 (b) is a schematic diagram of the predicted results of microseismic events corresponding to FIG. 5 (a);
FIG. 5 (c) is a schematic diagram of a waveform of noise;
fig. 5 (d) is a schematic diagram of the noise prediction result corresponding to fig. 5 (c).
Detailed Description
In order to make the objects, technical solutions and advantages of the embodiments of the present application clearer, the technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the drawings in the embodiments of the present application, and it is obvious that the described embodiments are only a part of the embodiments of the present application, and not all the embodiments. The components of the embodiments of the present application, generally described and illustrated in the figures herein, can be arranged and designed in a wide variety of different configurations. Thus, the detailed description of the embodiments of the present application provided below in connection with the appended drawings is not intended to limit the scope of the claimed application, but is merely representative of selected embodiments of the application. All other embodiments, which can be derived by a person skilled in the art from the embodiments of the present application without making any creative effort, shall fall within the protection scope of the present application. The invention is further described below with reference to the accompanying drawings.
As shown in fig. 1, the present invention performs filtering processing according to the frequency characteristics of different components, so as to better characterize the frequency components in the time-frequency plane. Compared with decomposition methods which rely on prior function bases, such as Fourier transform and wavelet, the method has the advantages that internal characteristics of signals are reflected more effectively, signal energy diffusion and leakage are avoided, the limitation of an inaccurate measurement principle in Fourier transform is overcome effectively, and the method is more suitable for processing nonlinear and non-stationary signals, so that frequency distribution of the signals at any moment can be obtained, and higher time-frequency domain resolution capability is provided, and the method specifically comprises the following contents:
dividing the processed original microseismic signal data into two paths, wherein one path is directly input into a U-shaped structure neural network, and the other path obtains IMF1 components through Empirical Mode Decomposition (EMD);
the input layer of the U-shaped structure neural network receives original microseismic signal data, and simultaneously, IMF1 components obtained by decomposing original microseismic signals by an empirical mode are added in the encoding stage of the U-shaped structure neural network, so that the characteristic extraction is guided and restrained;
and (3) performing dimension reduction on the IMF1 component through a pooling layer in the encoding stage to enable the IMF1 component to be matched with the size of the corresponding feature map, and then outputting a recognition prediction result after decoding through the decoding stage.
As shown in fig. 2, the encoding stage and the decoding stage are each composed of four sub-modules; the neural network input layer receives an original microseismic signal, simultaneously, an IMF1 component obtained by decomposing the original microseismic signal by EMD is added in a network coding stage, in order to ensure that the extracted features are combined with the IMF1 component in each sub-module, the IMF1 component is subjected to dimensionality reduction by utilizing the maximum pooling idea so as to be matched with the size of a corresponding feature map, then decoding is carried out, and finally a prediction result is output. The model comprises two stages of coding and decoding from an input layer to an output layer, wherein the coding stage mainly has the functions of extracting microseismic signals and signal component characteristics layer by layer, and a pooling layer is adopted for performing maximum pooling operation on all characteristic graphs, amplifying and highlighting effective signal characteristics, reducing model parameters and restricting the extraction of the signal characteristics by the component characteristics. And in the decoding stage, the deconvolution layer is adopted for feature recovery, and the fusion layer is adopted for fusing the output feature graph with the output feature graph corresponding to the encoding stage. The activation functions are classified by using a ReLU nonlinear activation function Relu (x) = max (0, x), and finally by using Softmax logistic regression.
The microseismic signal identification method further comprises a training step of a U-shaped structure neural network model, before training, a data format needs to be converted into three-dimensional data with the size of NxMxK, wherein N is the number of single-channel seismic waveform sampling points, M is the joint number of multiple channels, K is the number of channels, and 10 cross folding is adopted in the training for strict evaluation. The method comprises the following specific steps:
step 1: inputting microseismic signals according to a format;
step 2: the data set is divided randomly. Taking 10% as a test set, and dividing 90% of the rest 90% of data into a training set and 10% as a verification set;
and 3, step 3: the training set is amplified. Because the number of positive samples in the microseismic data set is often larger than that of negative samples, the classification performance of the model is low due to direct training, and higher accuracy can be obtained even if the samples are completely identified as the negative samples. Therefore, the amplification of the training set is realized by a method of randomly moving the time window, and in order to ensure that the effective signal in the positive sample still exists in the positive sample, the length of the left and right movement of the time window does not exceed 0.1 of the length of the sample, and the movement in the opposite direction is filled with zero;
and 4, step 4: and (6) cutting a sample. The training set is expanded in the previous step, and in order to remove zero padding parts and unify formats, the lengths of both ends of all samples are respectively cut to be 0.1;
and 5: and (4) EMD decomposition. Performing EMD on the signal sequence obtained in the step to obtain an IMF1 component matched with the size of the signal sequence;
and 6: and training the network model. The microseismic signal is input to the network for training, with epoch set to 50 and batch set to 20. Adding corresponding IMF1 components into each sub-module in the encoding stage to restrict the feature map, wherein the IMF1 components adopt the maximum pooling idea to reduce the dimension so as to ensure that the dimension of the feature map is matched with the dimension of the corresponding sub-module;
and 7: and testing the classification performance of the model. And since 10 cross-folding is adopted, the final identification accuracy is averaged for 10 times, and the classification performance of the model is further evaluated by drawing an ROC curve and calculating an AUC value.
EMD through 572 2 The non-stationary signal is decomposed into several Intrinsic Mode Functions (IMFs) to stabilize the signal. The natural mode signal needs to satisfy the following two conditions: (1) the number of extreme points and the number of zero-crossing points are equal or differ by 1 at most; (2) at any point, the average value of two envelope curves composed of the local maximum point and the local minimum point is 0. Any signal is composed of a plurality of different natural modes, each mode can be linear or nonlinear, the number of poles and the number of zeros are the same, the upper envelope line and the lower envelope line are locally symmetrical about a time axis, and at any time, one signal can contain a plurality of natural mode signals, and if the modes are mutually overlapped, a composite signal is formed. On the basis, Nordeng E.Huang et al screen out the natural modes of the signal by EMD. The method comprises the following steps:
1. finding out local maximum and minimum of original number series x (t), utilizing cubic curve to make interpolation connection to local maximum and minimum to respectively obtain maximum envelope x max (t) and a minima envelope x min (t);
2. Local maximum x for each time instant max (t) and minimum value x min (t) averaging to obtain an instantaneous average value m (t), where m (t) =1/2[ x [) max (t)+x min (t)];
3. Subtracting the instantaneous average value m (t) from the original number sequence x (t) to obtain a new number sequence h (t) with low frequency removed; wherein h (t) = x (t) -m (t);
checking whether h (t) meets two conditions of the inherent mode function, and if so, taking h (t) as an inherent mode function; if not, repeating the 3 steps by taking h (t) as an original sequence until two conditions of the inherent modal signal are met; thus, we obtain the first natural mode function c 1 (t) generally, this function represents the high frequency part of the original sequence, also called a vibration mode of the original sequence, c 1 (t) is separated from the original sequence of numbers, where r 1 (t)=x(t)-c 1 (t)。
The remainder r 1 (t) performing the above decomposition process as a new sequence until the remaining term r n (t) becomes a monotonic function or constant, where no IMF decomposition occurs, ending the decomposition, resulting in n normal mode function components (c) separated from the original sequence 1 (t),c 2 (t),...,c 1 (t)) and a trend term r n (t), when the signal can be expressed as:
Figure 864601DEST_PATH_IMAGE002
in practical application, because the frequency of each IMF component is different, if each component signal of the signal is analyzed, a filtering method is actually formed, so that different components can be selected according to actual needs to perform time-frequency analysis and signal reconstruction, and the signal-to-noise ratio and the resolution of the microseismic signal are improved.
In practice, data provided by Wilkins et al (2020), derived from a geophone in an unpublished mine in Australia monitored at 1000Hz, is used, each microseismic event consisting of data from eight seismic traces, each trace having 1500 samples, i.e. each microseismic segment is 1.5s long. The data set is obtained by acquiring 102 different microseismic events through expert identification, and acquiring 1087 events through a traditional automatic monitoring algorithm, wherein the 1087 events comprise 102 real events identified by the expert, and the rest are all noise events. It can thus be seen that 1087 potential events that are likely microseismic events were monitored using conventional methods, which is sufficient to demonstrate that the reliability of classification of microseismic events for low signal to noise ratios is low. The 1087 potential microseismic events are input into a network for training and prediction, and because the output result is also eight paths, the data of more than six paths of effective prediction results are judged as the microseismic events, otherwise, the data are noises, so that the classification of the events and the noises is realized. The neural network identification performance under the condition of inputting different data is compared, and the result is as follows:
TABLE 1 neural network identification results
Figure 113180DEST_PATH_IMAGE004
As can be seen from the results in table 1, the overall recognition accuracy is low because the training data set contains samples that are difficult to distinguish between events and noise, as shown in fig. 3, fig. 3 (a) is a schematic diagram of waveforms of microseismic events, fig. 3 (b) is a schematic diagram of waveforms of noise, and Wilkins et al. (2020) in the preprocessing of the training data set, sample augmentation is performed by exchanging seismic channels, and artificially synthesized data is also added to expand the data volume, but we do not perform similar processing in the actual research process, so as to make our model more universal, and can be applied to single data, and in addition, it is reduced that preprocessing of data can make more objective judgments. As shown in the table, when single data is input, the classification accuracy of the IMF1 component obtained by decomposing the signal by EMD is slightly higher than that of the original signal. Under the condition that the two data are input simultaneously, the classification effect is obviously better than the condition of inputting single data. Especially for real microseismic events, the network model has better robustness.
As shown in fig. 4, in the diagram, fig. 4 (a) is a schematic waveform diagram of an original microseismic signal, and fig. 4 (b) is a schematic waveform diagram of an IMF1 component, it can be clearly seen that the features of the IMF1 component obtained after EMD decomposition are more prominent, the resolution is improved, and the network is more facilitated to perform feature extraction. Although the energy of the original signal is concentrated, the original signal becomes more fuzzy under the background of large noise, and the IMF1 signal after EMD decomposition has clear characteristics, so that the original signal can be supplemented, and the model learning is helped to judge the effective signal. The model applied by the invention can fuse the information of the two, so that the IMF1 component after EMD decomposition supplements the original information for final judgment, and the characteristic capability of network learning is improved. As shown in fig. 5, fig. 5 (a) in fig. 5 is a schematic diagram of a waveform of a microseismic event, fig. 5 (b) is a schematic diagram of a prediction result corresponding to the microseismic event in fig. 5 (a), fig. 5 (c) is a schematic diagram of a waveform of noise, and fig. 5 (d) is a schematic diagram of a noise prediction result corresponding to fig. 5 (c). More than six of the data which can obtain effective prediction results are judged as microseismic events, otherwise, the data are judged as noise, and the classification of the events and the noise is judged according to the microseismic events and the noise.
The foregoing is illustrative of the preferred embodiments of this invention, and it is to be understood that the invention is not limited to the precise form disclosed herein and that various other combinations, modifications, and environments may be resorted to, falling within the scope of the concept as disclosed herein, either as described above or as apparent to those skilled in the relevant art. And that modifications and variations may be effected by those skilled in the art without departing from the spirit and scope of the invention as defined by the appended claims.

Claims (5)

1. The method for identifying the microseismic signal guided by IMF based on empirical mode decomposition is characterized by comprising the following steps: the microseismic signal identification method comprises the following steps:
dividing the processed original microseismic signal data into two paths, wherein one path is directly input into a U-shaped structure neural network, and the other path is decomposed by an empirical mode to obtain an IMF1 component;
the input layer of the U-shaped structure neural network receives original microseismic signal data, and simultaneously, IMF1 components obtained by decomposing original microseismic signals by an empirical mode are added in the encoding stage of the U-shaped structure neural network, so that the characteristic extraction is guided and restrained;
and (3) performing dimensionality reduction on the IMF1 component through a pooling layer in the encoding stage to enable the IMF1 component to be matched with the size of the corresponding feature map, and then outputting a recognition prediction result after decoding through the decoding stage.
2. The IMF guided microseismic signal identification method based on Empirical Mode Decomposition (EMD) of claim 1 wherein: the microseismic signal identification method further comprises a training step of a U-shaped structure neural network model, before training, a data format needs to be converted into three-dimensional data with the size of NxMxK, wherein N is the number of single-channel seismic waveform sampling points, M is the joint number of multiple channels, K is the number of channels, and 10 cross folding is adopted in the training for strict evaluation.
3. The empirical mode decomposition (IMF) -guided microseismic signal identification method of claim 2 wherein: the training step of the neural network model with the U-shaped structure specifically comprises the following steps:
step 1: inputting microseismic signals according to a format;
step 2: taking 10% as a test set, and dividing 90% of the rest 90% of data into a training set and 10% as a verification set;
and step 3: the amplification of the training set is realized by a random time window moving method with the length of the left and right movement of the time window not exceeding 0.1 of the length of the sample, and zero filling is carried out in the opposite direction of movement;
and 4, step 4: respectively cutting the two ends of all samples to be 0.1 of the length of the sample so as to remove zero padding parts and unify the format;
and 5: performing empirical mode decomposition on the signal sequence obtained in the step to obtain an IMF1 component matched with the size of the signal sequence;
step 6: inputting microseismic signals into a network for training, wherein epoch is set to be 50, batch is set to be 20, and each submodule in an encoding stage is added with a corresponding IMF1 component to constrain a feature diagram, wherein the IMF1 component adopts a maximum pooling idea for dimensionality reduction so as to ensure that the feature diagram size is matched with that of the corresponding submodule;
and 7: and since 10 cross-folding is adopted, the final identification accuracy is averaged for 10 times, and the classification performance of the model is further evaluated by drawing an ROC curve and calculating an AUC value.
4. The empirical mode decomposition (IMF) -guided microseismic signal identification method of claim 1 wherein: the encoding stage and the decoding stage are both composed of four sub-modules; each submodule in the encoding stage comprises a pooling layer and two convolution layers, and each submodule is added with an IFM1 component after empirical mode decomposition, so that feature extraction is restrained; and each module in the decoding stage comprises an anti-convolution layer, two convolution layers and a fusion layer, the characteristics are recovered through the anti-convolution layer, and the output characteristic graph is fused with the output characteristic graph corresponding to the encoding stage through the fusion layer.
5. The IMF-guided microseismic signal identification method based on empirical mode decomposition (EMF) according to any of claims 1-4 wherein: the obtaining of the IMF1 component by empirical mode decomposition specifically includes:
a1, finding out local maximum and minimum of original microseismic signal array x (t), utilizing cubic curve interpolation to connect local maximum and minimum to obtain maximum envelope x max (t) and a minima envelope x min (t);
A2, local maximum x for each time max (t) and minimum value x min (t) averaging to obtain an instantaneous average value m (t);
a3, subtracting the instantaneous average value m (t) from the original microseismic signal array x (t) to obtain a new array h (t) with low frequency removed;
a4, judging whether the new sequence h (t) meets two conditions of the intrinsic mode function IMF, if so, h (t) is taken as an intrinsic mode function, if not, the steps A1-A3 are repeated with h (t) taken as the original sequence until the two conditions of the intrinsic mode function IMF are met;
a5, obtaining a first inherent mode function c 1 (t) mixing c 1 (t) separating r from the original sequence 1 (t)=x(t)-c 1 (t);
A6, converting remainder c 1 (t) the decomposition process of step A5 is performed as a new sequence until the remaining term r n (t) becomes a monotonic function or constant, and the decomposition ends when no IMF is decomposed, resulting in n normal mode function components (c) separated from the original sequence 1 (t),c 2 (t),...,c 1 (t)) and a trend term r n (t)。
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