CN115061203B - Mine single-channel microseismic signal noise reduction method based on frequency domain singular value decomposition and application - Google Patents

Abstract

The invention relates to a mine single-channel microseismic signal noise reduction method based on frequency domain singular value decomposition, which provides a Hankel matrix construction method of a single-channel microseismic signal and provides a FSVD frequency domain noise reduction method based on Fourier transform and inverse transform and SVD singular value decomposition and a processing flow thereof aiming at the characteristics of low signal correlation of each channel of a mine microseismic system and low Hankel matrix dimension. Compared with the traditional method, the method has the characteristics of being not limited by a threshold value and considering the characteristics of high and low frequency bands, effectively eliminates interference components in the microseismic signals, improves the signal-to-noise ratio, smoothness and the like of the signals, and ensures the fidelity and resolution of the signals. The method has important significance for rapid analysis and treatment of the mine microseismic signals and subsequent accurate initial and time-to-time picking, mining and analysis of the characteristics of the mine microseismic signals.

Description

A method for reducing noise of single-channel microseismic signals in mines based on frequency domain singular value decomposition and its application

Technical Field

The present invention relates to the technical field of mine microseismic and image processing, and in particular to a method and application of mine single-channel microseismic signal denoising based on frequency domain singular value decomposition.

Background Art

It is difficult to reduce the noise of microseismic signals using conventional time domain and frequency domain analysis methods. For this reason, domestic and foreign experts have proposed many denoising methods for non-stationary, nonlinear, and transient change signals. At present, conventional filtering methods include bandpass filtering, EMD filtering, wavelet packet threshold filtering, Butterworth filtering, Chebyshev filtering, and other methods. There are also bandpass filtering, FK domain filtering methods, wavelet threshold, EMD, etc. based on Fourier transform. Xu Hongbin et al. used wavelet transform to study the denoising of microseismic monitoring signals under large-scale rock structures. Kimiaefar R. et al. used artificial neural networks and wavelet packet decomposition to suppress the random noise of seismic signals. However, wavelet packets have certain defects in adaptability, and will cause signal distortion when processing non-stationary and transient signals such as microseismic signals.

There are still some limitations: VMD is an adaptive signal decomposition method, which can overcome the modal aliasing phenomenon that occurs when processing signals, but this method only removes the modal components containing noise, and does not select the mode according to the signal spectrum characteristics, so the selected mode does not necessarily contain the signal characteristics of the original signal. In addition, after selecting the useful modal components, only the included power frequency noise is reduced, so the noise reduction effect achieved by this noise reduction method is not very good. The combination of wavelet packet decomposition and artificial neural network has a good effect on suppressing the random noise of seismic signals, but wavelet packets have certain defects in adaptability. When processing non-stationary and transient signals such as microseismic signals, it will cause signal distortion. For mine microseismic signals with weak energy, high frequency, transient non-stationary, and relatively single propagation medium, the existing microseismic signal processing methods are difficult to extract effective signals.

Summary of the invention

The purpose of denoising microseismic signals in mines is to extract effective signals from background interference, and then serve the links of waveform classification and recognition, arrival time picking, positioning calculation, and attribute feature mining. In order to improve the signal-to-noise ratio of microseismic signals in mines, the present invention provides a single-channel microseismic signal denoising processing method based on FFT and SVD.

In order to solve the above technical problems, the method for reducing noise of single-channel microseismic signals in mines based on frequency domain singular value decomposition of the present invention comprises the following steps:

Step S1: Fourier transform of microseismic signals

Perform Fourier transform on the microseismic signal _X1 and convert it into the frequency domain to obtain the corresponding frequency domain signal The conversion formula is:

Step S2: Establishment of key parameters

Establish the relevant parameters of singular value decomposition of single-channel microseismic data: time delay τ, reconstruction order k, and Hankel matrix length n and dimension m;

Step S3: Singular value transform SVD

The two-dimensional microseismic signal is divided into equal lengths, the Hankel matrix D is constructed, and the matrix is subjected to singular value decomposition: Assuming that the two-dimensional seismic profile is P, the number of channels is m, and the number of sampling points per channel is n, the m×n matrix P is subjected to singular value decomposition, and the following relationship can be obtained:

Among them, U and V represent the left and right singular matrices (orthogonal matrices), respectively, with U∈Rm ^×m and V∈Rn ^×n ; the rank of P is k (k＝min(m,n)), generally m is much smaller than n; S is a diagonal matrix composed of the eigenvalues σ of ^PPT or ^PTP in descending order; r is the rank of the matrix P, and the number of singular values k is equal to the rank r of the matrix.

The diagonal matrix S = diag (σ ₁ , σ ₂ , …, σ _k ) is the eigenvalue of the matrix R, where σ _k is the kth eigenvalue. The relationship can be expressed as:

The relationship between the singular value λ _k and the eigenvalue σ _k of the matrix PP ^T or P ^T P can be defined as Where λ ₁ ≥λ ₂ ≥…≥λ _k ≥0; in the process of signal reconstruction, the contribution of the kth characteristic quantity σ _k to the entire signal is proportional to the kth singular value λ _k . Therefore, using λ _k or σ _k ² to characterize the energy of the seismic signal in the channel, the energy contribution rate C _j of the signal in the jth channel can be expressed as:

It can be seen that the larger the component of the eigenvalue or singular value, the higher its contribution to the entire seismic signal.

Step S4: 2D signal reconstruction

Analyze the distribution law of singular values, and establish a reasonable reconstruction order k and singular value sequence number based on the singular value optimization principle; use SVD inverse transform to obtain the denoised single-channel two-dimensional microseismic signal;

Generally, since singular values are arranged in descending order, the seismic field will select the first few characteristic quantities (the part with concentrated contributions) to describe the original signal, that is, retain the first few valid singular values in the diagonal matrix S, set the other singular values to 0, and then use the inverse process of singular value decomposition to reconstruct the signal.

Step S5: Inverse Fourier Transform

The reconstructed spectrum is transformed using inverse Fourier transform Transformed into the desired target signal X ₂ , the inverse transformation formula is as follows:

Step S6: Determine whether the signal-to-noise ratio after denoising meets the requirement. If not, return to step S1.

Furthermore, in step S2, the delay time τ constructed by the SVD phase space matrix is obtained by using the autocorrelation function. Assuming that there is a single-channel microseismic time series X, the autocorrelation function R of the series can be expressed as:

Where N is the number of sampling points of the single-channel microseismic record; the delay time corresponding to the minimum value R _min is taken as τ.

Furthermore, in step S2, the relationship between the length n and dimension m of the Hankel matrix and τ is: (m-1)×τ+n=N; assuming m=n, then: In terms of the values of m and n, in order to avoid the shortcomings of the constructed Hankel matrix being too high in dimension, too many eigenvalues, and requiring high computing time and process, m and n can be considered to be approximately equal.

Furthermore, in step S2, the singular value energy difference spectrum is introduced to establish the singular value decomposition and reconstruction SVD order. The singular value energy difference spectrum E describes the change of energy represented by adjacent singular values, and its calculation formula can be expressed as:

Wherein, E(i) is the i-th singular value energy difference spectrum, i=1,2,…,k-1, E is a sequence consisting of k-1 singular value energy difference spectra; λ _i is the i-th singular value, λ _max and λ _min are the maximum and minimum values in the singular value matrix, respectively.

Furthermore, the judgment method in step S6 is: using the signal-to-noise ratio SNR, energy percentage ESN, root mean square error RMSE and signal smoothness STI of the signal to quantitatively describe the microseismic signals before and after noise reduction, respectively, and the formula can be expressed as:

Among them, _Sn and Microseismic signals before and after filtering, respectively. N is the number of sampling points of the signal.

The present invention also provides a computer program product, which includes computer instructions. When the computer instructions are executed by a processor, the computer device executes the above-mentioned method for reducing noise of single-channel microseismic signals in a mine based on frequency domain singular value decomposition.

The present invention also provides a computer-readable storage medium having computer-executable instructions stored thereon, which, when executed by a processor, are used to implement the aforementioned method for reducing noise of a single-channel microseismic signal in a mine based on frequency domain singular value decomposition.

The present invention also provides a mine single-channel microseismic signal denoising system based on frequency domain singular value decomposition, comprising:

one or more processors; and

One or more memories storing a computer executable program, when the computer executable program is executed by the processor, the above-mentioned method for reducing noise of single-channel microseismic signals in a mine based on frequency domain singular value decomposition is executed.

The single-channel microseismic signal denoising processing method based on FFT and SVD of the present invention aims at the characteristics of low correlation of each channel signal and low dimension of Hankel matrix in the mine microseismic system, proposes a method for constructing the Hankel matrix of a single-channel microseismic signal, and proposes an FSVD frequency domain denoising method based on Fourier transform and inverse transform and SVD singular value decomposition and its processing flow. Compared with the traditional method, this method has the characteristics of not being restricted by threshold and taking into account the characteristics of high and low frequency bands. While effectively eliminating the interference components in the microseismic signal, it improves the signal-to-noise ratio and smoothness of the signal, and ensures the fidelity and resolution of the signal. This method is of great significance for the rapid analysis and processing of mine microseismic signals, as well as the subsequent accurate picking of the initial arrival time, mining and analysis of mine microseismic signal features.

BRIEF DESCRIPTION OF THE DRAWINGS

The specific implementation of the present invention will be further explained below in conjunction with the accompanying drawings.

Figure 1 (a) Flow chart of SVD frequency domain noise reduction of mine microseismic signals of the present invention

FIG1( b ) is a schematic diagram of the noise reduction principle of the present invention;

FIG2 is a waveform diagram of a microseismic event in an embodiment of the present invention;

FIG3( a ) is a schematic diagram of FSVD singular value energy distribution of singular values in the interval of sequence numbers 1 to 5 in an embodiment of the present invention;

FIG3( b ) is a spectrum characteristic diagram of the reconstructed signal corresponding to the singular values in the interval of sequence numbers 1 to 5 according to an embodiment of the present invention;

FIG4( a ) is a schematic diagram of FSVD singular value energy distribution of singular values in the interval of sequence numbers 6 to 10 in an embodiment of the present invention;

FIG4( b ) is a spectrum characteristic diagram of the reconstructed signal corresponding to the singular values in the interval of sequence numbers 6 to 10 in an embodiment of the present invention;

FIG5( a ) is a schematic diagram of FSVD singular value energy distribution of singular values in the interval of sequence numbers 11 to 15 in an embodiment of the present invention;

FIG5( b ) is a spectrum characteristic diagram of the reconstructed signal corresponding to the singular values in the interval of sequence numbers 11 to 15 in an embodiment of the present invention;

FIG6( a ) is a schematic diagram of FSVD singular value energy distribution of singular values in the range of sequence numbers 16 to 20 in an embodiment of the present invention;

FIG6( b ) is a spectrum characteristic diagram of the reconstructed signal corresponding to the singular values in the interval of sequence numbers 16 to 20 in an embodiment of the present invention;

FIG. 7( a ) is a schematic diagram of FSVD singular value energy distribution of singular values in the interval of sequence numbers 21 to 25 in an embodiment of the present invention;

FIG. 7( b ) is a spectrum characteristic diagram of the reconstructed signal corresponding to the singular values in the interval of sequence numbers 21 to 25 according to an embodiment of the present invention;

FIG8( a ) is a schematic diagram of the analysis of the frequency domain SVD denoising results of a high signal-to-noise ratio signal in an embodiment of the present invention;

FIG8( b ) is a schematic diagram of the analysis of the frequency domain SVD denoising results of a low signal-to-noise ratio signal in an embodiment of the present invention.

DETAILED DESCRIPTION

The present invention proposes singular value decomposition (SVD) denoising for a single channel, and uses this method to decompose and reduce noise on microseismic signals in mines, mainly by utilizing the periodicity of microseismic signals in a single channel. By using SVD to decompose microseismic signals, the signal can be divided into several eigenvalues according to the energy size, and the effective bandwidth of the eigenvalue of the signal is broadened to a certain extent. The eigenvalue is compensated for the frequency according to the energy distribution, and the eigenvalue dominated by noise is eliminated at the same time, and the signal is reconstructed. This is the basic idea of the filtering method. The signal-to-noise ratio and resolution of the reconstructed signal are significantly improved compared with the original signal.

To realize the singular value decomposition of single-channel microseismic signals, it is necessary to first perform "fixed-length" division on the microseismic signals. Assume that the single-channel microseismic signal is expressed as X = [x ₁ , x ₂ , x ₃ ,…, x _N ], and the total number of sampling points is N. To facilitate SVD analysis, the single-channel signal is divided into m dimensions (channels), each dimension (channel) is a column of data with n sampling points, and the next column of data is an equal-length sequence of the previous column of data after delay τ. The decomposition matrix D _m constructed in this way can be expressed as:

Among them, m is the dimension of matrix reconstruction, τ is the time delay, and n is the number of sampling points of the signal in each dimension.

At this time, the microseismic signal can be regarded as consisting of the subspace D not disturbed by noise and the noise subspace N, and its Hankel matrix can be expressed as:

From this, we can see that U and V are just rotations of the original matrix, while S establishes the linearity (compression) degree of the matrix. The better the linearity, the closer D is to D. Using SVD for denoising is essentially seeking the best approximation to the undisturbed subspace D. The better the approximation, the better the denoising effect.

Using the above analysis, after the singular value decomposition SVD is performed on the decomposition matrix _Dm , the singular value consists of three parts, which can be expressed as: S _Dm = S _D + S _N + S _W , S _W represents the singular value corresponding to the strong interference component, S _N corresponds to the singular value corresponding to the random interference, and S _D is the singular value of the effective signal. Therefore, the process of using SVD to denoise the single-channel microseismic signal is to retain the effective signal corresponding to S _D , and set the singular values of the interference signal corresponding to S _W and S _N to 0, and then perform SVD inverse transformation to obtain the denoised microseismic signal. The process of setting the singular value of the interference signal to zero is actually the process of "compressing" the matrix Dm. As shown, ① corresponds to the S _W and S _N parts, and ② corresponds to the S _D part.

The method for reducing noise of single-channel microseismic signals in a mine based on frequency domain singular value decomposition in this embodiment includes the following steps:

Step S1: Fourier transform of microseismic signals

Perform Fourier transform on the microseismic signal _X1 and convert it into the frequency domain to obtain the corresponding frequency domain signal The conversion formula is:

Step S2: Establishment of key parameters

Establish the relevant parameters of singular value decomposition of single-channel microseismic data: time delay τ, reconstruction order k, and Hankel matrix length n and dimension m;

Step S3: Singular value transform SVD

The two-dimensional microseismic signal is divided into equal lengths, the Hankel matrix D is constructed, and the matrix is subjected to singular value decomposition: Assuming that the two-dimensional seismic profile is P, the number of channels is m, and the number of sampling points per channel is n, the m×n matrix P is subjected to singular value decomposition, and the following relationship can be obtained:

Among them, U and V represent the left and right singular matrices (orthogonal matrices), respectively, with U∈Rm ^×m and V∈Rn ^×n ; the rank of P is k (k＝min(m,n)), generally m is much smaller than n; S is a diagonal matrix composed of the eigenvalues σ of ^PPT or ^PTP in descending order; r is the rank of the matrix P, and the number of singular values k is equal to the rank r of the matrix.

The diagonal matrix S = diag (σ ₁ , σ ₂ , …, σ _k ) is the eigenvalue of the matrix R, where σ _k is the kth eigenvalue. The relationship can be expressed as:

The relationship between the singular value λ _k and the eigenvalue σ _k of the matrix PP ^T or P ^T P can be defined as Where λ ₁ ≥λ ₂ ≥…≥λ _k ≥0; in the process of signal reconstruction, the contribution of the kth characteristic quantity σ _k to the entire signal is proportional to the kth singular value λ _k . Therefore, using λ _k or σ _k ² to characterize the energy of the seismic signal in the channel, the energy contribution rate C _j of the signal in the jth channel can be expressed as:

It can be seen that the larger the component of the eigenvalue or singular value, the higher its contribution to the entire seismic signal.

Step S4: 2D signal reconstruction

Analyze the distribution law of singular values, and establish a reasonable reconstruction order k and singular value sequence number based on the singular value optimization principle; use SVD inverse transform to obtain the denoised single-channel two-dimensional microseismic signal;

Generally, since singular values are arranged in descending order, the seismic field will select the first few characteristic quantities (the part with concentrated contributions) to describe the original signal, that is, retain the first few valid singular values in the diagonal matrix S, set the other singular values to 0, and then use the inverse process of singular value decomposition to reconstruct the signal.

Step S5: Inverse Fourier Transform

The reconstructed spectrum is transformed using inverse Fourier transform Transformed into the desired target signal X ₂ , the inverse transformation formula is as follows:

Step S6: Determine whether the signal-to-noise ratio after denoising meets the requirement. If not, return to step S1.

In this embodiment, preferably, in step S2, the delay time τ constructed by the SVD phase space matrix is obtained by using the autocorrelation function. Assuming that there is a single-channel microseismic time series X, the autocorrelation function R of the series can be expressed as:

Where N is the number of sampling points of the single-channel microseismic record; the delay time corresponding to the minimum value R _min is taken as τ.

In this embodiment, preferably, in step S2, the relationship between the length n and dimension m of the Hankel matrix and τ is: (m-1)×τ+n=N; assuming m=n, then: In terms of the values of m and n, in order to avoid the shortcomings of the constructed Hankel matrix being too high in dimension, too many eigenvalues, and requiring high computing time and process, m and n can be considered to be approximately equal.

In this embodiment, preferably, in step S2, a singular value energy difference spectrum is introduced to establish the singular value decomposition and reconstruction SVD order. The singular value energy difference spectrum E describes the change of energy represented by adjacent singular values, and its calculation formula can be expressed as:

Wherein, E(i) is the i-th singular value energy difference spectrum, i=1,2,…,k-1, E is a sequence consisting of k-1 singular value energy difference spectra; λ _i is the i-th singular value, λ _max and λ _min are the maximum and minimum values in the singular value matrix, respectively.

Furthermore, the judgment method in step S6 is: using the signal-to-noise ratio SNR, energy percentage ESN, root mean square error RMSE and signal smoothness STI of the signal to quantitatively describe the microseismic signals before and after noise reduction, respectively, and the formula can be expressed as:

Among them, _Sn and Microseismic signals before and after filtering, respectively. N is the number of sampling points of the signal.

In order to verify the effectiveness of the single-channel signal SVD denoising method, this embodiment takes a microseismic event measured on site in a mine in Shandong as an example (time is 2014-06-10 20:13:42), and introduces the denoising process of the method proposed in the present invention. The waveform of the microseismic event is shown in Figure 2. The relevant parameters of the on-site microseismic monitoring system are as follows: sampling frequency 1000Hz, continuous acquisition buffer (continuous acquisition length 15min), and subsequent use of STA/LTA for event picking and interception; the sensor is a velocity type, with a frequency characteristic of 50-5kHz, a sensitivity of 30V/g, and a frequency range of 0-1000Hz. In order to perfectly collect the microseismic signal of coal rock fracture, the microseismic sensor is buried inside the coal seam (20-45m from the orifice).

1. Parameter selection and data processing

Taking the microseismic event shown in Figure 2 as an example, the following describes the selection process of each key parameter. First, taking single channel 9# as an example, it introduces how to obtain each key parameter and how to judge the effect after denoising.

(1) Calculate the delay time

According to the characteristics of single-channel microseismic records, the autocorrelation coefficient of the signal is obtained using the autocorr() function of MATLAB. The calculation results of the delay time τ and the autocorrelation coefficient R are as follows:

(2) Constructing the Hankel matrix

The delay time calculation result is τ = 9, and according to step S2, m = 100, n = 109 are finally solved. Thus, the key parameters for constructing the Hankel matrix are obtained, and these parameters can be used to realize the SVD decomposition of the microseismic signal of a single channel; the next step is to clarify how to select a reasonable SVD reconstruction order, that is, how to select the singular value corresponding to the effective signal.

(3) Establishment of reconstruction order

In order to illustrate the rationality of the reconstruction order selection, the signal will be reconstructed according to different singular value ranges to observe the contribution of each singular value to the original microseismic signal. The main frequency of the mine microseismic signal is concentrated in the range of 50-200Hz, and the noise energy is relatively strong and widely distributed. By performing singular value decomposition on the spectrum, it is determined that the energy spectrum of the original signal is mainly concentrated in the first 20. Therefore, the object of study is the signal components corresponding to the first 20 singular value numbers.

The constructed Hankel matrix is decomposed by FSVD, and the singular value sequence is selected and the signal is reconstructed according to a certain rule. The singular values in the intervals of sequence numbers 1 to 5, 6 to 10, 11 to 15, 16 to 20, and 21 to 25 are selected respectively. Finally, the FSVD singular value energy distribution is obtained, as shown in Figures 3(a), 4(a), 5(a), 6(a) and 7(a), respectively. The curves are energy proportions, and the lines correspond to the singular value numbers. The corresponding spectrum characteristic diagrams of the reconstructed signals are shown in Figures 3(b), 4(b), 5(b), 6(b) and 7(b), respectively. It can be seen from the figure that the signal characteristics reconstructed by selecting different sequences (orders) are different. Figures 3(a), 3(b) and 4(a), 4(b) fully reflect the waveform signal itself, while Figures 5(a), 5(b); Figures 6(a), 6(b) and 7(a), 7(b) show that the noise part has dominated. The noise in Figure 3(a) and Figure 3(b) is effectively suppressed, but more details are lost, which is mainly due to the incomplete selection of singular values. By analyzing Figure 4(a) and Figure 4(b), it is found that this series of singular values has both effective components and interference components, belonging to a transition zone; while Figure 5(a) and Figure 5(b); Figure 6(a), Figure 6(b) and Figure 7(a), Figure 7(b) spectral characteristics show that the influence on the effective components of the waveform is small. Therefore, 1 to 10 are selected as the effective singular value sequence. It can also be seen from the final denoising results that Figure 6(a) and Figure 6(b) have the best denoising effect, the main frequency components are effectively protected, the background noise is suppressed cleanly, and the initial jump point is obvious.

2. Spectrum Analysis Comparison

In order to illustrate the effectiveness of using the method provided by the present invention to denoise the microseismic signal of a mine, the 5# and 12# channels are taken as examples (representing high and low signal-to-noise ratio signals, respectively), and the waveform changes and spectrum changes of the data in the channel before and after denoising are compared. The results are shown in Figures 8(a) and 8(b). Comparing the effects before and after denoising in Figures 8(a) and 8(b), it can be seen that the noise of the microseismic signal is effectively suppressed, and the time-frequency distribution range is more concentrated, corresponding to the obviously suppressed background noise. From the time-frequency diagram Figure 8(a), the frequency of the microseismic signal before denoising is widely distributed in 0-400Hz, and the duration range is 200-800ms; after denoising, the frequency components of 600-800ms are removed, and the components of the frequency band above 320Hz are weakened. The denoising effect of the low signal-to-noise ratio signal in Figure 8(b) is more obvious, especially the frequency in the range of 300-400Hz in Figure 8(b) is completely removed, and the corresponding waveform noise is well suppressed.

This shows that the method provided in this embodiment denoises the microseismic signal from a frequency perspective. While retaining the main components of the original signal, it fully utilizes the small frequency range of the mine microseismic signal, suppresses and removes abnormal frequency components, effectively reduces the influence of interference components such as background noise, and obtains a higher signal-to-noise ratio.

This embodiment also provides a computer program product, which includes computer instructions. When the computer instructions are executed by a processor, the computer device executes the above-mentioned method for reducing noise of single-channel microseismic signals in a mine based on frequency domain singular value decomposition.

This embodiment also provides a computer-readable storage medium having computer-executable instructions stored thereon. When the instructions are executed by a processor, the instructions are used to implement the aforementioned method for reducing noise of a single-channel microseismic signal in a mine based on frequency domain singular value decomposition.

This embodiment also provides a mine single-channel microseismic signal denoising system based on frequency domain singular value decomposition, comprising:

one or more processors; and

One or more memories storing a computer executable program, when the computer executable program is executed by the processor, the above-mentioned method for reducing noise of single-channel microseismic signals in a mine based on frequency domain singular value decomposition is executed.

The single-channel microseismic waveform denoising method based on spectral singular value decomposition of the present invention is essentially to convert the microseismic signal into the frequency domain, and enhance the signal characteristics and suppress the interference noise from the frequency domain perspective by means of SVD singular value decomposition. The method avoids the defects such as serious loss of effective signals, and effectively realizes wavelength separation and denoising. The proposal of this method provides a guarantee for the interpretation and analysis of subsequent microseismic data. The present invention studies the construction method of the decomposition matrix Dm of the single-channel waveform by analyzing the waveform characteristics of the single-channel mine, proposes the FSVD denoising method based on Fourier transform and singular value transform, and then establishes the denoising process of the method and the key parameters (delay time τ, reconstruction order k, Hankel matrix) establishment method. The present invention improves the process and key parameter establishment of the spectrum denoising of the single-channel mine microseismic signal. Through comparative analysis, the method provided by the present invention can better retain the information of the original signal (high similarity, high energy percentage) compared with a variety of conventional single denoising methods, and can obtain a higher signal-to-noise ratio, effectively reducing the noise component in the signal, which has practical significance for the arrival time picking, feature extraction and analysis of microseismic signals.

Many specific details are described in the above description to facilitate a full understanding of the present invention. However, the above description is only a preferred embodiment of the present invention. The present invention can be implemented in many other ways different from those described herein, so the present invention is not limited to the specific implementation disclosed above. At the same time, any person familiar with the art can make many possible changes and modifications to the technical solution of the present invention using the methods and technical contents disclosed above without departing from the scope of the technical solution of the present invention, or modify it into an equivalent embodiment of equivalent changes. Any simple modification, equivalent change and modification made to the above embodiments according to the technical essence of the present invention without departing from the content of the technical solution of the present invention still falls within the scope of protection of the technical solution of the present invention.

Claims (8)

1. A mine single-channel microseismic signal noise reduction method based on frequency domain singular value decomposition is characterized by comprising the following steps of: the method comprises the following steps:

Step S1: fourier transform of microseismic signals

Fourier transforming the microseismic signal X ₁ to convert it into frequency domain to obtain corresponding frequency domain signalThe conversion formula is:

step S2: establishment of key parameters

Establishing relevant parameters of singular value decomposition of single-channel microseismic data: time delay τ, reconstruction order k, hankel matrix length n and dimension m;

step S3: singular value transformation

Equally dividing the two-dimensional microseismic signals, constructing a Hankel matrix D, and carrying out singular value decomposition on the matrix: assuming that the two-dimensional seismic section is P, the number of channels is m, the number of sampling points of each channel is n, and singular value decomposition is carried out on an m multiplied by n matrix P, so that the following relational expression can be obtained:

Wherein U and V respectively represent left and right singular arrays, wherein U is R ^m×m、V∈R^n×n; the rank of P is k (k=min (m, n)); s is a diagonal matrix composed of feature values sigma of PP ^T or P ^T P in descending order; r is the rank of the matrix P, and the number k of singular values is equal to the rank r of the matrix;

the diagonal matrix s=diag (σ ₁,σ₂,…,σ_k) is the eigenvalue of the matrix R, where σ _k is the kth eigenvalue, and its relation can be expressed as:

The relationship of the singular value of λ _k and the eigenvalue of σ _k of the matrix PP ^T or P ^T P can be defined as Wherein lambda ₁≥λ₂≥…≥λ_k is more than or equal to 0; the energy of the seismic signal in the channel is characterized by lambda _k or sigma _k ², and then the energy contribution rate C _j of the signal in the j-th channel can be expressed as:

step S4: two-dimensional signal reconstruction

Analyzing a singular value distribution rule, and establishing a reasonable reconstruction order k and a singular value sequence number according to a singular value optimization principle; obtaining a single-channel two-dimensional microseismic signal after denoising by utilizing SVD inverse transformation;

Step S5: inverse fourier transform

Frequency spectrum to be reconstructed using inverse fourier transformTransformed to the desired target signal X ₂, the inverse transform formula is as follows:

Step S6: and judging whether the signal to noise ratio after denoising meets the requirement, and if not, returning to the step S1.

2. The mine single-channel microseismic signal noise reduction method based on frequency domain singular value decomposition according to claim 1, wherein the method is characterized by comprising the following steps of: in step S2, the delay time τ of the SVD phase space matrix construction is obtained by using the autocorrelation function, and assuming that there is a single-channel microseismic time sequence X, the autocorrelation function R of the sequence can be expressed as:

Wherein N is the number of sampling points of single-channel microseismic recording; r takes the delay time corresponding to the minimum value R _min as tau.

3. The mine single-channel microseismic signal noise reduction method based on frequency domain singular value decomposition according to claim 1, wherein the method is characterized by comprising the following steps of: in the step S2, the relation between the Hankel matrix length n and the dimension m and τ is: (m-1) x τ+n=n; assuming m=n, then there are:

4. The mine single-channel microseismic signal noise reduction method based on frequency domain singular value decomposition according to claim 1, wherein the method is characterized by comprising the following steps of: in the step S2, a singular value energy differential spectrum is introduced for establishing singular value decomposition and reconstruction SVD (singular value decomposition) orders, the singular value energy differential spectrum E describes the change condition of energy represented by adjacent singular values, and a calculation formula can be expressed as follows:

Wherein E (i) is the i-th singular value energy differential spectrum, i=1, 2, …, k-1, E is a sequence consisting of k-1 singular value energy differential spectrums; lambda _i is the ith singular value, lambda _max and lambda _min are the maximum and minimum values, respectively, in the singular value matrix.

5. The mine single-channel microseismic signal noise reduction method based on frequency domain singular value decomposition according to claim 1, wherein the method is characterized by comprising the following steps of: the judging method in the step S6 is as follows: the signal-to-noise ratio SNR, the energy percentage ESN, the root mean square error RMSE and the signal smoothness STI of the signals are used for respectively quantitatively describing the microseismic signals before and after noise reduction, and the formula can be expressed as follows:

wherein S _n and And filtering the front and rear microseismic signals respectively, wherein N is the sampling point number of the signals.

6. A computer program product, characterized by: the computer program product comprising computer instructions which, when executed by a processor, cause a computer device to perform the method of any of claims 1-5.

7. A computer-readable storage medium, characterized by: having stored thereon computer executable instructions for implementing the method according to any of claims 1-5 when executed by a processor.

8. A mine single-channel microseismic signal noise reduction system based on frequency domain singular value decomposition is characterized in that: comprising the following steps:

one or more processors; and

One or more memories in which a computer executable program is stored which, when executed by the processor, performs the method of any of claims 1-5.