Tunnel environment noise suppression by SVD-DSW method

There is strong random noise in seismic records of tunnel seismic advance detection, which makes it difficult to obtain the underground lithology information in front of tunnel face accurately. Aiming at the problem that random noise is difficult to suppress in tunnel environment, a method of SVD-DSW is proposed in our research. Different from the directional seismic wave method, the proposed method is to stack the target signal after leveling. Then, the target signal with stronger coherence is extracted by singular value decomposition and target signal reconstruction, and finally reverse correct the extracted coherent signal to get the target signal. Simulation results and field data analysis show that the SVD-ICA theoretical approach is feasible for improving the SNR of the target signal in three-component seismogram, which is of great significance to increase detection range and resolution of tunnel seismic advance prediction.


Introduction
The geological conditions of underground space are very complicated, potential geological disasters such as karst caves, faults and hidden rivers may be encountered in tunneling or underground construction, which seriously threaten the life and property of the construction personnel [1,2].To ensure the safe and efficient construction of tunnels, many experts and scholars have studied a variety of tunnel geological prediction technologies [3][4][5], among which the most commonly used method is the TSP method [6,7].However, the acquired seismic records are often accompanied by strong environmental noise, which makes it difficult to extract high-quality target signals.Thus, it is easy to lead to the omission and misreporting of geological structure information [8][9][10][11][12][13].Aiming at the above problems, a TSP based Singular Value Decomposition (SVD) and Directional Seismic Wave (DSW) noise suppression method is proposed in our article.Different from the traditional DSW method, the proposed method does not introduce false multi-wave interference (FMWI), and has stronger ability to suppress random noise [14].Therefore, the SVD-DSW may be a better method for further improving the tunnel advance prediction effect.In this paper, the traditional directional seismic wave technology is improved, and SVD processing is introduced after the event stacking, so as to obtain the target signal with stronger coherence.Firstly, the working principle of TSP and the characteristics of seismic record collection are analyzed, and then the principle of SVD-DSW method is studied in detail.In addition, we quantitatively and qualitatively analyze the feasibility and effectiveness of SVD-DSW method in suppressing random noise by numerical simulation.Finally, we use SVD-DSW method to process and analyze the field test data, and the research results further validate the effectiveness of the proposed method in suppressing tunnel ambient noise.

Principle and analysis of SVD-DSW
In this part, we first construct the three-dimensional velocity model of the tunnel and analyze its observation system, then synthesize the corresponding seismic records, and finally study and analyze the principle of SVD-DSW method in detail.

Figure 1. Three-dimensional tunnel velocity model
To study the internal structure of the tunnel model more intuitively, Fig. 1 shows the P-wave velocity model of the three-dimensional (3D) tunnel that is closer to the real situation.Fig. 1 (a) shows the internal diagram of the 3D tunnel velocity model centered on x = 120 m, y = 200 m, and z = 200 m, from which the internal medium of the tunnel can be intuitively understood.Three-dimensional Cartesian coordinate system is established in the 3D geological model.The tunnel axis direction is x axis direction, perpendicular to the horizontal direction of the x axis is y axis direction.Perpendicular to both the x and y axes is the z axis direction.The medium in the tunnel is air, and the velocity of the sound wave in the air is 340 m/s.The velocity of P-wave is 2000 m/s in tunnel surrounding rock.Fig. 1 (b) shows the velocity model slice at z = 200 m, and points out the arrangement of the observation system of tunnel detection.The shot points array are arranged on the side wall of the tunnel.In order to facilitate numerical simulation, according to the principle of shot exchange, the original multipoint excited multipoint receiving is changed to the single-point excited multipoint receiving.The observation system is linearly arranged, with shot point coordinates (x = 40 m, y = 192 m, z = 200 m), offset of 40 m, and track spacing of 2 m.There is a vertical reflector 120 m ahead of the tunnel face, and the medium velocity (P-wave) is 2500 m/s.The spatial angle of the fault reflection interface is 90°.Figs.1(c)-(d) show the slices of the velocity model y = 200 m and x = 120 m, respectively, from which the interior of the tunnel velocity model can be understood from different perspectives.

Tunnel seismic prediction (TSP)
TSP is a reflection wave detection method with long detection distance and high precision [15].By processing the collected data, the lithologic changes ahead of the tunnel face are analyzed to provide geological lithologic information for tunnel construction.TSP adopts the observation system mode of "multi-point excitation and single point reception", and its detection principle is shown in Fig. 2(a).The observation system of TSP contains source array (generally no more than 24) and the high-sensitivity three-component (X, Y, Z) geophone arranged in a straight line [16].TSPwin software was used to process the collected data, and the location, size and lithologic of the undesirable geological bodies ahead of the tunnel work face were obtained.The planning parameters of the shot holes and detector holes are as follows: (1) The depth of the shot holes is 1.5 m, the spacing is 1.5 m, and the diameter is 40 mm.When the shot holes are arranged, they should be as close as possible to the face of the palm.Each hole is loaded with 50 g of emulsion explosive, 1 Instantaneous detonator, and anchor bolt sealing end.
(2) The detector hole is at least 20 m away from the nearest blasting hole, the depth is 2 m, and the diameter is not less than 50 mm.The three-component velocity detector probe is placed in the detector hole.
(3) All boreholes are 1.5 m from the bottom of the tunnel, and as far as possible in the same straight line, requiring the tunnel wall to be drilled vertically and slightly downward (less than 5°).The TSP equipment includes acceleration-type three-component seismic seismometers with a frequency range of 0.5-5000 Hz.The seismometer has a sensitivity of 1000 mV/g±5% and a recorded sampling interval of 62.5 us.

Principle of SVD-DSW method
To study the essential principles of suppression noise, we will analyze the principle of SVD-DSW theory in detail.In this paper, Z-component of three-component seismic record is selected for processing and analysis.Since the record contains target signal and noise, The jth trace record in the Z component can be expressed as: Where, ( ) zj s t and ( ) zj n t represent the jth trace seismic signal and the jth trace noise in the Z component record respectively; M is the total number traces of the Z component record.The delay correction of target signal is the key step of the method in our article.The time delay matrix ( τ ) of the target signal can be calculated by the local cross-correlation method [16,17], and the corrected record ( ( ) t A ) of the target signal is denoted as [ ( ), ( ), ( ] ) , ( ) , ( ) ，and . The 1th trace is usually selected as the reference trace, in which case 1 0 τ = .Since the corrected event in ( ) t A is horizontal, its coherence will be obviously enhanced.At the same time, the coherence of other nontarget signals or noise will be weakened to some extent.For a real matrix are variables in the following equation: Where, , O is the zero matrix, =min( , ) q m n , in the singular values of the matrix, 1 Since the coherence of the target signal in ( ) t A is the strongest, the first singular value is selected for reconstruction as signal and the rest singular values are used as noise for reconstruction, and the obtained target signal is denoted as [18,19] 1 1 1 ( ) According to the superposition mode of DSW method [17], the seismic record ( ) t E is obtained after multi-channel superposition processing of the records in ( ) t B .The final target signal obtained by reverse correction of ( ) t E is recorded as ( ) t F , and the expression is denoted as When the seismic record contains multiple target signals, the target signals can be extracted one by one from strong to weak according to the method presented in this paper.

Numerical simulation study and analysis
To article verify the effect of the SVD-DSW method, numerical simulation method was used to conduct a detailed study and analysis on the Z-component seismic records.The processing process and research results of the method are shown in Fig. 3.The Z-component seismic record with enhanced Gaussian noise is shown in Fig. 3(a), from which the event of Ds (Ds denote the direct S-wave) can be clearly observed.However, the Rs (Rs denote the reflected S-wave) is seriously disturbed by noise, and further processing is needed to improve the event of Rs.

Figure 3.
The process of target signal processing by SVD-DSW method The first step of SVD-DSW theory is to determine the location of the target signal and intercept the time window (t=210-280 ms) of the target signal according to its location.The obtained seismic record containing the event of the target signal (Rs) is shown in Fig. 3(b).For quantitative comparison, the SNR of the Rs in the original recording was calculated to be -10.641dB.According to the local crosscorrelation method by Yue et al [17], the time delay matrix τ of the Rs can be estimated.The event of Rs corrected by the delay matrix τ is shown in Fig. 3(c).Since the corrected event of the target signal is horizontal, thus enhancing the coherence of the target signal (Rs) in the recording.The target signal Rs is processed by multi-trace superposition after the event of Rs leveling, and the singular value results in order are obtained by SVD, as shown in Fig. 3(d).Fig. 3(e) shows that the coherence of the signal is the strongest.Since the first singular value corresponds to the target signal, the Rs target signal can be obtained by zeroing all the second and subsequent singular values, and then reconstructing the first singular value.We can clearly see that the quality of the target signal Rs has been obviously improved.In general, the sequence of multichannel superposition and SVD processing after correction is interchangeable.Finally, we used the reverse correction method to obtain the event of Rs as shown in Fig. 3(f), and the SNR of Rs has been increased to 7.982 dB.We can be clearly seen from the results that the random noise is well suppressed and the quality of the event of Rs is obviously improved.To qualitatively and quantitatively investigate the effectiveness of SVD-DSW theory for field experiment data processing, we adopted this method to process and analyze the X-component record of a TSP field experiment data, and the data processing results are shown in Fig. 4. Fig. 4 (a) shows the Xcomponent seismic record with the direct wave removed, from which it can be seen that the target signal (Rp) is almost completely overwhelmed by strong random noise.The result after processing by 7element array SVD-DSW method is shown in Fig. 4 (b), from which we be able to observe the event of Rs clearly.Through the quantitative comparison before and after recording processing, it can be found that the SVD-DSW method can improve the SNR of the target signal from -1.839 dB to 6.413 dB.Therefore, through the processing and analysis of field data, and the results further indicate that SVD-DSW method be able to suppress random noise well and extract high quality target signals.High quality target signal is the most important prerequisite for obtaining underground lithologic structure.

Conclusion
The environmental noise in the tunnel seriously affects the effect of seismic advance detection, which leads to the potential threat of tunnel construction.To solve the problem of difficult noise suppression in tunnel environment, this paper proposes the method of SVD-DSW.The principle of this method is to use local correlation method to calculate the time delay parameters of the effective signals.By using the delay parameters, the event of the corrected target signal becomes horizontal direction, and the coherence of the effective signals can be obviously improved.Then, the coherent signals are extracted by SVD method.Finally, the effective signals are obtained by multi-trace stack and reverse calibration of SVD records.In the numerical simulation part, TSP records are synthesized by finite difference method, and the effectiveness of SVD-DSW method is verified.The research results show that the SVD-DSW technique and method be able to isolate high quality effective signal from the target signal mixed with strong random interference.The SNR of target signal is increased from -10.641 dB to 7.982 dB, which can provide a good guarantee for the accuracy of the subsequent interpretation of the tunnel geological structure.Because of the commonality of seismic waves, the method in this paper is not only applicable to the field of tunnel environment, but also has important theoretical guiding significance for seismic exploration.

Figure 2 .
Figure 2. Tunnel advance detection principle and seismic record synthesis 3D finite difference method was used for numerical simulation to obtain Z-component seismic records as shown in Fig. 2(b).In the records of Z-component, Ds wave has the strongest energy, Rs wave has the strongest energy, and Dp wave has the weakest energy.This is mainly because in the threecomponent geophone, the Z-component mainly receives S-wave signals, while the X-component mainly receives P-wave signals.In seismic recording, the direct waves (Dp and Ds) are usually used to estimate the velocity, while the reflected waves are the target signal that needs to be extracted.

Figure 4 .
Figure 4. Field experiment processing and result analysis of SVD-DSW methodTo qualitatively and quantitatively investigate the effectiveness of SVD-DSW theory for field experiment data processing, we adopted this method to process and analyze the X-component record of a TSP field experiment data, and the data processing results are shown in Fig.4.Fig.4(a) shows the Xcomponent seismic record with the direct wave removed, from which it can be seen that the target signal (Rp) is almost completely overwhelmed by strong random noise.The result after processing by 7element array SVD-DSW method is shown in Fig.4 (b), from which we be able to observe the event of Rs clearly.Through the quantitative comparison before and after recording processing, it can be found that the SVD-DSW method can improve the SNR of the target signal from -1.839 dB to 6.413 dB.Therefore, through the processing and analysis of field data, and the results further indicate that SVD-DSW method be able to suppress random noise well and extract high quality target signals.High quality target signal is the most important prerequisite for obtaining underground lithologic structure.