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Improve HVNR Technique by Using Wavelet Transform

2013

The spectral ratio between horizontal and vertical components noise (H/V ratio) of microtremors has been used to estimate fundamental resonance frequency of the site. In this study we investigate the application of the wavelet analysis to improve the (HVNR) technique for site effect estimation. Wavelet analysis has been widely used in the last decade for its capacity to localise the signal in both the time and frequency domains. This property, which derived directly from multiresolution analysis provide us the ability to decompose a signal in a well localized set of coefficients and identify the non-stationary portions of it.In the present study we use the WT in order to eliminate the non-stationarities in microtremor signals before we calculate the spectrum of each one using conventional FFT algorithms.

The 1st Iranian Conference on Geotechnical Engineering, 22-23 October 2013 University of Mohaghegh Ardabili, Ardabil, Iran OHN10110191115 Improve HVNR Technique by Using Wavelet Transform H.Rahnema1, M.H.Bozorgi2 1- Assistant Professor, Department of Civil and Environmental Engineering, Shiraz University of Technology, Shiraz, Iran 2- Ms Candidate of Earthquake Engineering, Department of Civil and Environmental Engineering, Shiraz University of Technology, Shiraz, Iran [email protected] [email protected] Abstract The spectral ratio between horizontal and vertical components noise (H/V ratio) of microtremors has been used to estimate fundamental resonance frequency of the site. In this study we investigate the application of the wavelet analysis to improve the (HVNR) technique for site effect estimation. Wavelet analysis has been widely used in the last decade for its capacity to localise the signal in both the time and frequency domains. This property, which derived directly from multiresolution analysis provide us the ability to decompose a signal in a well localized set of coefficients and identify the non-stationary portions of it.In the present study we use the WT in order to eliminate the non-stationarities in microtremor signals before we calculate the spectrum of each one using conventional FFT algorithms. Keywords: HVNR, Wavelet transform, non-stationary, FFT algorithm. 1. INTRODUCTION During the last two decades Horizontal to Vertical Noise Ratio or Nakamura method (HVNR) has proved an invaluable tool for estimating a site’s fundamental (f0) frequency using cheap, rapid and fair accurate method. Since its first proposal by Nogoshi & Igarashi [1], and latest revision by Nakamura [2] the HVNR method widely used by many researchers but without following a de-facto standard for the stationarity of the selected microtremor signal. The use of HVNR method in urban areas and especially in densely populated areas seems to be the most demanding case since there will be artificial non-stationary signals from unknown sources which cannot be predicted. Nonstationary components contaminate the signal and reveals frequencies that are not related with site’s characteristics. Nonstationary signal caused by daily human activities such as movement of machinery in factories, motor cars, people walking and natural phenomena such as flow of water in rivers, rain, wind, variation in atmospheric pressure and ocean waves. In the present study we will estimate first the Horizontal to Vertical Noise Ratio (HVNR) using ordinary methodology and then we calculate the HVSR using wavelet-filtered microtremor signals in order to identify the variation of HVSR when the non-stationary components eliminated. 2. THE NAKAMURA TECHNIQUE A quick estimate of the surface geology effects on seismic motion is provided by the horizontal to vertical noise spectral ratio technique (HVNR). This technique firstly introduced by Nogoshi and Igarashi [1], was put into practice by Nakamura [2], and became in recent years widely used since it provides a reliable estimate of the fundamental frequency of soft soil deposits( Lermo and Chavez-Garcia and Bard et al)[3,4]. The resulting curves often show a clear maximum. The frequency at which this peak occurs is empirically found to correlate with the fundamental resonance frequency at the measurement site (e.g. Lachet and Bard; Lermo and Chávez-García; Dravinski et al.)[5,6,7]. such method is widely used since it significantly reduces field data acquisition time and costs. The evaluation of site response using the HVNR technique is largely adopted since it requires only one mobile seismic station with no additional measurements at rock sites for comparison. The principal two basic hypothesis explanations for using ambient noise are two. Nogoshi and Igarashi [1] showed through their investigations that HVNR on microtremors are directly related to the 1 The 1st Iranian Conference on Geotechnical Engineering, 22-23 October 2013 University of Mohaghegh Ardabili, Ardabil, Iran ellipticity curve of Rayleigh waves because of the predominance of Rayleigh waves in the vertical component. Nakamura [2] instead, asserted that the H/V-ratio on microtremors gives a good estimate of the S waves site response function. Dividing the horizontal component of surface ground motion by the vertical, a removal of the source as well as the Rayleigh wave effects can be obtained. Rayleigh waves, which is associated with an inversion of the direction of Rayleigh waves rotation (Nogoshi and Igarashi,; Lachet and Bard)[1,3]. Thus, the ratio between the horizontal and vertical spectral components of motion can reveal the fundamental resonance frequency of the site[9]. 3. SIGNAL PROCESSING The Fourier analysis (Papoulis)[10], which decomposes a time series into orthogonal frequency components or vice versa, has been widely used for geophysical signal processing. The fast Fourier transform (FFT) algorithm has made the Fourier analysis very attractive for many data processing applications, mainly because of the orthogonal properties of the Fourier series and of its simple expression. However, upon inspection of the expression of FT. F      (1) f (t ) e it dt  The FT yields information on how much but not when (in time) the particular frequency components exist. Such information is sufficient in a case of the stationary signals as the frequency content of such signals does not change in time and all frequency components exist all the time. the FT provides just information on the frequency content; however, the information on the frequency localization in time is essentially lost in the process thus the frequency information cannot be associated with time. The limitation of the Fourier transform, i.e. it gives only the global frequency content of a signal, is overcome by the short time Fourier transform (STFT). The STFT is able to retrieve both frequency and time information from a signal. The STFT calculates the Fourier transform of a windowed part of the original signal, where the window shifts along the time axis. This transform which also called Gabor transform is defined as [11] : G b,k ( )    f (t ) e it  g t  b dt k (2) Where g(t) is a Gaussian function : g t   2 k 1  .k  e t2 4k (3) which also called a window function. (Alternative formulations replaced the Gaussian function by other window functions). Thus the Gabor transform localizes the FT of a signal f(t) at around t=b. The width of the window is determined by the fixed positive constant k. In the majority of STFT methods there are undesirable computational complexities when either narrowing of the window is required for better localization or widening the window required to obtain more global picture [12]. The analysis of a non-stationary signal using the FT or the STFT does not give satisfactory results. Better results can be obtained using wavelet analysis. One advantage of wavelet analysis is the ability to perform local analysis. Wavelet analysis is able to reveal signal aspects that other analysis techniques miss, such as trends, breakdown points, discontinuities, etc. In comparison to the STFT, wavelet analysis makes it possible to perform a multiresolution analysis (MRA)[15]. By using MRA it is possible to analyze a signal at different frequencies with different resolutions. The change in resolution is schematically displayed in Figure 1. 2 The 1st Iranian Conference on Geotechnical Engineering, 22-23 October 2013 University of Mohaghegh Ardabili, Ardabil, Iran Figure1. Multiresolution time-frequency plane For the resolution of Figure 1, it is assumed that low frequencies last for the entire duration of the signal, whereas high frequencies appear from time to time as short burst. This is often the case in practical applications. Wavelet transform can be accomplished in two ways: Continuous Wavelet Transform (CWT) and Discrete Wavelet Transform (DWT). The CWT is defined as follows : w( a, b)  1 a    f (t ).g ( t b )dt a (4) Where g(t) is the wavelet function, and a and b are the scale and translation factors, respectively. The wavelet function g(t) decays rapidly to zero with increasing t and has zero mean. The domain (range) of nonzero values of the wavelet is called the support. The scale factor controls the dilation or compression of the wavelet, whereas at lower scales, the wavelet is compressed and characterizes the rapidly changing details of the signal. At higher scales, the wavelet is stretched over a greater time span and the slowly changing and coarse features are better resolved [13]. In practical applications, the DWT is generally preferred because waveforms are recorded as discrete time samples. DWT can be implemented quickly via the Mallat algorithm [14]. Figure2. Mallat algorithm As shown in Figure 2, in discrete wavelet analysis, a signal(S) is segregated into an approximation (A) and a detail (D) as Eq. (5): S=A1+D1=A2+D1+D2=A3+D1+D2+D3. (5) The approximations are the high-scale, low-frequency components of the signal. The details are the lowscale, high-frequency components. The approximation is then itself split into a second-level approximation and detail, and the process is repeated. For n-level decomposition, there are n+1 possible ways to decompose or encode the signal. 3 The 1st Iranian Conference on Geotechnical Engineering, 22-23 October 2013 University of Mohaghegh Ardabili, Ardabil, Iran 4. PROCESS OF ESTIMATION HVNR According to the following algorithm, using the wavelet transform, the signal is preprocessed,, see Figure 3 . Using by discrete wavelet for remove region high-frequency Using by continuous wavelet for select the local time zone that has a same frequency Estimation of hvnr Figure3. Signal preprocessing using wavelets Because, transient signals (non-stationary signals) should be removed from the original signal. So using continuous wavelet diagram (time - frequency), which has a similar frequency to the local time zone is selected. Then HVNR, is estimated, see Figure 5. The horizontal to vertical spectral ratio (HVNR) is estimated from the three components of the microtremor recordings (North-South, East-West and Vertical) through the following steps [11], see Figure 4. Figure4. Estimation of hvnr algorithm 4. RESULT AND DISCUSSION According to set of three microtremor recordings by record time 1m5.536s and sampling rate 128µs is presented below, see Figure 5. Figure5. Horizontal (East-West) component, Horizontal (North-south) component, Vertical component 4 The 1st Iranian Conference on Geotechnical Engineering, 22-23 October 2013 University of Mohaghegh Ardabili, Ardabil, Iran We estimate the HVNR following the steps defined in section 4. The calculated amplification factor over frequency is depicted in Figure 6. We can identify amplification for frequencies around 1.25Hz by amplitude 1.44 and around 3.33Hz by amplitude 1.513 and around 11.85 by amplitude 2.176, see Figure 6. Figure6. HVNR from unfiltered by wavelet microtremors In Figure 6, The black curve represents H/V geometrically averaged over all colored individual H/V curves. The two dashed lines represent the H/V standard deviation. The grey area, represent the averaged peak frequency and its standard deviation. The frequency value is at the limit between the dark grey and light grey areas. By using CWT, select local time between 24s and 44s which has a similar frequency, for three-component, see Figure 7. Figure7. Continuous Wavelet Transform (CWT) for three-component 5 The 1st Iranian Conference on Geotechnical Engineering, 22-23 October 2013 University of Mohaghegh Ardabili, Ardabil, Iran In the zone time between 24 s to 44 s, estimate HVNR, see Figure 8. Figure 8. HVNR from filtered by wavelet microtremors The latter estimation of HVNR indicates that the dominant frequency is around 0.894 Hz by amplitude 1.917 and 5.046 Hz by amplitude 1.161 and 11.46 Hz by amplitude 2.25. 5. CONCLUSIONS The precision of the HVNR method for site effect investigations depends on the stationarity of the recorded microtremors. This is not obtainable when measurements take place in urban areas. In the present study we apply wavelet transform in order to identify non-stationarities in microtremors and then eliminate short period transients using non-linear wavelet filtering. This approach does not nullify the commonly used HVNR method but it is incorporated with it by adding one more procedure in order to achieve better and trustworthy results. 11. REFERENCES 1. Nogoshi, M. and Igarashi, T. (1971). “On the Amplitude Characteristics of Microtremor (part 2) ”, Jour Seism. Soc. Japan, 24, 26-40 2. Nakamura, Y. (1989). “A method for dynamic characteristics estimation of subsurfaceusing microtremor on the ground surface”. Q.R. Railway Tech. Res. Inst. Rept., 30, 25-33. 3. Lermo J., Chavez-Garcia F. J. (1994). “Are microtremor useful in site response evaluation? ” Bull. Seism. Soc. Am., 84: 1350-1364. 4. Lermo, J, & Chavez-garcia, F. J. (1993). “Site effect evaluation using spectral ratio with only one station. Bull”. Seism. Soc. Am., 83, 1574-1594. 5. Dravinski M, Ding G, Wen KL (1996). “Analysis of spectral ratios for estimating ground motion in deep basins”. Bull Seismol Soc Am 86(3):646–654 6. Bard, P. Y. (1999). “ Microtremor measurements: a tool for site effect estimation? In The effects of surface geology on seismic motion”. Irikura et al. (ed.), Balkema, Rotterdam, 1279-1251. 7. Lachet C, Bard PY (1994). “Numerical and theoretical investigations on the possibilities and limitations of Nakamura’s technique”. J Phys Earth 42:377–397. 8. Brigitte Endrun (2011). “Love wave contribution to the ambient vibration H/V amplitude peak observed with array measurements”. J Seismol 15:443–472 .DOI 10.1007/s10950-010-9191-x. 6 The 1st Iranian Conference on Geotechnical Engineering, 22-23 October 2013 University of Mohaghegh Ardabili, Ardabil, Iran 9. F. Panzera, G. Lombardo, S. D’Amico and P. Galea (2013). “Speedy Techniques to Evaluate Seismic Site Effects in Particular Geomorphologic Conditions: Faults, Cavities, Landslides and Topographic Irregularities”, Engineering Seismology, Geotechnical and Structural Earthquake Engineering, Dr Sebastiano D'Amico (Ed.), ISBN: 978-953-51-1038-5, InTech, DOI: 10.5772/55439. 10. Papoulis, A., (1962). “The Fourier integral and its applications”. McGraw-Hill Press, New York. 11. G.Hloupis, F.Vallianatos, J.Stonham,(2004). “A Wavelet representation of HVSR technique”, Bulletin of the Geological society of Greece, vol 36, pp.1269-1278. 12. Chui, C.K., (1992). “An introduction to wavelets”, Academic press, New York. 13. Aa . Zhang, H., Thurber, C. and Rowe, C. (2003). “Automatic P-wave Arrival Detection and Picking with Multiscale Wavelet Analysis for Single-Component Recordings”, Bull. Seism.Soc. Am., 93, 19041912. 14. Mallat, S. (1989). “A Theory for Multi-Resolution Signal Decomposition: The Wavelet Representation, IEEE Trans”, Pattern Anal.Machine Intelligence, 11, 674-693. 7