SPECTRAL ANALYSIS OF GEOPHONE SIGNAL USING COVARIANCE METHOD

Transcription

1 International Journal of Pure and Alied Mathematics Volume 114 No. 1 17, ISSN: (rinted version); ISSN: (on-line version) url: htt:// Secial Issue ijam.eu SPECTRAL ANALYSIS OF GEOPHONE SIGNAL USING COVARIANCE METHOD SundeeVelagaudi 1, T.Phani Kumar Reddy,K.S.Ramesh 3, S.Koteswara Rao 4, V.Lakshmi Bharathi 5 Deartment of ECE, K L University, Vaddeswaram, Gunutr. sundeevelagaudi1188@gmail.com, rao.sk9@gmail.com Abstract Seismic waves carry the information of an earthquake. To develo an earthquake rediction system, data is taken from a geohone signal. In this work, the data collected is subjected to signal rocessing methods for effective analysis. Parametric aroach to sectrum estimation would make it ossible to roduce a more accurate and high resolution estimate. Covariance arametric method is used to find out the change in the sectrum of signals with and without disturbances in the signal. These studies in future may hel in designing rior warning systems for earthquakes. Keywords: Seismology, Adative signal rocessing, Stochastic signal rocessing, Alied statistics 1. INTRODUCTION The movement of rocks underneath the earth s crust along the fault lines due 51

2 International Journal of Pure and Alied Mathematics Secial Issue to stress, strain and ressure causes vibration of the earth s surface resulting in devastating natural disaster The Earthquake. Urbanization of rural areas, industrialization, and declination in the underground water level kindle the occurance of earthquake.insite of the advancement in technology and knowledge of these natural disasters, they remain unredictable. Research around the world has alied different techniques to estimate the arameters such as frequency, magnitude, energy of seismic data.geohones does not require electrical energy to work, they are light in weight, strong, used to recognize little ground dislacements. The movement of the ground and the movement of the mass inside a seismic sensor are connected by the basic harmonic oscillator condition, d d g λ ω d (1) t t t where g is the ground dislacement, d is the dislacement of the mass, is the resonant frequency and λ is the daming factor. Transfer function obtained by rearranging is: Y( ) T( ). X ( ) () where, T is the transfer function,x is inut and Y is outut. Taking Fourier transform for equation (1), by arranging as er a geohone requirement it is obtained as, d Va sc (3) t jω g Va sc (4) ω j ω t Where V a is analog voltage, s c is geohone sensitivity constant (in V.s/m). Earthquake rediction can be done through animal behavior. The behavior of various tyes of animals is analyzed before time of occurance of earthquakes and it is observed that animals disaear from disaster occurring sot or behave unusually rior to occurance of earthquakes [3]. Analysis of earthquake magnitude for detection of earthquakes using P and S waves, which redicts earthquake occurance if magnitude eceeds 4..[6] By alying Multile Signal Classification (MUSIC) algorithm on Global Positioning System Total Electronic Content for Earthquakes in which it is observed an indicative raise of energy of ionoshere on a quake occurring day[7]. By analyzing the seismogenic erturbations using Barlett method on GPS TEC in which signs of earthquake in ionoshere are identified and also observed PSD of erturbations has a huge initial value and a slow loss of intensity used in develoing rior detecting systems for earthquakes [5]. Parametric methods are known for obtaining a more accurate and higher 5

3 International Journal of Pure and Alied Mathematics Secial Issue resolution sectral estimates. In this work, one of the arametric methods for sectral estimation, covariance method is used for the urose of analyzing seismic data as collected from an elosion event using geohone. Data is recorded using rinciles of reflection seismology. The advantage of this method when comared to other methods is that no window is alied to data in estimation rocess.thereforefor data records, this method roduces sectral estimates with higher resolution. The sectral analysis of geohone signal using covariance method can be used as one of the method for earthquake rediction. Section- of this work deals with discussion about the methodology, arametric methods for sectral estimation and about covariance method. Section-3 consists of the results and a brief discussion of the results. The drawback of non-arametric methods is that they suffer sectral line slitting due to windowing of data techniques, while coming to the arametric methods the roblem of sectral slitting is avoided and also these methods rovide with better frequency resolution, than those obtained from sectral estimation using non arametric methods. The ower sectral density estimation in arametric or non-classical methods is estimated from a signal which is considered as the outcome of a system, and is driven by white noise. Autoregressive (AR) methods use a different methodology to rocess sectral estimation, they consider the data as the outcome of a linear system which is being driven by white noise instead of estimating it directly from the data and then try to estimate the characteristics of the system. In an all-ole filter all the zeros lie in the z-lane at the origin of the filter and is usually used as linear system model. That s why sometimes these methods are referred as sectral estimation using AR methods. Additionally the linear system equations obtained from an AR method are simler to solve. Before analyzing a signal it is necessary to subject it to adequate amounts of signal rocessing, and it rovides the following AR models for ower sectral density (PSD) estimation, they are; 1. Yule-walker method.. Covariance method. 3. Burg method. 4. Modified covariance method.. MATHEMATICAL MODELLING The arametric methods yield sectral estimation based on making use of a model for the rocess so as to obtain the ower sectrum estimation. For eamle,if (n) is the th order AR rocess then the measured values of (n) can be used in the rocess of estimation of arameters of all ole model,a (k) and ^ these a ( k) which are modelled arameters estimated may in turn be used for 53

4 International Journal of Pure and Alied Mathematics Secial Issue sectral estimation by following: ^ 1 P ( ej) (5) a^ P ( k) e k jk All Auto Regressive methods yield a sectral estimate given by, ^ 1 P( f ) (6) AR fs jkf / fs 1 a^ ( k) e k1 To estimate AR coefficients auto correlation normal equations are to be solved, r 1 () r * (1) r * ()... r * ( ) 1 r (1) r () r * (1)... r * ( 1) a (1) () (1) ()... * ( ) a () r r r r = r ( ) r ( 1) r ( )... r () a ( ) (7) 1 N where, 1 k r ( k) ( n k) *( n); k,1,..., n N (8) Now considering the covariance method which is used in this work, it is an aroach for estimation of AR constants. The solution to set of linear equations in covariance method requires solving, r (1,1) r (1,)... r (1, ) N 1 n r (,1)... r (,) r (, )... r (,1) a (1) r (,1) r (,) a () r (,) = r (, ) a ( ) r (, ) where, r ( k, l) ( n 1) *( n k). (1) (9) 3. SIMULATION AND RESULTS Ste-1: In order to obtain the required results of sectral analysis of geohone signal using covariance method, a synthetic trace which is better known as a synthetic signal on which covariance method is alied is taken from book_seismic_data.mat [9], in which the synthetic traces are recorded at a deth of 8-1 ft as shown in Fig.1. Ste-: For sectral estimation, non-classical covariance method is alied on the seismic trace. The PSD observed is reresented in Fig.. Ste-3: A raw seismic signal is obtained as shown in Fig.3. Ste-4: The detrended signal is shown in Fig.4. Ste-5: By alying the covariance method on the raw seismic signal, the 54

5 Am of the signal Mag mag International Journal of Pure and Alied Mathematics Secial Issue sectral analysis outut is obtained as shown in Fig.5. Ste-6: The frequency sectrum by alying a finite imulse resonse band ass filter is obtained in Fig.6..4 Ste-7: The FIR band assed signal is observed in Fig.7. ω = πf 5 =.847π = πf 5 =.847π We get, tonal frequency f=1.175 Hz, if f s5. Ste-8: FFT is alied on the signal as a art of the sectral analysis and is reresented in normalized frequency Vs magnitude (in db) is shown in Fig.8. Ste-9: The final sectral analysis signal after BPF by alying covariance method is observed in Fig Samle no Fig 1. Synthetic signal Fig.PSD using covariance Method Samle Number Fig 3. Raw seismic signal Samle Number Fig 4.Detrended raw Seismic signal 55

6 PSD in db mag of the signal am in db PSD in db Gain (db) International Journal of Pure and Alied Mathematics Secial Issue Normalized Frequency (rad) Fig 5.Raw signal sectral analysis using covariance Normalized Frequency Fig 6.FIR band ass filter frequency sectrum samle no normalized Frequency (Hz) Fig 7.FIR bandass filtered signal Fig 8.FFT sectrum seismic after BPF in normfreqvs mag in db reresentation X:.847 Y: 3.191e Normalized Frequency (rad) Fig.9.After BPF sig sectral analysis using Covariance. 56

7 International Journal of Pure and Alied Mathematics Secial Issue 4. CONCLUSION By using the covariance method on a synthetic signal taken from data which is collected using geohone, the sectral analysis results are observed by alying various signal rocessing otions available in order to obtain a better and higher resolution estimates. These results may be used as one of the earthquake rediction measure, whenever the same kind of results are observed. 5. REFERENCES [1] Snajit K Mitra, Digital signal Processing Comuter Based Aroach,second edition, McGraw-Hill Publication. [] Raju.G.V.S,Kishore, Kumar Reddy.C, NarsimhaPrasad.L.V, Revealing of Earthquake Magnitude using Seismic signals and Wavelet transforms, the fifth international conference on softcomuting and software engineering, , 15. [3] Neeti Bhargava, V. K. Katiyar, M. L. Sharma, P. Pradhan, Earthquake Prediction through Animal Behavior: A Review, Indian Journal of Biomechanics, , Mar. 9. [4] Monson H. Hayes, Statistical Digital Signal Processing and Modeling, John Wiley & Sons.inc. [5] R Revathi, S Lakshminarayana, S Koteswara Rao, K S Ramesh, K.UdayKiran. Alication of Maimum Entroy Method for Earthquake Signatures using GPSTEC. [6] Narasimha Prasad L V,Kishore Kumar Reddy C, Ramya Tulasi Nirjogi, A Novel Aroach for Seismic Signal Magnit ude Detection Using Haar Wavelet, 14, [7] S. K. Baji, R. Revathi, S. Lakshminarayana, S. Koteswara Rao and K. S. Ramesh, Alication of Multile Signal Classification Algorithm on GPS TEC for Earthquakes,Indian Journal of Science and Technology, Vol 9(17), May

8 International Journal of Pure and Alied Mathematics Secial Issue [8] K.Umamaheswari, P.Sushmachowdary and P.Rajesh, Estimation of Random Signals using Nonarametric and Parametric methods,.5-33, Vol 5, Jul. 13. [9] Wail A.Mousa and AbdullatifA.Al-Shuhail, Processing of Seismic Reflection data using MATLAB,11. 58

9 59

10 6