SEISMIC DETECTION AND TIME OF ARRIVAL ESTIMATION IN NOISYENVIRONMENTS BASED ON THE HAAR WAVELET TRANSFORM

Joannis A. Thanasopoulosithan@mail.ntua.gr

John N .Avaritsiotisabari@cs.ntua.gr

National Technical University of Athens, GreeceDepartment of Electrical and Computer Engineering

ABSTRACT

In this paper we propose a discrete wavelet transfonn(DWT) method for event detection and estimation of thetime of arrival (TOA) of seismic signals in a sensornetwork. The Haar wavelet is selected for its lowcomputational complexity and its good locality in timedomain which is essential for the analysis of transientsignals. The proposed method requires no a prioriknowledge about the spectral characteristics of thesignals, because the algorithm defines the optimum scalesfor the extraction of infonnation by time-domain featuresas the signal is acquired. The perfonnance of thealgorithm is verified using a computer program thatsimulates the propagation of surface seismic waves.Simulation results corroborate the suitability of theproposed method for source localization applications.

estimation with the use of the DWT.In the following sections, the Haar based algorithm

for seismic event detection and TOA estimation isdescribed. A program for the simulation of seismicpropagation is presented and the perfonnance of thealgorithm, based on simulated tests is discussed.

2. EVENT DETECTION AND TOA ESTIMATION

In this section we describe an algorithm based on the Haarwavelet transfonn for seismic event detection and TOAestimation.

The DWT allows hierarchical decomposition of timesequences. Using a mother wavelet function, the signal isdecomposed in approximation and detail coefficients,corresponding to lower and higher spectral components ofthe original signal, respectively.

The Haar wavelet function is expressed by:

2.1. Detection Algorithm

Real seismic signals were acquired using the single axisSiFlex-1500 accelerometers with very low noise spectraldensity over the range of 10-1000 Hz, suitable forperimeter monitoring applications [10]. The sampling rate

This gives the Haar wavelet its most importantadvantage, which is low computational complexity of thedecomposition process. Another feature that makes theHaar wavelet very useful in applications of impulsedetection and time delay estimation [6], [8] is its highlydiscontinuous nature that makes it very well localized intime domain.

A more comprehensive reading over the DWT can befound in [9].

In the following sections we describe the algorithmdeveloped for seismic event detection and time of arrivalestimation.

1. INTRODUCTION

Seismic and acoustic source localization has numerousapplications ranging from robotics and teleconference tomilitary surveillance systems and medical applications.Specifically, in the field of sensor networks the problemhas attracted considerable attention and the most popularapproach is the estimation of the time differences ofarrival (TDOA) between the received signals at spatiallyseparated sensors. In most approaches, the TDOA isestimated explicitly using direct cross-correlation methods[1 ]-[3]. Another common approach implements adaptivefiltering techniques [4]-[6].

The aforementioned methods, while providing goodresults in acoustic localization, are demanding incomputational resources which are valuable in a sensornode. Additionally, the perfonnances of these methodsgreatly rely on the high correlation between the signals.This, however, may not be the case in seismic signals, asthe attenuation due to soil material damping is frequencydependent [7] causing alterations in the spectralcharacteristics of the signals received by different sensors.For these reasons, we propose a method based on TOA

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Fig. 1. Time series plot of a recording that contains seismic events of different amplitudes. Area A shows a portioncontaining environment noise and area B shows a detected seismic event.

of the recordings was set at 10kS/s. A portion of arecorded signal is shown in Fig. 1.

First, a recorded signal of N =2J samples,containing environment noise is acquired and analyzed.This part of the signal (shown in area A, Fig. 1) isdecomposed with the use of the Haar wavelet transformdown to the coarsest possible scale, J-I. The finest scale,s=2°= I, for J=O, is the same as the original data and thecoarsest scale corresponds to a single data point giving thesignal average. For each scale, the detail waveletcoefficients' standard deviation, (J, is calculated and athreshold is set, given by the formula:

which indicates that signal level has exceeded noise level,the program sets this sample as the beginning of the eventand starts to record the time intervals between successivezero crossings and the amplitudes of the peaks betweenthem. The last sample of the detected event (see area B,Fig. 2) is attributed when three successive peaks fail tocross To, so it is considered that the signal has attenuatedbelow noise level.

The time between two successive zero crossingscorresponds to half a period of the sensor's oscillation.So, the central frequency of the signal is estimated as theinverse mean of all the periods from the detection of theevent to it's attenuation below noise level:

where ~ is the total number of coefficients at the scale i.Next, the recorded signal is divided in non­

overlapping blocks of N samples and each sample iscompared to the threshold value To. If the amplitude of therecorded signal exceeds To, it implies that theaccelerometer has detected an event, as shown in area Bof Fig. 1. In that case, the algorithm moves to the nextstate where the central frequency and the duration of thedetected signal are estimated and the possibility of falsealarm is ruled out.

In order to classify the detected signal as a positiveseismic event or a false alarm and, in the first case,estimate the TOA, first, we must determine the values oftwo basic spectral components. The first one is the centralfrequency of the signal, i.e. the frequency at which theseismic excitation causes the accelerometer to oscillate,and the second is the frequency of the signal's envelope.

When an event detection is triggered by To crossing,

where Z is the total number of detected zero crossings andZi is the time instant that the ith zero crossing occurred.

The envelope frequency, Fe, of the signal is half theinverse of the time interval Te between the initial detectionand the attenuation of the event. It is estimated as:

The dichotomization of the frequency domain thattakes place in each iteration of the DWT allows us todirectly assign a scale to the frequencies estimated by (3)and (4), given that the sampling frequency, Fs, is known.The bandwidth of a signal sampled at Fs ranges from 0 toF/2, so the scales are given by the formula:

(4)

(3)

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(5)

reaches at scale }=O, concluding in one single samplewhich is designated as the sample of arrival of the seismicevent.

3. SIMULATION OF PROPAGATION

where di and d1 are the distances of the ith and the firstsensor from the source respectively.

The amplitude decay can be expressed as the ratio ofthe signal amplitudes of different sensors and, for surfaceseismic waves, is given by the following formula:

where, s(k) is the signal emitted from the source at the

time instant k, Ai is the amplitude decay of the source

signal at the ith sensor, Di is the time of arrival and ni isthe additive noise.

The time delay between the sensor that is closer to thesignal source and the ith sensor can be expressed in termsof propagation speed c:

(6)

(7)

A program for simulating the propagation of the seismicsignals was developed in order to test the performance ofthe algorithm described in the previous sections. It takesas input a single recorded excitation of one sensor andgenerates shifted and decayed versions of it, taking intoaccount the propagation speed of the seismic wave and theattenuation factor of the soil.

In an array of M sensors, the discrete-time signalacquired by the ith sensor can be expressed as

where i stands for c or e, accordingly, and} is rounded tothe nearest integer.

The scales s = 2Je and s = 2Je are chosen as thee e

scale of the signal's envelope frequency and the scale ofthe signal's central frequency respectively. The scale Se

corresponds to the lower spectral band of the signal, so itis chosen as the deepest scale for decomposition anddenoising. The scale Se contains the wavelet coefficientswith the highest energy, and it is used to determinewhether the detected signal is a seismic event or a falsealarm.

A time interval of duration T/2 is selected around thepoint where the initial detection occurred, as the area atwhich the true time of arrival of the signal is expected tobe found. This portion of the signal, is decomposed downto the Se scale and denoised.

The denoising procedure consists of soft thresholdingof the detail coefficients at each scale, with the respectivethresholds that were calculated in (2). The inverse DWT isthen implemented at the thresholded coefficients torecompose the signal up to one level at a time.

When the scale of the central frequency, se, IS

reached, the variance of the denoised coefficients iscompared to the variance of the same level's noisycoefficients, as calculated from area A, Fig. 1. If theformer exceeds the latter by a factor R, a positive eventdetection is registered. Otherwise, the detected event isclassified as a false alarm. The value of R was setexperimentally at 1.5.

2.2. Time of Arrival Estimation

In the case of a positive event detection, the algorithmproceeds to the next stage, which is the estimation of theTOA.

When a seismic signal arrives it causes theaccelerometer to oscillate at frequency Fe, so a steepincrease in the amplitude of the coefficients of the Se scaleis expected. The algorithm searches within thosecoefficients for steep increases, after denoising them, asdescribed in the previous section. At this scale, a singlecoefficient corresponds to an area of je samples ofrecorded data, so the detection of a pair of coefficientswith distinct amplitude increase yields a time interval ofje+1 samples in which the TOA should be. The inverseDWT is then applied on those coefficients, and thealgorithm searches in the new set of coefficients for theinstant of the steepest amplitude increase. By iterativelynarrowing the search around a pair of coefficients andrecomposing the signal, up to one level, the algorithm

(8)

where Ai,} is the amplitude decay from the first to the ithsensor and a is the attenuation coefficient of the soil.

Both propagation speed and attenuation coefficientvary considerably for different types of soil [7]. Theattributed values are 500 mls for the propagation speedand 0.015 for the attenuation factor. They were selected toproduce a realistic model for the soil that the experimenttook place, based on preparatory in situ measurements.

The simulation program generates a set of M signals.For a known source position, the amplitude decay and theTDOA between each sensor and the first one is calculated.The recorded signal is appointed to the first sensor and aset of M signals is generated by shifting and decaying theoriginal signal, according to the formulas (6), (7) and (8).

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Fig. 2. Percentages of errors in (a) in TOA estimations (b)source distance, source angle bearing and speed ofpropagation.

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environments," IEEE Trans. Signal Processing, vol. 41, no. 7,pp.2289-2299,Jul. 1993.[5] H.C.So, "Noisy input-output system identification approachfor time delay estimation," Signal Processing, 82, pp. 1471­1475,2002.[6] D.H.Kim andY.Park, "Development of sound sourcelocalization system using explicit adaptive time delayestimation," Proc. ICCAS, Jeonbuk, Korea Oct. 2002.[7] D.S.Kim and lS. Lee, "Propagation and attenuationcharacteristics of various ground vibrations," Soil Dynamics andEarthquake Engineering, 19, pp. 115-126, 2000.[8] C.Capilla "Application of the Haar wavelet transform todetect microseismic signal arrivals," J. Applied Geophysics, 59,pp. 36-46, 2006.[9] I.Daubechies, Ten Lectures on Wavelets, SIAM,Philadelphia, 1992.[10] K.E.Speller and D.Yu, "A low-noise MEMS accelerometerfor unattended ground sensor applications," Proc. SPIE, vol.5417,pp.63-72,2004.[11] lZheng, K.W.K.Lui and H.C.So, "Accurate three-stepalgorithm for joint source position and propagation speedestimation," Signal Processing, 87, pp. 3096-3100, 2007.

4. RESULTS

[1] G.C.Carter, "Coherence and time delay estimation," Proc.IEEE, vol. 75, pp. 236-255, Feb. 1987.[2] P.Aarabi and S.Mavandadi, "Multi-source time delays ofarrival estimation using conditional time-frequency histograms,"Int 1. In! Fusion, vol. 4, no. 2, pp. 111-122, Jun. 2003.[3] lChen, lBenesty, and Y.Huang, "Robust time delayestimation exploiting redundancy among multiple microphones,"IEEE Trans. Speech Audio Processing, vol. 11, no 6, pp. 549­557, Nov. 2003.[4] K.C.Ho, Y.T.Chan and P.C. Ching, "Adaptive time-delayestimation in nonstationary signal and/or noise power

5. REFERENCES

Computer simulations are conducted in order to measurethe performance of the proposed algorithm. We considerfive sensors placed at the coordinates (0, O)m, (0, 10)m,(10, O)m, (-10, O)m and (0, -10)m. The source of theseismic signal is located at (-34, 15)m. Two kinds of testsare conducted.

In the first one, the set of signals generated by thesimulation program is used as input to the algorithm fordetection and TOA estimation. The signal set is added byuniform white noises of designated power in order to testthe algorithm for various noise conditions. For eachdetected event the TDOA between the first and each ofthe rest generated signals is estimated and compared to theknown time shifts originally made by the simulation. Allsimulation results are averages of 500 independent runs.Fig. 3(a) shows the error percentage of the estimation ofthe TDOAs for various SNR.

In the second, the source localization algorithmdescribed in [11] is implemented. This algorithm takes asinput the estimated TDOA and returns an estimation forthe source location and the propagation speed of theseismic signal. Fig. 3(b) shows the errors of theestimations of the source distance, the bearing angle andthe propagation speed.

During all simulations, no false alarms occurred andthe rate of missed detections remained below 1% for SNRas low as 6 dB.

The results show that the error levels in TOAestimation are kept low even for noisy environmentconditions. The resulting errors in the source localizationapplication are promising. Especially, the error in angle ofarrival remains always in very low levels. The distanceand speed estimation errors, while they are not as good,they remain below 10% for SNR as low as 12 dB.

The overall performance of the algorithm, as shownby the computer simulations, its low computationalcomplexity and its applicability in poorly cross-correlatedsignals, makes the proposed method a suitable solution forUGSN applications.

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