Near Optimum Detection of The P-Wave Arrival Using the Spectrograms

Dr. Hamed Abd-El Monam Nofal . National Research Inst. Of Astronomy and Geophysics

(NRIAG)

Prof. Dr. Farouk Abd-Elnaser Al Geldawy Electrical Engineering Dept

Faculty of Engineering, Minia University

Abstract- Through this paper, an automatic P-wave arrival detection and picking algorithm is introduced. This algorithm is based on the power of the different frequencies in the seismic data. The algorithm depends on checking the change in the power of the noise at certain frequency using the spectrograms as a Time Frequency Representation (TFR). The major power contribution in the spectrum of the noise is concentrated in the frequency range 4 . 3 3 Hz [l], while the power of the higher frequencies is much lower. To verify that, the power spectrum is concentrated in the frequency range 4 . 3 3 Hz, there is a study on the noise recorded at FYM, HAG and KOT stations using the spectrogram. Then the algorithm is applied to local events from Dahshour region recorded at FYM, HAG and KOT stations. And it will be tested also using two regional events. It is found that the maximum average error is 0.07 seconds of the corresponding analyst picks.

1 Introduction

Time-Frequency Representations (TFRs) such as the spectrogram are important two-dimensional tools for processing time-varying signals. These signals are important as they naturally occur in many real-world applications; examples include speech, music, biological signals such as dolphin echolocation sounds, biomedical signals such as electrocardiogram (ECG) waveforms, impulse responses of wireless channels, radar, sonar acoustic waves and seismic waves. They are specifically designed to process time-varying signals as they jointly display time and frequency information demonstrating which frequencies occur at a certain time, or, at which times a certain frequency occurs. They combine time domain and frequency domain information by displaying signals over a joint time-frequency (TF) plane. Through this paper we will use the spectrogram in a seismological application which is the detection and picking the P- wave arrival of the earthquake. Automatic time-picking continues to be a significant issue in seismogram analysis. Nowadays the automatic trigger algorithms are relatively ineffective when compared to a seismologist’s pattern recognition ability during reading of seismograms, which is based on years of experience and on the enormous capability of the human brain. On the other hand manual analysis of seismograms and phase

Dr. Elsayed Mohammed Ahmed

Faculty of Engineering, Minia University Computer and System Dept.

Eng. Ali Gama1 Rabie Hafiz National Research Inst. Of Astronomy and Geophysics)

(NRIAG)

picking is time-consuming and tedious. There is a need to provide a more efficient alternative. Especially in these days where there are large volumes of digital and real-time seismic data. That is also of great importance in event location, event identification, acquisition of triggered seismic data, and source mechanism analysis. Various techniques have been presented in the literature for detecting and picking the arrivals of different seismic waves from single-component as well as three-component recordings. These algorithms are presently known and used from a very simple amplitude and energy threshold. For example Earle and Shearer (1994) [2] have used an energy method to deal with the records from the Global Digital Seismic Network and compared the automated onset-time picking with analyst time picks previously reported to National Earthquakes Information Center (NEIC). Tong and Kennett (1996) [3] also used the energy technique to identify and pick the later phases of broadband records. Wagner and Owens (1996) [4] have proposed the use of the principal eigen value in the frequency domain as a detector. Withers et al. (1998) [5] have systematically compared several trigger algorithms currently used for onset-time picking and gave details of comparisons in the time and frequency domains and also for particle motion and adaptive processing. Also there were the sophisticated pattern recognition, adaptive methods and artificial neural network based approaches by Aki Hidani and Hiroaki Yamanaka (2003) 161, multi-scale wavelet analysis for single-component recordings by Haijiang Zhang et al. (2003) [7]. All these algorithms are either based on the amplitude, the envelope, or the power of the signal(s) in time or frequency domains of seismic signal. The simplest trigger algorithm is the amplitude threshold trigger. It simply detects any amplitude of seismic signal exceeding a preset threshold. The recording starts whenever this threshold is reached. This Algorithm is rarely used in weak-motion seismology but, it is a standard in strong motion seismic instruments that are in systems where high sensitivity is mostly not an issue, and-where consequently man-made and natural seismic noise amplitudes are much smaller than the signals which are supposed to trigger the instrument. The Root-Mean-Square (RMS) threshold trigger is similar to the amplitude threshold algorithm, except that the RMS values of the amplitude in a short time window are used instead of ’instant’ signal amplitude. It is less sensitive to

0-7803-8575-6/04/$20.00 02004 IEEE 710

spike-like man-made seismic noise; however it is rarely used in practice [8]. Today, the short-time-average through long-time-average trigger' (STALTA) is the most broadly used algorithm in weak-motion seismology. Although, as mentioned earlier, there are more sophisticated trigger algorithms than the STNLTA algorithm, they are rarely used in the seismic data loggers currently in the market. Only some of them are employed in the network's real time software packages available. When in the hands of an expert, they can improve the eventdfalse-triggers ratio significantly, particularly for a given type of seismic events. However, the sophisticated adjustments of operational parameters to actual signals and seismic noise conditions at each seismic site that these triggers require, has proven unwieldy and subject to error in practice. This is probably the main reason why the STALTA trigger algorithm still remains the most popular [SI. The STNLTA Algorithm is not empty-handed of this problem, as it also requires setting some parameters [8]. However, when dealing with the algorithm developed in this paper, we will find that this algorithm will not be in need to all these sophisticated parameter settings to make its decision. As the algorithm depends on checking the average power for the 1.33 Hz frequency component of the noise segment which proceed the event. And from this noise segment the algorithm calculates a power threshold above which the algorithm will make a trigger.

2 Studying The Noise Characteristics

When dealing with the seismic data one should be aware of every bit of these data. So, before rushing into analyzing the algorithm and the results obtained it is very important to deal with the back ground noise. Noise is a large part of the seismic data. It varies widely with period, time and geographic location. A precise evaluation of the noise at a particular time and place can only be obtained by field measurements. These measurements are available at our Institute (National Research Institute of Astronomy and Geophysics (NRIAG)).

2.1 Sources of Seismic Noise

Noise can be referred as the undesired signals which must not be magnified so strongly that they obscure the record [9]. There are many noise sources, some of these sources are natural and others are artificial. Examples of the natural sources are oceans, inland seas, high water falls, rapids of large rivers and small lakes. While the artificial sources are heavy machinery, railways, industrial machinery, highways with continuous traffic, big roads, high and low buildings and high trees . . . . . . ... etc. Another important noise source is the instrumental self- noise which may come from mechanical or electronic sources encountered in the sensing device and the communication system itself.

2.2 Spectrum representation of seismic noise

Site selection is a very important point explained by [9], so we must take care when choosing the site as it should be a low noise one; otherwise the events, especially weak ones, will be buried in noise. The United States Geological Survey (USGS) New Low Noise Model (NLNM) [lo] summarizes the lowest observed vertical seismic noise levels throughout the seismic frequency band. It is extremely useful as a reference for assessing the quality of seismic stations, for predicting the detectability of small signals, and for the design of seismic sensors. Fig. 1 is one of several possible representations of this model.

I I la' I- I \

Fig. 1 Velocity power spectra of ambient seismic noise at noisy and quiet conditions [ I ]

2.3 Noise Measurements

Noise is generated by nature, by weather and by industry. Its alternating behavior demands a measuring campaign covering all different activities around the year. So the measurements should include, Several times of day, Several points and Several methods.

2.4 Representing the Noise Spectrum Using The Spectrogram

This is a study on the spectrum of the noise segments in the FYM, HAG and KOT stations, which is made to verify that the power spectrum is concentrated in the frequency range 4 . 3 3 Hz. The noise measurements for FYM, HAG and KOT stations are taken according to the instructions listed in section (2-3). They are taken four times per day and one day per week to form sixteen records per month. The samples are taken in one month for every season of the year to account for 64 traces. The timing of the records is also chosen to avoid events by reviewing the bulletin published by NRIAG [ 111.

71 1

The following graphs indicate the spectrogram of the vertical, north-south and east-west components for the FYM stations. From these spectrograms we can recognize that the power is concentrated in the low frequency range. The parameters at which the spectrograms are estimated are: Window length = 256.

Number of overlap = length (window) / 2. Window is a periodic Hann window with window length.

Sampling rate = 10.

FVM7

Fig. 2 The noise in Fayoum station represented by the spectrogram

Then the 64 noise segments are checked with the same manner to ensure the homogeneous distribution of power over frequency and during the different periods. While checking the noise segments listed, there were some windows in FYM station in which there were irregular noisy spikes in the power at the 1.33 Hz as shown in Fig.3. The duration of each spike is about 20 samples (0.2 seconds). But when averaging the power, the power of these spikes is reduced. These spikes don't mislead the algorithm to indicate false triggers as the algorithm waits for 30 samples, after the average power exceeds the threshold calculated by the algorithm, to make its decision.

-m tux] mu m mu m axlo 7m samples

Power at 1 33 Hr

u t rm 2m m 4m 533.3 WO 7w xi0 samplcs

Fig 3 (a) The trace of the noise window (b) The power at 1 33 Hz Fs = 100 sample/second, count = Inm/second

3 Spectrograms in First Arrival Determination

3.1 Brief Description of The Algorithm

The algorithm depends on checking the change in the power of the noise at certain frequency. As shown in Fig. 4 the major power contribution in the spectrum of the noise is concentrated in the frequency range smaller than 1 Hz [l], while the power of the higher frequencies is much lower. The algorithm makes use of this feature and it sets a threshold for the average power at 1.33 Hz from the noise segment preceding the event and when that average exceeds that threshold the algorithm waits for a while to be sure that it is not a spike to avoid making false triggers. The reason behind the choice of the power of the 1.33 Hz component is as follows; As this frequency is in the margin between the range of event frequencies and the range of the noise frequencies so that, if we choose a lower frequency, the algorithm will be deceived by the noise power and the number of false triggers will increase. Meanwhile, if we choose a higher frequency, the algorithm will have a delay to trigger for a change. Fig. 4 indicates the spectrogram of a noise segment at FYM station. From which we can recognize the frequency range of the effective power in noise. The algorithm uses the spectrogram to calculate the power spectrum at different frequencies in the window under inspection.

FYMZ 1000 I

I 0 0.5 1 1.5 2 2.5

-1000 ' lo4

4 60 3-. 40 c 20

2

U

g 2 0 -20 -40

U

0 0 500 1000 1500 2000 2500

Samples "1 0 Fig. 4 (a) A noise segment recorded at FYM station.

(b) The corresponding spectrogram. Where the Count = 1 ndsec .

3.2 The Spectrogram In Local Event Triggering

When dealing with noise, as shown in the last section, the power in the spectrograms is focused within the low frequencies. However if we notice the spectrogram for a certain event, as shown in Fig. 5, we will derive another benefit from the spectrogram. It gives us a background of the change in power of a certain frequency component with time.

712

FYM-Z-1998-01-21-03 50 57 7201 HAG and KOT stations, have been extracted from the bulletin published by NRIAG [I21 and compared with the arrival times computed by our proposed technique. Table 1 shows the mean value and variance of the errors between the two measurement sets. While Fig. 8 shows the probability distribution function for the three stations.

100

80

60

I Station I Mean I Variance I -0.03 0.0027

0.02 1

KOT I 0.0009 I 0.01 0 500Tlme 1000

Fig 5 An event represented by the spectrogram

So that, by monitoring the average power at 1.33 Hz with time, with the start of any event, the power of that frequency component increases sharply as shown in Fig. 6. This change in power could be sensed easily. The block diagram of the suggested algorithm is also shown in Fig. 7.

H G P;%@:;?1 1x3 50 53% E

r2 Sa#t?-: Fig 6 (a) The trace as recorded at HAG station

(b) The power at 1 33 Hz with time

Calculate the threshold power at1.33 Hzfrom the data segment

at the begining of the trace

- Declare a local event and

calculate the P-wave arrival whenever the power at 1.33 Hz

check power averages

exceeds te threshold a : ~ : ~ ~ i ~ d ~ t ~ ~ ~ ~ s C e C s e m s e s f i v t e z+

Fig. 7 The block diagram of the suggested algorithm

Table 1 Mean and Variance for the three chosen stations

The algorithm is also tested on two regional events one from the Mediterranean Sea on 11 th. Feb. 2004 and the other from the Dead Sea on the same day. The overall average error of all stations, compared to the analyst picks, for each earthquake and the variance is presented in table 2 and the probability distribution function of the error of the two events is also shown in Fig. 8.

Event Variance

0.0127

No 2 -0.11 0.021

Table 2 Mean and Variance for the two chosen regional events

..................

..... .....

..... ......

.....

Enor 02 0.15 o i om o 005 0 1

4 Testing The Algorithm

The P wave arrival times computed manually for 53 earthquakes from Dahshour region and detected by FYM,

713

Fig. 8 probability distribution function for a- FYM b-HAG c-KOT

stations, (d) The Mediterranean Sea (e) The Dead Sea Events.

4.1 Advantages of the Algorithm

The algorithm doesn't need any parameter settings, in contrast to the other algorithms which depend on either the algorithm itself or the nature of the noise at the site. The algorithm also makes use of the nature of the noise frequency content as it doesn't compare the total power of the event with noise, but it divides this power to components. Then it only compares the component which is weak in noise and rather strong in the first arrival of the event. Thus the signal to noise ratio has a slightly different concept here as the ratio is only between the powers at the specified frequency. Considering the event in Fig. 9, when applying the STNLTA concept on this window we will notice that the amplitudes at the start of the event are quite equal to those of the noise preceding it but with higher frequency.

lb'

Fig. 9 (a) The complete event (b) The first arrival is zoomed in. (c) The power at 1.33 Hz.

So the STALTA algorithm will be deceived as it makes its trigger according to the amplitudes expressed in the short term averages through the long term averages, thus it won't alarm for a change unless there is an increase in the amplitudes. While, using the developed algorithm, the change is clear in the power at 1.33 Hz and there is no need to wait until there is an increase of the signal amplitude. The error in this event was 0.03 sec.

4.2 Limitations of the Algorithm

As discussed in the previous sections the algorithm is based on detecting the change in power of a certain frequency. As shown in Fig. 10, the algorithm doesn't accurately detect the first arrival of local or regional weak earthquakes. This limitation is mainly due to the weakness of these first phases. This limitation also exists when trying to calculate the arrival time manually due to the low SNR. It was noticed that the S/N power ratio must be greater than 3 in order to have accurate results from the algorithm.

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swlplm rZ Fig IO (a) The complete event (b) The first arnval is zoomed in (c) The power at 1 33 Hz

Another problem concerning any automatic picking algorithm based on one component is the false triggers. This problem is solved if the algorithm is applied on an array of stations, which is not discussed here. The algorithm alarms for a false trigger if the power of the noise at 1.33 Hz exceeds the threshold detected by the algorithm as shown in Fig. 11 .

**m@U* K2 Fig 11 (a) The complete event (b) The first arnval is zoomed in

(c) The power at 1 33 Hz

In Fig. 1 1 (b) The arrow points at the noise which have power exceeding the threshold and its duration is more than 0.3 seconds. The percentage of the false triggered events is 5.8% out of 153 events checked.

714

Conclusion [5] Withers, M., R. Aster, C. Young, J. Beiriger, M. Harris, S. Moore, and J. Tru-iillo,: A comparison of

.In this paper, we introduced a modern technique for determining the first arrivals of the earthquakes. This technique uses the Time-Frequency Representations (TFRs).The spectrogram is one of these representations. We used the spectrogram built in the Matlab environment. From the study made at the noise, We can say that the spectrogram could be used as a judging tool for site selection. In spite of the irregular noisy spikes appeared in the FYM station, the algorithm has not been deceived with such spikes and didn't alarm for a trigger. However the false triggers cannot be avoided absolutely as the algorithm works on a single site. To avoid this problem the algorithm could be applied on an array of stations. Many real cases have been studied in order to prove the effectiveness of the proposed technique. From this test we can draw the following features of the algorithm:

a. The algorithm depends on checking the change in the power at certain frequency.

b. The algorithm does not need any parameter settings to give its decision while most of the algorithms mentioned need sophisticated settings, which must be assumed by experts.

c. The algorithm is very sensitive to the small changes of the powers in the first arrival of the P-wave as their frequency is above 1.33 Hz.

d. The number of the false triggers the algorithm makes is 5.8% which is very small.

e. The signal to noise ratio has a slightly different concept here which is the ratio between the powers at the specified frequency of the noise and the event.

f. The mean value and variance of the errors computed when comparing the time of arrival computed by the proposed algorithm and that published by NRIAG could be neglected.

References

Peter Bormann: Seismic Signals and Noise, A chapter of the new Manual of Observatory Practice edited by Peter Bormann and Erik Bergmann. Global Seismological Services, 200 1. Earle, P., and P. M. Shearer,): Characterization of global seismograms using an automatic-picking algorithm, Bull. Seism. Soc. Am 1994, 84, 3 6 6 376. Tong, C., and B. L. N. Kennett, Automatic seismic event recognition and later phase identification for broadband seismograms, Bull. Seism. Soc. Am. 1996, 86,18961909. Wagner, G., and T. Owens, Signal detection using

multi-channel seismic data, Bull. Seism. Soc. Am. 1996,86,221-231.

select -trigger algorithms f i r auto-mated global seismic phase and event location, Bull. Seism. Soc. Am. 1998,88, 95-106. Aki Hidani and Hiroaki Yamanaka, Automatic picking of seismic arrivals in strong motion data using an artificial neural network, Environmental Sei. and Tech., T. I. Tech., T.I. Tech, 2003. Haijiang Zhang, Clifford Thurber, and Charlotte Rowe, Automatic P-Wave Arrival Detection and Picking with Multiscale Wavelet Analysis for Single- Component Recordings, Bulletin of the Seismological Society of America, Vol. 93, No. S. 2003, pp. I904- 1912. Amadej Trnkoczy, Kinemetrics SA, Z.I. Le Trksi, "Understanding and parameter setting of STNLTA trigger algorithm" 1999. Erhard Wielandt Seismic Sensors and their Calibration, Institute of Geophysics, University of Stuttgart. A chapter of the new Manual of Observatorv Practice edited bv Peter Bormann and Erik Bergmann. Global Seismological Services, 2001.

[lo] Peterson J., Observations and modeling of background seismic noise, Open-file report 93-322, US. Geological Survey, Albuquerque, New Mexico. Earth Planets Space, 1993, SO, 3-8, PP. 21-67.

[ l l ] The Egyptian National Seismological Bulletin of the Egyptian National Seismological Network (ENSN). National Research Institute of Astronomy and Geophysics (NRIAG),: Egyptian Seismological Bulletin, Volume ZZZ. 2003.

[12] The Egyptian National Seismological Bulletin of the Egyptian National Seismological Network (ENSN). National Research Institute of Astronomy and Geophysics (NRIAG), Egyptian Seismological Bulletin, Volume IV. 2004.

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