Automatic P-wave Arrival Detection and Picking with

Multiscale Wavelet Analysis for Single-Component Recordings

 

 

Haijiang Zhang, Clifford Thurber, and Charlotte Rowe

 

 

Department of Geology and Geophysics

University of Wisconsin-Madison

 

Draft

 

June 19, 2002

 

Abstract

An automatic P-wave arrival detection and picking algorithm is developed based on the wavelet transform and Akaike information criteria (AIC) picker. Wavelet coefficients at high resolutions show the fine structure of the signal, and those at low resolution characterize its coarse features. The main features such as the P-wave arrival in the signal will be retained over several resolution scales and irrelevant ones will decay quickly at larger scales. We apply the discrete wavelet transform to the data in a time window sliding through single-component recordings and determine if there is a P-wave arrival in the current window by comparing the nearness of the picks determined by using the AIC picker on the absolute wavelet coefficients at different scales. The arrival time is then determined by using the AIC picker on the time window chosen by the wavelet transform. The uncertainty of the arrival picking is also determined by the closeness of the picks at different scales. We test our method on regional earthquake data from the Dead Sea Rift region and find that it can detect about 95% of P-wave arrivals correctly.

 

 

Introduction

Quickly detecting and accurately picking the first P-wave arrival is of great importance in event location, event identification and source mechanism analysis, especially in the era of large volumes of digital and real-time seismic data. Analysts traditionally check the seismograms and pick phases based on their individual experiences, which is time-consuming and subjective. There is a need to provide a more reliable and robust alternative, which should be more efficient and objective.

There are a variety of techniques in the literature to detect and pick the arrivals of different seismic waves from single-component as well as three-component (3-C) recordings. In some cases, some seismic stations do not have 3-C seismometers or cannot provide consistent 3-C recordings due to a failure in one or more components. Consequently for the most general application, it is necessary to pick seismic arrivals from single-component recordings. Withers et al. (1998) have categorized previous trigger algorithms for onset picking into time domain, frequency domain, particle motion processing, or pattern matching. Some of current methods include energy analysis (Earle and Shearer, 1994), polarization analysis (Vidale, 1986), and auto-regressive techniques  (Maeta, 1985; Sleeman and Eck, 1999; Leonard and Kennett, 1999; Leonard, 2000).

Normally, the P-wave onset is characterized by a rapid change in amplitude and/or the arrival of high-frequency energy. Assume the seismogram can be divided into locally stationary segments as an autoregressive (AR) process and the intervals before and after the onset are two different stationary processes (Sleeman and Eck, 1999). Based on such an assumption, an autoregressive-Akaike information criteria (AR-AIC) method has been used to detect P and/or S phases (Sleeman and Eck, 1999; Leonard and Kennett, 1999; Leonard, 2000). For the AR-AIC picker, the order of the AR process must be specified by trial and error and the AR coefficients have to be calculated for both intervals. In contrast to the AR-AIC picker, Maeta (1985) uses a different AIC picker, which can be calculated directly from the records without fitting them with the AR processes. However, when the signal to noise ratio (S/N) is low, the AIC picker cannot pick the correct arrival. Also a time window must be chosen properly for the AIC picker to find the right arrival.

In this article, we use the wavelet transform to guide the work of the AIC picker. The wavelet transform has been used to detect and pick the arrival of several seismic phases. Anant and Dowla (1997) applied the discrete wavelet transform (DWT) to 3-C seismograms to identify the P and S phase arrivals of seismic events by using the polarization and amplitude information contained in the wavelet coefficients of the signals. Tibuleac and Herrin (1999) used the continuous wavelet transform to decompose the signal into different scales and applied a threshold detector to the wavelet coefficients at one scale to determine the arrival time. Gendron et al. (2000) jointly detect and classify seismic events via Bayes theorem by using features extracted from the wavelet coefficients of the records.

The wavelet transform decomposes the signal at different scales, thus adaptively characterizing its components at different resolutions.  Wavelet coefficients at high resolution show the fine structure of the signal, and those at low resolution characterize its coarse features. The main features in the signal will be retained over several resolution scales and irrelevant ones will decay quickly at larger scales (Daubechies, 1992).  The Akaike Information Criteria (AIC) picker is used on the corresponding wavelet coefficients over multiple scales. By comparing the nearness among the picks at different scales, we can determine if there is an arrival in the current time window. After the time window is chosen, we apply the conventional AIC picker to determine the arrival time. We test our method on regional earthquake data from Dead Sea Rift region and compare the autopicks with the analyst picks.

 

AIC Picker

 

We assume that the seismogram can be divided into locally stationary segments each modeled as an Autoregressive (AR) process, and the intervals before and after the onset time are two different stationary processes (Sleeman et al., 1999). The order and the value of the AR coefficients change when the characteristics of the current segment of the seismogram are different from before.  For example, typical seismic noise is well represented by a relatively low order AR process, whereas seismic signals usually require a higher order AR process (Leonard et al., 1999). The Akaike Information Criterion (AIC) is usually used to determine the order of the AR process when fitting a time series, which indicates the badness and the unreliability of the model fit (Akaike, 1973). This method has been used in onset estimation by analyzing the variation in AR coefficients representing both multi-component and single-component traces of broadband and short period seismograms (Leonard and Kennett, 1999). When the order of the AR process is fixed, the AIC function is a measure of the model fit. The point where the AIC is minimized determines the optimal separation of the two stationary time series in the least squares sense, and thus is interpreted as the phase onset (Sleeman and Eck, 1999). This approach is known as AR-AIC picker (Sleeman and Eck, 1999; Leonard, 2000).  The AIC of the two-interval model for seismogram of lengthis represented as function of merging point  (Sleeman and Eck, 1999):

                          (1)

where  is the order of an AR process fitting the data,  is a constant, and and indicate the variance of the seismogram in the two intervals not explained by the autoregressive process. To realize the AR-AIC picker, the order of the AR process must be specified by trial and error, and then AR coefficients can be determined by the Yule-Walker equations (Haykin, 1996). 

In contrast to the AR-AIC picker, Maeta (1985) calculates the AIC function directly from the seismogram, without using the AR coefficients. The onset is the point where the AIC has a minimum value. For the seismogram of length, the AIC value is defined as  

          (2)

where  ranges through all the seismogram samples.

Note that the AIC picker defines the onset point as the global minimum. For this reason, it is necessary to choose a time window that includes only the seismogram segment of interest. If the time window is chosen properly, the AIC picker can find the P-wave arrival accurately. For a seismogram with a very clear onset, AIC values have a very clear global minimum that corresponds to the P-wave arrival (Figure 1a). For a seismogram with a relatively low signal to noise (S/N) ratio, there may be several local minima in AIC values, but the global minimum still indicates accurately the P-wave onset (Figure 1b). When there is more noise in the seismogram, the global minimum cannot be guaranteed to indicate the P-wave arrival (Figure 1c). Thus, the S/N ratio in the seismogram affects the accuracy of the AIC picker to some extent.

If there are multiple seismic phases in a time window, the AIC picker will choose the strongest phase (Figure 2).  On the other hand, the AIC picker is not "smart" enough in that it will usually pick an "onset" for any segment of data no matter whether there is a true phase arrival in the time window or not (Figure 3), as there will almost always be one global minimum. For this reason, we need guide the work of the AIC picker by choosing an appropriate window for it.        

 

Wavelet Transform

The Fourier transform is conventionally used to analyze the frequency content of seismic signals. Assuming that the spectral content of the data does not change, Fourier analysis gives a global representation of the data and cannot analyze its local frequency content or its local regularity. It is known that seismic waves traveling through complex media are composed of time-frequency localized waveforms. Therefore it is wise to choose a basis that can represent the seismogram locally both in the time and frequency domains. The wavelet transform, which was actually initiated by work on seismic signals (Goupillaud et al., 1984; Grossmann and Morlet, 1984), is a very useful tool in the analysis of nonstationary signals such as seismic signals. The advantage of the wavelet transform over the Fourier transform is its ability to characterize the structure of the signal locally with a detail matched to its scale, i.e., broad features at a large scale and fine features on small scales.

The wavelet transform has been applied to seismic data in such aspects as improving the seismic data resolution and its S/N ratio (Chakra and Okaya, 1995), compressing seismic data (Lervik et al., 1996), characterizing the singularity structure of media (Goudswaard and Wapenaar, 1998), and seismic data inversion and migration (Wu and McMechan, 1998). It has also been used to detect P and S wave arrivals in 3-C seismograms (Anant and Dowla, 1997), determine arrival times of the regional phase Lg (Tibuleac and Herrin, 1999), and jointly detect and classify seismic events via Bayes theorem (Gendron et al., 2000).

The wavelet transform has two forms: continuous wavelet transform (CWT) and discrete wavelet transform (DWT) (Daubechines, 1992). The continuous wavelet transform of a functionis defined as:

                                                                (3)

whereis the analyzing wavelet, and a and b are the scale factor and translation factor, respectively. The analyzing wavelet g(t) decays rapidly to zero with increasing t and has zero mean. The scale factor controls the dilation or compression of the wavelet. At lower scales, the wavelet is compressed and characterizes the rapidly changing details of the signal, whereas at higher scales, the wavelet is stretched and the slowly changing and coarse features are better resolved.

In practical applications, the discrete wavelet transform (DWT) is used more often since the data are discrete time samples. DWT can be implemented quickly via the Mallat algorithm (Mallat, 1989).  A low-pass filter  and high-pass filter  are used to calculate recursively the wavelet coefficients of a discrete time series, as follows

                                                           (4)

where is the scale parameter and  is the maximum decomposition level. Through the decomposition, the original signal  can be represented as, from which the original signal can be reconstructed completely (Daubechies, 1992).  The wavelet coefficients characterize the details, or the fine structure of the signal, in different scales, or resolutions. In this way, we can analyze the signal at different resolutions.

 

Singularity Detection with Multiscale Wavelet Analysis

A singularity is defined as a discontinuity in the signal or its derivatives, which is characterized by the Lipschitz exponent (Mallat and Hwang, 1992). Noise usually has a Lipschitz exponent less than or equal to -1. For example, the Lipschitz exponent of white noise is  (Mallat and Hwang, 1992). If a point corresponds to the edge or regular part of the signal, its Lipschitz exponent is greater than or equal to zero.

The decay of the wavelet coefficients over scales depends on the singularity of the signal. When the signal singularity has a small or even negative Lipschitz exponent, the wavelet coefficients decay quickly. That is, the significant features in the signal will be retained over several scales, while noise or other trivial features will disappear at larger scales. Based on such interscale features of wavelet coefficients, the noise and the signal can be separated. Normally, the P-wave arrival is characterized by a rapid change in amplitude and/or the arrival of high-frequency energy.  That is, there is a singularity at the onset of the P-wave arrival. If the P-wave arrival is a significant feature of the signal, it will be retained across several scales, while the background noise will disappear at larger scales. This property allows the P-wave arrival to be detected. Figure 4 shows a noisy seismogram and its corresponding wavelet coefficients at scales 1, 2 and 3. The wavelet coefficients corresponding to the P-wave arrival decay more slowly than those of the noise with increasing scale.

 

Wavelet-AIC picker: Detecting and Picking the P-wave Arrival

As discussed above, the AIC picker is not "smart" enough to pick the P-wave arrival correctly unless it is guided by other methods. Our Wavelet-AIC picker combines the AIC picker with multiscale wavelet analysis, in which the AIC picker is applied to absolute wavelet coefficients at several scales (or resolutions). Since P-wave arrival information will be retained over several scales, the times picked by the AIC picker at several scales should be near each other (Figure 5a, b and c). If there is no P-wave arrival within the time window, there will be significant differences between the pick times at neighboring scales (Figure 5d). By this method, we can determine whether there is a P-wave arrival or not.  Table 1 lists pick times at three scales as well as manual picks, if applicable, for the seismograms shown in Figure 5. We have found that decomposing the seismograms into 3 scales is appropriate. If more scales are used, the singularity due to the P-wave arrival at the highest scale will be smoothed out. If only two scales are used, however, the singularity due to the noise will still be significant at scales 1 and 2 in some cases, thus resulting in false detections.

There are numerous wavelet families to choose from. The main criteria for choosing the wavelet function are its support, symmetry, regularity and number of vanishing moments (Wickerhauser, 1994). The wavelet function with tighter support has smaller border distortion of the DWT. In general, short wavelets are often more effective than long ones in detecting a signal rupture. So to detect a signal discontinuity, the best choice is to use the Harr wavelet. On the other hand, to detect a singularity in the derivative, the wavelet should be sufficiently regular with at least  vanishing moments.

For the seismogram shown in Figure 5(c), we use several wavelet functions to test the pick times at scales 1, 2 and 3. The results are shown in Table 2. For the same wavelet, the pick times at different scales are near each other, which indicates that there is a significant feature in this time window. It is noted that the Symmlet wavelet functions give the same pick times at scales 1, 2 and 3 as those by the Daubechies nonsymmetric wavelets. Except for this similarity, the pick times at different scales for different wavelets vary somewhat. This is due to the fact that the nonsymmetric filters can shift the signal by different amounts, an effect that can be estimated by the phase response of the filter (Wickerhauser, 1994). In addition, the wavelet coefficients cannot characterize the exact position of the singularity, but a region of the singularity. For this reason, if there is a P-wave arrival detected in the time window, then the conventional AIC picker is used to pick the arrival time.

When the S/N ratio is low, the Wavelet-AIC picker will usually detect and pick an incorrect arrival time. In this case, we automatically penalize the wavelet coefficients by soft-thresholding, which has a better mathematical property than hard thresholding (Donoho, 1995). The threshold is chosen by a wavelet coefficients selection rule using a penalization method proposed by Birge-Massat (1997). The Wavelet-AIC picker detects the P-wave arrival based on the thresholded wavelet coefficients, from which the de-noised signal can be constructed for the picker to use to pick a time. For the seismogram shown in Figure 5(c), the pick time with the AIC-picker is 49.56 seconds, which is very similar to the manual pick. For comparison with conventional band-pass filtering, this de-noising scheme based on the wavelet transform distorts the true P-wave arrival and reduces its amplitude to a lesser degree (Figure 6).

By evaluating the nearness of picks at three scales, we can estimate an uncertainty for the pick. If they are within 5 samples, weight 0 is set on the pick, which indicates the arrival is clear and strong. Weights 1, 2, and 3 are designated to the pick if the picks at 3 scales are within 10, 20 and 50 samples, respectively. Alternatively, the uncertainty can be expressed directly in terms of time.

 

Wavelet-AIC picker: Implementation Details

There are some aspects to take into account when implementing a Wavelet-AIC picker, as follows:

(1) Border effect of the wavelet transform

The basic algorithm for the DWT is based on a simple scheme: convolution and downsampling. When the convolution is performed on finite-length signals, there will be border distortion. The simple way to deal with  border distortion is to extend the signal on both sides, such as by zero-padding, smooth padding, periodic extension, or boundary value replication methods (Matlab Wavelet Toolbox, 2000). However, these methods will create some significant features at both ends of the signal. For example, zero-padding produces an edge singularity at both ends. Compared to the singularity of the noise, these singularities will be retained across several scales and thus be captured by the wavelet-AIC picker. In fact, the pick times at scales 2 and 3 for the seismogram shown in Figure 5d are due to such artificial singularities created at both ends. To prevent such false alarms due to the border effect, we define a border effect region at both ends of the time window. When the time pick at some scale lies in this region, we declare it to be the border effect and the time window continues to move. Considering the situation when a true arrival is located in the border effect region, the time windows are overlapped so that the overlapping time is larger than the border effect region. In this way, we can overcome the border effect of the wavelet transform. 

(2) Time window

The time window is important for finding the correct phase arrival for the wavelet-AIC picker. If the time window is too large, then there could be many phases within the time window and the picker may choose a later stronger phase. If the time window is too short, it will slow the detection process because the neighboring time windows need to overlap to reduce the border effect of DWT. Our Wavelet-AIC picker can specify the beginning and ending times for the time window.  If the user has no idea how much the time window should move, it will move from the first sample of the seismograms until the arrival is detected. If the picker declares a failure in detecting the P-wave arrival the first time, it will try again from a later starting time. This procedure can improve the detecting ability of the Wavelet-AIC picker.

 (3) Spikes problem

Spikes are typically one or two samples having anomalously larger values than the background signal (Dai and MacBeth, 1997). Spikes are significant features of the signal, and they could persist over several scales. When they are present in the time window the wavelet-AIC picker cannot distinguish them from phase arrivals. By using the feature of spikes that only one or two samples have much larger amplitudes than other samples, a spike amplitude ratio criterion can be defined to discard the spikes, as follows (Dai and MacBeth, 1997).

                                             (5)

where mean amplitude is calculated in the sliding time window except for the largest two peaks. If the ratio is smaller than a given threshold, it is considered a spike.

 

Application of Wavelet-AIC picker

We have applied the Wavelet-AIC picker to a set of  seismic events from the Dead Sea region that have been picked manually for comparison. Figure 7a and 7b show examples of arrivals picked by our picker for seismograms with high S/N ratio and low S/N ratio, respectively. It can be seen that in both cases, the Wavelet-AIC picker can detect and pick the P-wave arrival with considerable accuracy. We use Daubechies wavelet of order 2 (Dau2) to decompose the seismograms into 3 scales. If the pick times at these 3 scales are within 50 samples, and not within 20 samples from either end of the time window (border effect), we declare that the P-wave arrival exists in the time window and choose the pick at scale 2 as the preliminary pick. If no P-wave arrival is detected, the time window will shift to the right with an overlap of 50 samples until the end of the seismogram (or a predefined time) is reached. After the P-wave arrival is detected, the AIC picker will pick the onset from a time window of 40 samples before and 60 samples after the preliminary pick.  The uncertainty for the pick is based on the nearness of the picks at 3 scales, as mentioned above.

  Compared with manual picks, our picker provides onset times and uncertainties with high confidence. 92% of the autopicks are within 0.15 seconds of analyst picks for a set of Dead Sea region earthquakes from M 0.5 to M 4.2.

 

Conclusions and Future Work

A Wavelet-AIC picker is developed based on the Akaike Information Criteria combined with multiscale wavelet analysis. The P-wave arrival is a significant feature in the seismogram and will be retained over several scales, while noise or other trivial features will disappear quickly over larger scales.  The AIC picker is applied directly to the absolute wavelet coefficients. If the picks at 3 scales are close, then the P-wave arrival is declared and the AIC-picker is applied to the seismogram in the time window.

We apply the soft-thresholding scheme with the threshold chosen by the Birge-Massat penalization method to the wavelet coefficients. This approach is advantageous over the conventional band-pass filtering method, which is more likely to distort the P-wave arrival or reduce its amplitude. In this way, the Wavelet-AIC picker is more robust in detecting the P-wave arrival even for noisy seismograms. We test this method on a set of seismic events from the Dead Sea region. Compared with manual picks, this method provides high confidence picks with estimated uncertainties. 

The criteria to determine the closeness between picks at different scales should be investigated further. The criteria should be dependent on such features as the polarity and the impulsiveness of the P-wave arrival. The Wavelet-AIC picker will also be tested on picking the S phase in the future.

 

Acknowledgements

This research has resulted from a project supported by the Defense Threat Reduction Agency (contract number DTRA01-01-C-0085), US Department of Defense; the content does not necessarily reflect the position or the policy of the US Government, and no official endorsement should be inferred.  The first author acknowledges British Petroleum for partial support of his graduate studies in fall 2001.

 

 

References

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Akaike, H. (1973). Information theory and an extension of the maximum likelihood principle. In: Petrov, B. and F. Csaki (Eds.), 2nd Intermational Symposium on Information Theory, Budapest Akademiai Kiado, pp. 267-281.

Bai, C. Y., and B. L. N. Kennett (2000). Automatic phase-detection and identification by full use of a single three-component broadband seismogram, Bull. Seism. Soc. Am, 90, 187-198.

Birge, L. and P. Massart (1997). From model selection to adaptive estimation, in Pollard, D. (Ed.), Festchrifft for L. Le Cam, Springer, 55-88.

Chakra, A. B., and D. Okaya (1995). Frequency-time decomposition of seismic data using wavelet-based methods, Geophysics 60, 1906-1916.

Dai, H., and C. MacBeth (1997). The application of back-propagation neural network to automatic picking seismic arrivals from single-component recordings, J. Geophys. Res, 102, 15,105-15113.

Daubechies, I. (1992). Ten lectures on wavelets, CBMS-Conference Lecture Notes 61, SIAM Philadelphia.

Donoho, D.L. (1995). De-Noising by soft-thresholding, IEEE Trans. on inf. Theory 41, 613-627.

Earle, P., and P. M. Shearer (1994). Characterization of global seismograms using an automatic-picking algorithm, Bull. Seism. Soc. Am, 84, 366-376.

Gendron, P., J. Ebel, and D. Manolakis (2000). Rapid joint detection and classification with wavelet bases via Bayes theorem, Bull. Seism. Soc. Am, 90, 764-774.

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Goudswarrd, J., and K. Wapenaar (1998). Characterization of reflectors by multiscale amplitude and phase analysis of seismic data, 68th Ann. Internat. Mtg: Soc. of Expl. Geophys., 1688-1691.

Haykin, S. (1996). Adaptive filter theory, Prentice Hall Inc..

Leonard, M., and B.L.N. Kennett (1999). Multi-component autoregressive techniques for the analysis of seismograms, Phys. Earth planet. Int, 113, 247-264.

Leonard, M. (2000). Comparison of manual and automatic onset time picking, Bull. Seism. Soc. Am, 90, 1384-1390.

Lervik, J.M., T. Rosten, and T. A. Ramstad (1996). Subband seismic data compression: optimization and evaluation, IEEE Digital Signal Processing Workshop Proceedings, 65-68.

Mallat, S., and W. L. Hwang (1992). Singularity detection and processing with wavelets, IEEE Trans. Inform. Theory 38, 617-643.

Maeda, N. (1985). A method for reading and checking phase times in auto-processing system of seismic wave data, Zisin=Jishin 38, 365-379.

Sleeman, R., and T. v. Eck (1999). Robust automatic P-phase picking: an on-line implementation in the analysis of broadband seismogram recordings, Phys. of the Earth and Planet.  Int, 113, 265-275.

Vidale, J. E. (1986). Complex polarization analysis of particle motion, Bull. Seism. Soc. Am. 76, 1393-1405.

Wickerhauser, M. V. (1994). Adapted wavelet analysis from theory to software, Wellesley, MA

Withers, M. et al. (1998). A comparison of select trigger algorithms for automated global seismic phase and event detection, Bull. Seism. Soc. Am. 88, 95-106.

Wu, Y., and G. A. McMechan (1998). Wave extrapolation in the spatial wavelet domain with application to poststack reverse-time migration, Geophysics 63, 580-600.

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Table 1. Pick times at scales 1, 2 and 3 as well as manual picks (a-d, respectively) for seismograms shown in Figure 5 (with "Dau3" wavelet).

 

 

a

b

c

d

Scale1

37.58

70.34

49.70

27.70

Scale 2

37.62

69.98

49.26

26.70

Scale 3

37.46

70.22

49.90

30.94

Manual Pick

37.64

70.06

49.56

N/A

 

 

 

 

 

Table 2. The pick time at scale 1, 2 and 3 with different wavelets for the seismogram shown in Figure 5c

 

Wavelet

Dau2

Dau3

Dau4

Sym2

Sym3

Bior2.2

Bior2.4

Scale 1

49.70

49.70

49.70

49.70

49.70

49.82

49.78

Scale 2

49.74

49.26

49.74

49.74

49.26

49.82

49.34

Scale 3

49.26

49.90

49.26

49.26

49.90

49.58

49.90

 

 

 

Figure Captions

 

Figure 1 Seismogram and its corresponding AIC values. a) For seismogram with clear P-wave arrival, AIC value is a very clear minimum point. b)For seismogram with clear P-wave arrival with relatively lower S/N ratio, AIC function has many local minima, whereas the global minima still corresponds to the P-wave onset. c) For very low S/N seismogram, there are a few local minima close to each other. In this case, the global minima cannot be guaranteed to be the P-wave arrival.

Figure 2 Seismogram with two phases and the corresponding AIC values. It is noted that there are clear local minima with respect to each phase arrival. The global minimum indicates the arrival of the stronger phase.

Figure 3 Seismic noise data and its AIC values. The minimum value does not indicate any phase arrival although it divides the data into two different stationary segments.

Figure 4 Seismogram and the corresponding absolute wavelet coefficients at scales 1, 2 and 3.

Figure 5 Wavelet-AIC picker. For seismograms shown in a, b and c with a P-wave arrival, picks at different scales are near each other. However seismogram d does not have an arrival. Therefore the picks are different.

Figure 6 Comparison of wavelet de-noising and band-pass filtering methods. (a) Noisy seismogram. (b) De-noising by soft-thresholding the wavelet coefficients with the threshold chosen by the Birge-Massat method. (c) Band-pass filtering using the Butterworth filter of 1.5HZ to 10.0HZ.

Figure 7 Wavelet AIC-Picker applied to seismograms with (a) high S/N ratio and (b) low S/N ratio