Polarizacion Deteccion avalanchas

IEEE TRANSACTIONS ON SIGNAL PROCESSING, VOL. 46, NO. 1, JANUARY 1998 83

Three-Component Signal RecognitionUsing Time, TimeFrequency, and

Polarization InformationApplicationto Seismic Detection of AvalanchesBenoit Leprettre, Nadine Martin, Francois Glangeaud, and Jean-Pierre Navarre

Abstract A method for automatic signal recognition, ap-plied to seismic signals classification, is presented. It is basedon the fusion of data derived from the analysis of the signalin three domains: time, timefrequency, and polarization. Inthe time domain, two techniques are used for envelope shapeparametrization. In the timefrequency domain, the autoregres-sive and Capon (ARCAP) timefrequency method is used ona gliding time-window to estimate the spectral components ofthe signal versus time. For each window, the frequencies areestimated using AR modelization. The power at each frequencyand the corresponding filtered signal are estimated using Caponsmethod. A comparison with Fouriers narrow-bandpass filteringshows that Capons method produces a better filtering. In thepolarization domain, two original methods are proposed: one forchecking the linear polarization of a signal and one for localizingthe linear waves in the timefrequency plane.A system for automatic recognition of seismic signals associated

with avalanches is then presented as an application. Signal fea-tures are derived from the analysis to sum up the characteristicsof the signal in each domain. These features are combined usingfuzzy logic and credibility factors, according to rules derived fromphysical knowledge (generating processes and propagation rules),in order to decide whether a signal comes from an avalanche ornot. The global rate of correct recognition is over 90% for thatfirst version of the system.

Index Terms ARCAP timefrequency method, data fusion,nonstationary signal analysis, polarization, seismic detection ofavalanches.

I. INTRODUCTION

THE APPLICATION described in this paper is the auto-matic discrimination of three-component avalanche seis-mic signals from other types of signals. When an avalancheoccurs, seismic waves are generated into the ground by themoving snow packets and can be detected by appropriate sen-sors. The analysis of the ground seismic signal can thereforeenable us to detect and maybe localize avalanches at the timeof their occurrence. A reliable, real-time estimation of theavalanche activity of a massive occurence would allow a betterManuscript received June 16, 1995; revised March 7, 1997. The associate

editor coordinating the review of this paper and approving it for publicationwas Dr. Petar M. Djuric.B. Leprettre and J.-P. Navarre are with the Centre dEtude

de la Neige, Meteo-France, St. Martin dHeres, France (e-mail:[email protected]).N. Martin and F. Glangeaud are with the Centre dEtude des Phenomenes

Aleatoires et Geophysiques, ENSIEG, St. Martin dHeres, France.Publisher Item Identifier S 1053-587X(98)00533-9.

understanding of the avalanche phenomenon and a validationof the deterministic system for avalanche hazard estimationdeveloped by the Snow Research Centre (Centre dEtude dela Neige-Meteo France, Saint-Martin dHe`res, France). Theevolution versus time of the avalanche activity would alsohelp in making the decision to reopen roads after snowfallsonce the end of the rise of the avalanche has been detected.The feasibility of the seismic detection of avalanches has beenproved [20]. At present, other experiments are made in theSpanish Pyrenees [19], but as yet, no operational applica-tion has been considered. The main difficulty is that manyunwelcome nonavalanche signals are recorded in additionto avalanche signals. The recognition of avalanche signalscan prove difficult to perform, given their complexity andvariety. On the other hand, most of the nonavalanche signals(earthquakes, blasts, or helicopter signals) can be discriminatedbecause the associated physical processes are less complex.Thus, a complete analysis of the three-component signal isnecessary to discriminate avalanche signals with maximuminformation.Section II presents how several signal analysis methods are

combined to provide a complete description of the signal.It must be noted that this multidisciplinary approach of theproblem of signal recognition can also be used in otherapplications than the one presented here. Three main analysisdomains can be distinguished: time (envelope shape analysis),timefrequency analysis using the autoregressive and Capon(ARCAP) method, and localization of linear ground motionsin the timefrequency plane using Capons filtering. Signalfeatures describing the signal in each domain are derivedfrom the analysis. In Section III, the features are combinedusing fuzzy logic techniques in order to estimate the possi-bility of the signal being either type of signal. This allowsus to decide whether the signal has been produced by anavalanche or not and to estimate the reliability of this finaldecision. Three examples of signal classification are presented.Section IV concludes with a discussion about improvementsof our recognition system.

II. METHODS USED FOR SIGNAL CHARACTERIZATIONSome types of nonavalanche signals are well recognizable

in the time domain and can thus be discriminated on their

1053587X/98$10.00 1998 IEEE

84 IEEE TRANSACTIONS ON SIGNAL PROCESSING, VOL. 46, NO. 1, JANUARY 1998

envelope. Others can be recognized using their frequency orpolarization content. Several analysis methods must thus becombined to get a reliable description of the signal char-acteristics in each domain. The methods are presented inthe following sections. For each method, the derived signalfeatures used for signal recognition are described and labeledto make further reference easier.

A. Envelope Shape AnalysisThe avalanche phenomenon is very complex. The associated

seismic signal varies greatly from one avalanche to another,depending mainly on the size of the avalanche, the profileof the avalanche path, and the distance between the event andthe seismic sensor. From a seismic point of view, an avalanchecan be considered to be an emitter with an unknown (possiblyhigh) number of seismic sources of unknown amplitude, onunknown locations, at an unknown distance from the sensor.Given the complexity of the physical phenomenon, we cannotassume a particular envelope shape for the avalanche events.On the other hand, other seismic phenomena produce lesscomplex signals, the structure of which is known better, giventhe more simple characteristics of the associated physicalprocesses. Examining the signal envelope thus leads to a firstpiece of information for recognizing the events.Three types of signals are almost always identifiable ac-

cording to their time envelope shape: blasts, footsteps, andnonteleseismic earthquakes (i.e., local events). We proposetwo methods for characterizing the time envelope. First, acumulated histogram of the temporal amplitude maxima isused to discriminate sharp, well-defined signals, such as blastsor footsteps. Second, the signal envelope is compared with amodelization of a typical, simplified earthquake envelope. Thequality of the fit is estimated by calculating a mean distancebetween the signal envelope and the model. This allows us torecognize earthquakes with good reliability.The cumulated histogram method provides information on

how well the envelope maxima dominate background noise.The time envelope of a signal contains many temporal peaks:some of them being part of the signal and the others beingpart of the noise. Some types of nonavalanche events producesharp seismic signals, with a few temporal peaks towering overthe other peaks and noise. For example, a mining blast is abrief, energetic event. It produces a short, very sharp signal.Only one or two envelope amplitude peaks will emerge frombackground noise. In the same way, when an animal or aperson is moving in the vicinity of the sensor, its footstepsproduce numerous brief, very energetic waves. Hence, numer-ous temporal peaks of high amplitude appear on the envelopecurve, towering over the background noise peaks. There arevery few peaks of intermediate amplitude. These types ofsignal can easily be recognized with a cumulated amplitudehistogram that is defined as follows. Given a temporaldiscrete signal , its normalized envelope can be definedusing the Hilbert transform (HT) [16]

(1)

where is the Hilbert transform of , and isthe maximum amplitude of the envelope before normalization.For a given amplitude , let be the number of temporalpeaks of with an amplitude larger than . The curve

is monotonous and decreasing. Its shape depends on theamplitude distribution of the envelope peaks, and it can bemore or less steep. For a blast-type signal, where only a fewpeaks are significant, the cumulated histogram will besteeper than for other types of signals, such as avalanches,where the amplitude is more homogeneously distributed. Thesteepness of can be estimated by fitting it to a simplemodel of exponential decay

(2)

where is the total number of temporal peaks of. This model has the advantage of being very simple,

and the parameters and are easy to calculate:is easily computable, and is well estimated by a leastsquare method. The value of parameter is related to thesteepness of , that is, the amplitude distribution of thetime envelope of the signal. It is used to discriminate blast andfootsteps signals from other, more homogeneous signals. Ahigher value of denotes a blast or a footsteps signal [Fig. 1(a)and (b)], whereas a smaller value of is rather typicalof avalanches [Fig. 1(c)], earthquakes, or helicopter signals.The problem is as follows: How do we choose appropriatethresholds for when is used as a classification criterion?We have calculated this parameter for a set of unambiguouslyidentified signals and drawn distribution histograms of foreach class of signals (blasts, footsteps, avalanches, and others).The representativeness of this set of events will be discussedlater. These histograms allowed us to estimate boundary valuesof , that is, lower and higher thresholds. For an unknownsignal, if the calculated value of is smaller than the lowerthreshold, the signal is sure not to be a blast or a footstepssignal according to the time-related criterion . Inversely, avalue of larger than the higher threshold denotes a blast orfootsteps signal. For a few events, however, the value of islocated between the lower and higher thresholds. In that case,we cannot be sure of our decision. This has been taken intoaccount using fuzzy sets. This point will be explained morein detail in the third part of this paper. For a given three-component seismic signal, three values of are calculated inorder to be used in the decision process:K Z value of parameter in (2), estimated using the

vertical channel;K E value of parameter in (2), estimated using the

EastWest channel;K N value of parameter in (2), estimated using the

NorthSouth channel.For other types of nonavalanche signals, parameter isnot discriminating, but the shape of the envelope is easilyrecognizable and can thus be modelized. This is the case forlocal earthquake events. The idea is to compare the normalizedtime envelope of the signal with a model. The model is asimplified representation of the global aspect of the envelope.In order for the envelope to enhance the global temporal

LEPRETTRE et al.: THREE-COMPONENT SIGNAL RECOGNITION USING TIME, TIMEFREQUENCY, AND POLARIZATION INFORMATION 85

(a)

(b)

(c)Fig. 1. Example of signal discrimination using steepness parameter k. (a) Original signals: blast (left), footsteps (middle), and avalanche (right). (b) Signalenvelopes. (c) Calculated (solid line) and modelized (dots) N(x) curves with corresponding steepness parameter k.

trends of the signal, it must be smoothed using, for example, agliding rectangular time window. The smoothed envelope canbe defined as

(3)where

defined by (1);length of the smoothing time-window;maximum value of before normaliza-tion.

When a local earthquake occurs within a radius of about 200km from the sensor, the propagation of the seismic waves inthe ground produces a separation of the waves in two maingroups. A first group of waves (called the -waves) emergesfrom background noise and decreases slowly. Then, generallyafter several seconds, a second group of waves of higheramplitude (the -waves) appears and decreases more rapidly.One can modelize the resulting envelope using a constantamplitude in the -wave zone and a decreasing exponentialcurve in the -wave zone. A simplified earthquake envelope

model is thus defined by

(4)

(5)

wheredate when the signal emerges from backgroundnoise;date corresponding to the maximum envelope am-plitude ;date when the signal vanishes into the noise;mean envelope amplitude in the -wave zone;average envelope amplitude in the background noisearea;time constant of the exponential model, estimatedby least square method.

This model has the advantage of being very simple to cal-culate and is sufficient to allow a correct discrimination ofseismic local events on the basis of their envelope shape. Theparameters of the model must be adapted to each signal inorder to best fit the signal envelope. and are estimatedusing a segmentation algorithm and is equal to one due to


normalization, whereas and can easily be calculated.The -wave zone runs from to , but ,which is the mean amplitude of the waves, is estimated ona temporal window of length beginning at . mustbe less than because smoothing tends toincrease the envelope amplitude just before . In addition,smoothing generally causes the amplitude to start to increasea short moment before . We thus propose to estimate ona window of length , where isa fixed ratio, for example, .In order to estimate whether the signal envelope fits the

earthquake model or not, a distance criterion between the realenvelope and the model can be estimated using the averagedistance:

(6)

This distance has the advantage of being simple, easy tocalculate, and efficient. Events other than local earthquakeswill not fit the model correctly, and the associated valueof will thus be larger than for earthquakes. However, thechoice of , which is the length of the smoothing window,is very important. If is too small, the envelope is stilltoo hatched, that is, it does not represent only the globaltemporal aspect of the signal, and thus, parameter is notdiscriminating enough. On the other hand, if is too large,the amplitude of the smoothed envelope increases too slowlyin the beginning of the - and -wave zones, and the proposedmodel does not fit the envelope in a satisfactory way. Inaddition, for earthquakes that have close and waves, the

wave is no longer distinguishable on the smoothed envelopeif is too large. We have set up a simple method to estimatea suitable value of from the results of signal segmentation.The background noise level is relatively constant on theequipped site. Thus, a simple segmentation algorithm is used todetect the beginning and end of the effective signal. The meanamplitude of the noise is estimated on a 1-s window glidingalong the first 10 s of the signal. Then, the mean amplitudeof the signal is estimated on a similar gliding window. Assoon as the mean amplitude of the signal window exceeds themean noise level with a certain threshold (e.g., three timesthe noise level), the first sample of the gliding window issaid to be the beginning of the effective signal. The sameoperation is carried out from the end of the recorded signalto estimate the end of the effective signal. It is thus easy,using this simple segmentation algorithm, to cut the noisypre- and post-event parts of the signal. This method has theadvantage of allowing the user to choose the minimum signal-to-noise ratio (SNR) in the effective signal by modifying thedetection threshold. Unlike other applications in seismology,a high-precision signal segmentation is not necessary for ourstudy. The onset moment and the end of the effective signalare calculated using this method:ES BEG onset moment of the effective signal;ES END end of the effective signal.

We empirically established that for our signals, a value ofabout 10% of the length of the effective signal offers a good

compromise for , and distance parameter is then welldiscriminating. Fig. 2 shows three examples of model fitsand corresponding distance parameter . The top signal is alocal earthquake; the model thus fits the smoothed envelopecorrectly. The middle signal is an avalanche where envelopedoes not fit the model. The bottom signal, however, is oneof the few examples where a satisfactory fit to the earthquakemodel is obtained, although the signal is actually an avalanche.This indicates that the variety of behavior of avalanche signalsis high and that it will be necessary to combine several criteriaduring the decision process. Like for the previously describedsteepness parameter , lower and higher thresholds for theuse of as a classification criterion have been determinedfrom the calculation of for a set of unambiguously identifiedevents (earthquakes and others). One distance parameter canbe calculated for each of the three channels. Thus, three signalfeatures are obtained:D Z value of parameter in (6) for the vertical channel;D E value of parameter in (6) for the EastWest channel;D N value of parameter in (6) for the NorthSouth

channel.The last feature derived from the time domain is the meanamplitude of the effective signal on the vertical channel

MA ZES END ES BEG

(7)

where is the sampling frequency. The combination ofthe two proposed methods allows a good recognition of theblast and footsteps signals (cumulated histogram method,steepness parameter ), as well as local earthquakes (envelopemodelization method, distance parameter ). Details about therate of correct recognition and the estimation of the boundaryvalues for the fuzzy sets will be given in Section III. Othertypes of signals, such as helicopter noises, rolls of thunder,or teleseismic events, cannot be discriminated using this soletime-related information. For these, recognition criteria can befound in the timefrequency domain.

B. TimeFrequency Analysis (ARCAP Method)To interpret the spectral information contained in nonsta-

tionary signals, one needs a timefrequency analysis. In orderto do this, a possibility is to perform spectral analysis over atime window gliding along the signal with a local stationarityhypothesis [2]. If a detailed analysis versus time is needed,it must be performed over a short time window. In thatcase, Fourier analysis is often inadequate, as its resolutionis insufficient. For example, a Hanning time window of 1s gives a 1.5-Hz frequency resolution, which is defined asthe equivalent noise bandwidth [7]. That proves insufficientfor our application. The drawbacks of methods based on theFourier transform have been highlighted in [8]. As our finalaim is to use the analysis results in a decision process, wealso wanted the selected method to reduce the amount ofinformation in order to make the decision process easier. The


(a) (b)Fig. 2. Envelope modelization for earthquake discrimination. (a) Original signals: earthquake (top) and two avalanches (middle and bottom). (b) Smoothedenvelope (dotted line) with W equal to 0.1 times the length of the effective signal, estimated earthquake model (solid line), and corresponding distanceparameter d. The bottom signal shows an example where a good fit is obtained, although the signal is not an earthquake.

auto-regressive (AR) method, which estimates only a givennumber of frequency components, offers a good reduction ofinformation and has a high-frequency resolution. Its varianceis less than that of Fouriers method [9], and it directlyprovides the signal frequencies, whereas with the Fouriermethod, they must be derived from the numerous peaks ofthe estimated Fourier spectrum. However, the AR methodis a poor amplitude estimator, and it must thus be coupledwith another method. The use of Capons method togetherwith the AR method offers two major advantages. First,Capons estimator is a very good power estimator, whichmakes up for the bad amplitude estimation of the AR method.Second, it provides, with few additional computations, areliable frequency filtering. This filtering is used to improvethe performance of the polarization analysis method that willbe presented in Section II-C. The resulting ARCAP methodis a combination of the autoregressive (AR) and Caponsmethods, which combines the advantages of both methods.Its variance is less than the one obtained with a Fouriertransform method. To sum up, using the ARCAP method is aconvenient and efficient way of combinating timefrequency

and polarization analysis. The AR modelization leads to aconsiderable reduction of the amount of data to interpret,which is particularly interesting with a view to classifyingthe signals. That is, the timefrequency information is easilyextracted from the analysis results. The use of Capons methodis a way to make up for the low precision of the ARamplitude estimator. The ARCAP method proved to be a goodcompromise between nonmodel methods and methods usingmore sophisticated models. We first present a brief descriptionof the ARCAP method. We then explain how the results canbe used to estimate the evolution versus time of the dominantsignal frequencies. Finally, we list the features derived fromthe timefrequency analysis.The ARCAP timefrequency analysis method [2], [6] uses

a combination of autoregressive and Capons methods on agliding time window of length . Letbe the signal to analyze, let and , withto , be a signal window of length beginningat sample , where is the gap in samples betweentwo consecutive windows. Parameter is thus the windownumber. The signal is assumed to be stationary inside this


window. It can be modelized as the output of a linear filterwith white noise input

(8)where is the filter order, and the parametersare the filter coefficients for this signal window number .Let be the vector of the coefficients, and let the

correlation matrix of estimated by theforwardbackward covariance method. is estimated byminimization of the prediction error power

(9)where denotes the transposition operator. The least squaresmethod is used to compute the AR parameters. The estimationof the signal frequencies derives directly from those coef-ficients. Let be the th of the complex conjugatesolutions (poles of the AR model) of the equation

(10)

The s are characterized by their modulus andtheir phase . The signal window is assumed to be acomposition of signal frequencies plus noise. The signalfrequencies correspond to the s whose moduli are closeto one, that is to say, located near the unit circle in the complexplane [10]. They are estimated by

(11)

where is the sampling frequency. On the other hand, thepoles related to noise are randomly distributed inside a discof radius that is small compared with one, depending on theSNR. The corresponding frequencies can be rejected as theyare not part of the signal components.Once a signal frequency has been estimated using

the AR method on the th signal window, the associatedpower is estimated using Capons method [4]. It is based onthe estimation of a finite impulse response filter of orderwith two constraints: gain at frequency equal to one andminimal power contribution from the other frequencies.Let be the correlation ma-trix of the signal window , let be the

filter coefficients vector, and let. The power at fre-

quency is then estimated by [11], [15]

(12)

The corresponding filter coefficients can be estimated with fewadditional computations as

(13)

is called the ARCAP timefrequency representa-tion of signal . The time information is provided by the

window number , whereras the frequency information isgiven by frequencies .The parameters of ARCAP analysis are (length of the

sliding time window, inside which the signal is assumed tobe stationary), (shift between two windows), andand (orders for AR and Capons method, respectively).Because of complex conjugate symmetry of the poles,

frequencies can be estimated with an -order ARmethod. Thus, must be at least equal to twice the numberof expected signal frequencies. If the SNR is small, onemust increase the order to take the noise frequencies intoaccount. Of course, for our application, we do not know thea priori number of frequency components in a given seismicsignal. A solution is to estimate the AR order automaticallyfor each signal using, for example, Akaikes AIC criterion [1].This criterion is based on the prediction error. Other criteriatest the whiteness of the filter output [17]. The problem isthat from one window to another, the estimated order variesa lot. This can make the final choice of the analysis ordervery difficult. For our signals, the average order provided bythese criteria varies from 4 for narrowband signals, such asteleseismic events, to 14 or 16 for broader band signals (e.g.,avalanches or thunder). Once again, our current priority issignal recognition, and we have thus chosen for simplicityto set the AR order to 10. This proves sufficient for us toallow a correct estimation of the frequency content of thesignal and, hence, a satisfactory decision. On the other hand,there is no optimal value for . The larger is, thebetter the estimation. The choice of is limited byfor the statistical estimation of . However, beyond acertain value, the result is not much improved, whereasthe computation of becomes too long. For our signals,a value of between 16 and 20 offers a good com-promise.Unlike methods based on Fourier transform or wavelet

decomposition, which produce matrix pictures, the ARCAPmethod describes the timefrequency content of a signal inthe form of a cloud of points (examples will be presentedin Section IV). That is, only the dominant frequencies ofeach signal window appear. This type of representation iswell adapted to extract the timefrequency components ofthe signal and estimate their variations. This is done byfollowing up the poles with moduli close to one accordingto the time axis. The problem is thus to link the points of theARCAP picture automatically from one window to another.In order to do this, we have developed a simple nearest-neighbor method. First, a global ARCAP analysis is performedover the whole signal. For each window, the number andthe frequency of the signal components is determined. Themaximum number of signal components is the a priori numberof components in the signal. Then, for each window, eachestimated frequency is assigned to the nearest component. Thedifficulty is that many particular cases can occur, for which achoice has to be made in the algorithm. If there is a shorttime interval where no dominant frequencies are found, apolynomial interpolation of the components is made. If thefrequency gap between two consecutive values of the samecomponent is larger than a given threshold, then one considers


that they actually represent two different components. Thistechnique works well if the spectral content of the signaldoes not vary too quickly from one window to another andif the components are not too close to each other, which isgenerally the case for our signals. Nevertheless, for highlynonstationary signals, or signals with poor SNR, followingup the poles can be difficult, and it might prove impossibleto get a reliable description of the frequency componentsevolution versus time for the signal. Studies are being carriedout to check whether alternate methods based on trajec-tory modelization (e.g., Kalman filtering) could give betterresults [18].Once the timefrequency components have been extracted

from the ARCAP picture, features of the signal spectral contentare derived:NBCOMP number of extracted timefrequency compo-

nents.For each component, the mean frequency is calculated. The

components are then numbered from 0 to NBCOMP-1 inascending mean frequency order. The obtained features areMFRQ mean frequency of the th extracted

timefrequency component;NPTS number of windows for which a frequency has

been assigned to the th component.It is also of great utility for us to estimate whether a giventimefrequency component tends to increase versus time or,rather, to decrease or remain stable, especially for the lowesttimefrequency component. The trend of a given curve isgenerally difficult to estimate unless it is quite monotonous. Inorder to reduce the amount of information, the time axis is splitup into a small number of intervals (e.g., five intervals). Oneach interval, the mean frequency value of the component isestimated. The sign of the difference between two consecutivevalues allows estimation of its local frequency trend: increase,decrease, or stability. If the difference is less than a giventhreshold (typically 0.5 Hz), we consider that the frequencyremains stable. Thus, four features are obtained if five intervalsare used:VARF00, VARF01, VARF02, and VARF03: frequency vari-ation of the lowest timefrequency component from oneinterval to the other.

This simple method allows a good estimation of the globaltrend of a timefrequency component versus time. If weeventually decide to use Kalman filtering for following up thepoles of the ARCAP picture, the parameters of the Kalmanfilter might produce interesting information about the trend ofthe timefrequency components. Finally, two additional signalfeatures are derived from the timefrequency domain:F BEG mean frequency of the lowest component es-

timated on the first two seconds of effectivesignal;

F MAX mean frequency of the lowest component es-timated around the moment when the signalreaches its maximum amplitude. This moment iscalculated on the channel for which the distancebetween the envelope and the earthquake modelis minimal.

Those two features are very useful to detect -wave/ -wavefrequency patterns of local earthquake signals (see Section III).

C. Linear Polarization Detection in the TimeFrequency PlaneFor some applications, such as seismology, a multicompo-

nent signal is provided by the instrumentation, for example,one signal versus time for the vertical motions ( component),one for the WestEast motions ( component), and one forthe NorthSouth motions ( component). One can considerthese signals separately and perform an ARCAP analysis oneach component. Still, we lose a lot of interesting informationabout the signal. As a matter of fact, the componentsand are not completely independent: When a signal emergesfrom background noise, the motions along the three main axisare correlated. Several techniques can be used to detect rela-tionships between the components: correlation (time domain),coherence (frequency domain), or polarization (space domain).As for us, an interesting fact is the localization of the

linearly polarized waves in the timefrequency plane. Thiscan easily be derived from the previously performed ARCAPanalysis. The vertical channel can be considered to bethe most significant component for spectral analysis becausethis channel is not dependent on the arrival direction ofthe seismic waves. The principle of the proposed methodis thus to determine for each time window the frequencycomponents using the vertical channel signal with the ARmethod. Then, each channel is filtered at each detected fre-quency using Capons method. Finally, a linearity criterionis estimated from the three-component filtered signal, and itspolarized nature is checked using a simple, original method.Let be a three-component signal time window of length beginning atsample , where is the vertical component. Vector

represents the position of the moving pointat a given date with respect to a fixed reference pointfor the th signal window. An ARCAP analysis is performedon , as described in Section II-B, in order to estimatethe signal dominant frequencies . Then, for each ,the Capons filters (one filterper channel) are estimated, and the associated filtered signals

are calculated. The polarization researchis performed using these filtered signals in order to enhance theSNR. To decide whether the filtered three-component signalwindow is linearly polarized at frequency a linearitycriterion is estimated, followed by a check of the polarizednature of the wave.Let be the matrix defined by

(14)

where is theposition vector. is a positive symmetrical matrixwith eigenvalues andrespective eigenvectors and .A linearity criterion is directly derived from the


eigenvalues

(15)

where represents the linearity distribution in thetimefrequency plane in the form of a cloud of points asthe ARCAP method does for the power distribution. For acircular motion, one has . If the motion is actuallyalmost linear at frequency , thenand , and thus, . In practice, if islarger than a given threshold close to one (e.g., 0.8), the motioninside the th signal window is considered to be linear atthe corresponding frequency , i.e., the points are globallyelongated along vector . This allows us to estimatethe azimuth and inclination with respect to the horizontal planefor the incoming linear wave. This is, however, insufficient toconclude that the signal inside the window is actually linearlypolarized at frequency . As a matter of fact, the ends ofthe vectors can form an elongated set of pointswithout the motion actually being polarized. The polarizationstate of the signal must thus be checked. This can be doneusing, for example, coherence information or interspectralmatrix decomposition [14], [21]. We propose an alternate,very simple method, which uses the previously calculatedeigenvector to check whether the signal in the thwindow is actually polarized at frequency or is just anunpolarized, elongated set of points. This method allows us tolocate the linear wave precisely inside the signal window, thatis, to estimate its onset moment and duration. It is based onthe following principle: The linear polarization of the signalis actual only if all the motions are directed along the maineigenvector . A simple way of checking this pointis to estimate the angle between and themotion vector .If the motion is actually linearly polarized, and

stay parallel, and thus, . Thevalue of can easily be estimated to be

(16)

where is the direct product operator. The linearly polarizedparts of a real signal are thus identified by a plateau of valueclose to one in the curve . Note that for areal signal, a few values of close to zerocan appear even if the motion is well linearly polarized. Theycorrespond to the ends of the trajectory, where the length of theposition vector is close to its maximum value, and the motionslows down and reverses. They do not denote a change in thepolarization state. The position of the first plateau gives anestimate of the onset date of the polarized wave. The positionof the last one allows us to estimate the length in samples

of the linearly polarized motion. An example ofthis polarization study will be presented in Section II-D. Inpractice, we will consider that the motion inside the th signal

window is actually linearly polarized at frequency if

(17)

where is the estimated length of the linear motionat frequency in window number , and is the samplingfrequency. This means that at least one complete periodicpattern must be described by the position vector to considerthat the linear polarization is significant. Otherwise, the lin-ear polarization is nonsignificant, and the linearity parameter

is set to zero.The aim of detecting the linearly polarized waves in the

timefrequency plane is twofold. First, the azimuth of theselinear waves can be used to localize avalanche events ap-proximately with one single three-component sensor, whichis very interesting for our application. Second, polarizationinformation is likely to provide additional recognition criteriafor signals with typical timefrequency polarization patterns.For example, significant linearly polarized waves in thebeginning of earthquake events are easily detected by thismethod.

D. A Comparison of Fouriers and CaponsFrequency Filtering MethodsIn the previous section, we have proposed to filter the signal

windows using Capons method in order to enhance the SNRprior to polarization analysis. Since parameters are derivedfrom the filtered signal at frequencies (linearity andlength of the polarized wave), it is of prime necessity thatthe filtering is reliable. Another simple, classical possibilitycould be to use a Fourier bandpass filter centered atinstead of Capons filtering method. The question is thus: Isit worth using Capons filtering instead of Fouriers? We aregoing to show that Capons method provides a more reliablefiltering than Fouriers. When a Fourier bandpass filter is usedto filter a signal at a given frequency, the choice of both theshape and the bandwidth of the transfer function is alwaysdifficult. If the bandwidth is too narrow, the impulse responseof the filter is too long, and thus, the beginning of the incomingpolarized waves cannot be well detected. In addition, a Fourierfilter is based on an explicit sine and cosine decomposition ofthe signal (complex exponentials) and is not dependent on thedata. Thus, it will tend to find a polarized (linear or elliptical)motion at any frequency if the filter bandwidth is narrow, butthis polarization might have no physical reality. Even in abackground noise signal, almost perfect linear and ellipticalmotions can be detected at any frequency with a narrowbandfilter. Capons filter, on the other hand, is adapted to the signal.The user must choose the order of the filter, that is, the lengthof the impulse response, but the transfer function is calculatedfrom the input signal according to the filter constraints. Dueto this adaptation, Capons filter is more efficient is rejectingunwelcome frequencies than a Fourier filter with comparablefrequency resolution.An example is shown in Fig. 3. This input three-component

signal of length 1.28 s [Fig. 3(a)] is composed of a 13-Hzlinear motion beginning at s added to white noise and


to another linear motion of 11 Hz frequency beginning ats. The 11- and 13-Hz linear motions are perpendicular. Thesampling frequency is Hz. We want to extract the13-Hz linear motion from the input signal in order to estimateits onset moment. The SNR is about 3 dB. In order to do this,a Capon filter of order and a steering frequencyof 13 Hz is used. The associated frequency resolution is

Hz. The transfer function of the Fourier filter usedfor comparison is a Gaussian curve centered at 13 Hz and witha 5-Hz width. The result of the Fourier filtering operation isshown in Fig. 3(b). The Fourier filter is unable to eliminate the11-Hz component efficiently. The first part of the signal hasa very clear sinusoidal aspect, and the 11-Hz linear motion iswell visible on the diagram. On the other hand, when a Caponfilter is used [Fig. 3(c)], the 11-Hz component is much betterrejected, even though the frequency resolution is the same. Thefirst part of the signal is not linear, the filtered motion is morelinear, and the beginning of the 13-Hz motion at sappears to be much better.In Fig. 4, the method proposed in Section II-C for esti-

mating the onset moment of the linear wave is used on thefiltered signals produced by both methods. With the Fouriermethod (left), the emergence of the 13-Hz linear wave is veryprogressive: According to the curve derived from(16), the linear motion seems to start before s.With the Capon method (right), the distinction between thefirst half of the signal, where the power at 13 Hz is small,and the second half, where the 13-Hz linear wave emerges, ismuch sharper and is easily visible on the curve.The first plateau with a value close to 1 actually starts at

s, which is the right onset moment of the 13-Hzlinear wave.As a conclusion, Capons filtering method offers two major

advantages over Fouriers when the filtering context is difficult(small SNR). First, the user does not have to choose theshape of the transfer function explicitly: only the lengthof the impulse response. Second, due to its adaptation tothe input signal, Capons filter is more efficient in rejectingunwelcome frequencies than a Fourier filter with a similarfrequency resolution. The quality of the filtered signal isbetter with Capons method, which is a great advantagewhen a polarization study is carried out on the filtered sig-nal.In this part of the paper, we have described an original

way of combinating timefrequency and polarization analysisand a simple method to check the linear polarization of agiven signal. The existing ARCAP method is used to estimatethe spectral content of the signal and its evolution versustime. The AR method provides the frequency components ofthe signal. At present, these are estimated using the verticalchannel, which is considered a priori as the most significantchannel, but we can propose an alternate procedure thatis currently being studied. The principle is to perform aneigenvalue decomposition of the covariance matrix of theunfiltered three-component signal. If this decomposition showsthat there are one or two privileged directions for describingthe energy distribution of the signal, a solution is to estimatethe dominant frequencies according to that direction or plane

by projection of the original three-component signal. Once thedominant frequencies have been calculated, Capons methodprovides the power and the filtered signal at each component.We have shown that Capons frequency filtering methodis more reliable than Fouriers. The properties of Caponsfilter are to be more precisely investigated in a near futurebecause this filter may have some interesting applications.A linearity criterion is estimated on the filtered signal. Thepolarized nature of a detected linear wave is checked usinga projection of the motion vectors on the first eigenvector.This combination of several methods is an efficient wayof merging timefrequency and polarization analysis withgood performance: high resolution in time and frequencyand power and reliable filtering to improve the SNR priorto polarization study. It must be noted that computationalexpense was not our priority for this study. The ARCAPmethod needs two matrix inversions and several matrix mul-tiplications for every windowed segment, the calculation costis thus nonnegligible. The complete analysis of a 1-s timewindow takes about 1 s on a personal computer equippedwith a 486DX processor. Now that the proposed recognitionmethod has been used satisfactorily in an operational contextfor the discrimination of avalanche seismic signals, we aregoing to consider reducing computational cost using, forexample, recursive AR methods and optimal matrix inversionfunctions.

III. APPLICATION TO SEISMIC SIGNAL CLASSIFICATIONThe key point of our experiment is to decide whether a

seismic signal detected by the instruments has been producedby an avalanche or not. We have failed in finding distinctivecriteria for avalanches because their behavior in the time,frequency, and polarization domains is extremely varied fromone signal to another. Other types of signal, however, suchas earthquakes, teleseismic events, helicopter noises, blasts,or footsteps, often have typical characteristics in one orseveral of those domains. Our process is thus the eliminationof nonavalanche signals rather than actual recognition ofavalanche signals. In order to do this, we need to estimatepertinent signal features in each domain, the fusion of whichenables us to make a decision. When we started this study,we did not have a large enough collection of unambiguouslyidentified signals, particurlarly avalanche and thunder andhelicopter signals. We thus could not use statistical, Bayesian,or neural approaches for solving this data fusion problem.We therefore decided to use our knowledge of the generatingprocess of each type of event to set up recognition rules. Ouraim is to reproduce the reasoning of an expert confrontedwith the problem of identifying a given, unknown signal.The expert links the characteristics of the signal with hisown knowledge of generating processes and seismic wavepropagation to make a decision about the origin of the signal.We first present basic elements about fuzzy sets, decision rules,and credibility factors. Then, we list all the features derivedfrom the analysis results and give, for each type of signal, therelated decision rules. Finally, we present how these rules arecombined and how the final decision is made.


(a)

(b)

(c)Fig. 3. Comparison between Fouriers and Capons methods for signal filtering at a given frequency. (a) Three component synthetic signal of length 1.28 s(128 samples): a 13-Hz linear wave of amplitude 100 emerges at t = 0.64 s. An 11-Hz linear motion of amplitude 50 plus white noise is added to whole signalwindow. The RSB is about 3 dB. (b) Fouriers filtering around 13 Hz with bandwidth of f = 5 Hz. (c) Capons filtering at 13 Hz with order Mc = 20.

A. Dealing with Imprecision and Uncertaintyin the Decision ProcessFuzzy sets [23] allow modelization of imprecise linguistic

terms such as large, short, and high to take into accountthe variety of behavior of the signals inside a given class.

Let be a variable and a linguistic term referring to. In binary logic, the elementary proposition is can

only take two values: 1 (true) or zero (false). This does notrepresent the subtlety of reasoning of a human expert, whomight consider that, for example, is almost or is


Fig. 4. Estimation of the linear wave onset moment. Comparison of Fouriers (left column) and Capons (right column) filtered signals. The signals arethe ones obtained in Fig. 3. (a) Compared hodograms. (b) Compared filtered signals. (c) Length of the position vector V13Hz

(n) versus time. (d) Absolutevalue of the cosine of the angle (n) between the main eigenvector V1

of matrix M (13 Hz) and the motion vector dV13Hz

(n) versus time. Theplateaus with values close to one allow to localize the linearly polarized motions.

a little bit . Fuzzy logic modelizes using a so-calledmembership function of variable . To each value of isassociated a value ranging from 0 (false) to 1 (true),representing the so-called truth value of proposition is .

Any intermediate value of indicates that the propositionis neither totally true nor totally false. is called a fuzzy set.The truth values and of two elementary propositions is and is can be combined using operators to


estimate the truth value of more complex propositions such as( is ) AND ( is ) or ( is ) OR ( is ). The greatvariety of combination operators is surely the main differencebetween the probalistic (Bayesian) approach and the fuzzymodel for data fusion. Fuzzy combination operators allow us toreproduce various types of reasoning. A detailed comparisonand classification of information combination operators canbe found in [3]. Conjunctive operators allow us to modelizesevere behaviors. T norms such as the functionare conjunctive operators that generalize intersection of fuzzysets (i.e., the logical AND operator). Compromise operators,such as mean operators, express cautious behaviors. Finally,disjunctive operators modelize indulgent decision behavior. Tconorms such as the function are disjunctiveoperators used to represent the union of fuzzy sets (i.e.,the logical OR operator). For simplicity, we use only threecombination operators: the min function, which is the leastsevere T norm; the max function, which is the least indulgentT conorm; and the arithmetical mean for thecompromise operator. Finally, the complementation operator

allows us to estimate the truth value of is NOT. Using these four operators, we can reproduce various

types or reasoning. These have been chosen for convenience:We have not yet studied the effect of using other operatorsfor the decision system, but this will be done in a nearfuture.In the decision system that is presented in this part of the

paper, we combine the truth values of pertinent elementarypropositions, derived from the signal features, according todecision rules to obtain the truth value of each possibleconclusion about the origin of the signal. All rules withcorresponding fuzzy sets will be described in detail later.The uncertainty about the (sometimes semi-empirical) decisionrules we have set up is taken into account using credibilityfactors [22]. Using this technique, a decision rule can beschematized as

proposition conclusion

where is the truth value of the input proposition. CF, which isthe credibility factor of the rule, is a number ranging from 0 (atotally unreliable rule) to 1 (a totally reliable rule), representingthe confidence one has in the rule. is the truth value of theconclusion, which is calculated as

CF (18)If, in turn, the conclusion of the rule is used to estimate thetruth value of another proposition during the decision process,we will call it an intermediate proposition.

B. Use of a Training Set as a Guide forFuzzy Parameters EstimationWhen Bayesian or statistical approaches are used to solve

a data fusion problem, the constraints, in terms of exhaustive-ness, of the training sample are severe. The choice of operatorsfor combining probabilities is restricted. When working withfuzzy sets, the constraints are not very restrictive, and the useroften needs guidelines to choose the fuzzy sets, combination

operators, and credibility factors that are used in the decisionprocess. All the rules we have set up for identifying a givenrecorded event derive from our physical knowledge of thedifferent seismic generating processes and propagation rules.However, the user must estimate their reliability and define thefuzzy sets that are needed. In order to do this, we have useda population of 308 unambiguously identified signals to guidethe choice of the boundaries of the fuzzy sets. The constraintsabout the representativeness of this training sample areless strong than with statistical or neural methods as it isonly used by the expert as an aid in designing the decisionsystem in addition to the users own physical knowledge.Nine classes can be distinguished among the signals, accordingto their origin. Table I shows the distribution of the classesinside the training sample. It is clear that the avalancheand thunder classes, as well as the helicopter class, are notwell represented, but this is all we can afford if we want tohold a similar population of other signals for validating thesystem. It is this nonrepresentativeness of some classes thatlead us to reject statistical or Bayesian or neural methods atthe beginning of our experiment. This nonrepresentativenessof the training sample is somewhat compensated for by ourknowledge of the physical processes involved and propagationrules. How can this set of signals be used to help definingfuzzy parameters? Let us assume that two classes of signals

and can a priori be distinguished using variable(in our case, is a signal feature or an arithmetical

combination of several features). The principle is to draw adistribution histogram of variable for each class and

from the analysis of all the corresponding signals in thetraining set. If the values of for are completely disjointfrom the values for class , discriminates very well, andbinary logic can be used. However, it often happens that forour application, a given variable does not discriminate well.That is, the distribution histograms for classes andpartially overlap or are close to each other. In that case, itis necessary to define fuzzy sets according to to modelizethis imprecision. The histograms can be used as a gaugeto estimate the boundaries of the fuzzy sets, keeping inmind the nonexhaustiveness of some classes as well as ourphysical knowledge. In the same way, when two variablesare used simultaneously in the proposition of a given rule,two-dimensional (2-D) diagrams can be used in addition tophysical knowledge to determine which combination operatorshould be used and define the fuzzy sets. All the fuzzy setsthat are presented in the next section have been defined usingthis technique and have a trapezoidal shape for programmingconvenience.

C. Decision Rules and Corresponding Fuzzy SetsAll the signal features derived from the analysis results

are gathered in Table II. They will be useful to expressthe decision rules synthetically, and we will refer to themfrequently. We now state, for each type of signal, the decisionrules that are derived from our knowledge and used in thedecision system. For convenience, the rules and correspondingfuzzy sets are gathered in Table III and Fig. 5, respectively.


(a) (b) (c)

(d) (e) (f)

(g) (h) (i)

(k) (k) (l)

(m) (n) (o)

(p)Fig. 5. Membership functions of the fuzzy sets used in the decision process (in order of appearance in the text).

1) Recognition of Blast Signals: From a physical point ofview, a blast is a short, energetic event. These characteristics ofthe generating process are recognized in the associated seismicsignal: a short signal with few amplitude peaks dominatingbackground noise. A few blast signals are longer (these thathave been produced further away from the recording place),but they are still easily recognized. The shortness of the signalis estimated using variable ES ENDES BEG (which is the

duration of the effective signal). The fact that few peaks ofsignificant amplitude dominate is revealed using the steepnessparameter of the cumulated envelope amplitude histogram (seeSection II-A) for each channel, namely, K Z, K E, and K N.Therefore, we can set up a first recognition rule (rule no.1 in Table III). This rule can be considered to be totallyreliable (CF ) as the associated generating process isnot too complex. This reliability can easily be confirmed using


TABLE IDISTRIBUTION OF EACH TYPE OF EVENT IN THE TRAINING SAMPLEUSED AS A HELP TO ESTIMATE THE BOUNDARIES OF THE FUZZY SETS.

THE RELATIVE POPULATION OF EACH CLASS IS EQUIVALENTTO THAT OBTAINED DURING A WINTER RECORDING CAMPAIGN

distribution histograms of (ES ENDES BEG), K Z, K E, andK N, which is not shown here to be concise. Fuzzy sets inFig. 5(a) and (b) are involved in this rule.2) Recognition of Local Earthquakes: Local events are

earthquakes where the epicenter is located less than 200km away from the sensor. The generating process associatedwith an earthquake is more random than that of a blast signal.However, the short travel distance limits the distorsions of thesignal in such a way that local events often have a typicalenvelope shape. We have already presented, in Section II-A,the method for comparing the envelope of a given signalwith a simplified model of the earthquake envelope ( and

waves). The quality of the fit is estimated by deriving adistance parameter for each channel, namely, D Z, D E, andD N. Local events fit the model correctly, and thus, D Z,D E, and D N are smaller than other types of signals. Inaddition, we know that the frequency of the compressionwaves ( waves) located at the beginning of the signalis higher than that of the shear waves ( waves) locatedaround the zone with maximum amplitude. This can easily beestimated using features F BEG and F MAX. Another wayof interpreting this is to say that due to the dispersive effectof the propagation medium, the frequency of an earthquakesignal tends to decrease versus time. This decreasing trendcan be estimated by calculating the mean frequency variationMFVAR0 of the lowest timefrequency component extractedfrom the ARCAP analysis:

MFVAR0 VARF00 VARF01 VARF02 VARF03

These elements can be combined to give the recognition rule.As often happens, one channel to be distorted, depending onthe azimuth of the incoming waves, we will be indulgent whileexaminating the shape parameter. The recognition rule we haveset up is rule no. 2 in Table III. As avalanches can show agreat variety of shape and timefrequency behavior, we must

be cautious and consider this rule to be moderately reliable(CF ). Fuzzy sets in Fig. 5(c)(e) are used for this rule.3) Recognition of Mid-Range Earthquakes: Mid-range

events are earthquakes where the epicenter is about 150 to1000 km away from the recording place. We know that giventhe rather long travel distance, the amplitude of the signal islow, whereas the frequency content is intermediate betweenthat of teleseismic events and that of avalanches. Moreprecisely, the timefrequency components extracted from theARCAP analysis generally show at least one component withmean frequency value below 6 Hz and no high-frequencycomponent. In addition, the frequency decrease due todispersion appears better than for local events because of thelonger travel time. We thus have implemented rule no. 3:working with fuzzy sets in Fig. 5(e)(h). It is more reliablethan the previous one (CF ). The high frequencyfuzzy set will also be used later.4) Recognition of Teleseismic Events: Unlike local events,

teleseismic events are easily identified. These are earthquakeswhere the epicenter is located more than 1000 km awayfrom the sensor. Given the long travel time in complexgeophysical layers causing random changes to the signal, thesignal is often long and distorted. Our knowledge of seismicwave propagation reveals that only low-frequency waves areable to travel such a long way. We will thus use frequencyfeatures to distinguish teleseismic events from other classesof signals. We have built distribution histograms of parameterMFRQ 0 (mean frequency value of the lowest timefrequencycomponent extracted from the ARCAP picture) for both theteleseismic event and avalanche classes. These show thatvariable MFRQ 0 is sufficient for discriminating teleseismicevents in a very reliable way. Rule no. 4, with CF , canthus be set up. It uses the fuzzy set in Fig. 5(i).5) Recognition of Helicopter Signals: These signals are in-

duced by the pressure waves generated by the three-bladedpropeller of helicopters flying in the vicinity of the sensor. Airpressure waves generate seismic waves close to the sensor.The frequency content of the resulting signal is, thus, high(low attenuation and dispersion), that is, the mean frequencyof the lowest timefrequency component (namely, featureMFRQ 0) is high. Since the rotating speed of the propelleris constant, these signals have a distinctive timefrequencycomponent, which is almost perfectly confirmed by analyzingthe helicopter signals in the training sample, where the typicalfrequency is about 19 Hz. Rule no. 5 in Table III is usedto distinguish helicopter signals. It uses the previously definedhigh frequency fuzzy set and the new helicopter frequencyfuzzy set, respectively; see Fig. 5(h) and (j). It is almost totallyreliable, and thus, CF for this rule.6) Recognition of Thunder Signals: Like helicopter sig-

nals, thunder signals are produced by air pressure wavestransmitted to the ground. However, these are more energetic,and distant thunderclaps can thus be recorded. Numerousacoustic echoes are produced so that the travel distance ofthe seismic waves varies greatly. Consequently, the obtainedseismic signal is rather long and made up of well-separatedseismic phases (jerky aspect) with a broadband frequencycontent. The bandwidth of the signal can be estimated


TABLE IILIST OF THE SIGNAL FEATURES (LABLES AND DEFINITION) DERIVED FROM THE ANALYSIS IN BOTH TIME AND TIMEFREQUENCY DOMAINS

by calculating the difference MFRQ between the meanfrequency for the lowest timefrequency component extractedfrom the ARCAP picture (namely, feature MFRQ 0) and thatof the highest (namely, MFRQ p, where NBCOMP-1is the number of the highest extracted component). We havenot estimated a feature for specifically quantifying the jerkyaspect of a signal. However, we propose to use the followingvariable:

PWINNPTS

ES ENDES BEG-L

where is the duration of the gliding window used for thetimefrequency analysis, and is the time lag between twoconsecutive windows. PWIN 0 thus represents the proportionof windows for which a frequency has been assigned to thelowest timefrequency component MFRQ 0. For a thundersignal, the points in the timefrequency distribution are spacedout, and thus, PWIN 0 is smaller than for other types of signals(like avalanches) that are more compact according to thetime axis. As the spectral content of a thunder signal variesaccording to the distance between the source and the sensor,we will be cautious and adopt a compromise behavior. Thecombination of variables MFRQ and PWIN 0 is actuallyable to recognize thunder signals quite efficiently using ruleno. 6 and fuzzy sets in Fig. 5(k) and (l), referring to variablesPWIN 0 and MFRQ, respectively.

7) Recognition of Avalanche Signals: The behavior ofavalanche signals in either domain varies a lot from onesignal to another, depending on the characteristics of boththe avalanche and the transmission medium, as well asthe propagation distance. Still, we know that avalanchesgenerally have a rather homogeneous envelope (unlike blast-type signals) and do not fit the earthquake envelope modelcorrectly. In that case, we will say that the signal is likelyto be an avalanche according to its envelope shape. Thecharacteristics of the envelope can be slightly different oneach channel, and we will thus be cautious and adopt acompromise behavior to deal with this temporal information.Rule no. 7, using fuzzy sets in Fig. 5(m) and (n), can be set up.It gives an intermediate proposition that will be used later withcomplementary information. As this rule is an intermediaterule, defining what we call an avalanche envelope shape,the associated CF is 1.0.Additional information can be used. Avalanche signals

are more compact in the timefrequency plane than othersignals, such as thunder or footsteps. That is, their bandwidthis less broad, and the points in the ARCAP picture are lessspaced out. This timefrequency criterion can be combinedwith the envelope information to give rule no. 8. In additionto the intermediate proposition produced by rule no. 7, this ruleuses fuzzy sets in Fig. 5(o) and (p). These properties have beenobserved for most of the avalanche signals. The credibilityfactor assigned to this rule is 0.8 to take into account the


TABLE IIILIST OF THE RECOGNITION RULES IMPLEMENTED IN THE DECISION SYSTEM, WITH CORRESPONDING CREDIBILITY FACTORS (CF).

THE SIGNAL FEATURES AND FUZZY SETS THAT ARE USED ARE DESCRIBED IN TABLE II AND FIG. 5, RESPECTIVELY

fact that a great variety of behavior is, however, likely foravalanche signals.8) Recognition of Footsteps Signals: Footsteps signals

show a great variety of temporal shapes, depending on theproximity and behavior of the source. Some are as short asblast signals, and others are long, jerky signals that surprisinglyresemble thunder signals. However, given the small distancebetween the source and the sensor, the frequency content of theresulting signals is always much higher than that of avalanchesignals. Footsteps signals are thus easy to distinguish fromavalanche signals but not from other classes of nonavalanchesignals (e.g., blasts or thunder). We have tried to set up rulesfor recognizing footsteps signals specifically, but these provedunreliable, given the variety of these signals. However, veryfew footsteps signals are recorded apart from those producedduring our technical inspections because the equipped site isquiet and a long way from paths and animals. As footstepssignals are well discriminated from avalanche signals (thisis our main aim), this lack of specific recognition rules isunpleasant but not very awkward in practice.

D. Final DecisionAll the rules described in the previous section are gathered

in a base of rules separated from the program. The rules arestated using quasinatural language and are easily modifiable ifnecessary. A fuzzy logic inference driver has been programedto perform information combination according to the rules.This driver may, of course, be used in other applications than

automatic recognition of avalanche seismic events. We justhave to modify the base of rules. When the whole decisionprocess has been carried out, we obtain the truth valuesassociated with all the possible conclusions: blast, earthquake(local, mid-range, or teleseismic event), and helicopter, as wellas thunder, footsteps, or avalanche. In most cases, two or three(rarely four) conclusions are proposed with a nonzero truthvalue, and a choice has to be made. When one truth valueis far greater than all the others, the associated conclusionis the final choice. When the two greatest truth values areclose to each other (a difference less than 0.1 for example),one is in a situation of conflict. Some conflicts can beresolved by examinating the reliability of each informationelement according to the experts knowledge. For example,when a conflict between the local event and avalancheconclusions appears, the system examines the truth valuesconcerning the envelope shape of the signal [see the fuzzysets in Fig. 5(c) and (n)] to remove the ambiguity because thistemporal information is known to be more reliable than thetimefrequency information. For a few signals, however, theconflict remains, and we must consider this uncertainty as partof the decision process.

E. ExamplesFig. 6 shows an example of automatic identification of three

previously identified signals: two avalanches and a mid-rangeearthquake. The truth value of the input fuzzy propositions arelisted. From these fuzzy criteria, a conclusion is proposed by


the expert system. The corresponding ARCAP timefrequencypower representations are shown on Fig. 7. The signal on topof Fig. 6 is well recognized as an avalanche signal due to itsshape and its timefrequency behavior (limited frequency bandand well-grouped points along the horizontal axis). No otherdiagnosis is proposed. For the middle signal (earthquake),two diagnoses are proposed: mid-range earthquake (due tofrequency decrease and low mean amplitude) and avalanche(the signal has an avalanche shape, its band is limited, andthe points are relatively well grouped). As the truth valuerelated to the earthquake conclusion is far greater, the finaldecision is earthquake. On the other hand, the bottom signal(avalanche) is a situation of conflict. The shape of the signaland its timefrequency behavior tend to favor the avalancheconclusion. However, the points are not well grouped alongthe horizontal axis, and the frequencies in the top componentare slightly higher than the typical frequencies of avalanchesignals. Thus, the system is not able to decide whether thesignal has been produced by an avalanche or a roll of thunder.However, as this signal was recorded in January, soon aftersnowfalls, the user will eventually lean toward the avalanchediagnosis.

F. PerformanceA population of 280 other previously identified signals has

been used to validate the system and estimate its perfor-mance. The population of each class is equivalent to thatof the training sample. Out of 13 avalanche signals, 12are unambiguously recognized as such by our system, andone jerky, high-frequency avalanche signal is identified as athunder signal. Out of the 267 nonavalanche signals of thevalidation sample, only nine have been erroneously identifiedas avalanches by our system: three local events (out of 44such signals), five mid-range earthquakes (out of 26), and onehelicopter signal (out of nine), which was in conflict with thehelicopter class. None of the 188 blast signals, teleseismicevents, footsteps, or thunder signals has been identified asan avalanche. The global success rate for our system is thusabout 96%, although the representativeness of some classesin both training and validation samples is questionable. Blastsand teleseismic events are well discriminated by our systemas the criteria and rules concerning those types of signals arewell known and reliable. Thunder, footsteps, and helicoptersignals are quite recognizable as well. On the other hand, wehave difficulty in discriminating avalanches from some localor mid-range, small, noisy earthquakes. It must be noted that inthe past, the sensor was located only 150 m away from a smallroad that was frequently cleared by snowplows after snowfalls.In addition to the vibrations produced by snow chains and ablade scraping off the snow, snowplows dump the removedsnow into a ravine, thereby producing small avalanches that arerecorded as well. For two years, we tried to set up recognitioncriteria for this type of event, based on frequency content andazimuth distribution of the detected linear waves. However,the results remained unsatisfactory as these signals are almostidentical to avalanche signals, and the azimuth of the road isidentical to that of an avalanche prone zone. We eventually

decided to move 200 m further away from the road in order toavoid recording such unwelcome and not easily recognizableevents.

IV. CONCLUDING REMARKSWe have proposed an original way of combinating several

original or pre-existing signal analysis methods with fuzzylogic and credibility factors in order to discriminate differenttypes of signals with maximum information. Three domainsare involved in the signal analysis: time, timefrequency, andpolarization. In the time domain, two original methods havebeen proposed to discriminate some types of signals accordingto their envelope shape. In the timefrequency domain, theARCAP method is used to perform a timefrequency analysisof the signal. A simple method has been presented to extracttimefrequency components from the ARCAP analysis. In thepolarization domain, we have proposed to use Capons filteringmethod prior to polarization analysis,. and we have highlightedthe superiority of this method over Fouriers narrow-bandpassfilter. The proposed method allows us to localize the linearlypolarized waves in the timefrequency plane. A simple methodhas been proposed to check the linear polarization of a signaland estimate the duration of the linear motion.An application of this timefrequency polarization analysis

method to the recognition of avalanche seismic signals hasbeen presented. Signal features are derived from the analysis todescribe the signal in both time and timefrequency domains.As our collection of unambiguously identified signals is notwell representative, statistical or Bayesian or neural methodscould not be used to perform automatic classification ofthe signals. We thus decided to combine the signal featuresaccording to specific rules, these rules being derived from ourexpert knowledge of the generation and propagation of seis-mic waves for each type of event. Fuzzy logic and credibilityfactors provide a flexible theoretical frame for modelizing im-precision and uncertainty in the decision process. A populationof previously identified signals is used as an aid to estimatethe boundaries of the fuzzy sets and the credibility factors, inaddition to the experts physical knowledge. This approach canbe used in other problems of automatic identification, when arepresentative training set is not available and can be made upfor by physical knowledge.The presented application works satisfactorily in preoper-

ational conditions in one of the two instrumented sites sincethe Winter of 19941995. Seismic detection provides a farmore reliable estimation of avalanche activity than visualobservations [12]. Our system will improve our knowledge ofthe evolution of avalanche activity versus time and allow usto validate deterministic models for avalanche prediction. It isthe first actually operational system for automatic estimationof avalanche activity. An alternate solution lies in acousticdetection of avalanches [5], which leads to a similar problemof signal identification. However, this approach seems to beessentially suitable for big avalanches. A detailed review ofadvantages and drawbacks of seismic detection, as well asoperational results, is presented in [13]. We are currentlystudying the possibility of localizing the avalanche events


(a) (b)Fig. 6. Three examples of the proposed analysis/decision process. (a) Three-component input signals are two avalanches (top and bottom) and an earthquake(middle). (b) Corresponding output files of our system: truth values of the fuzzy input propositions and proposed conclusions (the final decision is in bold).

using polarization information. Polarization is also likely toprovide additional discrimination criteria when the azimuth ofa well-known source of unwelcome seismic signals is knownor when some types of signals have a typical polarizationpattern in the timefrequency plane. We used to include such

rules in our decision process, but these proved less reliablethan timefrequency rules for our recording site. However,we expect these polarization-related rules to be very useful inthe near future: We plan to carry out experiments of seismicdetection of avalanches at a ski resort. Unwelcome signals


Fig. 7. ARCAP timefrequencypower representation associated with the vertical channel of the signals in Fig. 6: (a) avalanche signal, (b) earthquakesignal, and (c) avalanche signal. The dots are linked using a hhnearest neighborii method in order to reduce the timefrequency information into acouple of unidimensional, easily interpretable curves.

produced by fixed sources such as ski lifts could be eliminatedusing polarization information.In order to improve the performance of our system, further

analysis of unambiguously identified signals will be performedin order to try to find complementary discrimination criteria.The domains to be more closely explored are the ambiguityfunction and the study of the elliptical polarizations. As soonas we get a large enough number of identified events inthe avalanche, thunder, and footsteps classes, we will tryto compare the proposed recognition method with statistical,Bayesian, or neural methods. Our method has the advantageof being easily adapted to new recognition criteria. As therules are expressed in almost natural language, a given userdoes not need to have any knowledge of statistics or neuralnetworks to modify the recognition process. The latter caneasily be adapted to external factors using several bases ofrules. For example, since thunderstorms are unlikely in theAlps in January and February, the user could thus choose to

set the credibility factor of the corresponding recognition ruleto zero during this period. As our recognition system is likelyto be used later on by nonspecialist nivologists, who will haveto adapt it to other sites, this ease of use and modification isessential.

ACKNOWLEDGMENTThe authors would like to thank the reviewers for their

pertinent comments and for their suggestion of including moredetails about the recognition process.

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[3] I. Bloch, Information combination operators for data fusion: A com-parative review with classification, IEEE Trans. Syst., Man Cybern. A,vol. 26, Jan. 1996.

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Benoit Leprettre received the Ph.D. degree fromthe Universite J. Fourier, Grenoble, France, in 1996for his work about seismic detection of avalanches.He set up an automated system for avalanche sig-

nal recognition, two examples of which are installedin the French Alps and are operational. He currentlyworks as a Research and Development Engineer forthe Centre dEtude de la Neige, Meteo-France, St.Martin dHeres, France, and the Centre dEtude desPhenome`nes Aleaoires et Geophysiques, Grenoble.His research interests include automatic classifica-

tion and decision making in uncertain and/or imprecise contexts, nonstationarysignal analysis, and adapted digital filtering.

Nadine Martin received the Ph.D. degree in 1984and the Habilitation a` Diriger des Recherchesdegree in 1994, both from the Polytechnic NationalInstitute, Grenoble, France.Since 1985, she has been in charge of research

with the French Scientific Research Centre (CNRS).Her research interests include nonstationary signalanalysis and timefrequency methods. She is partic-ularly involved in the processing of real signals invarious application domains (acoustics, mechanics,etc.). She is currently working on methodologies

for decision from timefrequency representation and on the diagnostics ofelectrical machines. She is involoved with a coordinated research programon timefrequency within the Signal and Image Processing Group managedby the CNRSDr. Martin was co-organizer of the Fourth European Conference (EU-

SIPCO) in Grenoble in 1988, of the Sixteenth GRETSI Symposium on Signaland Image Processing, in Grenoble in 1997, and of a pre-doctoral course onthe recent advances in signal processing in 1993.

Francois Glangeaud received the Doctor degree ingeophysics.He is Director of Research in French Scientific

Research Centre (CNRS). He is teaches at the EcoleNationale Superieure des Pe`troles et des Moteurs,Paris, France, and he teaches signal processing atthe Centre dEtude des Phenome`nes Aleaoires etGeophysiques, Grenoble, France. He is the authorof the book Traitement du Signal pour Geologues etGeophysiciens (Paris, France: Technip).

Jean-Pierre Navarre graduated in 1970 from theInstitut National Polytechnique, Grenoble, France.Since 1972, he has been working as a Research

Engineer with the Centre dEtude de la Neige(CEN), St. Martin dHe`res, France, which is part ofMeteo-Frances National Centre for MeteorologicalResearch. From 1975 to 1985, he successively dealtwith deterministic models of snow cover evolution,statistical forecast models concerning avalanchehazards or precipitation, and mechanical propertiesof snow. Since 1990, he has been the head of

the CEN Avalanche Research Group, where he has two main researchinterests: modeling of snow cover stability/instability and seismic detectionof avalanches.

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