Automatic P-Wave Arrival Detection and Picking with Multiscale Wavelet Analysis for Single-Component Recordings

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1 Bulletin of the Seismologicl Society of Americ, Vol. 93, No. 5, pp , Octoer 23 Automtic P-Wve Arrivl Detection nd Picking with Multiscle Wvelet Anlysis for Single-Component Recordings y Hijing Zhng, Clifford Thurer, nd Chrlotte Rowe* Astrct We hve developed n utomtic P-wve rrivl detection nd picking lgorithm sed on the wvelet trnsform nd Akike informtion criteri (AIC) picker. Wvelet coefficients t high resolutions show the fine structure of the time series, nd those t low resolutions chrcterize its corse fetures. Primry fetures such s the P-wve rrivl re retined over severl resolution scles, wheres secondry fetures such s scttered rrivls decy quickly t lower resolutions. We pply the discrete wvelet trnsform to single-component s through series of sliding time windows. In ech window the AIC utopicker is pplied to the thresholded solute wvelet coefficients t different scles, nd we compre the consistency of those picks to determine whether P-wve rrivl hs een detected in the given time window. The rrivl time is then determined using the AIC picker on the time window chosen y the wvelet trnsform. We test our method on regionl erthquke dt from the Ded Se Rift region nd locl erthquke dt from the Prkfield, Cliforni region. We find tht 81% of picks re within.2-sec of the corresponding nlyst pick for the Ded Se dtset, nd 93% of picks re within.1 sec of the nlyst pick for the Prkfield dtset. We ttriute the lower percentge of greement for the Ded Se dtset to the sustntilly lower signl-to-noise rtio of those dt, nd the likelihood tht some percentge of the nlyst picks re in error. Introduction Quickly detecting nd ccurtely picking the first P- wve rrivl is of gret importnce in event loction, event identifiction, nd source mechnism nlysis, especilly in the er of lrge volumes of digitl nd rel-time seismic dt. Mnul nlysis of s nd phse picking is timeconsuming nd sujective. There is need to provide more efficient lterntive. Vrious techniques hve een presented in the literture for detecting nd picking the rrivls of different seismic wves from single-component s well s three-component (3-C) recordings. Becuse some seismic sttions cnnot provide consistent 3-C signls, it is importnt to e le to pick seismic rrivls from single-component recordings. Withers et l. (1998) hve ctegorized previous trigger lgorithms for onset picking into time domin, frequency domin, prticle motion processing, or pttern mtching. Some of the current methods include energy nlysis (Erle nd Sherer, 1994), polriztion nlysis (Vidle, 1986), nd utoregressive techniques (Med, 1985; Sleemn nd Eck, 1999; Leonrd nd Kennett, 1999; Leonrd, 2). *Present ddress: EES-11, M.S. D48, Los Almos Ntionl Lortory, Los Almos, New Mexico Autoregressive techniques re sed on the ssumption tht the cn e divided into loclly sttionry segments s n utoregressive (AR) process nd the intervls efore nd fter the onset re two different sttionry processes (Sleemn nd Eck, 1999). On the sis of this ssumption, n utoregressive-akike informtion criteri (AR-AIC) method hs een used to detect P nd/or S phses (Sleemn nd Eck, 1999; Leonrd nd Kennett, 1999; Leonrd, 2). For the AR-AIC picker, the order of the AR process must e specified y tril nd error nd the AR coefficients hve to e clculted for oth intervls. In contrst to the AR-AIC picker, Med (1985) uses different AIC picker, which cn e clculted directly from the records without fitting them with the AR processes. However, when the signl-to-noise rtio (S/N) is low nd the rrivl is not evident, the AIC picker does not perform well. Further, for the AIC picker to identify the proper rrivl, limited time window of the dt must e chosen. We present n ppliction of the wvelet trnsform to guide the work of the AIC picker. The wvelet trnsform hs een used to detect nd pick the rrivl of severl seismic phses. Annt nd Dowl (1997) pplied the discrete wvelet trnsform (DWT) to 3-C s to identify the P- 194

2 Automtic P-Wve Arrivl Detection nd Picking with Multiscle Wvelet Anlysis for Single-Component Recordings 195 nd S-phse rrivls of seismic events y using the polriztion nd mplitude informtion contined in the wvelet coefficients of the signls. Tiulec nd Herrin (1999) used the continuous wvelet trnsform to decompose the Lg signl into different scles, nd pplied threshold detector to the wvelet coefficients t one scle to determine the Lg rrivl time. Gendron et l. (2) jointly detected nd clssified seismic events vi Byes theorem y using fetures extrcted from wvelet coefficients of the records. The wvelet trnsform decomposes the signl t different scles, thus dptively chrcterizing its components t different resolutions. The primry fetures in the signl (phse rrivls) re retined over severl resolution scles nd irrelevnt ones (noise) decy quickly t lrger scles (Duechies, 1992), lthough we note tht some seismic noise will lso e present t lrger scles (e.g., microseisms). We pply thresholding to the wvelet coefficients using the Birge-Mssrt penliztion method to denoise the (Birge nd Mssrt, 1997). Then the AIC picker is used on the penlized wvelet coefficients over multiple scles. By compring the consistency mong the picks t different scles, we cn determine whether there is n rrivl in the current time window. After time window is chosen, we pply the AIC utopicker to the denoised signl reconstructed from the thresholded wvelet coefficients to determine the rrivl time. We test our method on regionl erthquke dt from Ded Se Rift region nd locl erthquke dt from Prkfield, Cliforni region, nd compre the utopicks with nlyst picks. AIC Picker For the stndrd AR-AIC pproch, it is ssumed tht cn e divided into loclly sttionry segments, ech modeled s n AR process, nd tht the intervls efore nd fter the onset time re two different sttionry processes (Sleemn nd vn Eck, 1999). Either the order of the AR process or vlues of the AR coefficients or oth will chnge when the chrcteristics of the current segment of the re different from those of the previous one. For exmple, typicl seismic noise is well represented y reltively low-order AR process, wheres seismic signls grdully require higher-order AR process (Leonrd nd Kennett, 1999). The AIC is usully used to determine the order of the AR process when fitting time series, which indictes the dness nd the unreliility of the model fit (Akike, 1973). This method hs een used in onset estimtion y nlyzing the vrition in AR coefficients representing oth multicomponent nd single-component trces of rodnd nd short-period s (Leonrd nd Kennett, 1999). When the order of the AR process is fixed, the AIC function is mesure of the model fit. The point where the AIC is minimized in the lest-squres sense determines the optiml seprtion of the two sttionry time series, nd thus is interpreted s the phse onset (Sleemn nd Eck, 1999). This pproch is known s AR-AIC picker (Sleemn nd Eck, 1999; Leonrd, 2). The AIC of the two-intervl model for x of length N is represented s function of merging point k (Sleemn nd Eck, 1999): 2 AIC(k) (k M)log(r 1,mx) 2 (N M k) log(r ) C (1) 2,mx 2 where M is the order of n AR process fitting the dt, C 2 is 2 2 constnt, nd r1,mx nd r2,mx indicte the vrince of the in the two intervls not explined y the utoregressive process. To relize the AR-AIC picker, the order of the AR process must e specified y tril nd error, nd then AR coefficients cn e determined y the Yule-Wlker equtions (Hykin, 1996). In contrst to the AR-AIC picker, Med (1985) clcultes the AIC function directly from the, without using the AR coefficients. The onset is the point where the AIC hs minimum vlue. For the x of length N, the AIC vlue is defined s AIC(k) k log{vr(x[1,k])} (N k 1) log{vr(x[k 1,N])} (2) where k rnges through ll the smples. The AIC picker defines the onset point s the glol minimum. For this reson, it is necessry to choose time window tht includes only the segment of interest. If the time window is chosen properly, the AIC picker is likely to find the P-wve rrivl ccurtely. For with very cler onset, AIC vlues hve very cler glol minimum tht corresponds to the P-wve rrivl (Fig. 1). For with reltively low S/N rtio, there my e severl locl minim in AIC vlues, ut the glol minimum still indictes ccurtely the P-wve onset (Fig. 1). When there is more noise thn signl in the, the glol minimum cnnot e gurnteed to indicte the P-wve rrivl (Fig. 1c). Thus, the S/N rtio in the ffects the ccurcy of the AIC picker to some extent. If there re multiple seismic phses in time window, the AIC picker will choose the strongest phse (Fig. 2). On the other hnd, ecuse there will lmost lwys e one glol minimum in time window, the AIC picker will usully pick n onset for ny segment of dt no mtter whether there is true phse rrivl or not (Fig. 3). For this reson, we need to guide the work of the AIC picker y choosing n pproprite time window for it. Wvelet Trnsform The Fourier trnsform is conventionlly used to nlyze the frequency content of seismic signls. Fourier nlysis gives glol representtion of the dt ut cnnot nlyze its locl frequency content or its regulrity. (If the mth derivtive of the signl resemles x x r loclly round x,

3 196 H. Zhng, C. Thurer, nd C. Rowe AIC vlues 11 AIC vlues c AIC vlues Figure 1. Seismogrms nd their corresponding AIC vlues. () For with very cler P-wve rrivl (indicted y thick line), the AIC vlue is very cler minimum point (indicted y n rrow). () For with rther cler P-wve rrivl ut with reltively lower S/N rtio, the AIC function hs mny locl minim, wheres the glol minimum (rrow) still corresponds to the P-wve onset. (c) For very low S/N, there re few locl minim close to ech other. In this cse, the glol minimum (rrow) cnnot e gurnteed to e the P-wve rrivl. then the regulrity p m r with r 1. The signl is more regulr with greter p.) Becuse seismic wves trveling through complex medi re composed of time-frequency-loclized wveforms, it is etter to choose sis tht cn represent the loclly oth in the time nd frequency domins. The wvelet trnsform, which ws ctully initited y work on seismic signls (Goupillud et l., 1984; Grossmnn nd Morlet, 1984), is very useful tool in the nlysis of such nonsttionry signls. The dvntge of the wvelet trnsform over the Fourier trnsform is its ility to chrcterize the structure of the signl loclly with detil mtched to its scle, tht is, corse (low frequency) fetures on lrge scles nd fine (high frequency) fetures on smll scles. The wvelet trnsform hs een used in severl pplictions such s improving the seismic dt resolution nd its S/N rtio (Chkr nd Oky, 1995), compressing seismic dt (Lervik et l., 1996), chrcterizing the singulrity structure of medi (Goudswrd nd Wpenr, 1998), nd seismic dt inversion nd migrtion (Wu nd McMechn, 1998). It hs lso een used to detect P- nd S-wve rrivls in 3-C s (Annt nd Dowl, 1997), to determine rrivl times of the regionl phse Lg (Tiulec nd Herrin, 1999), nd to detect nd clssify seismic events (Gendron et l., 2). The wvelet trnsform hs two forms: continuous wvelet trnsform (CWT) nd DWT (Duechies, 1992). The CWT of function x(t) is defined s:

4 Automtic P-Wve Arrivl Detection nd Picking with Multiscle Wvelet Anlysis for Single-Component Recordings Figure 2. Seismogrm with two phses nd their corresponding AIC vlues. There re cler locl minim (indicted y rrows) with respect to ech phse rrivl (indicted y thick line). The glol minimum indictes the rrivl of the stronger phse Figure 3. Seismic noise dt nd their AIC vlues. The minimum vlue (indicted y n rrow) does not indicte ny phse rrivl lthough it divides the dt into two different sttionry segments. 1 t W (, ) x(t)g dt (3) where g(t) is the nlyzing wvelet, nd nd re the scle nd trnsltion fctors, respectively. The nlyzing wvelet g(t) decys rpidly to zero with incresing t nd hs zero men. The domin (rnge) of nonzero vlues of the wvelet is known s the support, denoted here y K. The scle fctor controls the diltion or compression of the wvelet. At lower scles, the wvelet is compressed nd chrcterizes the rpidly chnging detils of the signl, wheres t higher scles, the wvelet is stretched over greter time spn nd the slowly chnging nd corse fetures re etter resolved. In prcticl pplictions, the DWT is preferred ecuse wveforms re recorded s discrete time smples. DWT cn e implemented quickly vi the Mllt lgorithm (Mllt, 1989). A low-pss filter h nd high-pss filter g re used to clculte recursively the wvelet coefficients {d 1, d 2,...} of discrete time series s, s follows j 1 j s (k) h(l 2k)s (l) l j 1 j d (k) g(l 2k)s (l) (4) l j,..., J 1 where k nd l re the smple indexes, j is the scle prmeter, nd J is the mximum decomposition level. Through the decomposition, the originl signl s cn e represented s {d 1, d 2,...,d J, s J } from which the originl signl cn e reconstructed completely (Duechies, 1992). The wvelet coefficients {d 1, d 2,...}chrcterize the detils, or the fine structure of the signl, t different scles, or resolutions. The coefficients {s 1, s 2,...}represent the pproximtions of the signl t different scles. In sense, the s j coefficients indicte the residuls of the signl fter the high-frequency components t lower scles re removed. In this wy, we cn nlyze the signl t different resolutions. Singulrity Detection with Multiscle Wvelet Anlysis A singulrity t prticulr point of signl is defined s discontinuity in the signl or its derivtives t tht point, which is often chrcterized y the locl Lipschitz exponent (Mllt nd Hwng, 1992). For exmple, signl edges hve zero Lipschitz exponents nd regulr signls possess positive Lipschitz exponents, wheres Gussin noise usully hs negtive one. The chnge of the solute wvelet coefficients over scles depends on the locl singulrity of the signl (Mllt nd Hwng, 1992; Hsung et l., 1999). When point of signl hs negtive Lipschitz exponent, the corresponding solute wvelet coefficients inside the corresponding cone of influence (COI) decy s the scle increses, where the COI is the support of the wvelet function t different scles. The rdius of this cone is less thn or equl to the product K * 2 j, where K is the support nd j is the scle (Fig. 4). However, the solute wvelet coefficients corresponding to regulr signls nd signl edges increse or remin the sme s the scle increses. Tht is, the significnt fetures in the signl re retined over severl scles, wheres rndom noise or other incoherent fetures will dispper t lrger scles. On the sis of such interscle fetures of wvelet coefficients, the noise nd the signl cn e seprted. Usully, P-wve rrivl is chrcterized y rpid chnge in mplitude nd/or the rrivl of high-frequency or rod-nd en-

5 198 H. Zhng, C. Thurer, nd C. Rowe Scle 1 Scle 2 Scle Asolute wvelet coefficients t scle 1 Asolute wvelet coefficients t scle 2 Asolute wvelet coefficients t scle Figure 4. () Cone of influence (COI) of the Duechies wvelet of order 2 (Du2) t scles 1, 2, nd 3. () Seismogrm nd the corresponding solute wvelet coefficients using Du2 wvelet t scles 1, 2, nd 3. ergy. It usully hs positive or t lest zero Lipschitz exponent nd will e retined cross severl scles. This property llows the P-wve rrivl to e detected. Figure 4 shows noisy nd its corresponding wvelet coefficients t scles 1, 2, nd 3. The solute wvelet coefficients corresponding to the P-wve rrivl increse rpidly, wheres those of the noise or secondry fetures decrese or (in this cse) increse more slowly with incresing scle. Wvelet-AIC Picker Detecting nd Picking the P-Wve Arrivl Our wvelet-aic (W-AIC) picker comines the AIC picker with multiscle wvelet nlysis, in which the AIC picker is pplied to solute wvelet coefficients t severl scles (or resolutions). If P-wve rrivl informtion is retined over severl scles, the times picked y the AIC picker t severl scles should e in close proximity to one nother (Fig. 5 c). If there is no P-wve rrivl within time window, there will e significnt differences etween the pick times t neighoring scles (Fig. 5d). By this method, we cn determine whether there is P-wve rrivl. Tle 1 lists pick times t three scles s well s mnul picks, if pplicle, for the s shown in Figure 5. We hve found tht decomposing the s into three scles is pproprite. If more scles re used, the COIs of those singulrities tht re not isolted will hve more overlp nd cuse more miguities. If only two scles re used, however, the singulrity due to the noise will still e significnt t scles 1 nd 2 in some cses, resulting in too mny flse detections. There re numerous wvelet fmilies from which to choose. The min criteri for choosing the wvelet function re its support, symmetry, regulrity, nd numer of vnishing moments (Wickerhuser, 1994). The wvelet function with tighter support hs smller order distortion of the DWT nd COI. In generl, short wvelets re often more effective thn long ones in detecting signl singulrity. So to detect signl discontinuity, the est choice is to use the Hrr wvelet, which hs the support of only 2. However, it fils to detect singulrity in the jth (j ) derivtive. Insted, the wvelet used should e sufficiently regulr with t lest j vnishing moments. For the shown in Figure 5, we use severl wvelet functions from the Mtl Wvelet Toolox 2.2 to test the pick times t scles 1, 2, nd 3. The results re shown in Tle 2. For the sme wvelet, the pick times t different scles re within 16 smples or.32 sec, indicting tht there is significnt feture in this time window. It is noted tht the Symmlet wvelet functions (symmetric Duechies wvelets) give the sme pick times t scles 1, 2, nd 3 s those given y the Duechies nonsymmetric wvelets. Pick times t different scles for other wvelets vry somewht. This indictes the effect of the COI, nd demonstrtes tht the wvelet coefficients cnnot chrcterize the exct position of singulrity, ut region of the singulrity (Mllt nd Hung, 1992; Wickerhuser, 1994). For this reson, we use the wvelet detector to determine whether there is P- wve rrivl in the current time window nd dopt the pick t scle 2 s the preliminry pick. Then the conventionl AIC picker is used on the segment chosen on the sis of the preliminry pick. In our test using the Duechies wvelet of order 2 (Du2), whose support is 4, the mximum rdii of COI t scles 1, 2, nd 3 re 8, 16, nd 32, respectively. Thus we ssume tht picks t scle 1 nd scle 2 within 24 smples nd picks t scle 2 nd scle 3 within 48 smples re consistent. Note tht this criterion gives the worst-cse scenrio tht the theory llows. In prctice, the COI my e quite smll.

6 Automtic P-Wve Arrivl Detection nd Picking with Multiscle Wvelet Anlysis for Single-Component Recordings 199 c AIC vlues t scle AIC vlues t scle AIC vlues t scle AIC vlues t scle AIC vlues t scle AIC vlues t scle d AIC vlues t scle AIC vlues t scle AIC vlues t scle AIC vlues t scle AIC vlues t scle AIC vlues t scle Figure 5. W-AIC picker. For s shown in,, nd c, with P-wve rrivl, picks t different scles re ner ech other. Seismogrm d does not hve n rrivl, therefore the picks re different. P-wve rrivl is indicted y thick line, nd picks t different scles re indicted y rrows. When the S/N rtio is low, the W-AIC picker sed on the rw wvelet coefficients usully detects nd picks n incorrect rrivl time. For this reson, we penlize the wvelet coefficients y soft thresholding, which hs etter mthemticl property thn hrd thresholding (Donoho, 1995). (Let t denote the threshold. The hrd threshold signl is x if x t, nd is if x t. The soft threshold signl is sign(x)( x t) if x t nd is if x t.) The threshold t is chosen y wvelet coefficients selection rule using penliztion method (Birge nd Msst, 1997). The W-AIC picker detects the P-wve rrivl sed on the thresholded wvelet coefficients, from which the denoised signl cn e reconstructed for the AIC utopicker to pick time. For the shown in Figure 5, the pick time with the AIC picker is sec, which is exctly the sme s the mnul pick. In comprison to conventionl ndpss filtering, this denoising scheme sed on the wvelet trnsform decreses the distortion of the P-wve rrivl nd reduces its mplitude to lesser extent (Fig. 6). Implementtion Detils The principle purpose of using the wvelet trnsform is to guide the work of the AIC picker y choosing n pproprite time window for it, in which P-wve rrivl exists. The time window is chosen utomticlly vi tril-nderror process. First, preliminry time window is chosen nd pick times t scle 1, 2, nd 3 re checked to see if they re consistent. If so, the wvelet detector clims there is P-wve rrivl in this time window nd chooses the pick time t scle 2 s the preliminry pick. If not, the time window will continue to move until P-wve rrivl is detected or predefined ending time is met. After P-wve rrivl

7 191 H. Zhng, C. Thurer, nd C. Rowe Tle 1 Pick Times t Scles 1, 2, nd 3 nd Mnul Picks ( d, respectively) for Seismogrms shown in Figure 5 (with Du3 Wvelet) c d Scle Scle Scle Mnul Pick N/A is detected, the AIC picker will pick n onset within the time segment round the preliminry pick. There re two dditionl spects to consider when implementing W-AIC picker, s follows. Time Window. The time window for conducting the wvelet nlysis is importnt for finding the correct phse rrivl for the W-AIC picker. If the time window is too lrge, it my include mny phses tht could dominte the signl nd result in spurious pick. If the time window is too short, it will slow the detection process ecuse neighoring time windows need to overlp to reduce the order effect. Our W-AIC picker llows the user to choose the strting nd ending times for the sliding time windows. If the user does not select windowing time, the lgorithm will egin windowing from the first smple of the (with defult window length of 1 sec) until n rrivl is detected. Border Effect of the Wvelet Trnsform. The sic lgorithm for the DWT is sed on simple scheme: convolution nd downsmpling. When the convolution is performed on finite-length signls, there will e order distortion, tht is, there re not enough dt points ville ner the order to conduct the convolution. The simple wy to del with order distortion is to extend the signl on oth sides, such s y zero-pdding, smooth pdding, periodic extension, or oundry vlue repliction methods (Strng nd Nguyen, 1996). However, these methods will crete some significnt fetures (discontinuities) t oth ends of the signl. For exmple, zero pdding produces n edge singulrity t oth ends. Compred with the singulrity of the noise, these singulrities will e retined cross severl scles nd thus e detected y the W-AIC picker. In fct, the pick times t scles 2 nd 3 for the shown in Figure 5d re due to such rtifcts. To circumvent this prolem, we define order-effect region t oth ends of the time window. When the time pick t some scle lies within this region, we ssume it is n rtifct nd the pick is rejected. Time windows re overlpped so tht improperly rejected rrivls my e detected in djcent windows. Appliction of W-AIC picker We hve tested the W-AIC picker in comprison with mnul picks for two sets of seismic events, from the Ded Se region (46 s) nd the Prkfield, Cliforni region (1112 s). The erthqukes in the Ded Se region hve epicentrl distnces less thn 3 km nd mgnitudes from M.5 to M 4.2. For the Prkfield dtset, most of the erthqukes re within 25 km of the sttions nd hve mgnitudes less thn M 2.. We used Duechies wvelet of order 2 (Du2) to decompose the s into three scles. If the pick times t scle 1 nd scle 2 were within 24 smples nd those t scle 2 nd scle 3 within 48 smples, nd picks t scles 1, 2, nd 3 were lso not within 8, 16, nd 24 smples from either end of the time window, respectively (order effect), the W-AIC picker declred tht P-wve rrivl existed in the time window. The pick t scle 2 ws chosen s the preliminry pick. If no P-wve rrivl ws detected, the time window ws shifted to the right with n overlp of 5 smples, continuing until the end of the (or predefined time) ws reched. After the P-wve rrivl ws detected, the AIC picker picked n onset within time window of 3 smples (.6 sec for Ded Se dtset nd.3 sec for Prkfield dtset) efore nd 5 smples (1. sec for Ded Se dtset nd.5 sec for Prkfield dtset) fter the preliminry pick. Figure 7 nd shows exmples of rrivls picked y our picker for s from the Ded Se region with high S/N rtio nd low S/N rtio, respectively. In oth cses, the W-AIC picker detected nd picked the P-wve rrivl with considerle ccurcy in tht the picks re within.1 sec of nlyst picks. For the Ded Se dtset, our picker detected nd picked out 8% of P rrivls correctly, mong which out 81% re within.2 sec of mnul picks. The men vlue nd the stndrd devition of the differences etween the utopicks nd the mnul picks re.52 nd.15 sec, respectively. For the Prkfield dtset, more thn 9% of picks re detected nd picked within.5 sec of mnul picks, mong which out 93% re within.1 sec of Tle 2 The Pick Time t Scles 1, 2, nd 3 with Different Wvelets for the Seismogrm Shown in Figure 5 Wvelet Hr Du2 Sym2 Sym3 Coif2 Rio2.2 Bior2.2 Scle Scle Scle

8 Automtic P-Wve Arrivl Detection nd Picking with Multiscle Wvelet Anlysis for Single-Component Recordings c Figure 6. Comprison of wvelet denoising nd ndpss-filtering methods. () Noisy. () Denoising y soft-thresholding the wvelet coefficients with the threshold chosen y the Birge-Msst method. (c) Bndpss filtering using Butterworth filter of Hz. mnul picks. The men vlue nd the stndrd devition etween the utopicks nd mnul picks re.2 nd.63 sec, respectively. We cn ccount for the difference in results etween the Ded Se nd Prkfield dtsets. For the Ded Se, the events nd sttions re distriuted over wide re, nd the events lso hve wide rnge of mgnitudes. Therefore, the S/N rtio nd the wveform chrcteristics re highly vrile. As result, oth the nlyst nd the utopicker cn e expected to mke reltively lrge numer of errors. In contrst, the Prkfield dtset consists of events nd sttions from very loclized re, so tht rrivls re on verge more impulsive nd wveforms re generlly more similr. This leds to fewer picking errors oth y the nlyst nd y the utopicker. We lso performed the conventionl STA/LTA picker (pk from sc2) on the sme dt sets for comprison. For the Ded Se dtset, out 67% picks re detected nd picked within.5 sec of nlyst picks, mong which out 87% re within.2 sec of mnul picks. The men vlue nd the stndrd devition etween the utopicks nd mnul picks re.23 nd.133 sec, respectively. For the Prkfield dtset, out 87% of picks re detected nd picked within.5 sec of mnul picks, mong which out 93% re within.1 sec of mnul picks. The men vlue nd the stndrd devition etween the utopicks nd mnul picks re.3 nd.68 sec, respectively. Thus, the W-AIC picker performs notly etter thn pk for the noisier Ded Se dtset, wheres the performnces re more comprle for the less noisy Prkfield dtset. On the sis of these tests, we conclude tht the W-AIC picker provides us n efficient nd utomtic wy to pick P- wve rrivls. The picks otined y the W-AIC picker cn Figure 7. W-AIC picker pplied to s with () high S/N rtio nd () low S/N rtio. e treted s the preliminry picks for cross-correltion techniques. In this wy, the picks cn e further refined. Conclusions We developed n utomtic P-phse picker sed on the AIC comined with multiscle wvelet nlysis. The P- wve rrivl is significnt feture in nd will e retined over severl scles, wheres rndom noise or other incoherent fetures will dispper quickly over lrger scles. The AIC picker is pplied directly to the solute wvelet coefficients. If the picks t three scles re consistent, then P-wve rrivl is declred nd the AIC picker is pplied to the in the time window. To reduce the noise in the, we pply the soft-thresholding scheme with the threshold chosen y ppliction of the Birge-Msst penliztion method to the wvelet coefficients. This pproch is dvntgeous over the conventionl ndpss-filtering method, which is more likely to distort the P-wve rrivl or reduce its mplitude. In this wy, the W-AIC picker is more roust in detecting the P-wve rrivl even for noisy s. We tested this method on set of seismic events from the Ded Se region nd Prkfield, Cliforni region. We

9 1912 H. Zhng, C. Thurer, nd C. Rowe found tht out 81% of the utopicks re within.2 sec of nlyst picks for the Ded Se dtset nd out 93% of the utopicks re within.1 sec of nlyst picks for the Prkfield dtset. In the cses tht some spikes or glitches exist in the time window, the picker will erroneously clim tht there is n rrivl in the current time window. This prolem cn e corrected y pplying despiking lgorithm efore pplying the W-AIC picker. Acknowledgments We re grteful to Bill Ellsworth for providing us his AIC progrm. We lso thnk two nonymous reviewers nd ssocite editor Cezr Trifu for their constructive comments. H. Z. cknowledges British Petroleum for prtil support of his grdute studies in Fll 21. This reserch resulted from project supported y the Defense Thret Reduction Agency (Contrct DTRA1-1-C-85), U.S. Deprtment of Defense; the content does not necessrily reflect the position or the policy of the U.S. Government, nd no officil endorsement should e inferred. References Akike, H. (1973). Informtion theory nd n extension of the mximum likelihood principle, in 2nd Intermtionl Symposium on Informtion Theory, B. Petrov nd F. Cski (Editors), Budpest Akdemii Kido, Annt, S. K., nd F. U. Dowl (1997). Wvelet trnsform methods for phse identifiction in three-component, Bull. Seism. Soc. Am. 87, Birge, L., nd P. Mssrt (1997). From model selection to dptive estimtion, in Festchrifft for L. Le Cm, D. Pollrd, Editor, Springer, New York, Chkr, A. B., nd D. Oky (1995). Frequency-time decomposition of seismic dt using wvelet-sed methods, Geophysics 6, Duechies, I. (1992). Ten lectures on wvelets, in CBMS-NSF Regionl Conference Series in Applied Mthemtics, Vol. 61, Society for Industril nd Applied Mthemtics, Phildelphi, Pennsylvni, 357 pp. Donoho, D. L. (1995). De-noising y soft-thresholding, IEEE Trns. Inf. Theory 41, Erle, P., nd P. M. Sherer (1994). Chrcteriztion of glol s using n utomtic-picking lgorithm, Bull. Seism. Soc. Am. 84, Gendron, P., J. Eel, nd D. Mnolkis (2). Rpid joint detection nd clssifiction with wvelet ses vi Byes theorem, Bull. Seism. Soc. Am. 9, Goudswrrd, J., nd K. Wpenr (1998). Chrcteriztion of reflectors y multiscle mplitude nd phse nlysis of seismic dt, 68th Ann. Int. Mtg. Soc. Expl. Geophys., Goupillud, P., A. Grossmnn, nd J. Morlet (1984). Cycle-octve nd relted trnsforms in seismic signl nlysis, Geoexplortion 23, Grossmnn, A., nd J. Morlet (1984). Decomposition of Hrdy functions into squre integrle wvelets of constnt shpe, SIAM J. Mth. Anl. 15, Hykin, S. (1996). Adptive Filter Theory, Prentice Hll, Upper Sddle River, New Jersey, 989 pp. Hsung, T-C, D. P-K Lun, nd W-C Siu (1999). Denoising y singulrity detection, IEEE Trns. Signl Processing 47, Leonrd, M. (2). Comprison of mnul nd utomtic onset time picking, Bull. Seism. Soc. Am. 9, Leonrd, M., nd B. L. N. Kennett (1999). Multi-component utoregressive techniques for the nlysis of s, Phys. Erth Plnet. Interiors 113, Lervik, J. M., T. Rosten, nd T. A. Rmstd (1996). Sund seismic dt compression: optimiztion nd evlution, IEEE Digitl Signl Processing Workshop Proceedings, Med, N. (1985). A method for reding nd checking phse times in utoprocessing system of seismic wve dt, Zisin Jishin 38, Mllt, S. (1989). A theory for multiresolution signl decomposition: the wvelet representtion, IEEE Trns. Pttern Anl. Mchine Intelligence 11, Mllt, S., nd W. L. Hwng (1992). Singulrity detection nd processing with wvelets, IEEE Trns. Inform. Theory 38, Sleemn, R., nd T. vn Eck (1999). Roust utomtic P-phse picking: n on-line implementtion in the nlysis of rodnd recordings, Phys. Erth Plnet. Interiors 113, Strng, G., nd T. Nguyen (1996), Wvelets nd Filter Bnks, Wellesley- Cmridge Press, Wellesley, Msschusetts, 49 pp. Tiulec, I. M., nd E. T. Herrin (1999). An utomtic method for determintion of Lg rrivl times using wvelet trnsforms, Seism. Res. Lett. 7, Vidle, J. E. (1986). Complex polriztion nlysis of prticle motion, Bull. Seism. Soc. Am. 76, Wickerhuser, M. V. (1994), Adpted Wvelet Anlysis from Theory to Softwre Algorithms, A. K. Peters Ltd., Wellesley, Msschusetts, 54 pp. Withers, M., R. Aster, C. Young, J. Beiriger, M. Hrris, S. Moore, nd J. Trujillo (1998). A comprison of select trigger lgorithms for utomted glol seismic phse nd event detection, Bull. Seism. Soc. Am. 88, Wu, Y., nd G. A. McMechn (1998). Wve extrpoltion in the sptil wvelet domin with ppliction to poststck reverse-time migrtion, Geophysics 63, Deprtment of Geology nd Geophysics University of Wisconsin Mdison 1215 W. Dyton Street Mdison, Wisconsin 5376 hjzhng@geology.wisc.edu Mnuscript received 6 Decemer 22.