<strong>Null</strong> <strong>Detection</strong> <strong>in</strong> <strong>Shear</strong>-<strong>Wave</strong> Splitt<strong>in</strong>g <strong>Measurements</strong> 1209(9), a difference <strong>in</strong> fast axis estimate close to 45, that is 37 DU 53. Near-<strong>Null</strong> measurements can be classified by0 q 0.3 and 32DU 58. Rema<strong>in</strong><strong>in</strong>g measurementsare to be considered as poor quality (see Fig. 3 for furtherillustration).Real DataWe apply our <strong>Null</strong> criterion to the shear-wave splitt<strong>in</strong>gmeasurements of station LVZ <strong>in</strong> northern Scand<strong>in</strong>avia. Theanalyzed earthquakes (M w 6) occurred between December1992 and December 2005. The data were processed by us<strong>in</strong>gthe SplitLab environment (A. Wüstefeld et al., unpublishedmanuscript, 2006). This allows us to analyze eventsefficiently and to calculate simultaneously both the RC andSC technique. We mostly used raw data or, where necessary,applied third-order Butterworth bandpass filters with uppercornerfrequencies down to 0.2 Hz. Most usable events havebackazimuths between 45 and 100. Such sparse backazimuthalcoverage is unfortunately the case for many splitt<strong>in</strong>ganalyses, and we aim to extract the maximum <strong>in</strong>formationabout the splitt<strong>in</strong>g parameters from these sparse distributions.In total we analyzed 37 SKS phases from a wide rangeof backazimuths (Fig. 4). Many results resemble <strong>Null</strong> characteristicsby show<strong>in</strong>g low energy on the <strong>in</strong>itial transversecomponent, elongated to l<strong>in</strong>ear <strong>in</strong>itial particle motion and atypical energy plot. Such characteristics can be replicated <strong>in</strong>synthetic seismograms with near-<strong>Null</strong> parameters, that is,when the fast axis deviates less then 20 from backazimuth(Fig. 1). The average fast axis of the good events, as detectedautomatically and manually, is 14.3 and 14.7 for the SCand RC technique, respectively. Such orientation implies<strong>Null</strong>s at backazimuths of approximately 15, 105, 195, and285 and favorable backazimuths for splitt<strong>in</strong>g measurements<strong>in</strong> between. Indeed, good and fair splitt<strong>in</strong>g measurementsare found <strong>in</strong> backazimuthal ranges between 50 and 70 (Table1 and Fig. 4), where the energy on the transverse componentis expected to reach maximum possible values (seeequation 3) and the splitt<strong>in</strong>g can be <strong>in</strong>verted most reliably.Figure 4. <strong>Shear</strong>-wave splitt<strong>in</strong>g estimates from 33 good and fair measurements fromstation LVZ. The upper panels display fast-axis estimates for RC and SC methods. Notethat many RC estimates are situated near the dotted l<strong>in</strong>es that <strong>in</strong>dicate 45. The lowerpanels display the delay-time estimates. The solid horizontal l<strong>in</strong>es <strong>in</strong>dicate our <strong>in</strong>terpretationof the LVZ with fast axis at 15 and 1.1-sec delay time, based on the meanof the good splitt<strong>in</strong>g measurements.
1210 A. Wüstefeld and G. BokelmannTable 1Good Events of Station LVZ as Detected AutomaticallyDate Lat Long Bazi* U SC U RC dt SC dt RC SNR SC†corr RC‡01-Oct-1994 17.75 167.63 55.1 19.1 13.1 0.8 0.8 5.85 0.8917-Mar-1996 14.7 167.3 54.3 14.3 12.3 1.0 1.0 9.55 0.9305-Apr-1997 6.49 147.41 71.1 17.1 24.1 1.4 1.3 6.16 0.8806-Feb-1999 12.85 166.7 54.2 6.2 11.2 1.2 1.2 10.43 0.9710-May-1999 5.16 150.88 67.3 11.3 10.3 1.3 1.3 5.70 0.8706-Feb-2000 5.84 150.88 67.5 13.5 13.5 1.4 1.4 9.33 0.9118-Nov-2000 5.23 151.77 66.5 18.5 18.5 1.0 1.0 5.74 0.90*Bazi, backazimuth† SNR SC , signal-to-noise ratio of the SC technique.‡ corr RC , correlation coefficient of the RC technique.Also <strong>in</strong> good agreement are the detected <strong>Null</strong>s at backazimuthsbetween 80 and 110 and at about 270.Simultaneously, RC delay times systematically tend tosmaller values between backazimuths of 80 and 110, mimick<strong>in</strong>gthe trapezoidal shape <strong>in</strong> the synthetic RC delay times(Fig. 2). Mean delay time estimates of good SC and RC are1.2 and 1.1 sec. respectively.Discussion and ConclusionsWe have presented a novel criterion for identify<strong>in</strong>g <strong>Null</strong>measurements <strong>in</strong> shear-wave splitt<strong>in</strong>g data based on two <strong>in</strong>dependentand commonly used splitt<strong>in</strong>g techniques. The twotechniques behave very differently near <strong>Null</strong> directions,where the RC technique systematically fails to extract thecorrect values both for the fast-axis azimuth U RC and delaytime dt RC . That technique should therefore not be used as a“stand-alone” technique. On the other hand, the comparisonof the two techniques is valuable for f<strong>in</strong>d<strong>in</strong>g <strong>Null</strong> events.The backazimuths of <strong>Null</strong>s ambiguously <strong>in</strong>dicates either fastor slow direction. Thus, a <strong>Null</strong> measurement yields limited,yet important, constra<strong>in</strong>ts on anisotropy orientation, especiallyif the backazimuthal coverage of the station is onlysparse. Furthermore, <strong>Null</strong>s from a wide range of backazimuths<strong>in</strong>dicate either the lack of (azimuthal) anisotropy orweak anisotropy, at the limit of detection. Restivo and Helffrich(1998) analyzed the splitt<strong>in</strong>g procedure for effects ofnoise. They conclude that for small splitt<strong>in</strong>g filter<strong>in</strong>g doesnot necessarily result <strong>in</strong> more confident estimates of splitt<strong>in</strong>gparameters, s<strong>in</strong>ce narrow bandpass filters lead to apparent<strong>Null</strong> measurements. For SNR above 5 our criterion detects<strong>Null</strong> measurements and classifies near-<strong>Null</strong>s. Good eventscan still be obta<strong>in</strong>ed but only for exceptionally good SNR orwith backazimuths far away oriented with respect to theanisotropy axes (where the transverse amplitude is larger;see equation 3).The comparison of the two shear-wave splitt<strong>in</strong>g techniquesallows assign<strong>in</strong>g a quality to s<strong>in</strong>gle measurements(Fig. 1). Furthermore, the jo<strong>in</strong>t two-technique analysis of allmeasurements (Fig. 2) yields characteristic variations ofsplitt<strong>in</strong>g parameter estimates with backazimuth. This variationcan be used to extract the maximum <strong>in</strong>formation fromthe data, and to decide whether a more complex anisotropythan a s<strong>in</strong>gle layer needs to be <strong>in</strong>voked to expla<strong>in</strong> the observations.The practical steps for this should be: first, assumea s<strong>in</strong>gle-layer case with the most probable fast directionbased on the good measurements. Second, verify that<strong>Null</strong>s measurements occur near the correspond<strong>in</strong>g <strong>Null</strong> directions<strong>in</strong> the backazimuth plot (Fig. 4). In the vic<strong>in</strong>ity ofthese <strong>Null</strong> directions, the splitt<strong>in</strong>g parameter estimates U SCand dt SC should show a larger scatter with a tendency towardlarge delays. For dt RC we expect to f<strong>in</strong>d an arc-shaped variationwith backazimuth that should have its m<strong>in</strong>imums nearthe assumed <strong>Null</strong> directions. If these conditions are met, aone-layer case can reasonably expla<strong>in</strong> the observations. Onthe other hand, good events that deviate from these predictionsmay require more complex anisotropy (multilayer caseor dipp<strong>in</strong>g layer). Applied to station LVZ <strong>in</strong> northern Scand<strong>in</strong>avia,we were thus able to comfortably characterize theanisotropy by a s<strong>in</strong>gle anisotropic layer with a fast axis orientedat 15 and a delay time of 1.1 sec.ReferencesBarruol, G., P. G. Silver, and A. Vauchez (1997). Seismic anisotropy <strong>in</strong> theeastern US: Deep structure of a complex cont<strong>in</strong>ental plate, J. Geophys.Res. 102, no. B4, 8329–8348.Bowman, J. R., and M. Ando (1987). <strong>Shear</strong>-wave splitt<strong>in</strong>g <strong>in</strong> the uppermantlewedge above the Tonga subduction zone, Geophys. J. R. Astr.Soc. 88, 25–41.Brechner, S., K. Kl<strong>in</strong>ge, F. Krüger, and T. Plenefisch (1998). Backazimuthalvariations of splitt<strong>in</strong>g parameters of teleseismic SKS phases observedat the broadband stations <strong>in</strong> Germany, Pure Appl. Geophys.151, 305–331.Chevrot, S. (2000). 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