SKS splitting observed at Romanian broad-band seismic network

Tectonophysics 462 (2008) 89–98

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Tectonophysics j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / t e c t o

SKS splitting observed at Romanian broad-band seismic network Marian Ivan a,b,⁎, Mihaela Popa b, Daniela Ghica b a b

University of Bucharest, Department of Geophysics, 6 Traian Vuia str., 020956 Bucharest o.p.37, Romania National Institute for Earth Physics, P.O. Box MG-2, 077125, Bucharest, Romania

a r t i c l e

i n f o

Article history: Received 28 November 2006 Received in revised form 7 November 2007 Accepted 6 December 2007 Available online 9 August 2008 Keywords: SKS splitting Anisotropy Vrancea area Romanian upper mantle

a b s t r a c t Shear-wave splitting results are presented for the broad-band stations of the Romanian seismic network. For stations BUC1 and CRAR (located in Moesian Platform), IAS (in East-European Platform), TIRR and CVD (in Central Dobrudja–Black Sea microplate), TIM and DRGR (in Dacia-Tisza plate, including Apuseni Mts.), BURAR, BZS and GZR (in, or very close to the Carpathian Arc), the fast directions (φ) are around 135°. The mean delay values (δt) of the slow wave are slightly greater for the stations placed in platform areas (δt ~ 1.5 s) than for the stations situated in the (proximity) of Carpathians (δt~ 1.2 s). For the MLR station located in the South-Western part of Vrancea area, at the Carpathian Bend, the fast direction is 48°, similar to VOIR station (located in Southern Carpathians, 70 km West of MLR). At VRI and PLOR, located in the North-Eastern part of Vrancea, the fast axis is oriented approximately on North–South direction, with a possible dependence of the splitting parameters with back azimuth. At least for some stations, the splitting results are not consistent with vertical coherent lithospheric anisotropy. © 2008 Elsevier B.V. All rights reserved.

1. Introduction The broad-band stations of the Romanian Seismic Network are located in a variety of tectonic settings (Fig. 1): IAS in East-European Platform, TIRR and CVD in Central Dobrudja–Black Sea microplate, TIM and DRGR in Dacia-Tisza plate, including Apuseni Mts., CRAR and BUC1 in Moesian Platform, BURAR, BZS, GZR and VOIR in (or very close to) the Carpathian Arc. Stations MLR, VRI (and PLOR) are placed in Vrancea area, above a volume of highly confined, seismic activity, frequent in the 85– 220 km focal depth. Several geodynamic scenarios have been invoked in Southern East-Carpathians, in an attempt to explain the nature of the seismogenic volume, its age and the physical mechanism of the intermediate depth earthquakes. Fuchs et al. (1979) proposed a paleosubduction process of an oceanic slab, while Oncescu (1980) considered the basalt–eclogite phase changes. Mantle delamination/ continental collision, followed by a late roll-back stage (and break-off), have been also discussed (Linzer et al., 1998; Gîrbacea and Frisch, 1998; Chalot-Prat and Gîrbacea, 2000; Wortel and Spakman, 2000; Cloetingh et al., 2004). Various other models are summarized by Popa et al. (2005). Recent teleseismic body-wave tomographic studies of Martin et al. (2005, 2006) indicated in Vrancea a high velocity, near vertical anomaly (maximum P-velocity perturbation around 4%), down to 400 km. The high velocity body has a horizontal cross section of quasi-elliptical shape. The tearing of the slab at 200–250 km depth is accompanied by the rotation of the slab from NE–SW towards N–S orientation. Currently, there is no definite conclusion regarding the origin of the Vrancea seismicity (Milsom, 2005). ⁎ Corresponding author. University of Bucharest, Department of Geophysics, 6 Traian Vuia str., 020956 Bucharest o.p.37, Romania. E-mail address: [email protected] (M. Ivan). 0040-1951/$ – see front matter © 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.tecto.2007.12.015

Splitting analysis of SKS (or SKKS) waves from large distant events (Δ ≥ 87°) is considered a reliable tool for retrieving the anisotropy beneath a broad-band recording station (e.g. Vinnik et al., 1984; Vinnik et al., 1992), sampling the geological structure in a circular area around the station with a radius of approximately 70 km (first Fresnel zone, for a depth like 150 km and a wave period around 7 s) (Knapp, 1991; Pearce and Mittleman, 2002). The outputs of the shear-wave splitting analysis are the azimuth φ (positive clockwise from North) of the fast S wave polarization and the delay time δt of the slow wave. The first parameter is assumed to represent the direction of the fast crystallographic axis of the olivine (Nicolas and Christensen 1987). The value of δt is related to the thickness of the uppermost mantle anisotropic layer and strength of anisotropy, but there is always a trade-off between the strength of anisotropy and the length of the ray path within the medium. The main process responsible for SKS splitting is the lithospheric anisotropy characterized by a compression in the mantle perpendicular to the orogen, resulting by a mountain building (VCD — vertical coherent deformation). Other processes that could be considered in shear-wave splitting analysis are the “fossil” lithospheric anisotropy and the asthenospheric flow (e.g. Silver, 1996; Fouch and Rondenay, 2006). Hence, quantitative information about the direction of the tectonic strain/mantle flow in the investigated area can be obtained, assuming, in simple cases, a one-layer, transversely isotropic medium with a horizontal axis of symmetry (e.g. Vinnik et al., 1989). If such two or more horizontal layers are present, a 90° periodicity of the apparent splitting parameters is theoretically expected (Savage and Silver, 1993; Silver and Savage, 1994; Rumpker and Silver, 1998). Non-horizontal and/or non-planar structures having different tilted fast axis orientations can be also considered (Babuška et al.,1993; Šílený and Plomerová,1996), but such situations are almost impossible to resolve in the absence of a

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M. Ivan et al. / Tectonophysics 462 (2008) 89–98

Fig. 1. Tectonic sketch of Romania and adjacent areas and locations of stations of the Romanian broad-band network used in this study, with some previous results of shear-wave splitting at KIEV, LVV, UZH and KOV (Dricker et al., 1999), KWP (Wiejacz, 2001) and PSZ (Ivan et al., 2002).

great number of estimations from a broad azimuth range. Splitting analysis is of particular interest in subduction zones, where mantle anisotropy is routinely used to map the mantle flow (e.g. Margheriti et al., 2003; Civello and Margheriti, 2004; Long and van der Hilst, 2005). Here, shear-wave anisotropy seems to show predominantly trenchparallel fast directions for stations close to the trench (Yang et al., 1995; Audoine et al., 2000; Shimzu et al., 2003), with a possible reorientation of fast directions from trench-parallel adjacent to the plate boundary to trench-normal further away (Polet et al., 2000). A detailed discussion is presented by Levin et al. (2004, 2007), anisotropy parameters being also sensitive to the location of the slab edges (i.e., Peyton et al., 2001). This paper presents a shear-wave splitting analysis at the Romanian broad-band seismic stations, covering the last seven years, in an attempt to relate the splitting results to some geodynamic scenarios regarding Vrancea seismicity.

2. Method and data analysis We used digital broad-band data available at GEOFON DMC (for stations MLR, IAS, DRGR, BUC1, VRI), at IRIS DMC (for TIRR) and from NIEP Data Base (for BURAR, VOIR, TIM, BZS, CRAR, PLOR, GZR and CVD stations), routinely sampled at 20 Hz. Events below magnitude 6 have not been analyzed because their signal-to-noise ratios are very low to get reliable results. However, since SKS path is near vertical in the neighborhood of the focus, strike-slip crustal events do not radiate enough energy to provide clear SK(K)S observations in most cases. For crustal thrust events, a very long PP coda of significant, quasi-constant amplitude is routinely observed at the Romanian stations and consequently SK(K)S waves are contaminated by a high level noise, also associated to the proximity of the Black Sea. Further contamination by noise is provided by associated depth phases like p(s)SK(K)S. Consequently, crustal events can be used at the

Fig. 2. Geographic location of the earthquakes used in this study (see Table 1 for details) and of MLR station.

M. Ivan et al. / Tectonophysics 462 (2008) 89–98

91

Fig. 3. Example of unfiltered recording of event of 2006/08/25 (see Table 1 for details) at the BZS station.

Romanian stations for SKS analysis only in some particular cases. Like earthquakes of large magnitudes and/or stations placed in the proximity of a fault plane on the focal mechanism solution. Hence most of the splitting parameters derived in this study are from strong earthquakes, preferably deep or intermediate depth events, many of them presenting a normal or reverse fault plane solution (Harvard CMT). The Romanian stations have two major suitable sources of such earthquakes, i.e. Pacific (Java Sea, Minahassa, Banda Sea, Papua etc, at backazimuth values around 80°) and Central and South America (Mexico, Chile, Argentina etc, at 280°) (Fig. 2). Events from 1994/10/09 (opening date of MLR broad-band digital station) to 2000/08/09 have been processed by Ivan (2000). Arrivals of SK(K)S phases were also checked with respect to the travel times computed with the IASP91 TTIM software (Buland and Chapman, 1983; Kennet and Engdahl, 1991). Many procedures to retrieve the splitting parameters, including the one used here, assume implicitly that SK(K)S wave has the energy focused in a narrow frequency band (see Appendix A). It could be not true for most of the complex, multiple

earthquakes (two or more strong events occurring several seconds apart), best visible on broad-band instruments. Most of such events have been discarded by visual examination of the P wave train and by using International Seismological Centre (ISC) Catalogue. The theoretical predicted quasi-elliptical polarization along the approximate source to receiver path has been examined in all cases by using the Particle-Motion tool of PITSA software (Scherbaum and Johnson, 1992) and used to select the start and the end of time windows processed for splitting analysis (Figs. 3 and 4). Only 91 earthquakes listed in Table 1 (see also Fig. 2) were selected for analysis. Among them, 44 events recorded at MLR have been already presented by Ivan (2000). A zero-phase Butterworth band-pass filter (3 ÷30 s) has been used in all cases. The theoretical background of the processing algorithm is summarized in the Appendix A of this paper. 3. Results Previous results of splitting analysis at MLR station situated in the South-Western part of Vrancea seismogenic (Ivan, 2000) were derived

Fig. 4. Elliptical particle motion corresponding to the SKSac wave arrival shown on Fig. 3, after band-pass filtering. The beginning and the end of the processed time window are indicated. As a result of splitting, the major axis of the ellipse has an azimuth around 237° from the North, different from the event back azimuth, equal to 252°.

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M. Ivan et al. / Tectonophysics 462 (2008) 89–98 Table 1 (continued )

Table 1 Events used in this study (NEIC locations) Region

Date

Time

Latitude

Longitude

Depth (km)

Mag.

Java Sea⁎ Peru⁎ Peru⁎ Mexico⁎ Chile⁎ Banda⁎ Minahassa⁎ Flores Sea⁎ Mariane Isls.⁎ Mariane Isls.⁎ Minahassa⁎ Minahassa⁎ Ecuador⁎ Peru⁎ Jujuy⁎ Halmahera⁎ Peru⁎ Minahassa⁎ Peru⁎ Peru⁎ Minahassa⁎ Ecuador⁎ Mexico⁎ Mindanao⁎ Molucca⁎ Molucca⁎ Santa Cruz⁎ Celebes⁎ Panama⁎ Peru⁎ Mexico⁎ Mindanao⁎ Mexico⁎ Honduras⁎ Indonesia⁎ Sumatera⁎ Costa Rica⁎ Bolivia⁎ Mexico⁎ California⁎ Argentina⁎ South Indian⁎ Banda Sea⁎ Michoacan⁎ El Salvador Molucca Banda Sea Fiji S. Australia Chile Mariane Isls. Bali Sea Sumbawa Mexico Indonesia Halmahera S. Molucca Halmahera Mindanao Brazil Celebes Sea Molucca W. Irian Banda Sea Timor Costa Rica Banda Sea Costa Rica Mindanao Indonesia Banda Sea Argentina Chile N. Peru Chile–Bolivia Banda Sea

1994/11/15 1995/09/23 1995/10/03 1995/10/09 1995/11/01 1995/12/25 1996/01/01 1996/06/17 1996/07/06 1996/07/15 1996/07/16 1996/07/22 1996/08/05 1996/11/12 1997/01/23 1997/06/24 1997/10/28 1997/11/25 1997/11/28 1998/04/03 1998/05/21 1998/08/04 1998/08/23 1998/09/02 1998/11/29 1998/12/06 1999/02/06 1999/03/04 1999/03/31 1999/04/03 1999/06/15 1999/06/18 1999/06/21 1999/07/11 1999/08/12 1999/08/14 1999/08/20 1999/09/15 1999/09/30 1999/10/16 2000/04/23 2000/06/18 2000/08/07 2000/08/09 2001/01/13 2001/02/24 2001/03/19 2001/04/28 2001/12/12 2002/04/01 2002/08/14 2002/10/03 2002/10/06 2003/01/22 2003/03/25 2003/05/05 2003/05/11 2003/05/26 2003/05/26 2003/06/20 2003/07/01 2003/10/18 2004/02/05 2004/04/17 2004/04/23 2004/04/29 2004/06/25 2004/06/29 2005/02/05 2005/02/15 2005/03/02 2005/03/21 2005/06/13 2005/09/26 2005/11/17 2006/01/27

20:18:11.46 22:31:53.87 12:45:01.01 15:35:55.28 00:35:32.61 04:43:23.16 08:05:10.83 11:22:18.54 21:36:32.49 16:51:22.07 10:07:36.65 14:19:35.77 21:39:16.25 16:59:44.03 02:15:33.10 23:04:59.80 06:15:29.70 12:14:45.60 22:53:49.30 22:01:48.25 05:34:25.50 18:59:20.10 13:57:15.28 08:37:39.91 14:10:31.96 00:47:13.45 21:47:59.47 08:52:01.90 05:54:42.13 06:17:18.36 20:42:05.93 10:55:25.75 17:43:04.52 14:14:16.53 05:44:59.59 00:16:52.29 10:02:21.10 03:01:24.34 16:31:15.69 09:46:44.13 09:27:23.32 14:44:13.31 14:33:55.91 11:41:47.90 17:33:34.58 07:23:50.49 05:52:15.51 04:50:01.90 14:02:49.8 19:59:37.60 13:57:58.5 19:05:15.5 15:46:42.4 02:06:47.3 02:53:34.1 15:50:14.6 17:51:40.5 19:23:38.5 23:13:36.3 06:19:48.5 05:52:27.2 22:27:20.3 21:05:02.84 15:58:24.61 04:50:30.22 00:57:21.00 02:35:07.79 07:01:30.90 12:23:18.94 14:42:25.0 10:42:16.90 12:23:52.0 22:44:34.0 01:55:44.0 19:26:56.43 16:58:53.67

−5.618 −10.714 −2.781 19.116 −28.884 −6.921 0.729 −7.137 21.979 18.726 1.016 1.000 −1.996 −14.993 −22.03 −1.88 −4.48 1.44 −13.58 −8.148 0.207 −0.593 11.663 5.41 −2.071 1.253 −12.853 5.397 5.827 −16.66 18.386 5.514 18.324 15.78 −1.716 −5.885 9.044 −20.934 16.059 34.594 −28.307 −13.802 −7.018 18.198 12.997 1.334 −4.044 −18.07 −42.69 −29.54 13.99 −7.56 −8.13 18.77 −8.3 0.35 −0.94 2.58 6.92 −7.34 4.69 0.71 −3.62 −7.35 −9.6 10.81 −6.71 10.74 5.293 4.78 −6.5 −24.93 −19.91 −5.614 −22.319 −5.473

110.259 −78.58 −77.862 − 104.202 − 71.378 129.204 119.931 122.589 142.91 145.628 120.254 120.450 −81.0 −75.675 −65.85 127.12 −76.57 122.76 −68.98 −74.238 119.584 −80.393 −88.038 126.764 124.891 126.198 166.697 121.937 −82.616 −72.662 −97.436 126.639 −101.539 −88.33 122.46 104.711 −84.159 −67.275 −96.931 −116.27 −62.99 97.453 123.357 − 102.48 −88.729 126.335 128.013 −176.68 124.67 − 71.25 146.39 115.77 118.42 − 103.89 120.69 127.43 126.74 128.88 123.87 − 71.85 122.62 126.19 135.54 128.37 122.84 −86.0 130.38 −87.04 123.337 126.39 130.05 −63.36 −69.09 −76.371 −67.887 128.131

567.7 39.1 37.8 42.3 19.9 133 24 587.3 276.4 176.5 33 33 33 33 285.3 40.5 125.3 32.6 603.3 164.6 33 33 54.6 50 33 33 90.1 33 10 87.2 70 33 68.7 10 33 101.4 20 218 60.6 0 608.5 10 648.5 45.8 82.9 55.6 33(f) 367.4 16 73.7 45.7 316.2 20.6 32.6 28.4 124.3 26.9 34.8 576.7 554.2 604.4 30.1 16 128 65 10 70 9 525 39.7 196.7 557.8 119.2 132.3 162.6 397

6.0 6.0 6.2 7.4 6.5 6.2 7.8 7.9 6.4 6.2 6.6 7.0 6.2 7.7 6.4 6.4 6.9 6.8 6.3 6.0 6.2 7.1 6.0 6.7 7.6 6.2 7.3 6.5 6 6.2 6.5 6.1 6.0 6.0 6.0 6.0 6.1 6.1 6.5 6.3 6.9 7.9 6.5 6.5 7.7 7.1 6.2 6.8 7.1 6.4 6.5 6.0 6.2 7.4 6.4 6.4 6.0 6.9 6.8 7.0 6.0 6.3 7.0 6.1 6.6 6.2 6.1 6.3 7.1 6.6 7.1 6.8 7.8 7.5 6.9 7.6

Region

Date

Time

Latitude

Longitude

Argentina Papua N.G. Argentina Mariana Halmahera Guatemala Mexico Peru–Brazil Jujuy Molucca Java Mariane Isls. Mariane Isls. Peru–Ecuador Jujuy

2006/08/25 2006/10/17 2006/11/13 2007/01/30 2007/02/20 2007/06/13 2007/07/06 2007/07/12 2007/07/21 2007/07/26 2007/08/08 2007/09/28 2007/10/31 2007/11/16 2007/11/18

00:44:43.2 01:25:15.60 01:26:34.6 21:37:49.3 08:04:27.90 19:29:41.00 01:09:21.10 05:23:49.0 15:34:47.0 05:40:18.00 17:04:58.0 13:38:58.4 03:30:19.20 03:12:59.00 05:40:09.00

−24.32 −5.92 − 26.09 21.1 −1.06 13.613 16.68 −7.93 − 22.33 2.8 −5.968 21.98 18.84 −2.304 − 22.569

−66.89 151.01 −63.34 144.83 127.07 −90.822 −93.48 −74.36 −65.81 127.49 107.655 142.68 145.32 −77.793 −66.221

Depth (km)

Mag.

156.8 58.4 556.6 49.8 31.3 23 124.8 152.9 247.1 44.6 289.2 261.2 240 119 220.7

6.4 6.5 6.7 6.3 6.5 6.8 6.1 6.0 6.4 6.9 7.5 7.4 6.9 6.7 6.0

A star indicate events already processed by Ivan (2000) at MLR station.

using two different theoretical approaches on the same time widows. Using the ah_splitest2 software presented by Levin et al. (1999), a fast direction of 52° ± 7° (95% confidence level) and a delay time of 0.7 ± 0.1 s have been obtained from 46 estimations. Similar splitting parameters were derived by using the code summarized into the Appendix A, i.e. an average fast S polarization azimuth of 44 ± 5° and a delay time 0.9 ± 0.1 s. The good agreement between the two parameter sets might be considered as a validation of our computational method. Preliminary results on SKS anisotropy in Vrancea area have been also reported for four events by Achauer et al. (2001). The shear-wave splitting was evaluated at 15 temporary stations of the CALIXTO'99 experiment (e.g. Popa et al., 2005) and at MLR station. The fast S polarizations looks different when considering the two events from Mexico area (roughly North–South orientation) and the two events from Sulawesi and Sunda (generally N 56° E orientation), explained by a method deficiency or indicating a complex heterogeneous anisotropy beneath Vrancea. Previous splitting estimations in Romania and adjacent areas are summarized in Table 2 and displayed in Fig. 1 (for some permanent stations only). For MLR station we have processed 36 new events, leading to an average value of the fast direction of 48° ± 3° and a delay time of 1.0 ± 0.1 s from the total of 84 individual estimations. For all the other stations of the Romanian broad-band network, we present initial results. The individual estimations are presented in Table 3, SKS phase being used in most cases. For a limited number of earthquakes, well individualized SKKS phases have been used too. A Table 2 Previous results of splitting in Romania and adjacent areas (Dricker et al. (1999), Ivan (2000), Wiejacz (2001), Achauer et al. (2001) and Ivan et al. (2002)) Station Latitude Longitude Affiliation (°) (°) KWP KIEV LVV UZH KOV PSZ MLR A02 A10 A12 B04 C08 D04 D06 D15 E03 E17 E25 F09 F11 L02 S07

49.6316 50.6944 49.819 48.631 48.315 47.9184 45.4912 47.011 45.76 45.194 45.691 45.691 44.864 44.643 44.196 46.103 45.512 45.327 45.88 45.308 45.771 46.09

22.7075 29.2083 24.031 22.293 25.0667 19.8944 25.9456 27.431 26.271 25.893 26.08 24.795 24.391 24.762 25.501 26.831 25.508 26.738 27.857 27.829 26.509 25.692

Type

φ (°)

δt (s)

Poland Permanent 99 0.8 Ukraine 110 0.8 Ukraine 145 0.7 Ukraine 135 1.5 Ukraine 130 1.3 Hungary 133 0.7 Romania 44 0.9 Romania Temporary 1.5–2.0 CALIXTO'99 0

56

BAz dependence No

For two earthquakes from Mexico

For one earthquake from Sunda Strait and one earthquake from Sulawesi

M. Ivan et al. / Tectonophysics 462 (2008) 89–98 Table 3 Fast S polarization azimuths and split delay times measured at the Romanian Network Stations Station Event

Distance Back-azimuth φ φ error δt deg deg deg deg s

MLR MLR MLR MLR MLR MLR MLR MLR MLR MLR MLR MLR MLR MLR MLR MLR MLR MLR MLR MLR MLR MLR MLR MLR MLR MLR MLR MLR MLR MLR MLR MLR MLR MLR MLR MLR MLR MLR MLR MLR MLR MLR MLR MLR MLR MLR MLR MLR MLR MLR MLR MLR MLR MLR MLR MLR MLR MLR MLR MLR MLR MLR MLR MLR MLR MLR MLR MLR MLR MLR MLR MLR MLR MLR

90 108 102 101 115 115 104 92 100 92 96 92 92 103 109 107 99 102 94 103 103 92 102 98 94 98 96 134 90 99 108 98 94 100 95 96 86 97 107 100 93 109 109 87 100 101 97 96 96 101 147 124 115 115 100 95 97 101 99 98 98 97 91 101 91 101 97 98 91 94 105 107 108 103

941115 950923 951003 951009 951101 951101 951225 960101 960617 960706 960715 960716 960722 960805 961112 970123 970624 971028 971125 971128 980403 980521 980804 980823 980902 981129 981206 990206 990304 990331 990403 990615 990618 990621 990711 990812 990814 990820 990915 990930 991016 000423 000423 000618 000807 000809 010113 010224 010224 010319 010428 011212 020401 020401 020814 021003 021006 030122 030325 030505 030511 030526 030526 030620 030701 040423 040429 040629 050205 050215 050302 050321 050613 050926

98 273 278 313 253 253 85 87 90 56 56 86 86 281 267 255 83 276 84 264 272 87 281 295 79 85 82 58 82 288 264 307 79 310 298 87 102 291 257 305 330 249 249 113 90 311 297 82 82 84 42 119 253 253 58 95 94 312 92 82 83 79 80 270 82 92 293 294 81 79 84 252 259 275

14 18 72 54 69 47 26 36 38 38 28 30 38 32 60 33 20 20 10 66 16 64 32 72 18 26 38 48 61 41 54 47 50 51 38 57 60 76 74 46 68 60 52 61 44 42 35 52 46 34 51 40 56 54 68 58 44 65 47 55 59 65 48 66 54 47 53 31 52 58 60 55 63 63

– – 7 40 11 11 – 13 – – – – 11 15 11 12 – – – 28 – – – 10 – 12 15 9 24 13 12 17 3 – – 12 7 5 19 10 – – – 14 10 – 10 4 4 – 10 – 2 2 3 4 10 5 4 5 5 15 4 3 3 5 – 5 6 10 2 4 5 –

0.9 1.4 0.8 1.0 1.3 0.3 0.7 0.7 1.1 0.5 0.5 0.6 0.6 1.2 1.1 0.5 1.6 0.8 1.8 0.8 0.4 1.1 1.1 1.3 0.5 1.1 0.6 0.8 1.3 0.6 0.7 0.6 0.4 1.6 1.5 1.0 1.0 0.7 0.4 0.5 0.7 0.9 1.2 0.7 0.6 0.6 0.9 0.8 0.9 1.3 0.6 1.1 1.7 0.8 0.7 1.2 1.1 1.3 1.1 1.1 1.3 0.8 0.9 0.8 0.7 1.2 0.7 1.1 1.1 1.4 1.6 1.5 1.1 1.0

δt error Phase Quality s – – 0.2 0.4 0.5 0.5 – 0.6 – – – – 0.3 0.5 0.5 0.1 – – – 0.2 – – – 0.5 – 0.4 0.3 0.3 0.4 0.2 0.1 0.2 0.1 – – 0.2 0.1 0.2 0.2 0.1 – – – 0.2 0.1 – 0.1 0.1 0.1 – 0.1 – 0.5 0.5 0.1 0.1 0.2 0.5 0.3 0.1 0.2 0.2 0.1 0.2 0.1 0.2 0.1 0.1 0.3 0.3 0.4 0.1 0.1 –

SKS SKS SKS SKKS SKS SKKS SKKS SKS SKS SKS SKS SKS SKS SKS SKKS SKS SKS SKS SKS SKS SKS SKS SKS SKS SKS SKKS SKS SKS SKS SKS SKS SKKS SKS SKS SKS SKS SKS SKKS SKS SKS SKKS SKS SKKS SKS SKS SKS SKS SKS SKKS SKS SKKS SKS SKS SKKS SKS SKS SKS SKS SKS SKS SKS SKS SKS SKS SKS SKS SKS SKS SKS SKS SKS SKS SKS SKS

p p g f p p p f p p p p f f f g p p p p p p p f p f f f f f f f f p p f f f p p p f f f f f f f f p p p f f f f f f f g g f f f f f f f p f f f f f

(continued on next page)

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Table 3 (continued ) Station Event

Distance Back-azimuth φ φ error δt deg deg deg deg s

MLR MLR MLR MLR MLR MLR MLR MLR MLR MLR BURAR BURAR BURAR BURAR BURAR BURAR BURAR BURAR BURAR BURAR BURAR BURAR BURAR BURAR BURAR BURAR BURAR BURAR BURAR BURAR BURAR BURAR BURAR BURAR BURAR BURAR BURAR BURAR BURAR TIRR TIRR TIRR TIRR TIRR TIRR TIRR TIRR TIRR TIRR TIRR TIRR TIRR TIRR TIRR TIRR TIRR TIRR TIRR TIRR TIRR TIRR TIRR TIRR TIRR TIRR TIRR TIRR TIRR TIRR TIRR DRGR DRGR DRGR DRGR DRGR

109 118 108 99 103 107 96 88 96 101 99 96 99 98 97 91 92 96 91 94 105 107 107 107 102 108 108 103 109 109 99 97 96 102 96 89 91 95 100 95 105 105 102 100 99 103 100 90 92 103 109 104 110 110 101 110 110 117 117 93 97 100 99 99 105 108 95 87 91 103 104 95 106 100 106

060825 061017 061113 070220 070712 070721 070726 070808 071031 071116 020814 021003 030122 030511 030526 030526 030701 040629 050205 050215 050302 050321 050321 050613 050926 051117 051117 060127 060825 060825 070220 070613 070706 070712 070726 070808 070928 071031 071116 031018 040205 040205 040417 040423 040429 040625 040629 050205 050215 050302 050613 050926 051117 051117 060127 060825 060825 061017 061017 070130 070220 070613 070706 070706 070712 070721 070726 070808 070928 071116 040423 040429 050613 050926 051117

254 68 251 83 272 255 80 100 56 278 57 95 312 82 78 79 81 294 80 78 83 252 252 259 275 257 257 84 254 254 82 298 302 272 79 100 323 55 278 84 80 80 88 94 295 84 296 83 81 86 260 276 258 258 87 255 255 70 70 57 85 301 304 304 273 256 82 102 319 280 89 291 257 273 255

56 57 44 34 36 62 51 64 66 64 128 123 115 143 126 131 127 129 142 116 114 131 139 131 128 141 133 137 128 134 129 114 130 148 141 128 109 122 117 115 96 97 107 121 165 116 144 126 125 113 100 156 93 108 98 93 114 88 120 117 149 147 160 144 131 85 142 118 106 138 167 108 154 170 146

– – 10 15 – 2 17 – 11 24 5 4 5 – 8 11 5 5 – 3 9 5 5 5 5 8 8 – – – 5 – – 13 5 – 21 8 2 – 5 7 5 6 – – 3 9 12 2 14 – 8 9 – – – 17 15 19 3 7 16 16 – 1 1 1 – 1 6 – – – 2

0.8 1.2 1.4 1.0 0.7 1.5 1.1 1.3 1.6 0.8 1.0 1.3 1.3 0.6 1.5 0.9 1.0 1.6 1.0 1.0 1.2 1.2 1.2 1.1 1.0 1.2 1.5 0.8 0.8 0.9 1.1 1.0 0.9 0.8 0.7 1.5 0.7 0.7 1.9 0.6 1.1 0.9 1.3 1.0 0.8 0.6 1.0 1.2 1.4 1.0 1.2 0.8 1.7 0.8 0.9 1.1 0.6 1.4 1.0 0.7 0.9 1.3 1.0 1.5 0.9 2.2 0.7 1.2 0.7 0.8 1.7 1.1 3.2 1.2 1.7

δt error Phase Quality s – – 0.3 0.5 – 0.4 0.2 – 0.1 0.4 0.3 0.3 03 – 0.4 0.2 0.2 0.1 – 0.2 0.3 0.2 0.1 0.1 0.6 0.2 0.1 – – – 0.3 – 0.2 0.2 0.3 – 0.1 0.1 0.2 – 0.1 0.3 0.5 0.3 – – 0.1 0.8 0.1 0.1 0.4 – 0.8 0.1 – – – 0.2 0.3 0.1 0.2 0.1 0.3 0.2 – 0.4 0.1 0.3 – 0.1 0.4 – – – 0.1

SKS SKS SKS SKS SKS SKS SKS SKS SKS SKS SKS SKS SKS SKS SKS SKS SKS SKS SKS SKS SKS SKS SKKS SKS SKS SKS SKKS SKS SKS SKKS SKS SKS SKS SKS SKS SKS SKS SKS SKS SKS SKS SKKS SKS SKS SKS SKS SKS SKS SKS SKS SKS SKS SKS SKKS SKS SKS SKKS SKS SKKS SKS SKS SKS SKS SKKS SKS SKS SKS SKS SKS SKS SKS SKS SKS SKS SKS

f p f f p g f p p p f f f p f g f g p f f f f f f f f p f f g p f f f f p p f f g g f f f p g p f f f f f f p f f f f f g g g g p p g p p g f p p f g

(continued on next page)

94

M. Ivan et al. / Tectonophysics 462 (2008) 89–98

Table 3 (continued )

Table 3 (continued )

Station Event

Distance Back-azimuth φ φ error δt deg deg deg deg s

δt error Phase Quality s

Station Event

Distance Back-azimuth φ φ error δt deg deg deg deg s

δt error Phase Quality s

DRGR DRGR DRGR DRGR DRGR DRGR DRGR DRGR DRGR DRGR DRGR DRGR DRGR DRGR DRGR DRGR VRI VRI VRI VRI VRI VRI VRI VRI VRI VRI VRI VRI VRI VRI VRI VRI VRI VRI VRI VRI VRI VRI BUC1 BUC1 BUC1 BUC1 BUC1 BUC1 BUC1 BUC1 BUC1 BUC1 BUC1 BUC1 BUC1 BUC1 BUC1 IAS IAS IAS IAS IAS IAS IAS IAS IAS IAS IAS IAS IAS IAS BZS BZS BZS BZS BZS BZS BZS BZS CRAR

106 107 107 120 106 95 101 95 101 105 98 91 93 97 99 105 101 97 98 93 104 108 108 103 109 102 110 118 108 93 98 98 98 107 95 91 95 102 91 94 105 107 103 108 108 109 99 98 103 107 96 88 101 109 103 102 110 110 117 97 98 97 104 90 149 94 102 106 96 100 104 99 94 98 104 107

0.2 0.1 – – 0.4 0.2 0.1 – 0.1 0.1 0.3 – 0.1 0.2 0.2 0.2 – 0.4 0.2 – 0.2 0.1 0.3 – 0.4 – 0.1 – 0.1 0.1 – 0.2 0.1 0.1 – 0.2 0.2 0.2 0.4 0.6 0.1 – – 0.4 0.3 – 0.3 0.1 0.3 0.3 1.0 0.8 0.1 – – – 0.4 – – 0.2 – – 0.1 0.2 0.1 0.4 0.4 0.1 0.1 0.2 0.1 0.2 0.2 0.4 0.1 0.2

CRAR CRAR CRAR CRAR CRAR CRAR CRAR CRAR TIM TIM TIM VOIR VOIR VOIR VOIR VOIR VOIR VOIR PLOR PLOR GZR CVD

107 97 97 97 101 90 93 100 94 92 94 94 99 97 102 102 106 92 107 91 93 91

0.1 0.2 0.1 0.1 0.3 – 0.1 0.2 0.1 – 0.1 0.2 0.1 0.1 1.0 0.2 0.5 0.8 – 0.1 0.2 0.1

051117 060825 060825 061017 061113 070130 070220 070706 070712 070721 070726 070808 070928 071031 071116 071118 040423 040429 040629 050215 050302 050321 050613 050926 051117 060127 060825 061017 061113 070130 070220 070613 070706 070721 070726 070928 071031 071116 050205 050215 050302 050613 050926 051117 051117 060825 070220 070706 070712 070721 070726 070808 071116 050613 050926 060127 060825 060825 061017 070220 070613 070706 070712 070928 071016 071031 071116 060825 070130 070712 070721 070726 070928 071116 071118 051117

255 253 253 64 249 52 80 300 270 253 77 98 324 53 276 253 92 294 295 80 85 252 260 275 257 86 255 68 251 56 83 299 303 256 80 321 57 279 81 79 85 259 274 256 256 254 83 303 272 255 80 100 278 261 276 86 256 256 68 84 300 304 273 322 56 57 280 252 52 269 252 77 323 275 252 255

147 141 148 142 143 128 157 112 166 140 142 173 131 126 168 136 8 149 130 −1 12 18 12 29 29 8 8 17 14 8 2 149 133 5 0 163 167 12 152 157 160 161 164 145 149 152 154 174 152 146 160 143 133 161 137 146 140 147 129 145 148 151 135 131 126 133 126 148 128 155 140 124 139 130 143 153

3 2 – – 6 10 – – 2 6 5 – 1 4 7 9 – 11 3 – 6 7 5 – 6 – 2 – 2 5 – 22 5 5 – 4 1 3 5 2 5 – – 6 2 – 5 5 4 2 1 14 8 – – – 4 – – 2 – – 1 3 1 2 5 5 2 11 1 18 1 6 3 1

1.1 1.3 1.3 0.9 1.4 1.2 1.3 1.1 1.6 1.3 0.9 1.7 1.9 1.2 0.9 1.2 0.6 1.1 1.1 1.3 1.5 0.7 1.6 0.9 0.9 2.6 0.8 0.8 0.8 0.8 1.6 1.3 1.1 0.8 1.2 0.9 1.0 0.9 1.4 1.4 1.5 3.3 2.2 1.3 1.9 0.5 1.1 0.7 1.4 1.8 2.3 1.0 0.9 2.4 1.3 0.7 0.9 1.0 1.7 1.0 1.9 1.0 0.9 1.2 0.8 1.9 1.0 0.9 1.1 1.0 0.7 0.6 0.7 1.0 0.8 1.5

SKKS SKS SKKS SKS SKS SKS SKS SKS SKS SKS SKS SKS SKS SKS SKS SKS SKS SKS SKS SKS SKS SKS SKS SKS SKS SKS SKS SKS SKS SKS SKS SKS SKS SKS SKS SKS SKS SKS SKS SKS SKS SKS SKS SKS SKKS SKS SKS SKS SKS SKS SKS SKS SKS SKS SKS SKS SKS SKKS SKS SKS SKS SKS SKS SKS SKKS SKS SKS SKS SKS SKS SKS SKS SKS SKS SKS SKS

g f f f f f f p f g f p g g f g p f g p f g f f f p f p f f f f f f p g g g f f f p f f f f f g f g f p f p f p f f p f p p f g g f f g f f g g f f g f

060825 070613 070706 070706 070712 070808 070928 071116 070706 070808 070928 070130 070220 070706 070712 070712 070721 070928 070721 070928 070928 070928

253 297 301 301 270 99 321 276 299 97 323 54 82 302 271 271 255 321 256 321 322 319

155 136 154 140 112 134 160 117 125 123 119 41 59 7 76 72 59 40 7 0 132 157

1 2 14 – – – 1 2 8 – 5 – 3 4 2 – – 1 – 5 2 1

1.4 1.4 1.4 1.1 1.2 2.9 2.1 1.2 1.4 0.7 0.5 1.4 1.2 1.2 2.2 1.8 1.9 1.7 0.8 0.5 1.4 2.0

SKS SKS SKS SKKS SKS SKS SKS SKS SKS SKS SKS SKS SKS SKS SKS SKKS SKS SKS SKS SKS SKS SKS

g f f f p p g g g p p p g g f p f f f f f f

First 46 results at MLR are from Ivan (2000) and have been obtained with the method presented in the Appendix A. In this case, errors have been derived by evaluating the same time window by using the ah_splitest2 software (Levin et al., 1999). The rest of the results have been derived by using the method presented in the Appendix A. The corresponding errors have been obtained by slightly changing the beginning and the end of the input data strings. Quality: p = poor; f = fair; g = good.

quality factor (good, fair or poor) have been ascribed to all individual measurements, depending on the signal-to-noise ratio and to the similarity between the observed particle motion and the predicted elliptical shape of the processed time window. The average splitting measurements are presented in Fig. 5 and Table 4. For the first 46 events from Table 1, errors have been estimated by using the ah_splitest2 software presented by Levin et al. (1999). For the rest of the estimations, errors have been derived by slightly modifying the beginning/end of the processed data strings. For a very small number of events, “null measurements” have been suspected to be observed, especially at VRI station. In such cases, transverse component (roughly the North–South channel), which should display no energy, is also contaminated by a high seismic noise. Consequently, “null measurements” have not been presented here. 4. Discussion The average splitting parameters (φ=129°, δt=1.1 s) derived from 29 estimations at BURAR station, located in Eastern Carpathians, are close to the observations at Ukrainian stations KOV, UZH and LVV (Dricker et al., 1999) and at the Polish station KWP (Wiejacz, 2001) (Table 2). The fast S polarization direction is parallel to the local trend of the arc, a situation quite common in Central and Western Europe (Bormann et al., 1993; Nicolas, 1993; Bormann et al., 1996; Barruol et al., 1998; Plomerová et al., 2007). Apparently, it is consistent with a lithospheric anisotropy characterized by a compression in the mantle perpendicular to the Carpathians (VCD mechanism). However, the fast polarization direction observed at IAS station is also parallel to Eastern Carpathians, but that station is located in East-European Platform at almost 200 km away of BURAR. A value of φ around 135° is also observed at GZR station (one estimation only, but fair quality), where the local trend of the arc is normal to the observed fast direction. Similar values of the fast S polarization azimuth are obtained for CRAR and BUC1 stations (located in Moesian Platform) and at TIM and BZS (in Dacia-Tisza plate). DRGR station is located in Apuseni Mountains (having no preferred orientation of the structure), but the fast S polarization azimuth is also around 135°, close to the previous PSZ (Ivan et al., 2002) observation. Similar values are obtained at TIRR and CVD (located in Central Dobrudja), close to splitting observed at KIEV (Dricker et al., 1999). For CVD station, only one estimation was available,

M. Ivan et al. / Tectonophysics 462 (2008) 89–98

95

Fig. 5. Average fast shear-wave polarization azimuths and split delay times at Romanian broad-band network.

so an error of the angle determination like 30° cannot be excluded, especially because the higher noise due to the proximity to the Black Sea. Consequently, we consider our results inconsistent with a VCD lithospheric anisotropy for the above mentioned stations. Splitting values at stations located above the Vrancea seismogenic area are quite different from the above regional trend. At station MLR, located in the South-Western part of Vrancea, 44 values are from events with back-azimuth values around 80°, leading to φ = 46° ± 5° and δt = 1.0 ± 0.1 s. For the rest of 40 values from earthquakes around 280°, the splitting values are φ = 51° ± 5° and the same δt value as above. Hence, the results from both back-azimuth ranges are quite similar, leading to an average fast polarization roughly parallel to the local NE–SW strike of the Carpathians. A similar fast polarization angle is obtained at VOIR station, located 70 km West of MLR, but the delay time here is 1.6 s. The δt difference with respect to MLR is considered to be statistically significant (Student t-test criterion) with a probability exceeding 95%. Assuming the anisotropy strength shows no important lateral variations, it suggests a thickening of the anisotropic layer at VOIR with respect to MLR.

At VRI (and PLOR) stations, located in the North-Eastern part of Vrancea, approximately above the boundary of the vertical seismic volume, most fast directions are roughly North–South (Table 3) from 18 events located both in South America and Pacific. For four events in Central America (Mexico, Guatemala and Costa Rica) the average fast polarization azimuth is 140°. Most likely, this indicates a possible azimuth dependence (Fig. 6), associated to the location of VRI in a transition area from φ ~ 50° (like VOIR and MLR) to φ ~ 135° (like BURAR). The splitting results at Vrancea stations are consistent with a fossil lithospheric anisotropy, if a thermo-mechanical controlled continental collision (Cloetingh et al., 2004) is assumed in the SE Carpathians (Fig. 7). Lithospheric thickness beneath stations is inferred from δt values assuming an anisotropic strength of 0.1 s delay per 10 km of anisotropic layer (Barruol and Mainprice, 1993; Barruol and Kern, 1996) and an isotropic asthenosphere. Because δt values from both temporary or permanent stations in Vrancea do not exceed 2 s, the above assumed anisotropic strength value requires a thickness of the anisotropic material less than 200 km. It suggests the high velocity body in Vrancea to be isotropic beneath a depth around 200–250 km.

Table 4 Average splitting parameters at Romanian broad-band stations and 95% confidence errors Station

Latitude

Longitude

Instrument

Date

Number of estimations

φ

φ error

δt

δt error

MLR TIRR BURAR DRGR VRI

45.4912 44.4581 47.63967 46.7917 45.8657

25.9456 28.4128 25.20017 22.7111 26.7277

STS-2 STS-2 KS5400 KS2000 CMG-3ESP

1994.10.09–present 2003.10.13 2002.08.01–present 2004.02.24 2004.02.24

BUC1 IAS CRAR

44.3479 47.1933 44.325

26.0281 27.5617 23.8

3 8 4 8 6 17 6 6 13

1.0 1.0 1.1 1.4 1.0 1.1 1.5 1.3 1.6

0.1 0.1 0.1 0.2 0.2 0.2 0.4 0.3 0.5

45.6188

21.6401

8

138

9

0.8

0.1

VOIR

45.4371

25.0495

7

51

22

1.6

0.4

TIM PLOR GZR CVD

45.7365 45.8512 45.3933 44.351

21.2211 26.6499 22.7767 28.039

2004.09.07 2005.02.01 2004.06.28–2005.08.16 2005.08.16–present 2004.12.14–2005.11.23 2005.11.23–present 2004.08.05–2007.08.23 2007.08.23–present 2007.04.27–present 2005.01.04–present 2006.06.08–present 2007.06.23–present

48 120 129 145 8 140 153 141 140

BZS

KS2000 CMG-40T CMG-40T KS2000 CMG-40T STS-2 CMG-3ESP CMG-40T CMG-40T CMG-40T CMG-40T CMG-40T

84 31 29 21 18 4 15 14 9

3 2 1 1

122 3 132 157

– – – –

0.9 0.7 1.4 2.0

– – – –

96

M. Ivan et al. / Tectonophysics 462 (2008) 89–98

some stations, delay time values suggest the anisotropic layer is thicker in platform areas with respect to the Alpine regions. At least for some stations, the splitting results look to be inconsistent with a vertical coherent lithospheric anisotropy mechanism. The spatial distribution of the broad-band stations and the small number of available data for most stations (except MLR, TIRR and BURAR) does not allow one to clearly identify the source of SKS splitting as a fossil lithospheric anisotropy or an asthenospheric mantle flow. But the first hypothesis is compatible to a continental collision in South-Eastern Carpathians (Cloetingh et al., 2004). In any case, thermo-mechanical modelling in Vrancea area could be refined if anisotropy parameters are included and compared to the splitting results. Fig. 6. Individual splitting measurements at station VRI and PLOR located in the Vrancea area. Fast S polarization azimuth and split delay times are projected into piercing points at 150 km depth. The ellipse is approximately the epicentral area of intermediate depth earthquakes.

In such a case, the presence of lithospheric contacts (possible faults) is required in order to separate the Vrancea block (φ ~ 50°) from the rest of the Romanian territory (φ ~ 135°). Such candidates are Danube fault, Intra-Moesian fault and Peceneaga-Camena fault (Fig. 1). A geodynamic model explaining the rotation (by almost 90°) of the Vrancea block with respect to the Eastern Carpathians is asked too. An alternative explanation for the splitting values at the Romanian stations could be also represented by a parallel, large scale mantle flow (φ ~ 135°), similar to the assumption of Dricker et al. (1999). Note, however, that the absolute plate motion direction in the area is around 248° from North, relative to hotspots frame (Gripp and Gordon, 2002). In this case, fast polarization values at VOIR, MLR, VRI (and PLOR) could indicate a toroidal asthenospheric flow around the Vrancea slab. 5. Conclusions Most stations of the Romanian broad-band network show fast polarization azimuths around 135°, with a notable exception in Vrancea area. At VOIR and MLR, φ is like 50°, with no apparent variation of the splitting parameters with back azimuth. Delay time is significant greater at VOIR than MLR, indicating an increase of the anisotropic layer. Splitting values at VRI display a possible variation with back azimuth, or, less probable, a considerable scattering of the results due to the proximity of the slab edge. Despite the small number of estimation at

Acknowledgements The authors express their deep gratitude to Winfried Hanka, GEOFON staff and IRIS DMC people for continuously maintaining the digital database. We thank Jaroslava Plomerová, Vadim Levin, Lucia Margheriti, Pawel Wiejacz, Petru Negraru and one anonymous referee for very constructive comments and suggestions to improve our manuscript. Some figures were produced using Generic Mapping Tools of Wessel and Smith (1996). Appendix A Here we summarize the theoretical background of shear-wave splitting algorithm (Ivan, 2000). Considering the Radial–Transverse (R–T) coordinate system, an input monochromatic wave sinωt, crossing an anisotropic region, gives the following output (Vinnik et al., 1992): Rðt Þ ¼ cos2 β sin ωt þ sin2 β sin ωðt−δt Þ

ð1Þ

and T ðt Þ ¼ 0:5 sin 2β½sinωt− sinωðt−δt Þ

ð2Þ

where β is the angle between the direction of the fast shear wave and the radial axis, assumed in the range β a (−π/2;π/2), β ≠ 0.

Fig. 7. 2-D cartoon based on Cloetingh et al. (2004) illustrating anisotropic lithosphere in Vrancea area. See Fig. 5 for geographical location. Stars show intermediate depth foci.

M. Ivan et al. / Tectonophysics 462 (2008) 89–98

References

Let x = R(t) and y = T(t). From Eqs. (1) and (2) it follows ðx−ycot2βÞ2 þy2 cot2 ðωδt=2Þ=sin2 2β ¼ cos2 ðωδt=2Þ

ð3Þ

For β ≠ ±π/4, a rotation of the coordinates system is considered x ¼ X cos θ−Ysinθ

ð4Þ

y ¼ X sin θ þ Y cos θ

ð5Þ

with the rotation angle given by
 tan2θ ¼ sin 4β= cos4β þ cot2 ðωδt=2Þ

ð6Þ

In the new (X, Y) coordinate system, Eq. (3) becomes X 2 =a2 þ Y 2 =b2 ¼ 1

ð7Þ

showing that the particle motion due to the shear-wave splitting is an ellipse (or an elliptic arc). For β = 0 or , transverse component vanishes in Eq. (2) and the particle motion is a straight line (“null measurement”). Differentiating the transverse signal of Eq. (2) with respect to time it follows dT=dt ¼ −ωsin2β sinðωδt=2Þ sin ωðt−δt=2Þ

ð8Þ

Hence the time-derivative of the transverse signal depends linearly on the radial signal and on transverse signal itself dT=dt ¼ ωtanðωδt=2ÞðT ðt Þ cos 2β−Rðt Þsin2βÞ

ð9Þ

Let zk ¼ dT=dt ðtk Þ;

yk ¼ T ðtk Þ;

xk ¼ Rðtk Þ

ð10Þ

Eq. (9) shows that the instantaneous values xk, yk and zk are placed on a plane in the appropriate 3-D space, i.e. zk ¼ Axk þ Byk þ C;

ð11Þ

where C takes into account the baseline corrections of the recordings. The coefficients of the plane are related to the unknown value of β and to the time delay δt by β ¼ −0:5atnð A=BÞ

ð12Þ

and δt ¼

 pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Tw Tw atn A2 þ B2 ; π 2π

ð13Þ

where Tw is the wave period. The coefficients of the plane can be obtained by a standard regression procedure, i.e., by minimizing N

∑ ð Axk þ Byk þ C−zk Þ2 ¼ min;

ð14Þ

k¼1

where N is the number of data samples. The derivatives of the transverse signal are evaluated by cubic spline procedure (e.g. Ahlberg et al., 1967; Bhattacharyya, 1969). Note that the azimuth φ of the fast S polarization is related to the back-azimuth bAz and to the value of β obtained from Eq. (12) by u ¼ bAz−β  180 o

97

ð15Þ

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