Guilhem Barruol

Hartmut Kem

Seismic anisotropy and shear-wave splitting in lower-crustal and upper-mantle rocks from the Ivrea Zone-experimental and calculated data

Keywords: plagioclase: Kspar, K-feldspar, hom, hornblende, gar, gamet, sill, sillimanite, pyrox, pyroxene: cpx, clinopyroxenc, opx, orthopyroxene, biot, biotite, spi, spinel, ol, olivine, serp, serpentine, cr, chromite, ox, oxide

To quantify the relationships between anisotropy. S-wave splitting and tectonics, we determined the seismic properties of lower-crustal and upper-mantle rocks outcropping in the lvrea Zone (Northem Italy). We obtained P-and S-wave seismic velocities by laboratory direct velocity measurements and/or by calculations based on the modal compositions of the rocks, the lattice preferred orientations (LPOs), and the single crystal stiffness coefficients. Measured P-and S-wave velocities (6.0-7 .5 km s -1 and 3.6-4.2 km s -1 ) are typical of the lower crust. The P-wave anisotropy is in the range 0-l 0%. Shear-wave birefringence is in the range 0.0-0.6 km s -1 , with typical values between 0.0 and 0.2 km s -1 • In many cases, the birefringence is clearly related to fabric elements (foliation, lineation). Mafic rocks such as anorthosite or pyroxene-bearing gabbros exhibit low P-wave anisotropies ( < 5%) and low shear-wave birefringences (less than 0.1 km s -1 ). In contrast, the seismic properties of felsic rocks such as biotite-bearing gneisses and mafic rocks such as amphibolites display high V P anisotropy ( 10%) and strong birefringence (0.3 km s -1 ). Biotite and amphibole preferred orientations clearly control seismic anisotropy and particularly shear-wave splitting. In these rocks, maximum splitting is observed in directions parallel to the foliation with the fast split shear wave polarized parallel to the foliation plane. To have an overview of the seismic properties of this lower-crustal section at a broader scale, we calculated from our data the anisotropie seismic properties of several hypothetical samples that are perhaps more representative of the regional anisotropy than each sample individually. For instance, the average lower-crustal sample displays an anisotropy of 5.5% for P waves and a birefringence around 0.14 km s I for S waves propagating parallel to the foliation. We observe little splitting for waves propagating at high angle to the foliation. • Ultrnmafic rocks (pyroxenites, pcridotites) 1111 Gabbro, me1agabbro and amphibolitc.� • Gamet pyroxene gabbros (pyriclasitcs) D Mctasedimcnts (stronalites and kinzigitcs) • Marblcs • Strona Ceneri Zone me!apelitcs 11ii Pcrmian granites

Introduction

The Ivrea Zone, northem Italy, is considered to be one of the best examples of an exposed lower-crustal terrane. It provides a unique opportunity for geo physicists and petrophysicists to observe and study a large area (several tens of square kilometres) of rocks formed or metamorphosed at lower -crustal conditions. This zone has been studied by several workers as a potentially good example of layered lower crust (e.g. [START_REF] Hurich | Compositional variation and the origin of deep crustal reflections[END_REF]Hol-liger and Levander, 1994). [START_REF] Fountain | The lvrea-Verbano and Strona-Ceneri Zones, northem Italy: a cross-section of the continental crust -new evidence from seismic velocities of rock samples[END_REF] and [START_REF] Burke | Seismic properties of rocks exposure of extended continental crust-new laboratory measurements from the lvrea zone[END_REF] made laboratory seismic measurements on Ivrea Zone rocks. In these studies, however, no birefringence measurements were made. [START_REF] Burlini | Seismic anisotropy of metapelites from the lvrea-Verbano zone and Serie dei Laghi (N. Italy)[END_REF] measured shear-wave splitting in Ivrea Zone samples, but their work was focused on mid-crustal metapelite of the 'Serie dei Laghi'. In this study, we concentrate on the shear wave velocities and particularly on birefringences of rocks from the westemmost part of the lvrea Zone, which represents the former, pre-tilting, lowermost level of the crust and possibly the uppermost mantle.

The investigation of shear-wave splitting (SWS) in lower-crustal rocks is important for two closely related reasons. First, quantification of possible crùstal contributions to teleseismic SWS may lead to a more precise information of actual upper-mantle delay times and may therefore better constrain the location and magnitude of anisotropy in the Earth. Splitting of teleseismic S waves (SKS and SKKS waves, for instance) has been generally considered to occur in the upper mantle (e.g. [START_REF] Silver | Shear wave splitting and subcontinental mantle deforrnation[END_REF][START_REF] Bormann | Teleseismic shear-wave splitting and deformations in central Europe[END_REF], but particularly in continental regions, one cannot rule out that the crust may contribute to the total splitting. Second, SWS may be used to investigate the nature of the crust. Until now, most splitting measurements were per formed using either teleseismic sources and inter preted in terms of mantle flow, or using local, mid crustal seismicity and interpreted in term of upper crustal, microcrack-induced anisotropy related to up per-crustal stress states (e.g. [START_REF] Kaneshima | Evidence from shear-wave splitting for the restriction of seismic anisotropy to the upper crust[END_REF][START_REF] Peacock | Shear wave splitting in the Anza seismic gap, southern Cali fornia: temporal variations as possible precursors[END_REF][START_REF] Gledhill | Evidence for shallow and pervasive seismic anisotropy in the Wellington region, New Zealand[END_REF]. Sorne recent seismic studies have nevertheless shown that it was possible to obtain an independent measurement of lower-crustal shear-wave splitting either by using P to S conversion at the Moho transition [START_REF] Mcnamara | Azimuthal shear wave velocity anisotropy in the Basin and Range province using Moho Ps converted phases[END_REF] or by using wide-angle seismic reflection experiments to detect this phenomenon [START_REF] Clement | Shear wave splitting in the lower crust beneath the Archean crust of southwest Greenland[END_REF]. In these two studies, a delay time in the range 0.1-0.2 s has been measured and attributed to lower-crustal anisotropy. Laboratory seismic measurements performed by [START_REF] Christensen | Shear wave velocities in metarnorphic rocks at pressures to !Okilobars[END_REF] have already shown that crustal rocks can be strongly anisotropie for shear waves. More recent petrophysical investigations indicate that there is generally a close relationship between the intrinsic anisotropy (generated by preferred crystal orienta-tions), the birefringence, and the rock structure (foli ation and lineation). This relationship may yield information on the crustal structure from shear-wave splitting studies [START_REF] Kem | Fabric-related velocity anisotropy and shear wave splitting in rocks from Santa Rosa mylonite zone[END_REF][START_REF] Kem | The velocity and density structure of the 4000 m crustal segment at the KTB drilling site and their relationship to lithological and mi crostructural characteristics of the rocks: an experimental ap proach[END_REF]Barruol and Mainprice, 1993a). Thus, both petrophysical and seismological developments are pointing the way towards use of SWS as a tool to investigate crustal nature and structure. lt is therefore important to acquire new petrophysical data and particularly birefringence data on lower-crustal rocks.

In this paper, after a brief description of the geologic setting of the study area, we characterize the seismic properties of selected lower-crustal-up per-mantle samples. We used two different ap proaches: ( 1) direct laboratory measurements of seis mic velocities on typical rocks from the lvrea lower-crustal section; (2) calculations of the com plete three-dimensional seismic properties of three samples based on the modal composition, the crystal lographic preferred orientation of major minerais and the single crystal elastic constants. Both methods (direct laboratory measurements and calculations) were applied on several samples. We compare results and analyse discrepancies in Section 5. ln Section 6, we attempt to characterize seismic properties at a more regional scale. Using the experimental data sets, we calculate average anisotropie seismic proper ties of hypothetical rocks that may be representative of the Ivrea lower crust. We finally discuss shear wave splitting in the lower crust in light of these new results.

Geological description

The Ivrea-Verbano Zone and the Serie dei Laghi are classically described as a crustal section through the lower crust of the Apulian plate which was uplifted and tilted during the alpine orogeny (e.g. [START_REF] Berckemer | Topographie des • lvrea korper' abgeleitet aus seismichen und gravimetrischen Daten[END_REF][START_REF] Zingg | Tectonometamorphic history of the Ivrea zone and its relation ship to the crustal evolution of the southem Alps[END_REF]. Generally, structures trend NE-SW (Fig. 1) and layering is steeply dipping. The Ivrea-Verbano Zone and the Serie dei Laghi are separated by vertical faults: the Pogallo line, which is interpreted as pre-tilting low angle fault [START_REF] Hodges | Pogallo line, south Alps, northem Italy: an intermediate crustal level, low-angle normal fau!t ?[END_REF][START_REF] Handy | The structure, age and kinematics of the Pogallo fault zone, southern Alps, northem Italy[END_REF], and the Cossato-Mergozzo-Brissago line [START_REF] Boriani | The Cossato Mergozzo-Brissago line and the Pogallo line (Southern Alps, Northern Italy) and their relationships with the late Hercynian magmatic and metamorphic processes[END_REF], whose nature remains unclear. Severa! high-temperature shear zones have been rec- [START_REF] Zingg | Regional metarnorphism in the Ivrea Zone (Southern Alps, N. Italy): field and microscopie investigation[END_REF]Bro<lie and Rutter, 1987). Sample locations and sample numbers are indicated. e, Sam pies used for the laboratory seismic measurements; 0, samples used for the velocity calculations; () . samp les for which both methods were applied.

ognized in the exposed lowermost parts of the crust and interpreted as ductile normal faults that accom modated post-Hercynian crustal extension [START_REF] Brodie | Deep crustal extensional faulting in the Ivrea Zone of northem ltaly[END_REF][START_REF] Rutter | Structural geome try, lower crustal magmatic underplating and lithospheric stretching in the Jvrea-Verbano zone, Northern ltaly[END_REF]). The regional metamorphism increases to the west from green schist to amphibolite facies in the Serie dei Laghi and from amphibolite to granulite facies in the Ivrea Zone (e.g. Si lis and Tarney, 1984). Our study fo-cuses on the Ivrea-Verbano Zone, the lowermost level of this crustal section.

In the northem part of the study are a, in the V al Strona and Valle d'Ossola (Fig. 1), the outcropping section comprises mainly a metasedimentary se quence composed of metapelites (kinzigites and stronalites) and marbles, and metabasic rocks such as amphibolites and pyriclasites (gamet-bearing

z -0.2 1 1 1 1 1 0 0 0 0 0 0 0 s 0 0 0 0 0 N "' sr v; "" Pressure (MPa) *'• ' • ' • '• *•'•'• '•'•*• '• '•'• '• "'•'•'•'•'
• *-----4:.:. :.:-:$ This rock is composed of hornblende (60%) and plagioclase (40%) . The three P-wave velocities measured along the three structural directions ( x, lineation; y and z, pole of the foliation) and the corresponding average velocity are plotted in (a). The six shear-wave velocities are presented in (b). The shear-wave notation carries information about orientation and is similar to stress and strain notation (e.g. [START_REF] Nye | Physical properties of crystals their representation by tensors and matrices[END_REF]: the first index indicates the direction ofparticle motion and the second the direction ofwave propagation (see the insert). Ys,,, for instance, is a shear wave propagating along the z structural axis and polarized parallel to the x axis. The birefringence along each direction is plotted in (cl. The measured P-and S-wave velocities display hexagonal symmetry: P waves propagate with nearly identical velocities along the x and y structural directions, whereas they propagate at a signifi cantly lower velocity along the z axis. The birefringence is also high and constant for propagation directions parallel to the foliation, whereas it is very low for waves propagating at high angle to the foliation. This property is generally due to a high amphibole or phyllosilicate content. The velocity anisotropy and the birefringence are not significantly affected by pressure and temperature.

• • 1 1 • -� 0----o- - ---O-- ---D------0------0-----D 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 s 0 0 0 0 0 r-- N "' sr "' "" r=t=::=1-it: • � 87=8 � § § q 0 0 0 0 8 8 8 0 0 s 0 0 r-- N "' sr V-. "" Ô"==à====t
metagabbros). The petrography and metamorphism of these units have been extensively studied (e.g. Schmid, I 967;Zingg, I 980;Pin and Sills, I 986;[START_REF] Zingg | Tectonometamorphic history of the Ivrea zone and its relation ship to the crustal evolution of the southem Alps[END_REF]. The whole section displays layering at a I O m to 100 m scale. Several ultramafic bodies outcropping in the western part of the zone are thought to represent upper-mantle slices now incorporated within this lower-crustal section.

In the southem part of the area, in the Val Mastal lone and the Val Sesia, a large vertically layered mafic body, 10 km thick, is exposed. This body is clearly intrusive into the metasedimentary sequence and displays clear magmatic microtextures (e.g. [START_REF] Quick | Synmagmatic deforrnation in the underplated igneous complex of the lvrea-Verbano zone[END_REF]. It is mainly composed of gab broic material differentiated to diorites towards the top of the intrusion. The basal zone, defined as the Lower Layered Group by [START_REF] Rivalenti | Existence of different peridotite types and of a layered igneous complex in the Ivrea Zone of the western Alps[END_REF], is located between the Balmuccia peridotite massif and the mafic intrusion. It is about I km thick and made up by a layering (up to 50 m) of mafic to ultramafic materials such as gamet-bearing metagabbros, pyrox enites, dunites, and also some lenses of metapelitic felsic rocks such as stronalites. These rocks display microstructural evidence to varying degree of plastic deformation under high metamorphic grade condi tions. Numerous rock samples were collected from surface outcrops throughout the area in order to select samples with typical petrography, modal com position and microstructures for the laboratory mea surements.

Experimental measurements of seismic veloci ties

Experimental deuices

Laboratory seismic velocity measurements were made in a 'cubic' pressure apparatus using the pulse transmission technique. Cubic samples (43mm edge) were eut parallel to the main structural directions x, y and z (see insert Fig. 2). The P-and S-wave velocities were measured simultaneously along these three directions, first at increasing confining pressure (up to 600 MPa) at room temperature, and then at increasing temperature (up to 600 or 700 °C) at 600 MPa confining pressure. Splitting of shear waves is obtained for each direction of propagation by two sets of oriented transducers with perpendicular polar ization planes, and with the fast and the slow shear waves polarized parallel and normal to the main structural planes ( xy, yz and xz ). Each set of results is composed of nine velocities: three P-wave veloci ties and six S-wave velocities.

V s(.n --,y> V S(yx-:.,) (km s-1 ) (kms 1 > (kms-1 ) (%)

(kms-1 ) (kms-1 ) (km s-1 ) (kms-1 ) (km s-1 ) (kms-1 ) (km s-1 ) (kms

Experimental results

Fourteen lower-crustal samples and two mantle rocks were selected for the laboratory seismic mea surements. Sample numbers, along with the modal compositions of the rocks, are listed in Table 1. The modes were determined by scanning electron mi croscopy (SEM) image analysis techniques using backscattered electrons (e.g. [START_REF] Lloyd | Review of instrumentation, techniques and applications of SEM in mineralogy[END_REF].

The P-and S-wave velocities of the 16 specimens measured at 600 MPa confining pressure (room tem perature) are summarized in Table 2. For each sam ple we report the three P-wave velocities, the V P anisotropy, the six shear-wave velocities and the three corresponding birefringence values. At increas ing pressure, P-and S-wave velocities typically show a steep non-linear velocity increase up to 200-300 MPa, which is interpreted as closure of microc racks (e.g. [START_REF] Kem | Laboratory seismic measurements: an aid in the interpretation of seismic field data[END_REF]. At higher pressures, a slight, linear increase of velocities is observed (see Fig. 2). lncrease of temperature at high confining pressure (600 MPa) results in a slight, linear decrease of the

Pressure derivatives

Temperature derivatives (r oom temperature) (600MPa) (lo-4 kmÇ I MPa-1 ) (-l0-4 kms-10 c- wave velocities. These linear velocity variations re flect the intrinsic rock properties which are con trolled by the volume percentage of major minerais, their single crystal elastic properties, and their lattice preferred orientations (LPO). The pressure and tem perature derivatives (see Table 3) were calculated from these linear trends and they allow one to ex trapolate seismic velocities for any P-T condition within the stability field of the constituent assem blage of rock-forming minerais. On the basis of the isotropie seismic velocities of these lower-crustal rocks, we also calculated their Poisson's ratios.

Calculation of seismic velocities from lattice preferred orientations

Seismic properties of three rock samples were calculated through the Christoffel equation [START_REF] Crosson | Voigt and Reuss prediction of anisotropie elasticity of dunite[END_REF] combining single crystal densities, single crystal stiffness coefficients and LPO of the constitutive minerai phases, in their modal propor-tions. This enables us to determine the 21 elastic coefficients (the 6 X 6 symmetric matrix) character izing the aggregate intrinsic elastic behaviour and the complete anisotropie seismic velocities (V p , V 5 1 , V 52 , seismic birefringence, orientation of the shear-wave polarization planes ... ). Details of the calculation methods may be found in several studies (e.g. Baker and Carter, 197 2;[START_REF] Peselnick | Velocity anisotropy in a mantle peridotite from the lvrea Zone: applica tion to upper mande anisotropy[END_REF][START_REF] Siegesmund | Anisotropy of Vp and Vs in an amphibolite of the deeper crust and its relationship to the mineralogical, microstructural and texturai characteristics of the rock[END_REF]. We used a computer program devel oped by [START_REF] Mainprice | A FORTRAN program to calculate seismic anisotropy from the lanice preferred orientation of minerais[END_REF] for the calculations and the spatial representation of the seismic velocity variations. We made these velocity calculations on three samples: an amphibolite, a kinzigite and a lherzolite. Obviously, these three samples cannot be representative of the whole study area but they repre sent important lithologies and they add new and complementary data to the work of Barruol and Mainprice (1993b). The crystallographic measure ments were perfonned with an optical microscope equipped with a universal stage using the methods already described by Barruol and Mainprice (1993b).

Amphibolite 90VS33

Automorphous and elongated grains of amphibole define a clear lineation. The grain size is typically in the range 0. 2-1.0 mm. The hornblende crystallo graphic c-axes (Fig. 3(a)) form a strong maximum close to the lineation. b-Axes are grouped around the y structural axis and the poles of the ( 100) planes are statistically oriented close to the pole of the foliation. Subautomorphous plagioclase grain size is around 0.5 mm. In thin section, most of grains exhibit an albite twin (parallel to the (010) crystallographic plane) roughly parallel to the foliation. This kind of microstructure is typical of those observed in other Ivrea Zone mafic rocks. For this reason, we took as representative the plagioclase LPO measured in the pyroxene-rich gabbro 87VS14a sampled in the Val Sesia, in the same metamorphic grade (Barruol and Mainprice, 1993b). This plagioclase fabric is charac terized by b-axes concentrated close to the pole of the foliation and c-axes statistically oriented close to the lineation.

Single crystal elastic stiffness coefficients used in these calculations were reported by [START_REF] Aleksandrov | The elastic proper ties of rock forming minerais Il: Layered silicates[END_REF] for hornblende and by [START_REF] Aleksandrov | Velocities of elastic waves in miner ais at atmospheric pressure and increasing precision of elastic constants by means of EVM (in Russian)[END_REF] for plagioclase. P-Wave velocities in the hornblende single crystal exhibit a maximum close to the c-axis and a minimum close to the pole of the (100) plane. In the plagioclase single crystal, the maximum V p is sub-parallel to the b-axis and the minimum is close to the a-axis. Despite the fact that plagioclase and hornblende fabric have some de structive effects on the resulting anisotropy when summed together, hornblende (60% of the rock) clearly controls the resulting P-wave velocity distri butions. The maximum V p (7.2 km s-1 ) corresponds to the amphibole lineation and the minimum (6.5 km s-1 ) to the pole of the foliation (Fig. 3(b)). The P-wave anisotropy is significant (10.9%). The shear-wave properties of the amphibolite are also controlled by the amphibole fabric. The plagioclase single crystal birefringence displays a complex pat tern (e.g. [START_REF] Siegesmund | The effect of plagioclase textures on velocity anisotropy and shear wave splitting at deeper crustal levels[END_REF] and induces a weak birefringence for the plagioclase aggregate. On the other hand, the high birefringence (greater than O. 7 km s -1 ) of hornblende single crystals in the (100) crystallographic plane and the low birefrin gence parallel to the a-axis are responsible for the pronounced shear-wave splitting (greater than 0.25 km s -1 ) parallel to the foliation ( xy-plane) with the fast shear wave polarized parallel to the foliation. Birefringence is very weak for propagation direc tions normal to the foliation.

Kinzigite 87VS57b

This metapelite (sedimentary rock metamor phosed in the amphibolite facies) was sampled in the G Opxke3 e

Val Sesia (Fig. 1). The rock exhibits a foliation strongly marked by fiat biotite crystals. Biotite and sillimanite crystals are automorphous and their grain long axis is about 5 mm. The biotite main cleavage (crystallographic plane (001)) is systematically ori ented parallel to the foliation. Biotite LPO (Fig. 3(c)) was measured in a similar kinzigite (87MA161; see location, Fig. 1) by Barruol and Mainprice (1993b).

The quartz is xenomorphous and the grain size ranges from 0.2 to 1.0 mm. Plagioclase grains are subauto morphous and their grain size is 0.5-1.0 mm. Thin section study revealed that quartz and pla gioclase do not display evidence of preferred orienta tion. We therefore assumed a random orientation for these two minerais. The seisrnic properties of this metapelite were hence calculated using the biotite LPO. Muscovite single crystal stiffness coefficients [START_REF] Vaughan | Elasticity of mus covite and its relationship to crystal structure[END_REF] were used for these calculations. Sillimanite has not been taken into account in these calculations. Burlini and Foun tain ( 1993) quantified the role of the sillimanite in the seismic properties of the 'Serie dei Laghi' metapelites by direct velocity measurements and cal culations. They showed that the crystallographic c axes oriented close to the lineation generate a high P-wave velocity in that direction. Sillimanite-rich metapelites (volume content greater than 15%) there fore display orthorhombic properties for compres sional waves. Sillimanite content in the kinzigite VS57 being around 5%, we assumed this minerai may have only a second-order effect on the seismic properties. The whole-rock seismic properties (Fig. 3(d)) display a P-wave pattern with high velocities (greater than 6.8 km s-1 ) for waves propagating par allel to the foliation and significantly lower velocities (Jess than 5 .8 km s -1 ) normal to the foliation, giving rise to a high P-wave anisotropy (21 %). The shear-wave birefringence pattern displays a band of very high values (greater than 0.55 km s -1 ) parallel to the foliation. Fast split shear waves are further more systematically polarized parallel to the foliation plane. On the other band, birefringence is very weak (Jess than 0.05 km s -1 ) for shear waves propagating normal to the foliation.

Lherwlite ke3

This lherzolite crops out within the Balmuccia peridotite massif. It is characterized by a typical coarse granular texture and displays evidence of plastic deformation. Olivine shows a classic LPO {Fig. 3(e)) with a strong maximum of [010]-axes close to the pole of the foliation whereas the [100] are parallel to the lineation. The orthopyroxene LPO is typical of upper-mantle rocks (e.g. [START_REF] Boudier | Structural study of the Balmuccia massif (western Alps): a transition from mantle to lower crust[END_REF]: a-axes are grouped in a maximum close to the pole of the foliation. The c-axes form a band in the foliation plane with a maximum close to the lineation.

The stiffness coefficients of the olivine and py roxene single crystals used for the calculations are those determined by [START_REF] Kumazawa | Elastic moduli, pres sure derivatives and temperature derivatives of single crystal olivine and single crystal forsterite[END_REF] and by [START_REF] Weidner | Elasticity of orthoen statite[END_REF], respectively. The whole-rock seismic properties, and particularly the P-wave properties, are controlled by olivine, which represents the major volume of the rock (about 80%). The rock slow P-wave direction (7.95 km s-1 ) is parallel to the olivine [O 10]-axes (Fig. 3(f)). The [100]-axes (fast P-wave direction in olivine single crystals) concentrated close to the lineation induces a high V P (8.87 km s -i) in this direction. The shear wave properties of this rock are also controlled by the olivine fabric. The [010] olivine single crystal crystallographic direction is characterized by a weak birefringence. This explains the very weak birefrin gence (Jess than 0.05 km s -1 ) for shear waves propa gating at high angle to the foliation. The olivine single crystal maximum birefringence is located be tween the [100] and [001] crystallographic axes. The band of [001]-axes parallel to the foliation with a maximum corresponding to the y structural axis generates a highly birefringent zone (greater than 0.20 km s -1 ) within the foliation, with a maximum (0.40 km Ç 1) close to y. S-Wave seismic properties of kimberlite nodules [START_REF] Mainprice | An evaluation of the factors affecting shear wave splitting in the mantle from petrofabric measurements of mantle xenoliths[END_REF] display the same patterns of high birefringence close to the y direction. In the foliation plane, fast split shear waves are systematically polarized parallel to the foliation.

S. Comparison between measured and calculated seismic properties

Seismic properties were determined using labora tory measurements made on rock samples and/or calculations from petrofabric data. Both methods were applied to several samples. This enables us to compare the data and to analyse the discrepancies of the results obtained by both methods on four sam ples: the three samples studied in the present work (the metapelite VS57, the lherzolite ke 3 and the amphibolite VS 33) and one sample (the magmatic gabbro MA203) for which calculations were performed by Barruol and Mainprice (1993b). In this section, we compare measurements obtained at 600 MPa confining pressure (to minimize the influ ence of the microcracks) with those calculated from the LPO.

Fig. 4 displays the ratio (in per cent) between measured and calculated seismic properties consider ing the medium as anisotropie for the P-waves using the seismic velocities measured along each structural axis ( x, y or z) and considering the corresponding P and S velocities. Severa! features stand out: ( 1) most of the calculated values show discrepancies in the range of about ± 5% compared with the measured ones; (2) for a given sample. variations between the various structural axes show little scattering (in a range of about 5%); the average value between the three directions may hence be considered as repre sentati ve and suitable for the comparison; (3) there is no systematic trend. The measured velocities are sometimes higher but also sometimes lower than calculated ones. The only parameter displaying a systematic variation is density. The measured density (obtained from the size and the weight of the cubic specimen) is systematically higher than the calcu lated density (obtained from the rock modal compo sition and the single crystal densities). Calculation derived densities are smaller than those derived from the volume and the mass of the sample cubes be cause the calculations do not take into account high density accessory minerais, such as Fe-oxides.

Rock composition

The modal composition of the rock is one of the main factors that contrais the final results. Composi tions were determined by image analyses of digitized views of thin sections obtained from SEM backscat tered electrons. This approach enables us to deter mine directly for each image the surface area of each minerai phase. Samples (about 10cm 2 ) were digi tized in several images (10-20, depending on the rock grain size). Discrepancies between our mea sured and calculated results arise in two ways: ( 1) The composition measured from thin sections may differ from the cube specimen; (2) in the calculations we do not take into account minerai phases that represent Jess than 5% of the rocks. For example, oxides may strongly influence the seismic properties.

Seismic properties

Measured/calculated-Voigt ( % )

115 -.------------------, 110 - X 0 105 ----• -------.. ----------------• --- 2 e D 100 -t---iî=J-----40 �----,î=--------t 95--------------------------------- 90 - 85 1 1 1 1 r-- cr, "' "' "' .l;l V) > > D Vp//Z t,. Vp//Y 0 Vp//X + Vp mean (Voigt) X Vs Mean (Voigt)
• Density (g/cm3)

Fig. 4. Comparison between measured and calculated seismic properties of four samples on which both methods were applied. Ratio (in per cent) between the measured and calculated values of the P-wave velocities (Voigt average) along the three structural axes ( x, lineation; y and z, pole of the foliation) and also between the measured and calculated density, and V5 • A ratio of 1 00% means that we obtained the same results from laboratory measurements and calculations. This diagram clearly shows that the differences between measured and calculated properties are in the range ± 5%.

Vp (km/s) 8.0--.------------, 7.5

Sample 7

• 0 Sample V S 33 7•0 Amphibolite 6.5 6.0 ,8.5

VS57 6.5 Kinzigite 6.0 -a--Yp//X voigt -----•----Yp/Nv oigt •• • •••• •••••• y� -1(!igt
� •-•-----•---••& •.. . .. ••••••• • •••••••• • ••••• •••••-. . .. 5 .5 -'--.---r---.--..---.,..-.J � %amph-%plagio 9.0-
Sample 8•0 ke3 7.5 Peridotite 7.0 6.5 6.0 ----------7.5

•• •• ••••• • ••••• •••••---••• • ••• ••••• 5 .5 -'--
Sample 7.0 MA203 Magmatic 6 • 5 Gabbro 6_0 ,;
"'

;:ls %plagio-%opx

Birefringence (km/s) -----------, 3.3 3.2 3.1 3.0 2.9 2.8 2.7 2.6 _._...,...._..,.._.....,.._.....,.._....,..__.

0.8-.----------� 0.6 0.4 0.2 -a--Birefr.//X voigt • • • • ••-• • • Birefr.//Y voigt ••••••••••••• ••••• Birefr.//

zj � %plagio-%opx

To quantify the influence of the composition on the resulting seismic properties, we calculated for the four samples the three most important seismic pa rameters for various compositions: the P-wave veloc ity, the birefringence and the rock density, and we compare these values with the measured ones. Re sults for each sample are grouped together in Fig. 5. Each diagram displays the values measured at 300 and 600 MPa confining pressure (this allows one to have an idea of the pressure derivatives), the calcu lated values for measured composition, and the cal culated values with slightly different compositions: for each rock we calculated the seismic properties considering variations of ± 10% in the proportions of each minerai phase (see explanation in the figure caption).

The diagrams in Fig. 5 display the following general features: 1. there is no systematic variation. Calculated V P is generally higher than measured for the kinzigite and the lherzolite sample but the gabbro MA203 displays lower calculated P-wave velocities. 2. The general behaviour of the anisotropy compares fairly well: for both P-wave velocities and bire fringences, the hierarchical organization between the three structural axes is well preserved (for example V P ,• > V P y > V p ), except when the abso lute differences are small. For instance, the kinzigite VS57 has the following birefringence pattern: a very small value along the z structural axis and high values along the x and y axes. The highest measured birefringence is along the y axis whereas the highest calculated birefringence is along the x axis, but in both cases the interme diate birefringence is very close to the maximum. This qualitatively important discrepancy (the maximum calculated is oriented along the x and not the y structural direction as measured) is not quantitatively fondamental because the absolute variations are small. The measured and calculated birefringence patterns of the gabbro MA203 are differently organized but the absolute values are very weak (Jess than 0.10 km s-1 ) and this differ ence may not be considered as inconsistent. 3. Fig. 5 shows that a relatively small number of minerai phases controls the main seismic proper ties. Biotite and amphibole control the anisotropy of the kinzigite and the amphibolite, respectively. On the other hand, plagioclase does not appear to play an important role: the variations of the pla gioclase content ( ± 10%) in the gabbro MA203 generate minor variations in the P-wave velocities and weak and complex variations in the birefrin gence.

Densities

The difference between the measured and the calculated densities cannot directly explain the dif ferences between the two methods. Comparisons of densities in Fig. 5 show that calculated values are generally lower than measured. On the other hand, calculated P-wave velocities are generally higher than measured. For a given rock, characterized by its elastic stiffness matrix, the effect of a higher density in the velocity calculations would be to increase the calculated velocities and therefore to separate the calculated velocities from the measured slightly more. Only the gabbro MA203 displays compatible V P and density trends: both calculated velocities and densi ties are lower than measured velocities and densities.

Microfractures and porosity

The effect of microfracturing on seismic anisotropy may be inferred from Fig. 6, in which the measured V P anisotropy is plotted against the confin ing pressure. These curves display the variation of anisotropy, i.e. the variations of the differences be tween the minimum and maximum V p• In a medium Fig. 5. Influence of the rock composition in the comparison between measured and calculated seismic properties for the four samples on which both techniques were applied. V P is shown on the left, birefringence in the middle and density on the right. The diagrams show the measured properties for the three structural directions (at 300 and 600 MPa) and the calculated ones for different modal compositions. From the initial composition of the rock, seismic properties were calculated for variations of ± 10% of the amount of each minerai phase in the rock. For the kinzigite VS57, for example, 50-30-20 (horizontal axis) means that the calculation was perfonned using 50% biotite, 30% plagioclase and 20% quartz. with a randomly distributed crack fabric, the overall anisotropy should remain constant with increase of pressure (isotropie sample compaction). The lherzo lite ke3 and the amphibolite VS33 do not display strong variations of anisotropy with increasing pres sure. This means that either there are no cracks in the specimen or these cracks have no preferred orienta tions. Above 300 MPa, anisotropy varies slightly and the slope is quasi-linear. This is controlled by the preferred orientation of minerais (e.g. [START_REF] Kem | Fabric-related velocity anisotropy and shear wave splitting in rocks from Santa Rosa mylonite zone[END_REF][START_REF] Siegesmund | Complete seismic prop erties obtained from microcracks fabric and textures in an amphibolite from the lvrea Zone, Western Alps, Italy[END_REF]. Below 200-300 MPa, the anisotropy may be strongly affected by pressure variations. This is related to the preferred orientation of microcracks which are pro gressively closed as pressure increased. The strong variation of seismic anisotropy for the kinzigite VS57 and the gabbro MA203 clearly indicates the presence of preferred orientation of the microfractures in the specimen.

-•-•••••O-•••••• Kinzigite VS57 ----�----AmphiboLiteVS33 ---o---Gabbro MA203 -• -• -o-• -• Lherzolite ke3 • • u.•••o .... D•-••D•--•�----o � ••D••••-D•••-0---• 1�&c�--Q---o-.. -�--_-"ê---�---�• --:s.•.--s-:.-� . •- o, 0

Measured lattice preferred orientations (LPO)

Two major problems related to the petrofabric data may arise when calculating seismic properties: 1. owing to the difficulty of acquiring the crystallo-graphie orientations of some minerais, caused by their low crystallographic symmetry (the plagio clase triclinic, for instance), or because of the small grain sizes, the orientation fabrics of these minerai species may have to be considered as random. We made this assumption for the quartz and the plagioclase in the kinzigite sample, and in that particular case the comparisons with the di rect velocity measurements show fairly good agreements. This is a result of the overwhelming control of the biotite on the seismic properties. 2. The measured LPO may not be representative for the rock. This can arise if the number of mea sured grains is too small. Moreover, a representa tive measurement of the LPO for low-symmetry minerais (monoclinic and triclinic minerais; pla gioclase, for instance) is difficult to obtain, be cause many crystals are not appropriately oriented to be measurable. This may result in a grain selection in the fabric. To avoid or at least to minimize this problem, plagioclase crystallo graphic orientations were measured on two per pendicular sections (Barruol and Mainprice, 1993b).

The calculation assumptions

The calculation of the elastic properties of polymineralic aggregates is based on the Voigt, Reuss or Hill approximations. The Voigt average assumes a uniform strain inside the sample, the Reuss average a uniform stress, and the Hill assumption corresponds to the arithmetic mean of the Voigt and Reuss bounds. [START_REF] Mainprice | Methods of caJculating petrophysical properties from lattice preferred orientation data[END_REF] showed that the differences between the two approximations in crease with increase in the aggregate anisotropy. In particular, shear waves are more affected than P waves. We have calculated the velocities of these rocks with the different average assumptions and compared the results with the data. The results show no systematic trend. The V oigt assumption is more consistent with the measured values for samples VS57 and VS33, but the Reuss assumption is slightly better for the Iherzolite ke3 and the gabbro MA203. Except for the gabbro MA203, the calculated P-wave velocities generally give a better fit (in the range ± 5%) to the measurements than do the S-waves (in the range ± 10%). These observations clearly indi-cate that some differences between measured and calculated velocities may be explained by these as sumptions.

In conclusion, the calculated and measured seis mic properties are comparable, at least to a first approximation. Despite some simplifications used for two samples (minerai phase considered as isotropie and LPO obtained on a different sample), qualitative (orientation of fast and slow velocities, for example) and quantitative (magnitude of the velocities, bire fringence) results are in reasonable agreement, within the 95% confidence interval. Part of the observed discrepancies may be attributable to inaccuracies in the determination of the modal composition of the rock, to the calculation assumptions, to inaccuracies in the single crystal elastic constants (particularly for the plagioclase) and to non-modelled variations of the lattice preferred orientations. But we cannot rule out other factors, such as the degree of alteration and the effect of grain shapes and phase contiguity that are not taken into account in the calculations. Also, experimental problems such as the fixed shear-wave transducer orientations or the presence of large ve locity gradients within some samples may affect our results.

Bulk anisotropie properties of the lower crust

The extrapolation of laboratory measurements to results from field seismic experiments is problematic for seismologists and petrophysicists. Laboratory-de rived seismic properties are obtained using a wave length of a few millimetres and the results are inter- The 'intrusion Val Sesia' sample is our attempt to characterize the seismic properties of the gabbro to diorite mafic intrusion. Its elastic constants were determined using 75% of the magmatic gabbro MA203 and 25% of the diorite MA188. The corre sponding calculated seismic properties define the same pattern as the gabbro MA203, but the overall anisotropy is lower than for this rock ( V P anisotropy 3.5% and maximum birefringence 0.1 O km s -1 ).

We used the nine seismic velocities (three P waves and six S waves; see Table 2) of each hypo thetical sample to determine the stiffness coefficients characterizing their elastic properties (Table 4). These constants enable one to extrapolate the seismic ve locities to the whole space. The number of direct measurements enables us to determine only the elas tic coefficients assuming the medium has an axial symmetry. We used the transformation relationships reported by [START_REF] Christensen | Seismic anisotropy in the upper mantle[END_REF] and made the two required assumptions: (1) the medium has transversely isotropie elastic properties around the z structural axis (this holds particularly for the S waves; see, for instance, Fig. 7, but is sometimes Jess true for the P waves); (2) the P-wave velocity in a direction at 45 ° between the x and z structural axes corresponds to the average value between Vr, and Vr,• The calculation of the elastic stiffness coeffi cients is based on the P-wave velocity parallel to the z-axis. on the P-wave velocities parallel to the folia tion (defined as V P x= V r y = (V P x+ V p y )/2), on the values of the two fast shear waves (defined as V s y x = V s ,y = (V s ,y + V s y )/2), and on the other four S-wave velocities corresponding to the average of the four velocities (V 5 ,, = V s , y =Vs,,= V sy : = Calculated stiffness coefficients of the elastic tensor C, 1 characterizing the elastic properties of the three selected samples and the hypothetical average sam pies ( VSzx + Vsz y + Vsxz + Vs y )/4). The resulting stiff ness tensors (C;) describing the average elastic properties of these hypothetical samples are listed in Table 4.

Shear-wave splitting in the lower crust

Our calculations clearly show that the mafic rocks such as gabbros and pyroxenites are not efficient generators of significant shear-wave splitting. On the other band, as already shown by several workers [START_REF] Siegesmund | Anisotropy of Vp and Vs in an amphibolite of the deeper crust and its relationship to the mineralogical, microstructural and texturai characteristics of the rock[END_REF][START_REF] Burlini | Seismic anisotropy of metapelites from the lvrea-Verbano zone and Serie dei Laghi (N. Italy)[END_REF][START_REF] Ji | Shear-wave velocities, anisotropy and splitting in high grade mylonites[END_REF]Barruol and Mainprice, 1993a), amphibole-and phyllosilicate-bearing rocks are strongly anisotropie and may generate shear-wave splitting in the lower crust. Considering the wave length of a teleseismic shear wave such as an SKS wave, the crust may contribute to the total splitting if the crustal anisotropy appears at a similar scale. Thus, one may expect a crustal contribution to the teleseismic shear-wave splitting if the crustal compo sition and structure homogeneous enough at a large scale. From the calculated average samples, the birefringence displays some pervasive features: high birefringences for waves propagating parallel to the foliation and weak birefringences for waves propa gating at high angle to the foliation. The regional structure of the study area has furthermore a region ally nearly constant orientation. The present-day lay ering is generally oriented NE-SW and is steeply dipping. In a seismic shear-wave experiment record ing crustal splitting of vertically propagating shear waves, one can expect to measure fast split shear waves oriented NE-SW (i.e. parallel to the regional foliation and particularly to the kinzigite foliation). The magnitude of the delay time is more difficult to predict because it depends on the thickness of the anisotropie layer and on the magnitude of its anisotropy. For a seismic ray propagating in a given direction, the S-wave anisotropy is controlled by the composition of the medium but also by the orienta tion of the layering (Barruol and Mainprice, 1993a). The laboratory data and the seismic properties of the hypothetical mean rock calculated above may give some quantitative constraints and a reasonable upper and lower bound for the delay time. A maximum delay may be obtained by considering the kinzigite sample VS57. We calculated delay times of about 0.3 s for waves propagating parallel to the foliation through a 10 km thick layer with this composition. This value may be considered as an upper bound for the delay time because the rock is strongly anisotropie and because the calculations do not take into account several factors that would be included in a real field seismic experiment using longer wavelengths, such as lithological heterogeneities, fractures of the upper crust and variation of structural orientations. These three factors will almost systematically reduce the delay time except if microcracks are oriented parallel to the regional foliation. A second calculation has been done using the seismic properties of the aver age crustal sample. The calculated delay times are in this case about 0.1 s per 10 km of rock. Given the method by which the seismic properties were ob tained, one may assume this calculation takes into account important compositional heterogeneities and that this delay time may represent a more realistic lower bound.

Conclusions

We investigated the seismic properties, particu larly the shear-wave birefringence, of lower-crustal rocks by combining two different methods: (!) labo ratory seismic measurements at various pressures and temperatures; (2) velocity calculations, based on modal composition, LPOs of major minerais, and single crystal stiffness coefficients and densities. Both methods were applied to four samples.

The measured seismic velocities, particularly of P waves, are typical of those of the lower crust. In numerous samples, significant velocity anisotropy is evident, and shear waves generally display strong splitting parallel to the foliation. At normal incidence to the foliation, shear-wave splitting is practically absent. The laboratory-derived and calculated veloci ties are in good qualitative and quantitative agree ment. We discussed the basic effects that may ex plain the discrepancies, such as rock composition, density, microfracturing, accuracy of the LPO and the basic assumptions used in the calculations.

To make a link between direct velocity measure ments performed on hand specimens and large-scale seismology, we determined the elastic properties of hypothetical samples, which we consider to be more representative of large-scale lithological units. The calculated mean properties of the Ivrea Zone lower crust display important characteristics of hexagonal symmetry. The biotite and hornblende fabrics and the single crystal properties of these minerais clearly control the anisotropy and the S-wave splitting in the lower crust.

From our birefringence measurements performed on lower-crustal samples and assuming the anisotropy is mainly controlled by the rock fabric, we predict fast crustal split shear waves oriented NE-SW in a field seismic experiment, i.e. parallel to the present day regional banding in the Ivrea Zone. Sorne simple calculations on the amplitude of the delay time leads us to predict high values, of around 0.1 s per 10 km of anisotropie layer.

Fig. 1 .

 1 Fig. 1. Schematic map of the Ivrea Zone showing the various lithologie units (after[START_REF] Zingg | Regional metarnorphism in the Ivrea Zone (Southern Alps, N. Italy): field and microscopie investigation[END_REF] Bro<lie and Rutter, 1987). Sample locations

  -o----Yp-Z (Km/s) ........ + ........ Yp-Y (Km/s) -----6----Yp-X(Km/s) V p average (Km/s) -0--a--a-a-o,cô-�Ô'=Ô'�o Y � ........ ,0 ........ Ys(xz-yz) (Km/s) "' 0 . 2-D ----{J----Ys(xy-zy) (Km/s) ao.1-.. o .. --o . . -0---o--•0 ... 0 .. -0 ... 0 ... -0 ci'i-0.1-é? o .. .

Fig . 2 .

 2 Fig .2. Effect of pressure (at room temperature) and of temperature (at 600MPa) on P-and S-wave velocities, for the amphibolite 90VS33. This rock is composed of hornblende (60%) and plagioclase (40%) . The three P-wave velocities measured along the three structural directions ( x, lineation; y and z, pole of the foliation) and the corresponding average velocity are plotted in (a). The six shear-wave velocities are presented in (b). The shear-wave notation carries information about orientation and is similar to stress and strain notation (e.g.[START_REF] Nye | Physical properties of crystals their representation by tensors and matrices[END_REF]: the first index indicates the direction ofparticle motion and the second the direction ofwave propagation (see the insert). Ys,,, for instance, is a shear wave propagating along the z structural axis and polarized parallel to the x axis. The birefringence along each direction is plotted in (cl. The measured P-and S-wave velocities display hexagonal symmetry: P waves propagate with nearly identical velocities along the x and y structural directions, whereas they propagate at a signifi cantly lower velocity along the z axis. The birefringence is also high and constant for propagation directions parallel to the foliation, whereas it is very low for waves propagating at high angle to the foliation. This property is generally due to a high amphibole or phyllosilicate content. The velocity anisotropy and the birefringence are not significantly affected by pressure and temperature.

Fig. 3 .

 3 Fig. 3. (a), (c) and (e): lattice preferred orientations (LPOs) of three selected samples, presented on equal-area projection, in the structural reference frame (x, y and z). Foliation is north-south (continuous line) and lineation north-south. Contour intervals: 1, 2, 3, 4, 6, 8, 12, 14%. (b), (d) and (f): three-dimensional variations of the elastic properties of the corresponding rocks: P-wave velocities (left), variations of birefringence (middle) and orientation of the polarization planes of the fast split shear waves (right); each arc segment is part of a great circle corresponding to the orientation of the polarization plane. The modal composition of each rock is displayed in the pie diagram (right). (Note that contour intervals are not the same.)

�

  .... Ji. . . . .. . . .. . . . . . 5 . 5 ��,--,--,--,--:;:-..-..--..-J

  r---.---.--..---.,..-.J � ;:s %oliv-%opx 8.0 ........

  ...L.....,....-..,..-.....--....... -....... ..J

  0

Fig. 6 .

 6 Fig.6. Effect of confining pressure on P-wave anisotropy for the four samples on which seismic properties were calculated and experimentally determined. The large variations of anisotropy for the kinzigite and the gabbro indicate that these rocks are affected by non-randomly oriented microfractures. The velocity vs. pres sure relations of the amphibolite and the lherzolite indicate that either there are few initial microcracks or that the microcracks are randomly oriented.

Table 3

 3 Bulk densities, average P-and S-wave velocities and pressure and temperature derivatives of wave velocities

	Samples	Density	Poiss on	Average
		(g cm-3 )		velocities (km s-1 )
				V p	V s
	90VSl2	3.183	0.27	7.02	3.94
	90VSl9	3.096	0.26	6.91	3.94
	90VS33	3.111	0.26	6.92	3.95
	90VS46	2.753	0.17	6.09	3.83
	90VS48	2.897	0.28	6.85	3.80
	90VS53b	3.280	0.27	7.23	4.04
	90VS54a	3.016	0.22	7.03	4.21
	90VS77	3.154	0.27	7.22	4.07
	9IV07	3.087	0.27	7.18	4.05
	91V08	3.01 l	0.23	6.74	4.00
	87VS57	2.864	0.24	6.31	3.69
	91MA203	2.942	0.29	6.95	3.80
	9lVS26l	3.255	0.28	6.99	3.87
	9lV09	2.847	0.22	6.17	3.69
	ke3	3.360	0.25	8.25	4.75
	Per. 475	3.316	0.27	8.37	4.72
	Averages
	Metapelites	2.962	0.24	6.57	3.84
	Trans iti on	3.030	0.24	6.87	3.98
	Crust	3.035	0.25	6.83	3.92
	Ali samples	3.070	0.25	7.01	4.02

Table 4

 4

  c, 1 characterizing geologic units but calculated from direct velocity measurements. Null values are derived from the fact that the nine measured seismic velocities do not enable one to determine the complete elastic tensor. b C, 1 characterizing a single rock elastic properties, calculated from the lattice preferred orientations (LPO) of the constitutive minerai phases, the single crystal elastic constants and densities.

	ci} (GPa) metapelites a transition • lvrea Zone lvrea Zone Average Average Average Average ( 14 crustal (16 samples) •	Intrusion Val Sesia c Val Sesia c Amphibolite Kinzigite Lherzolite Transition VS33 b VS57 b ke3 b
				samples) •
	C1 1 C22 C 33 C 44 Cs, c66 C,2 C i , C14 C15 C16 C 2.1 C2• Cz5 C26 C 3 4 C3 5 c36 C 4 5 c46 Cs6	134.47 134.47 114.89 41.85 41.85 47.83 38.80 42.89 0.00 0.00 0.00 42.89 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00	145.52 145.52 137.65 47.76 47.76 48.97 47.58 46.34 0.00 0.00 0.00 46.34 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00	145.76 145.76 133.41 45.45 45.45 48.80 48.15 49.34 0.00 0.00 0.00 49.34 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00	156.07 156.07 141.96 48.63 48.63 51.73 52.60 52.57 0.00 0.00 0.00 52.57 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00	158.15 126.42 139.46 38.66 45.45 38.45 57.73 58.99 -1.10 -0.56 1.44 53.84 1.38 -1.31 -0.56 1.99 -0.59 0.19 0.15 -0.24 1.34	125.53 88.60 131.11 35.60 47.49 35.32 29.70 33.63 0.49 -1.54 -0.14 29.59 1.71 0.34 0.26 4.31 -1.86 -0.30 -0.36 -0.33 2.02	260.06 210.10 236.46 73.80 83.83 77.63 70.57 74.55 0.04 -2.70 1.79 72.47 -0.79 -0.07 1.74 -1.89 -3.50 0.77 0.81 -1.60 -0.40	193.74 199.19 194.96 65.74 64.83 65.10 64.99 65.36 -0.11 0.02 1.15 65.27 1.57 0.46 0.69 0.77 0.69 0.20 0.72 0.40 0.58	136.78 144.29 140.44 45.16 43.44 44.81 53.05 50.71 0.21 0.15 -1.52 53.49 0.28 0.01 -1.59 0.36 0.53 -0.05 0.56 0.05 0.05

a c C, 1 characterizing a geologic unit by averaging several single rocks' elastic matrixes.

Acknowledgements

We appreciate the help of M. Schroetel in per forming the experiments. H.K. is grateful to the Deutsche Forschungsgemeinschaft; G.B. thanks the Accompagnement ECORS 91 /92 Programme and the DBT programme Thème Géodynamique for fi nancial support, and also the Carnegie Institution of Washington, Department of Terres trial Magnetism and Geophysical Laboratory, in which part of this work has been done. This manuscript benefited from constructive reviews by N. Christensen and E. Rut ter, and comments by R. Russo and A. Vauchez.

'''' ,,,, ,, ..... . ''"' '''' '''' '''' X Anisotropy:;;: 5.55% y z 0 4.0 i " 3.9 [; 3.8 X preted at a scale of a few centimetres. ln seismic field experiments, by contrast, seismic waves sample the anisotropy at scales of hundreds of metres to tens of kilometres. Geophysicists therefore require an overview of the crustal seismic properties at a larger scale. To characterize better the regional seismic anisotropy of the lower crust in the lvrea Zone, we calculated the seismic properties of hypothetical samples which could be more representative of the 'average' lower crust than each sample considered individually. The seismic properties of these hypo thetical samples are obtained by averaging individual seismic properties of rocks that can be found in the same area, based on the velocities measured at 600 MPa confining pressure and room temperature (see Table 2) or on the calculated velocities. The regional structure (foliation and lineation) of the study area is found to be roughly constant so that most of the rock samples were similarly oriented originally. Averaging the physical properties is there fore based on the assumption that their structural axes Oineation, pole of the foliation) have similar orientations in the geographic reference frame [START_REF] Burlini | A mode! for the calculation of seismic proper ties of geologic units[END_REF]. This enables us to average simply the seismic velocities measured along the various structural axes.

From the laboratory data, we calculated the aver age properties of the crust, using the 14 crustal samples and the average properties of the lvrea Verbano Zone through the 16 crustal and mantle rocks. A striking feature is that the average velocities of the 14 crustal samples do not yield an isotropie result. Furthermore, there are clear relationships be tween the anisotropy and the structural reference ,,,,,''''' ''''' ,,,,,,,,,,''''' ,,,,,''''' , ... ,,, ''''' ''''' ''''' ''''' X '''' '''' '''' '''' ,,,,,,,,,... ,, ,,,,'''' '''' ,,,,,,,... '''' '''' '''' ... ,,, ,, .. . , '''' '''' y z Fig. 7. Anisotropie seismic properties of the hypothetical sample representing the mean properties of the lower crust in the lvrea Zone. The data correspond to the average of the laboratory-derived seismic properties of the 14 crustal samples. Despite the number of samples taken into account and their different natures, the P-wave velocities Oeft), the S-wave velocities (middle) and the birefringence (right) for the three structural axes (x, y and z) clearly indicate that the average sample is not isotropie at all. frame: the average crustal P-wave velocities (Fig. 7, left) are fast (7.0 km s -i) parallel to the lineation ( x structural direction) and slow ( 6.6 km s -1 ) normal to the foliation. The calculated average velocity anisotropy for P waves is 5.55%. The average crustal S-wave velocities are also strongly related to the structural reference frame. The mean anisotropie shear-wave velocities display a variation pattern al ready described in several samples (e.g. amphibolite VS33). The mean velocities calculated from the 14 crustal samples (Fig. 7, middle) display the follow ing properties: S-waves propagate at high velocities ( 4.01 km s -1 ) when the y are polarized parallel to the foliation plane (V sy , and V 5 ,/ S waves have much lower velocities (average 3.87 km s-1 ) when they are polarized normal to the foliation. The birefringence (Fig. 7, right) is therefore high for waves propagat ing parallel to the foliation (O. JO I and 0.146 km s -1 parallel to x and y, respectively), and smaller (0.036 km s-1 ) in directions at a high angle to the foliation plane.

Considering the fact that seismic waves in real seismic experiments may not sample the whole Ivrea Zone, we calculated the seismic properties of two other hypothetical samples more representative of the actual geology: one sample representing the metapelitic part of the study area and the other representing the lower-crust-upper-mantle transition zone. We based our calculations on lithologies that can be found in Val Strona and Valle d'Ossola (Fig. 1). The hypothetical 'metapelite' sample could be representative of the eastem part of the Val Strona or Valle d'Ossola, which is dominated by metapelitic lithologies. The seismic properties of this sample are calculated on a basis of 75% of metasediments (using the seismic properties of the kinzigite VS57 and stronalites V08 and V09) and 25% of mafic rocks (metagabbro V07 and amphibolites VS33 and VS 12). These ratios roughly represent the outcropping pro portions of the different lithologies.

'Metapelite' seismic properties

The second hypothetical sample, called 'transi tion', could be representative of the crust-mantle transition of the northem Ivrea Zone, i.e. of the westermost 5 km of the study area. The lower part of this crust is not dominated by a particular lithology and therefore we calculated the 'transition' sample properties from the arithmetic mean of the seven westemmost samples: 'Transition' seismic properties = [V08 + V077 + VS46 + VS19 + VS48

The 'metapelite' sample is characterized by much lower mean seismic velocities (V p = 6.57 km s -1 , V 5 = 3.84 km s-1 ) than the 'transition' sample (V p = 6.87 km s -1 , V 5 = 3.98 km s-1 ). The main difference between these two samples is their birefringence. The 'metapelite' sample displays a birefringence pat tern typical for metasedimentary rocks: a weak bire fringence (0.067 km s-1 ) for waves propagating nor mal to the foliation and a relatively high birefrin gence (greater than 0.23 km s -1 ) for waves propagat ing parallel to the foliation. On the other band, the 'transition' sample is weakly birefringent (less than 0.06 km s -1 ) in the three structural directions. This is mainly due to mafic rocks (gabbros, pyroxenites), which are generally Jess anisotropie than biotite-or amphibole-bearing rocks.

The lithologies found in the northem part of the Ivrea Zone cannot be extrapolated to the southem part of the studied area (Val Sesia and Val Mastal lone). For this reason, we have calculated the elastic properties of two supplementary hypothetical aver age samples that characterize the large-scale seismic properties of the Val Sesia section, from the petro fabric data obtained by Barruol and Mainprice (1993b).

The seismic properties of the 'transition Val Sesia' sample are the average of five typical samples that can be found in the I km thick layered mantle-crust transition at the contact with the Balmuccia peri dotite body (the pyroxenite VS28b, the dunite VS 148, the sheared pyroxenite VS 14a, the sheared gabbro VS26 and the stronalite VS31). The seismic proper ties of this hypothetical sample are almost isotropie for both P waves (2.2% anisotropy) and shear waves (maximum anisotropy 1.7%). This is a consequence of the weak anisotropy of mafic rocks such as pyrox enites and gabbros. Among these five samples, only the dunite displays an important V p anisotropy (9.7%) and a strong birefringence (0.30 km s -1 ).


Guilhem Barruol

David Mainprice

Hartmut Kernt

Michel De Saint

Patrick Co

3D seismic study of a ductile shear zone from laboratory and petrofabric data (Saint Barthélémy Massif, Northern Pyrénées, France)

In order to constrain interpretations of seismic reflection records more effectively, the seismic properties of a middle crustal section exposed in the Saint Barthélémy Massif have been determined. The massif, transected by a 200 m thick shear zone has been systematically sampled for density measurements and modal analysis has been performed in order to define the spatial variations of physical properties. Seismic velocities (V p , V 5 , shear wave birefringence), have been measured on five representative samples to 600 MPa and 600 °C simultaneously in the three structural directions (X, Y and Z). For two samples, the expep.mental data have been compared with calculated values, based on petrofabric analyses. The Lattice Preferred Orientation (LPO) is determined using universal stage, electron channelling microscopy and neutron diffraction goniometry. Using the experimental and calculated velocity data, we establish a lateral homogeneous anisotropie model.

INTRODUCTION

Deep seismic profiling of the lower con tinental crust has revealed many strong reflections. Up to now, their origins have been poorly understood. Low angle reflections are often interpreted as ductile shear zones, e.g. COCORP and the Brevard Fault (Cook et al., 1979), ECORS-Alps and the Penninic front (Nicolas et al., 1990), ECORS-Pyrcnees and the Variscan t h rust (Choukroune et al., 1989). Laboratory seismic measure ments have shown that preferred ori entation of anisotropie minerais (in particular phyllosilicates), may have a significant effect on seismic rock prop erties (e.g. [START_REF] Fountain | Seismic reflectivity of mylonite zones in the crust[END_REF]Jones and Nur, 1984). The gently dipping reflections observed across geological Present address: IFP, BP 311, 92506 Rueil Malmaison, France.

structures such as the Brevard mylonite zone (Christensen and Szymanski, 1988) and the Kettle river mylonite zone• (McDonough and Fountain, 1988) have been directly related to a large volume of oriented biotite minerais in ductile shear zones. Recently, [START_REF] Kern | Fabric related velocity anisotropy and shear wave splitting in rocks from Santa Rosa mylonite zone, California[END_REF] have shown that, at constant bulk composition, seismic anisotropy in my lonites increases significantly with the amount of strain, i.e. with the degree of preferred Lattice Orientation (LPO) of phyllosilicates.

The aim of this study is to understand better the seismic response of a middle crust ductile shear zone. Different but complementary methods have been used for deterrninations of seismic properties of rocks: laboratory velocity mcasurements and velocity calculation based on petrofabric data.

The samples were collected from a geological structure exposed in the Saint Barthélémy Massif (Northern Pyrénées) representing a middle crustal section transected by a thick ductile shear zone. Its structure, composition and geometry was already well con strained by previous studies [START_REF] Passchier | Mylonitic defonna tion in the St-Barthélémy massif, French Pyrénées, with emphasis on the genera tion relationship between ultramylonite and pseudotachylite[END_REF]Saint Blanquat, 1989).

We have chosen five samples repres enting the main lithological units for the laboratory measurements and for two of these samples the seismic ve locities have been calculated from the elastic constants of the constituent minerais and their LPO. Using a com bination of experimentally and petro fabric-derived (cross-checked) rock elastic constants, we have modelled the seismic response of this exposed struc ture. The synthetic seismograms are the result of a calculation taking into account the 21 elastic constants charac terizing the elastic properties of each unit.

GEOLOGICAL SETTING

Lithology of the Saint Barthélémy Massif

The Saint Bathélémy Massif [START_REF] Passchier | Mylonitic defonna tion in the St-Barthélémy massif, French Pyrénées, with emphasis on the genera tion relationship between ultramylonite and pseudotachylite[END_REF]Saint Blanquat, 1989) is located in the North Pyrenean Zone (Fig. la). It is scparated from the Variscan Axial Zone by •a major crustal structure, the North Pyrenean Fau.lt. The crustal section consists of the following bottom-to-top sequence (Fig. 1988). Based on the modal composition and the density measurements we have selected 5 representative samples, 3 from the shear zone (SB2a, SB89b, SB114a) and 2 from the lower unit (SB83, SB122b). The upper unit com posed of migmatites, Jeucogranites and micaschists, has been considered, at a first approximation, to be isotropie due to the extreme variability of lithologies and structures. Localities of these samples are indicated in the schematic geological map (Fig. ;;.,..

5,5

5,0 1.

LABORATORY SEISMIC MEASUREMENTS

Method

The velocity measurements at PT con ditions were carried out in a cubic pressure apparatus at the Mineralo gisch-Petrographisches Institut, Kiel (Germany) using the pulse-transmis sion technique. The method allows simultaneous measurements of P and S wave velocities in the three structural directions (X, Y and Z) of the cube shaped specimens [START_REF] Kern | Elastic-wave velocity in crustal and mantle rocks at high pres sure and temperature: the role of the high-low quartz transition and of de hydration reactions[END_REF]. Velocit ies were generally measured as a function of pressure (up to 600 MPa) and as a function of temperature (up to 600 °C) at a constant confining pressure of 600 MPa. For the determination of acoustic birefringence we used two sets

SB122b SB2a SB83b ... • • SB89b • • • T=25 °C

P=600MPa

of shear wave transducers with perpen dicular polarization directions. S-waves were polarized in the XY, XZ and YZ planes. Assuming the fastest and the slowest velocities were generally meas ured parallel and normal to the foliation plane respectively, we determined the velocity anisotropy. The velocities of the two perpendicularly polarized shear waves propagating in the X, Y and Z directions allow in addition the calcu lation of acoustic birefringence. Jn the following text, V,,j represents the veloc ity of a shear wave propagating in the ij plane, in the j direction.

P-wave measurements

At low pressure conditions, average values increase rapidly with increasing pressure (Fig. 2), reflecting the closure of microcracks. Above 200 MPa the curves become linear and represent the intrinsic elastic properties of the 7,0 6,5 samples. The P-wave velocities are not strongly influenced by the pressure increase above 200 MPa. For the phyl lonite SB2a, for example, a pressure increase of 400 MPa generates a V P increase of about 0.15 km s-1 • At 600 MPa a temperature increase results in a slight linear decrease of velocities. The derivatives of seismic velocities (Table 2) refer to the (quasi) linear slopes of the velocity-pressure and velocity-temper ature relation, respectivcly between 200-600 MPa and 20-SOO °C. The 600 MPa (room temperature) P-wave velocities are in a range of 5.8 and 6.8 km ç 1 , which was found to be typical for acidic rocl<s of Jow (phyllonite, mylonite) and high (granulite) metamorphic grade (Kem and Schenk, 1988;[START_REF] Kern | Fabric related velocity anisotropy and shear wave splitting in rocks from Santa Rosa mylonite zone, California[END_REF].

• • • ... 6,0 • • ---.
The studied samples exhibit signi ficant velocity anisotropy. Slowest velo cities were generally measured normal to the foliation plane, i.e. parallel to Z (Table 2). Anisotropies (A% = 100 (V max-V m ;n)/V max) vary between 2% (gneiss SB 83b) and 16 % (phyllonite SB2a) at 200 MPa. At and above this pressu re, where most of the cracl<s are closed, anisotropy is mainly caused by crystallographic and shape-preferred

G. BARRUOL ET AL.
orientation of minerais (texture). In the very low pressure range, however, oriented microcracl<s make a major con tribution to velocîty anisotropy pro ducing the highest anisotropy values. The present results also confirm earlier observations (B arruol, 1988;[START_REF] Mainprice | De velopment of shape and lattice pre ferred orientations: applications to the seismic anisotropy of the lower crust[END_REF] ) that anisotropy de creases with the number of minerai species in the rocks (Table 2), and is most pronounced in phyllosilicate rich rocl<s. The phyllonite SB2a illustrates this phenomenon well: P-wave velocity within the foliation plane is very homogeneous and fast, whereas the slowest is normal to the foliation (Fig. 3 bottom). It displays a strongly transverse isotropy characteristic of textured bio tite-rich rocks (see also [START_REF] Kern | Laboratory seismic meas urements: an aid in the interpretation of seismic field data[END_REF]. lt is important to recognize that apart from the a-13 quartz transition, the texture related anisotropy is almost pressure and temperature independent [START_REF] Kern | Laboratory seismic meas urements: an aid in the interpretation of seismic field data[END_REF].

The quartzite mylonite SB114 a dis plays well the influence of a-13 quartz transition on anisotropy. At room tem perature, the fast V P velocity is parallel to the Y structural direction and the slow velocity is parallel to the X direction (Fig. 3 top). With increasing pressure, the anisotropy remains almost constant (about 10%). At 200 MPa, an increase in temperature up to 630 °C reveals an important decrease of V P of almost 1 km ç 1 . Simultaneously, the properties change from strongly anisotropie (1 0%) to nearly isotropie (2 %). Above the transition, V p increases markedly by about 2 km s-1 and exhibits only a small directional dependence in the 13 -field (see also [START_REF] Mainprice | The seismic properties of alpine quartz mylonites determined from the orientation distribution functions[END_REF].

S-wave measurements

Pressure and temperature influence on S-wave velocîties are qualitatively very similar to P-waves. The difference 6. V, = v.o-V,90 (see Table 2 for def initions) for each structural direction characterizes the shear wave birefrin gence. T � ical values range fom O to 0.3 km s-. Pressure and temperature derivatives determined from the linear slope of the seismic velocities (Table 2) yield values in agreement with previous determinations (Christensen, 1979;Kem and Richter, 1981 ).

In elastically arùsotropic rocks, shear wave velocities strongly depend on their polarization directions. Pro nounced acoustic birefringences (shear Table 2. Laboratory velocity measurements summary, for the three structural directions, for the P-waves (velocities, anisotropies, pressure and temperature derivatives) and for the S-waves (velocities, birefringence, pressure and temperature derivatives). The temperature derivatives have not been calculated for sample SB114 a due to the non linearity of the curves.

Sample P-waves S-waves Derivatives

vP

AV p V.o Vs90 6.VS dV!dP -dV!dT°( kms-1 ) % (kmÇ 1 ) (kmÇ 1 ) (kms-1 ) (x 10-4 km Ç 1 MPa-1 ) (xl0 -4 kms-1 •c-

Sample SB114a

6,8 ---------------,.,-6,8 6,6 6,4 ,\-ave splitting) were observed in the ?hyllonite and mylonite samples (SB2a, SB89b and SB114a). Birefringence as :::.:gh as 1 km ç 1 was observed within fue foliation plane (Table 2). Shear wave E?Utting is closely related to the struc =i -al framework. The fast and slow s"'lear-waves are respectively polarized ::iarallel and normal to the foliation. ln �e phyllonite SB2a, for example (Fig. 4) � -;;:q and V sy x are the fastest S-waves �use both their propagating direc ::ons and their polarization planes are ;:ontained in the XY plane. In such bio =-� rich rocks, therefore, S-waves prop =-sating either normal to the foliation or ?'.'Iarized perpendicularl y to it have low �ocities.

3D seismic properties extrapolated from direct measurements

The technique we used to model the anisotropie seismic properties of our geological object requires the 21 elastic constants for each element of the mode!, that means we need to extra polate the velocities (V p , V s ) measured in the three mutually perpendicular directions (X, Y,Z) to an arbitrary direc tion. To determine the shape and the axial ratio of the velocity ellipsoid, the Flinn diagram has been used. The ratio

V p )V PY versus V 1 ,!V 1 ,,
is plotted for each sample (Fig. 5). In an ideal transverse isotropie case, the point would be placed on the K = 0 or K = co axes ( cor-responding to pancake-like and cigar like ellipsoids, respectively). The points representing the three studied samples (SB2a, SB89b and SB122b) fall close to the line K = 0 (K = 0.064, 0.038 and 0.273, respectively). The K values are defined as K = ((V p ,!V py )-l)l((V pyl V p z )-l). The velocity ellipsoids deter mined for these three samples are close to the transversely isotropie case (K = 0), especially for the two mylo nites (SB2a and SB89b). Their elastic constants (Fig. 9) can now be deter mined for these three samples as suming the symmetry to be transverse isotropie, using the method described in Christensen and Crosson (1968) 2 for the notion of V Jwith increasing pressure (left ) and with increasing temperature (right). V si j represent a shear wave velocity within the ij plane and in the j direction.

tropy (1.4 % ) of the gneiss SB83 explains why the shape of its velocity ellipsoid is not significant. The quartzite SB114a is close to the line K = -l, and cannot be describcd as a transverse isotropie case. Two specimens (SB114a and SB83b) were selected for the velocity calcu lations. The microstructures of the specimens are illustrated in Fig. 6. Pole figures of quartz in sample SB114a were measured by neutron diffraction goniometry. A solid cylinder (10 mm diameter and 20 mm length) of this monomineralic and fine-grained rock (10 µm) provides a good statistical representation of the crystallographic texture. LPO of minera! phases of the gneiss SB83 were obtained either using the universal stage on an optical microscope (biotite) or by scanning electron microscopy (SEM) using the se lected area electron channelling pattern (SAECP) method (Quartz, Plagioclase and K-feldspar) [START_REF] Lloyd | Selected-area electron channel ling patterns frorn geological materials: specimen preparation and representa tion of patterns and applications[END_REF]. SEM provides a powerful tool for measuring partial textures in polyphase material, in particular for minerais optically difficult to measure (plagioclase) or from which it is impossible to obtain complete crystallographic information (quartz). The SEM determination of the complete crystallographic orientation 3D SEISMIC VELOCITIES E!, 6. .Yficrophotographs of the morwmineralic quartzite, optical microscopy, crossed nicols � .;;r.d of the polymineralic gneiss, SEM backscattered image (bottom), bath in the XZ -==. -:-lie quartzite is very fine grained (10 µm) and strongly textured. In the gneiss, quartz ___._ _,ùucture is typical of plastic deformation. Grains are ribbon shaped and often bent ----:d strain free feldspar porphyroclasts. Despite the intense plastic defomzation, quartz

•-"""::i iisplay no sign of dynamic recrystalli z ation. Q = quartz, K = K-feldspar, -= -::ï.;.gioclase and B = biotite.

-=n grain is obtained by indexing the ��aj channelling pattern (Lloyd et �7) using a computer program .... � and Olesen, 1989). llloo:x:nre calculation �.:::L.-:tlation of the three dimensional ::s:=_fion of elastic seismic velocities (V p , V s , shear wave splitting) in an anisotropie polymineralic rock is based on the knowledge of the Lattice Pre ferred Orientation (LPO or petrofabric) of each minera! species, the volume fraction of each minerai, the crystal densities and the elastic stiffness coefficients. The grain shape preferred orientation is not taken into account in these calculations. The procedure of cal culation is described in detail by Cros son and Lin (1971) andPeselnick (1974). Computations were performed using an interactive program [START_REF] Mainprice | A FORTRAN pro gram to calculate seismic anisotropy from the lattice preferred orientation of minerais[END_REF].

The elastic constants of a-quartz single crystal (trigonal) used were those reported by [START_REF] Mcskimin | Elastic moduli o: quartz versus hydrostatic pressure at 25 ° and -195[END_REF], and for biotite (monoclinic, pseudohexa gonal) we used those recently reported by Vaughan and [START_REF] Guggenheim | �--tidty of muscovite and its relation �� rocrystal structure[END_REF] for muscovite. The seismic properties of muscovite are very close to those deter mined by biotite (considered as hexa gonal) by [START_REF] Aleksandrov | The elastic properties of rock forming minerais, II: Layered silicates, elasticity of dunite[END_REF]. The data for feldspars used in these calculations were determined by Aleksandrov et al. (1974) for microcline and plagioclase (An29% ).

Lattice Preferred Orientation (LPO) and calculated velocity distributions

The lattice preferred orientations of the major minerais constituting sample SB114a (quartzite) and SB83 (gneiss) are documented in Figs 7 and8, respectively.

In the quartzite SB114a, (Fig. 7 The Quartz c-axes form a broad girdle in the YZ plane, with a maximum close to the Y axis. The corresponding a-axes scatter around Yin the projection plane. This fabric is typical of amphibolite facies metamorphic conditions (Main price and Casey, 1990;Schmid and Casey, 1986). The Biotite c-axes ( close to the pole of the main cleavage of the crys tal, the (001) plane) form a strong maximum normal to the foliation, with a larger' angular spread toward X than toward Y, mainly due to deflection of the foliation around the feldspars por- ,,,,,' ,, .

' -o _ /

. ,, .. phyroclasts. For seismic properties computation, the a-axis orientation of each biotite grain, has been generated randomly in a plane nom1al to the pole of the cleavage (c*), assuming biotite to be transverse isotropie. Pole figures of K-feldspar and plagioclase a-axes and of the +(001) planes do not exhibit any preferred orientation. Tt should be mentioncd, however, that the small number of measured grains may not give a statistical representation of the �egate.

Pigure 7 (right) presents the calculated ••elocity surfaces of the monomineralic quartzite SB114a. The minimum P -... •ave velocity (V p m ;.J is close to X and correlates to the a-axes maximum. The a-axis represents the slowest velocity in the quart".G single crystal. V prn; n parallel to X is in good agreement with experi mental measurements (see Table 2). V p m.,x lies between the X and Z axis and is related to the z crystallographic axis (not shown) which represents the dir ection of the fastcst P-wave in quartz single crystal. The corresponding shear wave properties (V. and polarization planes) have been calculated and are shown in Figs 9 and7, respectively. ln an anisotropie aggregate shear waves split into two waves with different vel ocities and polarization directions (Crampin, 1985). The two shear waves V,l (fast) and v.2 (slow) are polarized in mutually perpendicular planes. ln equaJ area projection (Fig. 7), the shear wave polarization is indicated by a little arc segment of a great circle. The arc marks the orientation of the fastest shear wave (sl).

Considering the quartzite specimen in its structural framework, it follows from Fig. 7 (orientation of the polariza tion planes) and of Fig. 9 (spatial dis tribution of v., and V s l) that significant shear wave splitting occurs for 5-waves propagating parallel to the foliation plane. The fast shear waves (sl) close to the lineation are polarized normal to the foliation plane, and the corresponding slow shear wave (s2) parallel to it. This is in excellent accordance with the ex perimental results (see Table 2). On the

()11111'1 Z Biotite •••-5,, ••• •• .. _ ,.,., 0 �.

Microcline a axes

•. ...

-.e hand, retuming the quartzite x=ple to its crustal setting assuming its -::-oe_tion is horizontal, and considering x'ÎSIIÙC wave propagating upward -e.:xally, the shear waves will split at = lowest interface of the quartzite � and will propagate with different --=Iocities. The fastest (sl) will propa � vertically within the XZ plane, i.e.

a plane parallel to the lineation. The =�est (s2) will propagate vertically ;;:,o, but in the YZ plane, i.e. in a plane -c::mal to the lineation. In real seismic :-=--mrds, measurements of the delay =e between the two shear wave arri �:Js, the shear wave splitting and the _:entations of their polarization ===.nes, allows one to extract structural .c:rematic information. The polarization ::ane of sl may be a marker of the linea :ion, and the magnitude of the shear ra\•e splitting may indicate the com ':=ed values of anisotropy and the �ckness of the layer. �e velocity distribution of the ?Olymineralic gneiss SB83 (Fig. 8) is :esed on the partial textures and the �.Jiume percentages of the major min• =Is. The direction of the fastest P-wave � dose to X within the foliation plane =d the calculated bulk velocity aniso :::ü?Y is found to be around 5.6%. The �ocity distribution in the composite �ssregate is dominated by the biotite =:5tals, due to their strong preferred --:;:ientation and the pronounced veloc =:anisotropy (33.9%) of this minerai �es.

à Fig. 10 This small value could be explained by the shape preferred orientation of grains, not takcn into account in these calculations. The calculated velocity anisotropies are generally higher than those measured experimentally.

SEISMIC MODELLING

The synthetic seismogram program (DRT4) uses a 3D ray tracing method. lt generates seisrnic traces for three com ponent receivers. The receivers and the source may be in any geometrical dis position, at the surface or at any depth. The geometric mode! is a parallel epiped divided in homogeneou� or heterogeneous Jayers. Each layer is defined by its physical properties (the density and the 6 by 6 elastic stiffness (C;j) matrix) and by its three dimen sional geometry, excepting discon tinuities. The program may generate ail types of seismic signatures (reflection, transmission or multiples) for P and 5waves but they must be explicitly specified in the input parameters. The ray path in each layer is obtained cal culating first the isotropie case and then cakulating the pertubation due to three dimensional velocity distribution. The obtained seismic traces are not true amplitude.

Schematically, the algorithm used by DRT4 is the following: the first step is a scan to find the rays joining source and receivers. The second step is a ray trac ing inciuding amplitude computation along the selected rays which allows a modelling using the 'Gaussian Beams . --------------.-7 ].

Geometry of the model -seismic parameters

We have considered the St Barthélémy section at the end of the period of exten sion, under upper crustal conditions (about 4 km depth), with the structures horizontal. The model was composed of 13 layers (Fig. 11). The anastomosing character of the shear zone is rep resented by three repeated sequences of mylonites separated by a layer of gn eiss several hundred metres in thickness. Bach mylonite layer was 10 or 20 metres thick. This very simple approach is dearly not a true 3D seismic modelling. Layers are indeed planes, horizontal and laterally homogeneous. Only the seismic velocities have three dimen sional variations. The corresponding isotropie modelling using the average elastic parameters has not been carried out because the main interest of such a model is to study the first-order seismic si gn ature it can generate rather than the influence of anisotropy.

()

2K. m

G. BARRUOL ET AL.

The characteristics of the seismic line were as follows: the source was omni directional with a ricker centred at 30 Hz situated at one end of the seismic line on surface. 80 receivers were ali gn ed in a parallel array every 100 metres. The rock layers were plane and horizontal. The calculated seismic signatures are P p and P-S reflections on each interface.

Results

On seismic traces (Fig. 12) vertical movements display well the three P wave reflections generated by the three shear zones, between 1.3 and 1.6 s. The contact gneiss/granulites also generates a strong P reflection (at about 2 s). The first P-S reflections are also visible at about 1.7 s but have a S!f1aller ampli tude. On the radial movement traces, P-wave reflections become visible at about 1.5 km offset (at about 1.3 s) and their small amplitudes increase with in creasing offset whereas P-S reflections

4K111

() have a stronger amplitude and are visible even at small offsets (0.5 km and 1.7 s).

CONCLUSIONS

In this study, the seismic properties of a ductile shear zone have been studied. Whereas the rock types have been rep resented by a small number of samples (5), the results provide much informa tion and show the usefulness of the methods.

The seismic properties have been determined using different but com plementary methods. Bach one has its own advantages: (i) Laboratory meas urements give direct and accurate control of seismic properties, in an im portant range of geological conditions (pressures up to 600 MPa and temper atures up to 600 °C). In addition to the classic P-wave velocity measurement we have also measured the S-waves (velocities, polarization planes and bi- -:efringence) which are an important seismic and kinematic diagnostic. (il) Jte calculation of the elastic properties .:rom petrofabric data allows the deter mination of the true 30 variations of the .:omplete seismic properties ( charac !erized by the 21 elastic constants). An interesting approach, shown here, is to study the respective influence of each mineral phase on the seismic properties of the aggregate as a whole. The know ledge of petrofabrics has also a struc tural and kinematic interest.

Petrofabrics have been determined using different and complementa. ry tools: (i) Optical microscopy allows the determination of LPO of simple mineral phases (orthorhombic crystal symmetry ior example). (ii) Neutron diffraction goniometry gives a very good represent ative LPO of a single phased rock and (iii) SEM is a powerful tool for the study of complex aggregates of low symmetry minerai phases (trigonal, monoclinic or triclinic for example).

The results measured (in laboratory) and calculated (from petrofabrics) for the two samples on which the two methods have been applied (SB114A and SB83b), are in good agreement.

The seisrnic inodelling shows that such a schematic representation of a geological structure may generate re flections looking like those commonly observed on seismic profiles.

Finally, the main potential value of 3D seismic anisotropy is the extraction of the kinematic information carried by shear waves. Real, three component seismic records of S-wave polarization planes and of S-wave splitting may provide structural and kinematic in formation (Silver and Chan, 1988). This study has shown how one may deter mine the three dimensional shear wave properties (velocities, polarization planes, birefringence) of complex rocks. The 3D synthetic seismogram and the 3 component recording give us the opportunity to mode) the shear wave splitting.

Fig. 1 .

 1 Fig. 1. (a) Location mapof the Saint Barthélémy (NPF: North Pyrenean Fault, NPTF: North Pyrenean Frontal Thrust, SPTF: South Pyrenean Frontal Thrust). (b) Schematic geological map of the massif, withsample locations (from Saint Blanquat, 1989). (c) Schematic cross section (the sample loaitûms are projected onto the cross secti.on).

  ) and projected on a cross section plane (Fig.le). The

Fig. 2 .

 2 Fig. 2. Average measured P-waveî1elocities from the three structural directùms of the five samples as a function of pressure at room temperature (left) and as a function of ternperature at 600 MPa confining pressure. The sample SB114a has been measured only up to 200 MPa and is absent on the right-hand diagram.

Fig. 3 .

 3 Fig. 3. Laboratory measurernents ofVp for the quartzite SB114a (top) and of the phyllonite SB2a (bottom), with increasing pressure (left) and ::iih increasing temperature (right). The velocities measured in the three structural directions are plotted. The caption is the same for the two 521nples.

Fig. 4 .

 4 Fig. 4. S-wave measurements forphyll<mite SB2a a long the sixpolarization planes (cf Table2for the notion of V Jwith increasing pressure (left ) and with increasing temperature (right). V si j represent a shear wave velocity within the ij plane and in the j direction.

Fig. 5 .

 5 Fig. 5. Flinn representation of the anisotropy of the laboratory measured P-wave velocities for =l-, e five samples. (see text for explanations).

  left) the maximum of quartz a-axes is close to the lineation and the c-axes are grouped in two maxima between the Y and Z structural axis. The m-axes pole figure (not shown) is very sirnilar to the a-axes pole fi gu re and the r+z measured pole figure (not shown) exhibits two maxima between the Y and X directions, in the foliation plane. The fabric does not exhibit any clear obliquity with respect to the structural frame (XYZ). These pole fi gu res could arise from intra crystalline slip mainly on the rhom bohedral r crystallographic plane, in the [a) directions. The pole fi gu res of the polymine.ralic gneiss SB83 are shown in Fig. 8 (left).

Fig. 7 .

 7 Fig.7. Quartzite SB114a: a and c-axes pole figures (left) and some calculated seismic properties from these petrofabrics (P-wave velocity distribution at 25 °C and the orientation of the fastest 5-wave polarization planes). The equal area projections are in the lower hemisphere, the foliation is EW, nonna/ to the paper and the lineation EW.

Fig. 8 .Fig. 9 .

 89 Fig.8. Gneiss S883b: Calculation of the P-wave velocity distribution of a complex aggregate from the knowledge of the preferred orientation of each minerai phase. On the left, preferred orientation of the a and c crystallographic axes of quartz, biotite, K-feldspar and plagioclase. In the middle part of the figure are shown the P-wave velocity distributions of each virtual single phased aggregates. The modal composition is used to calcula te the V P spatùû distribution taking into account each minerai phase in its bulk proportion. The equal area projection characteristics are the same as in Fig.7.

  comparison is made be-cren measured and calculated P-wave -ciOCÏties in the three structural direc-::cns of the gneiss and ultramylonitic ?rtzîte. The results obtained by the two methods compare fairly well. The maximum deviations are around 4%.

  Fig.11. lD geological mode!, composedbya succession o f the fi ve samples studied. The relative thicknesses are not drawn to scale. The left column indicates the sample name and the thickness is in the right column .

Fig. 12 .

 12 Fig.12. Seismic traces corresponding to the mode! shown in Fig.12. The vertical movements and the radial movement are displayed, respective/y on the left and on the right.

Table 1 .

 1 Modal composition and density of the five selected samples

	Sample	Rock type
	SB2a	Phyllonite
	SB89b	Biotite rkh ultramylonite
	SB114A	Ultramylonitic quartzite
	SB83	Amphibolitic gneiss
	Sb122b	Acid granulite

Rock samples

115 samples were collected from two N S cross sections transecting the whole massif. Bulk densities were measured and lie within a narrow range of 2.6-2.8 g cm -3 indicating a relatively ho mogeneous, silica rich crustal section. .The modal compositions of 40 of the samples were measured by an image analysis technique (Allard and Sotin,

Present address: Laboratoire pét rophysique et téctonique, Université Paul Sabatior, 3214090 Toulouse, France.

ACKNOWLEDGEMENTS

This study has been supported by the Accompagnement ECORS 89/90 pro gram. Thanks to G. Lloyd for the useful help and advice for the SEM measure ments undertaken at Leeds University (England), to E. Rutter and K.J. Sand-30 SEISMIC VELOCITIES meier for their constructive comments, to the C.E.A. (Saclay) for the neutron diffraction measurements kindly un dertaken by T. Baudin, to the Compag nie Générale de Géophysique (Massy) for the program for 3D seismic model ling, to the Centre National Univer sitaire Sud de Calcul (Montpellier) for the computation time on the IBM 3090.

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