LOCAL DEFORMATION AND RHEOLOGICAL PARAMETERS BY MEASUREMENTS IN TALAYA STATION GALLERY ( BAIKAL REGION )

Tilt measurements have been taken in the underground gallery at Talaya Seismological Station for almost three decades, from March 1985 till 2014. Based on such data, deformation curves were constructed and analysed in the frame of elastic and viscous-elastic models of the geological medium. From estimated annual deformation rates, it became possible to reveal deformation cycles ranging from 3 to 18 years with amplitudes up to 5 arc-seconds (2·10–5). For the bedrock in the Talaya stream valley, the elastic modulus was estimated at 20 GPa. In frame of the Kelvin viscoelastic model, the apparent viscosity of the medium was estimated at 1019 Pa·sec by deformation delay curve for 1989–2014 epoch. Observed vertical rates were used to estimate the size of the studied area (from 0.1 km to 6.0 km). The values estimated in our experimental investigation are used in a wide range of geophysical studies: modelling tectonic, co-seismic and post-seismic processes.


INTRODUCTION
In studies of recent movements, which are an integral part of geophysical monitoring of the Earth's crust, recent deformation of the crust and mantle is described by elastic, plastic, viscoelastic models and combinations of such models.Obtaining field experimental results is essential for development of theoretical models of recent shear and deformation fields.Variations of such fields are determined for periods from a few days to decades.In such studies, measurements by extensiometers and the horizontal pendulums installed in special underground gallery is one of the common methods.Upon analyses of strain variations in time, a model showing deformation and rheology is selected, and it becomes possible to reveal factors and forces that influence the process of deformation.Interpreting of the obtained data can be challenging due to the fact that strain measurements are taken at the surface of the Earth and may be distorted by local impacts.Besides, there is an uncertainty of a total value of accumulated strain.Actually, accumulated strain can be estimated only at the qualitative level from neotectonic reconstructions, knowledge of the stage of seismic activation, and structural models of the region.Observed periods of deformation are indications of current regional activity; for instance, in the Baikal rift, i.e. in the intracontinental area, representative earthquakes occur in periods of 3 to 150 years.Determination of rheological parameters of the geological medium and estimation of deformation or strain rates are major objectives of our studies.We study processes on the data basis collected by long-term observations using tidal quartz tiltmeters that were installed in the underground gallery at Talaya Seismological Station (TSS, 51.68°N, 103.65°E) in March 1985 and ensure non-stop data recording.TSS situated near the northern boundary separated of the south-western part of the Baikal rift zone and the Siberian platform.The Main Sayan fault, being the boundary between the Siberian platform and the mobile area [Levi et al., 1997;Solonenko, 1993], is located a few kilometres to the north.In this region, lateral inhomogeneities of the crust and upper mantle cause deviatoric stresses of 35-40 МPа, according to calculations published in [Kaban, Yunga, 2000], and such stress values are close to maximum stresses estimated for the Baikal Rift.Left-lateral shift motion takes place at the Main Sayan fault.According to the available geological data and tectonic models of south-western part of the Baikal rift zone, horizontal displacement rates are from 0.8 to 2.0 mm per year, and displacements are mainly directed to the east [San'kov et al., 1999[San'kov et al., , 2000;;Calais et al., 2002;Lukhnev et al., 2010;Timofeev et al., 2012Timofeev et al., , 2013]].

STRAIN RECORD
The first measurements of tidal and technogenic tilting were obtained in 1960s when a tiltmeter designed by A.E. Ostrovsky was used; the tiltmeter mechanism included steel springs [Ostrovsky, 1978].A pilot quartz tiltmeter NK-1 (Zöllner suspension type) was designed in 1973, manufactured and tested in 1974; it provided for photoelectric recording, and a new calibration method was proposed for calibration of the tiltmeter [Bulanzhe et al., 1975].Stations in Siberia used pilot NK-1 units and sets of tools manufactured at the pilot plant of the Siberian Branch and in the Institute of Geology and Geophysics SB.In the TSS gallery, quartz horizontal pendulums have been in use since March 1985 [Gridnev et al., 1990].Analogue records of measurements were collected from 1985 to 1998.Digital records are available since 1998.The tiltmeter is calibrated in laboratory conditions under the impact of elastic force of a quartz spring, and regular calibration checks are conducted on the permanent measurement inside the TSS tunnel.In the laboratory conditions, the calibration error amounts to 0.1 %.In situ conditions, when operator approaches the tiltmeter installed in the underground gallery (Fig. 1), an error may increase to a few percent.Maintaining stable recording of metrological parameters in time is challenging as measurements are impacted by the following factors: the electric power network of the seismic station is unstable, elements of the photo-electric sensor need to be periodically replaced, voltage may vary, it may be needed to disconnect the tiltmeter when seismological and geophysical equipment is in service operation.Such factors cause gaps in records and disturb stabilization of temperatures inside the TSS tunnel (+1°±1°C).
At Talaya Seismological Station, the tiltmeters were calibrated with the use of a quartz-spring micrometer or an electromagnetic calibration device [Gridnev, Timofeev, 1990].For example, calibration for the period from 29 September 1999 to 01 October 1999 was done by shifting with a quartz spring, as shown in Figure 1. Figure 2 shows examples of tiltmeter calibration and attenuation of natural oscillations of the pendulum after shifting.The tiltmeter base ranges from 300 to 100 millimetres.Measurements are conducted on a pedestal (0.7 m × 1.4 m) mounted on the bedrock.
The horizontal pendulums were installed in two azimuths, N-S and E-W.Examples of digital records of tilting for every component are shown in Figures 3 and 4. Tidal tilt amplitudes amounted to 0.03 arc-seconds.Tilt records in analogue and digital formats were analysed at the IPGG SB RAS, and the Royal Observatory of Belgium [Timofeev et al., 2000[Timofeev et al., , 2008]].Then tidal parameters, i.e. amplitude and phase-lag factors, were compared with models of tidal deformations of the Earth.A good correlation was revealed with the DDW99 tidal model (static part) and SCW80 tidal ocean model (dynamic part) [Schiwiderski, 1983;Dehant et al., 1999;Ducarme et al., 2008].Deviations from the global tidal tilt model amounted to 7 % for amplitudes (E-W) and +9° for phases (N-S), which can be explained by the effect of the geological structure of the Main Sayan fault.This fault is located 3 km to the north of Talaya Station and strikes sub-latitude the region where the station is located.

SHORT-PERIOD VARIATIONS AND EFFECTIVE ELASTIC MODULI
Based on measurements of short-period variations associated with atmospheric pressure drops, we calculated effective elastic moduli of rocks in situ [Gridnev, Timofeev, 1989a, 1989b].Variations were recorded in periods from a few minutes to hours in case of rapid air pressure variation.A simple Young modulus (E) ratio was used for interpretation: where ΔP is an atmospheric pressure drop; Δε is a corresponding variation of vertical strain.The first data were received using a vertical quartz extensometer, quartz tiltmeters and a quartz microbarograph [Gridnev, 1975].Calculations based on records by the vertical strain meter yielded an effective elastic modulus of the rocks which is quite low, Е=4.7⋅10 9 Pa.In this case, significant impacts of cavity effects should be noted as such effects are maximum when the tool is installed (in a vertical or horizontal position) across the tunnel.According to calculations reported in [Harrison, 1976;Blair, 1977], horizontal strain is variable: where exx and eyy are horizontal strain values for the homogeneous medium.
A similar reduction of the modulus value is due to the strain value as follows: e zzп ≅ 3ezz. ( The effect of the triple increase of the tidal amplitude of vertical strain was also revealed in Osakayama (Japan), an old tunnel where vertical strain meters were installed [Ozawa, 1967[Ozawa, , 1974;;Melchior, 1982].The effect disappears when a vertical strain meter is installed in the tunnel in a specially drilled hole.
In case of short-period pressure variations (half a minute, less than 1 hour), it is possible to determine the effective modulus from records by tidal tiltmeters.In such cases, the following ratio is used: where: ΔP i ΔP i is a load; r i is a distance between tilt and load measurement points (in case of rapid variations, frontage orthogonally to isolines) normalized to the tiltmeter base; ∆ψ i is a tilt balance in the azimuth, orthogonal to the atmospheric front, i-th individual determination.
Our experiments show that the accuracy in this case is low because of difficulties in determining the position of the atmospheric front and challenges related to local mapping of pressure isolines in case of rapid variations (errors from 50 to 100 %).The effective modulus calculated from the tilt measurements is much closer to that estimated from petrophysical data, E=1.5⋅10 10 Pa.
Based on petrophysical studies of core samples (Archean marble from Well 1608 located 100 m from the tunnel entrance in the TSS territory) (Fig. 5 The obtained values are as follows: for Poisson ratio, ν=0.17; for bulk modulus, К=2.34•10 10 Pa; for shear modulus, ⁄ , Young modulus is E= =4.63•10 10 Pa, and Lamé parameter is The most effective reference to short-period strain variations was demonstrated in the study of co-seismic deformations near earthquake locations.When an earthquake (M=5.5-5.7,51.71°Ν, 102.70°Ε) took place on 29 June 1995, it was for the first time when a tilt change was recorded at a distance of 67 km to the west of the station.The anomalous tilt amounted to 0.25 microradian (extension, +2.5•10 -7 ) at azimuth 124°Ν, which correlates with the solution of the earthquake mechanism [Melnikova, Radziminovich, 1998].The most striking example is the Kultuk earthquake of 27 August 2008 (M=6.5, 51.61°Ν, 104.07°Ε) which occurred at a distance of 25 km from the station [Melnikova et al., 2009], when extension of +1•10 -6 was registered [Boiko et al., 2012].This result is in good agreement with the model making by seismological data of the Baikal Branch GS SB RAS, Irkutsk.
Tilting runs manifest strain recurrence from 3 to 18 years (Fig. 6, 7, 8, and 9).In the vector diagram, this is reflected in the time period from 1985 to 2003 (Fig. 8).The average annual strain rate in some periods is variable from 0.05 second of arc to 2 second of arc per year (10 -8 ÷10 -6 ), and such values are consistent with data obtained by space geodesy techniques in this region [San'kov et al., 1999;Lukhnev et al., 2010, Timofeev et al., 1994, 1999, 2012].
After the earthquake, the stress state changed.The measurements had lasted for ten years before the next group of strong earthquakes (М>5) was registered to the west and east of the station.The first strong event occurred on 29 June 1995 (М=5.5), and the second on 25 February 1999 (М=5.8).For 50 km zone around the    station, it is possible to distinguish two periods: the first period until 1990 (weak earthquakes, М=3.5÷4.0;one or two events per year), and the second period from 1990 to 1994 (no earthquakes) (Fig. 9).
Continuous tilt underground sites measurements allow us to estimate both elastic and viscous parameters of the geological medium.Structural rock mass elements are known to have rheological properties, i.e. they can be deformed with time under constant loading or release stresses in case of constant deformation.In simulations, equations of state generally include elastic and viscous elements.The number of such elements and their combinations (serial, parallel) are determined by the available experimental data.Definitely, the basic model envisages elastic deformation (Hooke body).As shown above, the elastic response is clearly manifested in case of rapid pressure changes and nearby strong earthquakes (co-seismic effect).Data on long-term variations of strain provide for estimation of effective viscous parameters, and the simplest viscoelastic models consisting of two elements are analysed as follows: and where σ and ε are tangential stresses and strain; µ is shear modulus; η is viscosity; ε' is differentiation of strain in time, t.The deviatoric form of ( 5) and ( 6) is due to the fact that viscous deformation does not change the volume.
Based on the experimental results concerning shear deformation progress / tilting and the simple concepts of stress changes from 1985 to 1989 σ ≠ 0 and later on σ = 0, we use the Kelvin model and consider the strain attenuation curve at azimuth -33°Ν in the main gangway of the shaft tunnels; this direction is orthogonal to the Talaya stream valley, where in a zone of fracturing is revealed [Timofeev et al., 2012], and to the Main Sayan fault located a few kilometres to the north of the station (Fig. 10).There is an approximate correlation between the notion of the zero component at azimuth -33°Ν and principal strain orientations in the given period according to strain data obtained by rod-and laser measurement systems.
The rheological equation for a solid Kelvin body is obtained from a simple algebraic combination of equations for a solid Hooke and a Newtonian fluid.For strain, it can be written as follows: where e is deformation at time t; e o is initial deformation; P o is instant stress; η is viscosity; t is time; T = η  ⁄ is time constant or lag time for rigid-viscous movement; µ is shear module.
Figure 10 shows attenuation in case of recalculations of variations for azimuth -33°Ν in the N-S and E-W directions, and the curve based on experimental data covering 30 years of observations at Talaya Seismological Station.In our analysis of these data, time constant, T is 10 years.For   = 20GPa, the effective viscosity of the crustal material, η  amounts to 6.3•10 18 Pa⋅sec.
Based on the available measurement data, it is possible to estimate an additional local stress of the crust from the maximum tilt value: For  = 5 х 4.8 • 10 −6 and   = 20GPa, the variable portion of the tectonic crustal stress,   amounts to 5 bar (0.5 MPa).
Estimating the size of the area being representative for tilt observations is complicated due to the following factors: in the area of Talaya Seismic Station, the terrain is strongly dissected; a zone of fracturing strikes along the Talaya stream valley; the Main Sayan fault zone is located 3 km to the north of the station.Based on the recorded tilt variations (from 0.1 to 3 arc-seconds per year) and velocities of vertical movements (according to space geodesy techniques, 1-3 mm per year) [Timofeev et al., 2013], the size of the zone can be estimated from the following ratio of the annual tilt rate: where l is size of deformation area; ∆ℎ is velocity of vertical movements.
For different rate, the estimated size of the deformation zone varies from 100 m to 6 km.
Рис. 11.Gangway located 50 m from the entrance to the shaft tunnel.
Quartz tidal slope meters installed on the pedestal (April 2014).In the zone of intrusion, the shaft tunnel walls are composed of crystalline schist and skapolite-amphibole-diopside gneiss.See zoomed-in photos of points marked by arrows in Fig. 12 and 13.

CONCLUSION
Determining the rheological parameters of rocks in situ is discussed.In the shaft tunnel of Talaya Seismological Station, it is possible to measure deformations from 0.1 nanostrain level (1 nanostrain = 10 -9 ).How-ever, cavity and thermal effects can distort the obtained parameters.Such effects should be taken into account during developing observation in well or in tunnel.The petrophysical studies of the core samples yielded elastic parameters of the bedrocks in the Talaya stream valley (Archean marble) as follows: μ=G=2•10 10 Pa for the shear modulus, and ν=0.17 for the Poisson ratio.The tilt measurement database covering 30 year period provided for strainattenuation analyses.Using the viscoelastic Kelvin model and the experimental curve, we estimated the apparent viscosity of rocks in the shaft tunnel: ηs≈10 19 Pa⋅sec.
In our experiments, the obtained parameters are representative for the area ranging from 0.1 km to 6.0 km, i.e. may be valid to the underground gallery, the Talaya stream valley and the Main Sayan fault zone.In the shaft tunnel, viscoelastic behaviour of the rocks may be outcome of their composition and fine structure (see Fig. 5,11,12 and 13).In the Talaya stream valley and the Main Sayan fault zone, viscoelastic behaviour may be caused by the impact of the linear fracturing zone (striking along the valley and along the fault strike) which is characterized by high water-cut.The reported rheological parameters of the geological medium can be useful for modelling of tectonic, coseismic and post-seismic effects.
The study was supported by Integration Project No. 76 in the Siberian Branch of RAS, RAS Presidium Project No. 4.1,
63. Core studies were conducted at IPGG SB RAS.

Fig. 5 .
Fig. 5. Geological map and mining plan, underground gallery No. 9, Talaya seismic station.Scheme and cross section of the tunnels, Talaya seismic station.