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6и в восточной (Кук-Караук, Гадельша, Атыш, Абза-новский, Шариповский, Ассинский, Шульган, Тю-люк, Инзер и др.) высотой от 5 до 25 м [1].
Для широкого развития туризма и рекреации в Башкортостане имеются ряд положительных, привлекательных факторов. Наряду с большим количеством водных туристско-рекреационных объектов, здесь присутствуют множество уникальных геологических, геоморфологических, археологических, антропогенных объектов (природные геотермальные явления и горы Янгантау («горящая гора», историко-культурные заповедник «Аркаим», горы-одиночки, пещера Шульганташ с рисунками эпохи палеолита, граница «Европа-Азия» и др.).
Республика Башкортостан находится в центре России, через ее территорию проходят транспортные (ж/д, авиа, авто) дороги, соединяющие запад и восток. Республика имеет хорошо развитую промышленность, сельское хозяйство, инфраструктуру, является одной из стабильных в Российской Федерации.
Литература
1. Абдрахманов Р.Ф. Пресные подземные и минеральные лечебные воды Башкортостана. Уфа, 2014. 414 с.
2. Гареев А.М. Реки и озера Башкортостана. Уфа: Китап, 2001. 260 с.
3. Гареев Э.З. Геологические памятники природы. Уфа: Тау, 2004. 295 с.
4. Сайфуллина Е.Н. География и геоэкологическая оценка рекреационных и туристских объектов юга Западного Приуралья (в пределах Башкортостана): монография. Уфа: Вагант, 2008.168 с.
5. Фаткуллин Р.А. Природные условия Башкортостана. Уфа: Китап, 1994. 176 с.
6. Фаткуллин Р.А., Файзуллина А.А., Санни-кова Е.Н. Охрана гидроцентров Южного Урала // Труды XI съезда русского географического общества). Т.5 - С - Петербург, 2000. - С. 122-123.
7. Фаткуллин Р.А., Сайфуллина Е.Н., Абдрахманов Р.Ф., Батанов Б.Н. Возможность использования водных объектов Западного Приуралья (в пределах Башкортостана) в рекреационных и туристских целях // Мелиорация и водное хозяйство. М., 2007. С. 10-14.
8. Фаткуллин Р.А., Сайфуллина Е.Н., Япаров И.М. Качественная оценка рекреационных и туристских объектов Западного Приуралья (в пределах Башкортостана) // Вестник ВГУ, Воронеж, 2007. С. 43 - 45.
9. Фаткуллин Р.А., Халиуллина Г.Ф. Лечебно-оздоровительные центры Башкортостана как туристские объекты // Региональный туризм - 2009: Сб. статей Межрегиональной науч. -практ. конф. Уфа, 2009. С. 136-139.
NEWTONIAN VS. NON-NEWTONIAN MANTLE WEDGE PALEOZOIC THERMAL CONVECTION AS THE MECHANISMS OF NON-ORGANIC HYDROCARBONS TRANSPORT IN TIMAN-PECHORA OIL- AND GAS-BEARING PROVINCE
Gavrilov S.V.
Schmidt Institute of Physics of the Earth, Russian Academy of Sciences, Moscow
Kharitonov A.L.
Pushkov Institute of Terrestrial Magnetism, Ionosphere and Radio Wave Propagation, Russian Academy of
Sciences, Moscow
ABSTRACT
Small-scale thermal 2D finite-amplitude convection in the mantle wedge with extremely small subduction angle has never been investigated previously by other authors, despite the subduction of this kind takes place in the case of underthrusting of continental plates, e.g. Indian plate, and apparently occurred at Paleozoic during the East-European plate subduction in the course of closing of the former Urals ocean. Alternating relief depressions and uplifts and associated with the latter oil- and gas-bearing zones parallel to south-western border of Timan-Pechora plate may evidence of topography undulations to have originated owing to 2D convection in the mantle wedge. Numerical models accounting for phase transitions at 410 km and 660 km depths and temperature, pressure and viscous stress (for non-Newtonian rheology) dependence of viscosity for wet olivine show the subduction velocity ~6 cm*yl to correspond to the dimension of the cells of convection aroused by fictional heating in the mantle wedge to be of the same scale as the Timan-Pechora relief undulations wavelength, total horizontal extent of convecting region being of the order of horizontal extent of Timan-Pechora oil- and gas-bearing province. In the case of non-Newtonian rheology the velocity in convection vortices exceeds ~1 m*y-1, mean water concentration is ~10-1 weight %%, the convective zone is ~103 km closer to the mantle wedge edge as compared to Newtonian rheology case.
Keywords: thermal convection in the mantle wedge, subduction angle and velocity, mantle rheology parameters, phase transitions, oil bearing zones
INTRODUCTION folded Timan mountain range while the eastern and the
Western and south-western borders of Timan-Pe- north-eastern borders are situated at Urals and Pie-chora oil- and gas-bearing province coincide with the Khoy. The northern border is mapped with the help of
geophysical means along nearly latitudinal deep fault ~50 km distant off Kolguev island at Barents sea. The province is characterized by a number of big relief depressions (viz. Izhma-Pecherskaya, Denisovskaya, Khoreyverskaya, Korotaikhinskaya, Kosyu-Rogovskaya ones) parallel to Timan range and separated by the regional uplifts (viz. East Timan and Pe-chora-Kolvinskiy mega rolls, Shapkin-Yuryakhinskiy, Layskiy, Varandeyskiy and Sorokin rolls). The zones of oil and gas accumulation are noticeably well associated with the abovementioned rolls. Alternating topography uplifts and depressions are parallel to the southwestern border of the Timan-Pechora plate the density anomalies being located quasi periodically as well [4]. That may serve an evidence for the origin of these structures be due to the small-scale convection in the mantle wedge formed in the course of closing of the former Urals ocean and the subduction of the East-European plate under the Timan-Pachora one at Paleozoic. On the ocean having closed $t the end of Paleozoic the subduction ceased [12]. However, the tilted zone of increased seismic velocities observed on the "Quarts" profile in the mantle at depths of 50 - 100 km dropping downwards at the angle ~8° - 9° in eastern direction [10] probably shows the subduction of the East-European plate under the Timan-Pechora one actually took place the greater density tilted zone being the remnant of the formerly subducting East-European plate. The zones of oil and gas accumulation aligned parallel to Timan-Pechors range may as well be regarded to be associated with the upwelling small-scale convective flows in the mantle wedge. This flows might have been transporting non-organic mantle hydrocarbons to the plate surface. Assuming the hydrocarbons were transported to the surface of the Timan-Pechora plate by the
mechanism of thermal convection of the form of variable thickness rolls aligned perpendicular to subduction the scale of convective rolls being the same as the scale of the relief and density variations wavelength, one can estimate the mean velocity of the former subduction of the East-European plate at closing Urals ocean at Paleozoic (~5-6 cm*y-1); this is done similarly to [4] taking into account total extent of the Timan-Pechora oil- and gas-bearing province. As this estimate was obtained on the assumption that the mantle wedge is a constant viscosity fluid, it seems important to calculate the scale and the intensity of convection for more realistic mantle rheology accounting for the temperature, pressure and viscous stress dependence of viscosity. The viscosity in the mantle wedge is probably rather low, i.e. ~1018 Pa*s or less, because of the presence of water upwelling to the mantle wedge from the subducting slab [15]. As is indicated by [3], additional 102-103 g of water in the tone of rock reduces viscosity by two orders of magnitude as compared to dry conditions. The model proposed accounts for the mentioned characteristics of the mantle wedge rheology i.e. rather low pressure-, temperature- and (for non-Newtonian rheology) stress-dependent viscosity.
MODEL
Thermomechanical model of the mantle wedge between the base of the Timan-Pechora plate and the upper surface of the East-European plate subducting under the Timan-Pechora one with a velocity V at an angle p is obtained for the infinite Prandtl number fluid as a solution of non-dimensional 2D hydrodynamic equations in the Boussinesq approximation for the
stream-function V and temperature T [11]:
(3-3L-3L)y + = RaTt - Ra^r - Rtf66«»!™
5 tT = AT - y J x + y J +
Dl x t,
Ra 2n
+ Q,
(1)
(2)
where n is non-dimensional dynamic viscosity, ^ and indices denote partial derivatives with respect to coordinates x (horizontal), z (vertical)) and time t,
A is the Laplace operator, P(410) and p(660) are volume ratios of heavy phases at phase transitions at 410
km h 660 km depths, the velocity components Vx and
Vz are expresses through the stream-function V as
Vx = Vz , Vz =-¥x , (3)
non-dimensional Rayleigh numberRa, phase
Ra^410*, Ra(660) and dissipative number Di are
Ra = ap gd T = 5.55 x108.
Dr = Ogi = 0.165, (4)
Ra(410) =
nx
ôp (410)gd
= 6.6 x108
nx
(660) j3
Ra(660) = ôp _gd = 8.5xi08
nx
where a =310-5 K-1 is thermal expansion coefficient, p =3.3 gxcm-3 is density, g is gravity acceleration, cp = 1.2*103 J ' kg-1K-1 is heat capacity at constant pressure, T1 = 1950 K is the temperature at the mantle transient zone (MTZ) base at 660 km depth, regarded the lower boundary of the modeled domain, Q= 6.2510-4 mWxm-3 is the volumetric radiogenic heat relies power in the crust, Trk is the viscous stress tensor, d=660 km is the vertical dimension of the modeled domain, n = 1018 Pa*s is the viscosity scaling factor, x =10-2 cm2 xs-1 is thermal diffusivity, ôp(410) = 0.07p
and ôp(660) = 0.09p are the density changes at phase transitions at 410 km h 660 km depths. In (1), (2) the
scaling factors for time t, stresses Trk and stream-function y are d2 • x—, nx ' d 2 and % respectively.
c
Previously in [6] convection was modeled in the assumption of linear rheology for the diffusion creep mechanism, dominating in the mantle at depths over ~200 km [1], and temperature T and lithostatic pressure
p viscosity n dependence was taken as [15]
П =
2 A
h b*
exp
E * + pV* RT
(5)
where for wet olivine A=5.3*1015 s-1, m=2.5, the grain size h=10-2 - 1 cm, Burgers vector is 6*=5*10-7 mm [14], activation energy is E"=240 kJ*mol-1, activation volume V*=5 cm3 xmol-1, ^ =300 GPa is normalizing factor of the shear modulus, R is universal gas
constant. At grain size h=10-2 cm, n = 1018 Paxs and abovementioned values of constants non-dimensional
viscosity also denoted n is
П = 5.0x10"7 exp
14.8 +1.34 x (1 - z)
T
(6)
П =
1
2 ACr t n -1
w
r^m
b
E + pV
exp--—, (7)
RT
where, according to [13], for "wet" olivine n=3, =1.2, m=0, t=(т2а)1/2 , £*=480 kJxmol-1, V*=11
cm3*mol, A=102 s-1x(MPa)-°, Cw ^ 10-3 for "wet" olivine is the weight ratio of water (in %). It should be noted, that the constants in (7) differ considerably in papers referred to by [13], and here we give averaged values. Accounting for
Tk = 4n2[(V, "Vxx*)2 /2 + 2¥L] (8)
at Cw =10-3 non-dimensional viscosity is
1.00 10.0 + 5.0X (1 - z) (9)
П =-i-^-tttX exp-'v '
[(Vzz- ¥xx)2/2 + 2yLf3 T
The modeled domain aspect ration is 1:6, i.e. for
diagonal subduction the angle of subduction is ß ~ 90 , while the trial subduction velocity V=6 cm*y-1 scaled by X' d— is V=1.25 103 its components in subducting
plate being Vx = - 1.233 103 и Vz = -0.164103 . Following [13], we take phase functions ) as (mind, z-axis is pointing upwards, thus the signs here are altered):
Г (l) = 11 - th
z - z W(T )
JJ )
Y (l )
z(l)(T) = z(l) -(T-T0(l)), (10) P&
where z(l )(T ) is the /-th phase transition depth, (l) r(l)
z0 and 1 g are averaged depth and temperature of
l-th phase transition, y(410) = 3 MPa*K_1 and Y(660) = -3 MPa^K'1 are the slopes of the Clapeyron curves,
w(l ) is the characteristic breadth of l-th phase transi-
T (410) tion, To
^(660)
= 1800 K, T o =1950 K are averaged
phase transition temperatures. Phase transition heats are here neglected as in [13] as these are inconsequent in the case of finite-amplitude convection. From (10) it follows:
г ?) =--
2pgw
-ch
z - z 0l) + Y (l)(T - To(l ))/pg ^ (11)
X T V
where T is non-dimensional temperature, and z, normalized by d, is vertical coordinate measured upwards from the MTZ base (x -axis is pointing along the MTZ base against subduction). To judge as to how the estimate ~6 cmxy-1 of Paleozoic subduction velocity V of the East-European plate is "sensitive" to the rheology law accepted, here we carry out computation for non-Newtonian rheology with Eqs. (5)-(6) rewritten as:
wherefrom it is clear the phase transition with Y(l) > 0 facilitates convection (at l=410), and phase transition with Y(l) < 0 ( at l=660) impedes convection. In non-dimensional form z(410) =0.38, z(660) =0,
w
(l )=n
0.05, Y(410) =2.55X109, Y(0°0) = -2.55X109
(660) _
T0(410) = 0.92, T0(660) =1, and in (1)
fin<" Y0
Г0 __Y— ch-1
Г pR«®2w(i)
z - 4° + Y(i)-^(T - T())
pRa1'
-x T,
.(12)
Boundary conditions are accepted as isothermal horizontal and insolent vertical no-slip impenetrable boundaries (but for the "windows" of in- and outgoing subducting plate where the velocity components are specified and for the distant from the trench vertical boundary crossed at right angle. The latter condition seems not too imposing for the case of flat subduction. Q in (2) is vanishing everywhere outside continental and oceanic crust 40 km and 7 km thick respectively. Initial temperature of vertical boundaries are taken according to half-space cooling model during 103 Myr for Timan-Pechora plate and during 102 Myr for East-European plate.
RESULTS AND DISCUSSION To construct self-consistent model of 2D small-scale thermal convection in the mantle wedge between overriding Timan-Pechora plate and subducting East-European plate it is necessary first, in order to raise the accuracy of computation, to put Ra П0, Di =0 in (1)-(2), i.e. to model thermo-mechanical state of the plates and the mantle wedge without taking into account viscous dissipation and convective instability. This approach is necessary as with Ra and Di (4) the convection modeled reaches too great a velocity thus making it necessary to choose extremely small time-steps to reach quasi steady-state temperature and velocity distributions within the plates. Integrating (1)-(2) with
Ra J 0, Di =0 with respect to spatial coordinates x
m
Y
2
w
w
2
and z by the finite element method on the uniform grid where the stream-lines are depicted with intervals 0.25,
of 104x104 size and with respect to time t by the 3-rd and isotherms with intervals 0 05 (vertical scale in
order Runge-Kutta method, one obtains quasi steady- Fig.1 is extended by a factor of 2).
state non-dimensional V and T = Tr shown in Fig. 1
330 HO 990 132» 1650 19» 2310 2640 2970 3330 M0
*J X ^■lIMIt^sk «1 ^^^ Newtonian rheology
1 .......
11 mo m 13» iuo m m wo m b «t
Fig. 1. Quasi steady-state non-dimensional stream-function and temperature in the zone of subduction of the East-European plate under the Timan-Pechora plate with no effects of viscous dissipation and convection for (a, c) - Newtonian and (b,d) - non-Newtonian rheologies. Parallel quasi equidistant streamlines correspond to
subducting East-European plate. The streamlines with negative y correspond to the mantle flow, induced by
subduction.
Fig. 1 shows the results for both Newtonian (equations (5)-(6)) and non-Newtonian (equations (7)-(9) ) rheologies. The plate subducting at the velocity V is considered rigid, the viscosity in the zone of friction of the lithospheric plates at temperatures below 1200 K is reduced by 2 orders of magnitude in comparison with (5) and (7). This accounts for lubrication by subducted sediments partially entrained by subducting plate and preventing lithospheric plates from gluing to each other
[8]. Assuming then the parameters in (1)-(2) according to (4), i.e. switching on the effects of dissipation and convection, and integrating (1)-(2), we find out the induced mantle flow shown in Fig. 1 by negative streamlines to be destroyed by convection during non-dimensional time interval ~1.5x10-4 (in dimensional form ~1.3 Myr) for Newtonian rheology. The quasi steady-state convective vortices are shown in the upper part of Fig.2 by the streamlines with the interval 25.
Fig.2. Quasi steady-state non-dimensional stream-function in the mantle wedge with the effects of viscous dissipative heating and convective instability for (a) - Newtonian and (b) - non-Newtonian mantle rheologies. AB is the Earth's surface portion whereto the convective flows shown by the arrows a, b, c, d can transport
mantle hydrocarbons.
The convective cells scale is of the order of 300 km and the streamlines density correspond to the velocity in convective vortices of the order or less than 10 cmxy1. Computation for non-Newtonian viscosity (7)-(9) shows convection not to be aroused at all. This result holds for viscosity reduced by an order of magnitude what may be due to a greater concentration Cw of
water, e.g. Cw ~10-2 weight %%. Small-scale convection turns out to be aroused only in the case of 3 orders of magnitude less viscosity than that given by (7)-(9),
what may be effected at Cw ~10-1 weight %% or greater. In this case the small-scale convection assumes the form of the vortices shown in the lower part of Fig.2 by the streamlines depicted with the interval 2.5*103, which corresponds to convective velocities over ~1 mxy1. Such the considerable convective velocities may be due to the local stress concentration resulting in the viscosity drop in convective vortices. It should be noted that convection in the non-Newtonian mantle wedge goes on in the oscillatory regime, and Fig.2 shows some transient phase of convection. Total horizontal extent AB of the zone with convection amounts to ~103 km, which for the rheology of both types is close to the observed horizontal extent of the Toman-Pechora oil- and gas-bearing province. Mean separation of upwelling convective flows (shown in Fig.2 by the arrows a, b, c, d) equals ~300 km, which is of the order of spatial wavelength of location of topography uplifts and associated oil- and gas-bearing zones on the Toman-Pechora plate. Fig.2 shows clearly the westward ~103 km shift of convective zone AB in the non-Newtonian mantle wedge in comparison to Newtonian case, and this favors non-Newtonian rheology case, which in this
respect fits in better with the observed distance between the Timan-Pachora range and the oil- and-gas-bearing zones.
Perpendicular to subduction convective rolls in the mantle wedge, as in Fig.2, are worth noting to be aroused exclusively in the case of extremely small subduction angle, such transversal rolls being not aroused already in the case of subduction angle ß=30° [5, 8]. At the angle ß=9° under consideration transversal convection is not aroused at subduction velocity V<5 cm xy-1. 2D small-scale transversal convection in the narrow mantle wedge is obviously associated with the greater viscous stresses and consequently greater dissipative heat release than in the wider mantle wedge. In the case of non-Newtonian mantle rheology transversal convection is aroused at subduction velocity V~6 cmxy' if water content is Cw >10-1 wight percent. It should be noted that numerous thermo-mechanical mantle models in the zones of subduction (see, e.g. [7, 8] and the vast number of references there) showed convection in the form of transversal rolls never to occurre as the models with extremely small subduction angle and sufficiently great subduction velocity were not investigated.
CONCLUSIONS
For both Newtonian and non-Newtonian rheolo-gies the characteristic cells scale ~300 km of 2D transversal convection in the mantle wedge formed in the course of closing of the former Urals ocean and subduction of the East-European plate under the Timan-Pechora plate at Peleozoic is approximately the same as the spatial wavelength of topography variations in the Timan-Pechora region. For both rheology types horizontal extent of Timan-Pechora oil- and gas-bearing
province (in which the zones of oil and gas accumulation are associated with the relief uplifts) is of the same size as the model horizontal extent of convecting region. The velocity in convection rolls for non-Newtonian rheology is over ~1 m xy1 which probably is sufficient to efficiently transport basaltic partial melt to the Earth's surface and thus to contribute to the crustal relief formation. Non-Newtonian rheology model shows the small-scale 2D convection to be aroused at the water concentration of the order or over 10-1 weight %%, the convecting region being shifted south-westward by ~103 km as compared to the Newtonian rheology model. The scale of convection cells is of the order of wavelength of localization of oil- and gas-bearing zones associated with topography uplifts this coincidence serving an evidence for the estimate ~6 cmy1 of the velocity of subduction of the East-European plate under the Timan-Pechora one at Paleozoic.
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