Annals 47, 1, 2004, 01/07def 151 ANNALS OF GEOPHYSICS, VOL. 47, N. 1, February 2004 Key words Baikal rift zone – electromagnetic mon- itoring – transfer functions – resistivity changes of the fault 1. Introduction It is generally accepted that one of the pos- sible precursors of earthquake in the seismical- ly active Baikal region may be the change in the electrical resistivity of the saturated porous rock in deep-water rift faults. In accordance with the modern concept of the Baikal region geoelectrical structure (Merklin et al., 1979), there is a narrow fault there that is galvanically connected with a deep-seated conductor. Berdi- chevsky et al. (1989) showed that for two-di- mensional (2D) model of marine deep magne- totelluric investigations the vertical electric field at the ocean bottom is highly sensitive to the resistivity of the underlying cross-section. Besides, Berdichevsky et al. (1996) showed that certain 2D Earth models would generate considerable vertical electrical currents if the models include vertical faults of low resistivity. These authors used horizontal magnetotelluric field as an incident field. The latter work deals with magnetotellurics in the Lesser Caucasus but the first one deals with deep marine magne- totellurics. Meanwhile, Baikal water is fresh and much more resistive as compared with the oceanic water, however, Shneyer et al. (1998) proved that in 2D model of Southern Baikal the vertical electric field, Ez, is again sensitive to the presence of thin vertical fault of low resis- tivity. Though these results are valuable, we de- cided to explore the behaviour of Ez for a three- dimensional (3D) Baikal model, bearing in mind that the fault is a body of limited length but not of an infinite one. In this paper we build Ez-response as a monitor of a Baikal rift fault electrical resistivity: 3D modelling studies Oleg V. Pankratov, Alexei V. Kuvshinov, Dmitry B. Avdeev, Vitaly S. Shneyer and Igor L. Trofimov Geoelectromagnetic Research Institute, Russian Academy of Sciences, Moscow Region, Russia Abstract 3D numerical studies have shown that the vertical voltage above the Baikal deep-water fault is detectable and that respective transfer functions, Ez-responses, are sensitive to the electrical resistivity changes of the fault, i.e. these functions appear actually informative with respect to the resistivity «breath» of the fault. It means that if the fault resistivity changed, conventional electromagnetic instruments would be able to detect this fact by meas- urement of the vertical electric field, Ez, or the vertical electric voltage just above the fault as well as horizontal magnetic field on the shore. Other electromagnetic field components (Ex, Ey, Hz) do not seem to be sensitive to the resistivity changes in such a thin fault (as wide as 500 m). On the other hand, such changes are thought to be able to indicate a change of a stress state in the earthquake preparation zone. Besides, the vertical profile at the bottom of Lake Baikal is suitable for electromagnetic monitoring of the fault electrical resistivity changes. Altogether, the vertical voltage above the deep-water fault might be one of earthquake precursors. Mailing address: Dr. Oleg V. Pankratov, Geoelectroma- gnetic Research Institute, Russian Academy of Sciences, 142190 Troitsk, P.O. Box 30, Moscow Region, Russia; e- mail: o.pankratov@mtu-net.ru 152 Oleg V. Pankratov, Alexei V. Kuvshinov, Dmitry B. Avdeev, Vitaly S. Shneyer and Igor L. Trofimov a simple 3D model of Southern Baikal and ver- ify: 1) whether Ez is detectable over the fault, and 2) whether Ez-response is sensitive to the resistivity changes of the fault. 2. Model Lake Baikal is located in the southern part of Eastern Siberia (see fig. 1). It is the oldest exist- ing freshwater lake on Earth (20-25 million years old), being the deepest continental body of water. It is 636 km long and 48 km wide. Baikal lies in a deep structural hollow surrounded by rock. The fault that we are interested in, is located at the southern part of Lake Baikal, not far from the town of Slydyanka. A simplified 3D resistivity model of the Baikal deep fault is shown in figs. 2 and 3. The geometry of the model was taken mainly from seismic data by Merklin et al. (1979), whereas the resistivity data were taken from electromagnetic data by Popov (1977), and Kieselev and Popov (1992). In the model the 2 km thick, 40 Ω⋅m water layer is underlain by Fig. 1. Map of the region of Lake Baikal. Modelling region is marked with a rectangle. The fault is marked with a thick line. 153 Ez-response as a monitor of a Baikal rift fault electrical resistivity: 3D modelling studies the 1 km thick, 60 Ω⋅m sedimentary layer. Both layers are surrounded and underlain by 1000 Ω⋅m rock. Below, at a depth of 15 km, there is a 10 km thick conductive layer of 10 Ω⋅m. As for the fault in the model, it is 28 km long in y-di- rection (parallel to the shore) and 0.5 km wide in x-direction (perpendicular to the shore). The ver- tical size of the fault is 13 km. The fault outcrop is located at lake bottom exactly where the 35° steep slope of the north-western shore of the lake is ending. The shape of the south-eastern shore slope has been proved not to affect the electro- magnetic (EM) field calculated in the vicinity of north-western shore. Thus, the fault appears to be galvanically connecting the deep conductive layer under the lake and the lake itself. 3. Numerical modelling In the 3D resistivity model proposed we have performed a series of simulations of the Fig. 2. 3D resistivity model of the Baikal Fault (side view). Line A-B is the profile where behaviour of Ez is studied. C is the coast site where components Hx and Hy are taken to obtain Ez response (see details in the text). Fig. 3. 3D resistivity model (plane view). 154 Oleg V. Pankratov, Alexei V. Kuvshinov, Dmitry B. Avdeev, Vitaly S. Shneyer and Igor L. Trofimov vertical electric field, Ez, along vertical profile A-B as well as horizontal magnetic field on the shore. This 2 km long profile (from lake surface to the bottom) is located just over the center of the fault (see fig. 2). The amplitude of the inci- dent plane wave electric field is chosen to be equal to 10 mV/km, resembling typical ampli- tudes of mid-latitude disturbances. Period of the incident field is taken to be 100 s and 1 h. While modelling, we varied the fault resistivity, ρfault, the values taken to be 10, 11 and 20 Ω⋅m. To perform the simulations we used X3D code which is based on the solution of modified scat- tering equation by the Krylov subspace itera- tions (Avdeev et al., 1997, 2000). The model- ling region of 44 km × 80 km × 15 km is divid- ed into 440 × 100 × 14 cells. Figure 4 presents the vertical electric field, Ez, along vertical profile A-B for Ex-polarized incident plane wave, with fault resistivity being 10 Ω⋅m. Left and right panels of the figure re- veal the results for the periods of 100 s and 1 h respectively. The figure demonstrates that the values of |Ez| are ranging, depending on depth, from zero (at the surface) up to 9 mV/km (at the bottom). In practice during the future experi- ment we are going to measure the vertical volt- age, V(A, B), between points A and B. In our model, V(A, B) can be calculated as .,V E z dzA B z A B = #^ ]h g . The left plot in fig. 4 implies that the vertical voltage, V(A, B), should exceed 5 mV, which is very promising, since 5 mV could be readily de- tected by conventional EM instruments, their measurement precision accounting for 0.01 mV. In addition, it is also seen from the figure that Fig. 4. Electric field components Ez and Ex along profile A-B. The source is Ex-polarized plane wave. The re- sults are presented for periods 100 s (left panel) and for 1 h (right panel). The fault resistivity is 10 Ω⋅m. 155 Ez-response as a monitor of a Baikal rift fault electrical resistivity: 3D modelling studies near the fault outcrop, Ez-field even dominates the primary field Ex. Note that only real parts of the components are discussed, since imaginary parts are two orders of magnitude less. It can be seen from fig. 4 Ez(z) that can be approximated as follows: h E z E b ez z z b . - ] ] ] g g g (0 < z ≤ b) (3.1) when we evaluate integral ,V E z dz E z dzA B z z b A B 0 = =# #^ ] ]h g g . Here b = 2 km is the bottom depth. Also, h = 621 m and h = 586 m for period of 100 s and 1 h re- spectively. As a consequence, the vertical volt- age is directly proportional to the vertical elec- tric field measured at the bottom ,V k E bA B z$=^ ]h g (3.2) where proportionality coefficient is k = h (1− e− b/h). We can show that coefficient k does not depend on the amplitude of the incident field. The other consequence: higher values of the vertical electric field are accumulated near the bottom, so that it is not necessary to locate point A exactly at the surface. We can locate point A, say, 100 or 200 m deeper without significant change in the value of V (A, B). As for the other polarization of the incident field (Ey-polarized plane wave), the vertical electric field is at least two orders of magnitude less than that for Ex-polarized incident field. So far we demonstrated the amplitudes of the fields themselves. But it is known that while monitoring, the external field should be exclud- ed from consideration. For this purpose, we in- troduce Ez-response as the expansion coeffi- cients in ,V u H u HA B zx x r zy y r = +^ h (3.3) where Hxr and Hyr are the horizontal magnetic field components at the coastal reference site (site C, see figs. 2 and 3). Expansion (3.3) can be used in the following way. Let V1(A, B) and V 2(A, B) be the vertical voltage values measured for any two different polarizations of the incident field. Let (Hx1, Hy1) and (Hx2, Hy2) be the horizontal magnetic fields measured at the coastal reference site for the first and for the second polarization respective- ly. From expansion (3.3) it follows that: , , V u H u HA B A B zx x zy y zx x zy y 1 1 1 2 2 2 = + .V u H u H= + ^ ^ h h (3.4) Therefore, we obtain final formulae for transfer functions uzx and uzy as follows , ,detu u H H H H H V V A B A B 1 zy zx y x y x 2 2 1 1 1 2= - - d e ^ ^ en o h h o (3.5) where detH = (Hx1Hx2 − Hy1Hy2). Then these transfer functions uzx and uzy are called the Ez- responses because bigger values of the vertical electric field, Ez, are accumulated near the bot- tom and because V(A, B) is proportional to Ez (b) (eq. (3.2)). Table I presents the absolute value of the Ez- response, |uzy|, shown with respect to the fault resistivity and period. Table I shows |uzy| trans- fer function alone, since response uzx appears to be negligibly small compared to uzy. This is due to the fact that only TM-polarized incident field generates major vertical electrical current through the fault. Although electromagnetic field components Ex, Ey, Hx, Hy, Hz appear to be insensitive to the Table I. Absolute value of Ez-response, |uzy|, with respect to the fault resistivity and period. Ez-response (mV/nT) 100 s 1 h ρfault = 10 Ω⋅m 776 ⋅10 − 9 186 ⋅10 − 9 ρfault = 11 Ω⋅m 743 ⋅10 − 9 180 ⋅10 − 9 ρfault = 20 Ω⋅m 526 ⋅10 − 9 128 ⋅10 − 9 precision of 14 ⋅10 − 9 5 ⋅10 − 9 experimental Ez-response 156 Oleg V. Pankratov, Alexei V. Kuvshinov, Dmitry B. Avdeev, Vitaly S. Shneyer and Igor L. Trofimov resistivity of the fault, we still need components Hx and Hy on the shore in order to obtain trans- fer functions uzx and uzy. Indeed, transfer func- tions uzx and uzy do not depend on the polarization of the incident field but the vertical voltage does. The second row of table I shows that for a 100 s period, an operator should measure the values of 776, 743, and 526 and distinguish them from each other having the measurement precision equal to 14. Obviously it is possible. For a 1 h period, the measurement precision is just enough to distinguish the 10 Ω⋅m fault from the 11 Ω⋅m fault; and it is far enough to distinguish the 11 Ω⋅m fault from the 20 Ω⋅m fault. Altogether, for both periods the changes in the fault resistivity lead to detectable changes in Ez-responses. More explicitly, 10% and 100% fault resistivity changes result in 4% and 30% Ez-response changes, respectively. It should be also stressed that traditional imped- ance responses (simulated but not shown here) have appeared to be practically insensitive to the changes of the fault resistivity. Further nu- merical modelling (performed but not shown here) reveals that the link between the Ez-re- sponses and the fault resistivity holds valid for bigger resistivity values. Namely, for the values ρfault = 10, 11, 12, 20, 40, 80, 160 and 320 Ω⋅m we calculated the Ez-responses and found that |uzy (ρfault)| can be approximated as follows: uzy fault fault$.t o t c _ i (3.6) where γ = γ (T ) and ν =ν (T ) depend on the peri- od, T, of the incident field. Approximation (3.6) now follows that though we could hardly distin- guish the 10 Ω⋅m fault from the 11 Ω⋅m fault at 1 h period, the 10 Ω⋅m fault can easily be distin- guished from the 14 Ω⋅m fault at this period. Though our model is an estimate, we realize that the link between the Ez-responses and the fault resistivity is rough enough and it must be detected while in situ measurements. 4. Conclusions 3D numerical studies have shown that the vertical voltage is detectable above the Baikal deep fault, and that Ez-responses are sensitive to the resistivity changes of the fault, i.e. Ez-re- sponses appear actually informative with re- spect to the resistivity «breath» of the fault. Further studies should include more detailed modelling and field operations. It should an- swer the question whether changes in Ez-re- sponses (and ρ fault) are connected with changes in a stress state in the fault vicinity and whether Ez-responses can be used as one of earthquake precursors. Acknowledgements The research has been partly made possible through grants No. 00-05-64182 and No. 00-05- 64677 from the Russian Foundation for Basic Research. We are also grateful for both review- ers’ valuable comments. REFERENCES AVDEEV, D.B., A.V. KUVSHINOV, O.V. PANKRATOV and G.A. NEWMAN (1997): High performance three-dimensional electromganetic modelling using modified Neumann series. Wide-band numerical solution and examples, J. Geomag. Geoelectr., 49, 1519-1539. AVDEEV, D.B., A.V. KUVSHINOV, O.V. PANKRATOV and G.A. NEWMAN (2000): 3D EM modelling using fast integral equation approach with Krylov subspace accelerator, in Extended Abstracts of the 62nd Meeting of Eropean As- sociation of Geoscientist and Engineers, vol. 2, p. 183. BERDICHEVSKY, M.N., O.N. ZHDANOVA and M.S. ZHDANOV (1989): Marine Deep Geoelectricity (Nauka, Moscow), pp. 90. BERDICHEVSKY, M.N., V.P. BORISOVA, N.S. GOLUBTSOVA, A.I. INGEROV, YU.F. KONOVALOV, A.V. KULIKOV, L.N. SOLODILOV, G.A. CHERNYAVSKY and I.P. SHPAK (1996): An experience of interpretaion of MT soundings in the Lesser Caucasus mountains, Fiz. Zemli, 4, 99-117 (in Russian). KIESELEV, A.I. and A.M. POPOV (1992): Asthenospheric di- apir beneath the Baikal rift: petrological constraints, Tectonophysics, 208, 287-295 MERKLIN, L.R., V.E. MILANOVSKYI, V.I. GALKIN and M.V. ZAKHAROV (1979): Structure of sedimentary layer and basement relief, in Gelologic-Hydrophysical and Deep- Water Studies at Lake Baikal, 104-110. POPOV, A.M. (1977): High conductive deep layers as they found from magnetotelluric data, in Deep Structure of the Baikal Rift (Nauka, Novosibirsk), (in Russian). SHNEYER, V.S., E.YU. SOKOLOVA and I.L. TROFIMOV (1998): Two-dimensional electromagnetic field modelling re- sults in the South-Baikal depression region, in Abstract of 4th International Conference: Modern Methods and Techniques of Oceanological Research, Moscow (in Russian).