ИСТИНА

Abstract Volume IAGR Conference Series No. 17, pp. 22-23 Ill-posed problem of regional modeling and major geodynamic periodicity V.D. Kotelkin Faculty of Mechanics and Mathematics of Lomonosov Moscow State University, Moscow, Russia Appearance of detailed data about the internal structure of many regions of the Earth led to growth a new branch of geodynamic modeling - real regional modeling with using data from seismic tomography. The recent calculations [1] of Ismail-Zadeh et al. (2013) are impressive example of such modeling. On the one hand such realistic simulation is very attractive, since it promises important forecasts, but on the other hand a new approach raises serious questions about the correctness of the simulation in the separate region. At first sight the use of real (ie correct) data should lead to correct results. However, mathematicians are well aware that in elliptic problems (geodynamics is such task) solution into any point (any local region) depends of the whole domain (of all mantle). Geologists also know many examples of coherence events in removed from each other regions. Explanation of this contradiction is that the complete solution of the mathematical problem is composed of homogeneous and inhomogeneous parts. Seismic tomography data allow (under additional assumptions on the viscosity) find only an inhomogeneous part of the solution. Homogeneous part of the solution satisfies the boundary conditions. In modern regional studies, based on the data of seismic tomography, boundary effects usually just ignored, which is equivalent to discarding the homogeneous part of the solution. Therefore, the accuracy of results (predictions) remains uncertain. Conditions for the absence outer actions are valid only at the upper boundary of the mantle, whereas at the lower boundary of the region and on its lateral boundaries the forces, heat and mass fluxes in the general case are different from zero. To improve the accuracy of regional modeling may be offered some arrangements. The general recommendation is that to allocate the study region out of the mantle should be done on natural boundaries without cutting it into pieces. As the lower boundary of the computational domain is preferable to take a natural border between the upper and lower mantle. In this case, according to [2] the condition of impermeability for the convection will be most justified, and for the thermal problem we obtain the reliable condition that a temperature is equal the temperature of the endothermic phase transition. As the natural lateral boundaries of the mantle (on which no forces and fluxes are acting) should be regarded the boundary of the convective cells, ie mid-ocean ridges and subduction zones. Besides, there is uncertainty of geodynamic modeling associated with well known fact that thermal convection admits a set of stationary solutions, in other words our modeling is ill-posed problem. Therefore, for geodynamic simulation is desirable to use additional conditions of regularization. As the regularizing conditions may be used a seismic tomography data [1] or geological data [3]. These recommendations were used in the study of thermal convection in an elongated upper mantle region, on the lateral boundaries of this region are supported ascending flows to simulate presence and action of mid-oceans ridges. The numerical 2D-modeling took into account changes in viscosity caused by temperature, phenomenon of solidus and exothermic phase transition at a depth of 410 km. Also was modeled the presence of lightweight crustal material over the mantle and was simulated his behavior. Dynamic visualization of calculations shows that a lightweight material forms a continent which is floating in the central part of region, and near the edges of the continent are functioning two active subduction zones. In this case, convection in the upper mantle has a clearly pronounced cyclical character. There is a phase during which is watching the oblique subduction of plates beneath the continent, and the continent at this time is stretched. When the space under continent will be filled by slabs, the convection rebuilds. Now is realizing another convective phase during which is watching the vertical subduction with overturn of slabs and their movement in the inverse direction, at this time the continent is compressed. When switching modes of convection takes place known to geologists misterious phenomenon when the background of the total extension there are local pieces with a compression and vice versa. Sea level is lowered when the continent is compressed and increases when the continent is elongated. References 1. Ismail-Zadeh, A., Honda, S. & Tsepelev, I. Linking mantle upwelling with the lithosphere decent and the Japan Sea evolution: a hypothesis. Scientific Reports, 3, 1137(2013). DOI:10.1038/srep01137 2. V.D. Kotelkin, L.I. Lobkovskii Thermochemical Theory of Geodynamical Evolution Doklady Earth Sciences, 438 (1) (2011), pp. 622–626. DOI: 10.1134/S1028334X11050333 3. V.D. Kotelkin, L.I. Lobkovskii Modeling of Regional Geodynamics Using Geological Data Doklady Earth Sciences, 2013, Vol. 450, Part 1, pp. 521–525. DOI: 10.1134/S1028334X13050048