Scientific interests of Sergei Medvedev

My main research interests are in modeling in geodynamics. That includes analytical and numerical modeling and investigations of new methods of modeling.  The particular projects are:
  1. ETSA
  2. Conceptual models orogenesis
  3. MWMB
  Starting back in 1988, I have worked on improving the so-called "thin sheet approximations" often applied to geodynamic modeling where the horizontal scale of lithospheric structures is greater than the vertical scale. These approximations attempt to estimate the depth dependence analytically and reduce the dynamic system to a set of 2D equations for numerical calculations. The main target of such investigations is to reduce a volume of computations and simplify them.
         The aims of my Ph.D. research were to reduce limitations of existing thin sheet approximations and increase their accuracy. Deep analytical investigations resulted in a new Extended Thin Sheet Approximation (ETSA), outlined in Medvedev & Podladchikov (1999 a, b) (hereafter "MP99").
 MP99a classified variations of geodynamic thin sheet approximations and discussed the advantages and limitations of 3 basic types of approaches (taking the following references as representatives of different branches: Medvedev 1993 and Royden 1996; England & McKenzie 1983; Ramberg 1970 and Burov & Diament 1992). Investigations in MP99a showed that the main disadvantage to previous approaches, their limited boundary conditions, is overcome in ETSA. It was also shown that most previous approaches can be derived by simplification of ETSA under specified boundary conditions. The rheological stratification of thin sheets is included as part of the unification behind ETSA. This allows accurate modeling of lithospheric structures involving layering with strongly varying properties.
         The results of linear analyses applied to 2D problems compared well with exact analytical solutions over a wide range of wavelengths for modeling isostatic adjustment, Rayleigh-Taylor instabilities and the development of instabilities due to lateral compression and extension (MP99b). These problems were not tractable to previous generations of thin sheet approximations. The results allow us to claim that ETSA will be a powerful tool for realistic modeling of complicated 2 and 3D geodynamic structures.
         The proposals below follow on naturally from my recent work which has been largely theoretical. I now recognise practical applications of ETSA as my main goal for the next few years. 1. Analytical modeling. A big advantage of thin sheet approximations, the possibility of solving some geodynamic problems analytically, was demonstrated by linear analyses in MP99b. Similar techniques can be used for investigations of instabilities in the spreading of ice sheets. Unpublished tests have also used Green's function to solve point-load problems that are relevant to the modeling of deformations in the lithosphere due to mountain growth and subduction (Medvedev & Podladchikov (a), in preparation).
2. Analogue modeling. The clear analytical background of ETSA allows applications to analysis and interpretation of deformations in analogue models (Sokoutis et al., 2000). Further combinations of analogue and analytical/numerical investigations would be very profitable. One of the main problems in analogue modeling is the restricted range of materials to represent the layered lithosphere. Analysis of boundary design provided in MP99a allows choice of the most appropriate construction using available materials for modeling particular problems in lithospheric dynamics
3. Numerical modeling is the main part of my further work. ETSA was always intended as a simplification of numerical modeling of 3D deformations. The conversion of ETSA to Fortran code was started about a year ago based on Medvedev (1993). This code describes the lithosphere as a fluid with depth dependent viscosity. The particular interests of this model are the flow in the lower crust and associated deformations near a Moho taken as a high viscosity discontinuity. Preliminary results were presented at the AGU Fall meeting (December 1997) and are a basis for Medvedev & Podladchikov (b, in preparation). Other potential applications include modeling of geodynamic problems such as: the dynamics of salt extrusions started in Talbot et al. (2000), evolution of orogens and rift zones separately or linked (preliminary results were presented at the Europrobe meeting, October 1997, Zurich) and the spreading of ice sheets. Particular advantages of ETSA, its simple and fast computing properties and flexibility with regard to boundary conditions allow grafting ETSA into other codes. 1. Rheology. Creep rheology was used in MP99a,b, and only a linear viscous rheologies have been employed in Fortran codes so far. MP99a illustrated the potential application of visco-elastic rheology and increasing the realism of rheology is one of the main goals for improving  ETSA. The possibility of incorporating plastic models within the frame of ETSA is under discussion with Drs. Yuri Podladchikov, Vladimir Lyakhovsky, and Philippe Fullsack.
2. Thermal model. The high temperature dependence of lithospheric materials requires additional thermal modeling. So far, this property has been modeled by the introduction of depth dependent rheology and lateral variations in depth of lithospheric discontinuities. Improving thermal aspects will increase the accuracy of modeling.
3. Programming. The development of the Fortran codes has always benefited from the simplicity of 2D numerical modeling behind ETSA which allows computer codes to be based on the simplest methods. The codes could be further accelerated using advanced techniques and potential parallel computing has already been under consideration.
          Burov, E. B. & Diament, M., 1992. Flexure of the continental lithosphere with multilayered rheology, Geophys. J. Int, 109, 449-468.
        England, P., & McKenzie, D., 1983. Correction to: a thin viscous sheet model for continental deformation, Geophys. J. R. Astr. Soc., 73, 523--532.
        Medvedev S. E., 1993. Computer simulation of sedimentary cover evolution, in: Computerized Basin Analysis: The Prognosis of energy and Mineral Resources, pp. 1--10, eds Harff, J. & Merriam, D.F., Plenum Press.
        Medvedev S. E., and Y.Y. Podladchikov, 1999. New Extended Thin Sheet Approximation for  Geodynamic Applications - I. Model formulation. Geophys. J. Int., 136, 567-585 (Summary)
        Medvedev S. E., and Y.Y. Podladchikov, 1999. New Extended Thin Sheet Approximation for  Geodynamic Applications - II. 2D examples. Geophys. J. Int., 136,  586-608 (Summary)
        Medvedev S., and Y. Y. Podladchikov (a). Point-source deformations in lithosphere: solutions by thin viscous sheet approximation. In preparation.
        Medvedev S., and Y. Y. Podladchikov (b). Extended Thin Sheet Approximation for Geodynamic  Applications - III. 3D examples. In preparation.
        Ramberg, H., 1970. Folding of laterally compressed multilayers in the field of gravity,1. Phys. Earth Planet. Interiors, 2, 203--232
        Royden L., 1996. Coupling and decoupling of crust and mantle in convergent orogens: Implications for strain partitioning in the crust. J. Geophys. Res., 101, 17679--17705.
        Sokoutis D.,  M. Bonini, S. E. Medvedev, M. Boccaletti, C. J. Talbot,  and H. Koyi, 2000, Indentaion of a  continent with a built-in thickness change: experiment and nature. Tectonophysics,  320, 243-270. (Summary) (Full paper in PDF)
        Talbot C.J.,  S. Medvedev, M. Alavi, H. Shahrivar, and  E. Heidari, 2000. Salt extrusion rates at Kuh-e-Jahani, Iran: June 1994 to November 1997.  In: Salt, Shale and Igneous Diapirs in and around Europe. Edited by B. C. Vendeville, Y. Mart and J. -L. Vigneresse, Geological Scociety Special Publication, 174, 93-110.
  The main goal of this project is to provide conceptual models, and analytical or approximate solutions in order to improve understanding of complex numerical results and to support recent research by the  Geodynamics Group at Dalhousie University.
        Although these approximations cannot give exact solutions, they can outline the mechanics behind processes much better than direct numerical methods. Moreover, the low level of accuracy of our knowledge about rheology and forces acting in the Earth's interior often requires a clear understanding of fundamental behaviour, rather than very detailed results.
        This idea was presented at the Spring AGU Meeting in Boston (June, 1999) and in Medvedev (submitted). Several simplified approaches were applied to modeling the evolution of a single rheology wedge and their analytical results were tested by exact numerical modeling. It demonstrates that simplified analysis of force and mass balance can predict many significant parameters of evolution of orogenic wedges.
        More complex model was considered  describing wedge-plateau transition during orogenesis. Prior to constructing the conceptual model, more than 300 full-size numerical experiments were conducted, several integrated parameters we introduced in order to accumulate knowledge about deformations in depth or temperature dependent rheology materials (Vanderhaeghe et al, in preparation). The further conceptual model is aimed to explain parameters of transition "wedge-plateau" and several features of deformations of plateau. This will require more detailed investigation of thermal-mechanical coupling, integration of analytical and semi-analytical models. The preliminar results were presented on AGU Fall Meeting, 2000 (see poster).
          Buck W. R., & D. Sokoutis, 1994. Analogue model of gravitational collapse and surface extension during continental convergence, Nature, 369, 737-740.
        Medvedev S., 2001. Mechanics of viscous wedges: modeling by analytical and numerical approaches. (submitted to JGR)
        Medvedev S., C. Beaumont, O. Vanderhaeghe, P.  Fullsack, and R. A.  Jamieson, 2000. Evolution of Continental Plateaus: Insights From Thermal-Mechanical Modeling. AGU Fall Meeting, San Francisco, USA. EOS Transactions, 81, p. F1094
        Royden L., 1996. Coupling and decoupling of crust and mantle in convergent orogens: Implications for strain partitioning in the crust. J. Geophys. Res., 101, 17679-17705.
        Vanderhaeghe O., Medvedev S., Beaumont C., Fullsack P., and Jamieson R. A. Dynamic evolution of orogenic wedges and continental plateaus: Insights from thermal-mechanical modelling of convergent  orogens. (to be submitted sometime)


Sand-box experiments and many natural examples of faulted structures are often characterised by "natural discretisation": faults are distributed regularly and deformations are concentrated along faults leaving space between faults low-deformed. This forced our attempts in searching of simple model of development of trust belts. Several existing approaches were adopted. However, there is not much progress to report so far, except critisism of those existing models and acknowledgments for that criticizm (Yin and Kelty, 2000)         Dahlen, F. A., 1990. Critical taper model of fold-and-thrust belts and accretionary wedges,  Ann. Rev. Earth Planet. Sci., 18, 55-90.
        Hardy, S., Duncan, C., Masek, J. and Brown, D., 1998. Minimum work, fault activity and the growth of critical wedges in fold and thrust belts,  Basin Res.,10, 365-373.
        Masek, J. G. and Duncan, C. C., 1998. Minimum-work mountain building, J. Geophys. Res.,103, 907-917.
        Medvedev S. What we can learn from simplified models of evolution of plastic wedges? (in preparation?)
        Yin A., 1993. Mechanics of wedge-shaped fault blocks. 1. An elastic solution for compressional wedges, J. Geophys. Res., 98, 14245-14256.
        Yin A., and T. K. Kelty,  2000. An elastic wedge model for the development of coeval normal and thrust faulting in the Mauna Loa-Kilauea rift system in Hawaii, J. Geophys. Res., 105, 25909-25925