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:

ETSA

Conceptual models orogenesis

MWMB

Thin sheet approximations
Starting back in 1988, I have worked on improving the socalled "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, RayleighTaylor
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 pointload 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 viscoelastic 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, 449468.
England, P., & McKenzie,
D., 1983. Correction to: a thin viscous sheet model for continental deformation,
Geophys. J. R. Astr. Soc., 73, 523532.
Medvedev S. E., 1993. Computer
simulation of sedimentary cover evolution, in: Computerized Basin Analysis:
The Prognosis of energy and Mineral Resources, pp. 110, 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, 567585 (Summary)
Medvedev S. E.,
and Y.Y. Podladchikov, 1999. New Extended Thin Sheet Approximation
for Geodynamic Applications  II. 2D examples. Geophys. J. Int.,
136, 586608 (Summary)
Medvedev
S., and Y. Y. Podladchikov (a). Pointsource 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, 203232
Royden L., 1996. Coupling
and decoupling of crust and mantle in convergent orogens: Implications
for strain partitioning in the crust. J. Geophys. Res., 101, 1767917705.
Sokoutis D., M. Bonini,
S. E. Medvedev, M. Boccaletti, C. J. Talbot,
and H. Koyi, 2000, Indentaion of a continent with a builtin
thickness change: experiment and nature. Tectonophysics, 320,
243270. (Summary) (Full paper
in PDF)
Talbot C.J., S. Medvedev,
M. Alavi, H. Shahrivar, and E. Heidari, 2000. Salt extrusion rates
at KuheJahani, 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, 93110.

Conceptual models of orogenesis
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 wedgeplateau transition during orogenesis. Prior to constructing
the conceptual model, more than 300 fullsize 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
"wedgeplateau" and several features of deformations of plateau. This will
require more detailed investigation of thermalmechanical coupling, integration
of analytical and semianalytical 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, 737740.
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 ThermalMechanical 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, 1767917705.
Vanderhaeghe
O., Medvedev S., Beaumont C., Fullsack P., and Jamieson R. A. Dynamic evolution
of orogenic wedges and continental plateaus: Insights from thermalmechanical
modelling of convergent orogens. (to be submitted sometime)

Minimum work mountain building
Sandbox
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 lowdeformed.
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 foldandthrust belts and accretionary wedges, Ann.
Rev. Earth Planet. Sci., 18, 5590.
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, 365373.
Masek, J. G. and Duncan,
C. C., 1998. Minimumwork mountain building, J. Geophys. Res.,103,
907917.
Medvedev S. What we can learn from simplified models of evolution of
plastic wedges? (in preparation?)
Yin A., 1993. Mechanics
of wedgeshaped fault blocks. 1. An elastic solution for compressional
wedges, J. Geophys. Res., 98, 1424514256.
Yin A., and T. K. Kelty,
2000. An elastic wedge model for the development of coeval normal and thrust
faulting in the Mauna LoaKilauea rift system in Hawaii, J. Geophys.
Res., 105, 2590925925