Laboratory of Mathematical Geophysics and Joint Inversion of Geophysical Data
The main fields of our activity are:
- Numerical modeling of formation and evolution of tectonic structures
Here our attention now focusses on study of interactions in the system the lithosphere - asthenosphere - uppermost part of
the upper mantle. Solving numerically direct and inverse problems we try to reveal the role of different
tectonic processes, including small-scale mantle convection in development of specific tectonic structures. These works have
given us new insight into geodynamics of continental rifts, sedimentary basins and orogenic belts formation.
- Local and regional state of stress in the lithosphere
To simulate deformation and stress it is necessary to assign initial data, which are distribution of density and mechanical properties
and a set of boundary conditions reflecting affect of external forces that may be plate boundary forces or mantle movements or their
interference. Density and mechanical properties distribution are derived from seismic and gravity data but boundary conditions can be
specified only on the basis of some qualitative hypothesis which are usually ambiguous. To determine boundary conditions we solve an
inverse problem: we seek for boundary conditions on the side boundaries and at the bottom of the model under condition that calculated
vertical movements on the surface match the observed movements in accordance with the neotectonic data. A number of models for various
platform and shield areas was obtained using this technique. Among them are: The Baltic Shield, the Caucasus, Crimea and the Northern Black Sea,
the Southern Beaufort Sea.
- Sedimentary basins analysis
In parallel with development of new models and modeling of specific structures we deal with the problems of uniqueness and stability
of back stripping in solution of the appropriate inverse problems. Our recent investigations were devoted to study of the North Caucasus
foredeep and Moscow basin. We also investigated analytically the processes of compression and extension of the lithosphere in order to
study when and where the models using the "necking level" can be applied.
- Methods of joint inversion of geological and geophysical data
Our approach is based on construction of models of formation of tectonic structures. These models provide relationships between different
data such as topography, thickness and physical properties, such as density, elastic modules, viscosity of the layers, thickness, depth of
deposition, and age of sediments, rate of subsidence or uplift, stresses, heat flow, gravity field etc. Using these models the joint
interpretation of any geological and geophysical data reduces to determination of almost the same parameters of geodynamic model. It has been
proved that the solution of this inverse problem is unique and stable. This approach was applied in particular to the analysis of the data
on platform sedimentary basins, oceanic rift zones and passive continental margins.
- Processing and interpretaion of potential fields
We put forward new methods, such as: the spectrum analysis and separation of gravity field into components associated with density
inhomogeneities situated at different depth; methods to estimate depth to the crystalline basement, methods of potential fields interpretation
based on the artificial intelligence (including new algorithm for Euler solutions selection). We have all necessary software for the 3D gravity
field calculation and transformations on the spherical Earth based on efficient and accurate algorithms.
We use gravity field analysis in conjunction with the geomechanicall modeling in order to constrain important rheological parameters of the
lithosphere including depth to the necking level. We are working on gravity field interpretation using regional tomography
models focusing on density - velocity relationship at high temperature and pressure. We perform a various statistical methods
for the investigation of the main features of the lithosphere and mantle inhomogeneities, such as mean anomalous mass dispersion
and concentration, etc. We started new project devoted to processing and interpretation of new satellite data of the GRACE and GOCE projects.
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