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Virtual Laboratory for Elastisity Problems


Virtual Laboratory on Fundamental and Applied Problem of Elastisity Theory

Tech Area / Field

  • INF-COM/High Performance Computing and Networking/Information and Communications
  • OBS-NAT/Natural Resources and Earth Sciences/Other Basic Sciences
  • PHY-SSP/Solid State Physics/Physics
  • SAT-AER/Aeronautics/Space, Aircraft and Surface Transportation

8 Project completed

Registration date

Completion date

Senior Project Manager
Komashko B A

Leading Institute
Research Institute of Aviation Systems, Russia, Moscow

Supporting institutes

  • Institute of Physics of the Earth, Russia, Moscow


  • Institut de Physique du Globe, France, Paris\nNational Geophysical Data Center, USA, CO, Boulder\nUniversidad Politecnica de Madrid / Escuela Universitaria de Ingenieria Técnica Topografica, Spain, Madrid

Project summary

The aim of the project is to revise certain theoretical and applied problems of geophysics on the basis of newly obtained exact solutions to boundary value problems of the elasticity theory. The solutions concern finite domains containing angular points, and have been obtained by researchers participating in the project.

The proposed approach to resolving these problems is not a development of any existing method: It is based on the absolutely novel ideas that generalize a fundamental notion of mathematics that of the function’s basis on a segment. The mathematical apparatus which has been elaborated and the results obtained on its basis are novel and no references to similar exist in the Russian or foreign literature.

For the first time, exact solutions will be obtained to the classical boundary problems of the elasticity theory, the solutions that have important applications for both theoretical and applied geophysics. Testifying to significance of the problem is the fact that intensive theoretical studies have been conducted in this field for more than 100 years now.

In particular, the work is expected to pursue the following main objectives:

· To revise the classical point source models with respect for domain’s finiteness and the presence of angular points at the boundary;

· To consider (with respect for the newly obtained solutions) the problem of stress distribution in triple junctions. Clear understanding of phenomena that occur in these domains is impossible without a revision (on the basis of theory proposed herein) of the classical solutions of the elasticity theory for infinite wedge;

· To elaborate a model explaining the phenomenon of sharp alteration of stress distribution pattern caused by relatively minor changes in the magnitude of external influence at the boundary in lithospheric slabs of the Earth in the vicinity of junctions and fault intersections or in the vicinity of sites where their strike undergoes sharp changes. Such changes may be triggered by minor (small magnitude) earthquakes or local non-seismic creep along faults in the vicinity of irregular points of the boundary. These changes in stress conditions propagate immediately along faults and can transform these faults from low-active state into active state and vice versa. Within the framework of the project, it is planned to study possible temporal bifurcations of regional stress fields for a number of typical geometric form tectonic plates (Arabian, African and Indian) and effects of initial geometry of fault intersection zones (intersection angles) and deformation mechanisms in the sources of weak earthquakes occurring in the vicinity of the boundary’s angular points;

· To analyze the relationships between changes in the elastic stresses at the boundaries of lithospheric plates in the Earths history and rapid changes in sea depth in sedimentary basins which were associated with the formation of lenses of coarse sands. During the last decade, numerous hydrocarbon fields were discovered in sediments which have been formed in this way. Many short impulses of changes in sea depth in sedimentary basins with magnitudes of 20-100 m and duration of 1-3 mln. years, which interrupted long periods of relative stability, have been identified for the last 600 mln. years. It is commonly believed that these events were associated with global fluctuations of sea level. However, it was recently shown that many rapid changes of sea depth actually occurred due to uplifts and subsidences of the Earths crust which took place under a stable sea level. This result can completely change a strategy for prospecting oil and gas fields of the above type. For this purpose, it is necessary to determine basic regularities and physical mechanism of rapid crustal movements which occur episodically in relatively stable areas. It is known that changes in the force acting along the Earths lithosphere with a laterally variable thickness produce vertical displacements of this layer. It has been found that, at certain epochs, strong weakening of the lithosphere occurs in some regions. When this phenomenon takes place near to the boundaries of lithospheric plates, it results in changes in the stresses at the boundaries, as well as in plate interiors, which is associated with vertical crustal movements. This can be a cause of many rapid changes in sea depth in sedimentary basins. The exact solutions for the state of stresses in a thin shell under complicated boundary conditions is an ideal tool for the studies of this problem, which is very important for prospecting of oil and gas;

· To determine an exact picture of mantle motion in the vicinity of irregularities, like inclusions and angular points of boundary;

· To figure out new models of earthquake origin and relevant methods of their prediction;

· To demonstrate that the approximation-based methods of solving boundary value problems of the elasticity theory are generally inapplicable to domains containing angular points of boundary. The results obtained herein permit to determine accuracy tolerances, which is very important for obtaining reliable numerical results in both theoretical and applied geophysics.

The list of objectives will be appended in the course of project’s realization and consultations between the project’s participants and their foreign collaborators, as more exact solutions are found to various kinds of problems.

The decision to revise former approaches was prompted by the following discoveries that have been made on the basis of the newly found refined solutions:

· The method based on the substitution of infinite space or semi-space for a finite elastic domain which is widely applied in geophysics for obtaining analytical solutions (for example, in various point source models) is generally incorrect for domains containing angular points of boundary and this incorrectness cannot be overcome during the transfer to a finite domain if an approximate or numerical solution is generated thereby. Nevertheless, the results obtained herein permit to determine accuracy tolerances for such solutions, which is very important for obtaining reliable numerical results in theoretical and applied geophysics;

· Stress field in the vicinity of angular points of the boundary (for example, at triple junctions) and at points of the boundary condition’s type change is characterized by instability, which cannot be detected with conventional methods but can be revealed with the help of the approach proposed herein;

· Contrary to the deeply-rooted belief, boundary-value problem of the elasticity theory for finite domain containing angular points of boundary has more than one solution. In practice, this means that minor changes in boundary conditions along faults at sites of their intersection or sharp changes of their strike may lead to major changes of stress field inside the domain. Such changes may be triggered by low-magnitude earthquakes propagating along faults in the vicinity of irregular points of boundary (angles, inclusions). The change of stress field propagates instantly along faults and can transform these faults from latent into active and hence cause strong earthquakes. This phenomenon is of great importance for explaining some mechanisms of earthquake origin and for developing methods of earthquake prediction.

To fulfill the tasks that have been set it is planned to establish a “virtual laboratory” which will include the main participating institutions (Federal Research Institute of Aviation Systems, Institute of Physics of the Earth) and foreign collaborators (Institute of Physics of the Earth of Paris, National Geophysics Data Center of the United States and Polytechnic University of Madrid). By “virtual laboratory” we mean a network structure comprising several research groups belonging to different scientific centers and cooperating for mutual benefit via the Internet. The project will maintain a Web-site displaying frequently updated information on project’s progress.

Foreign participants of the "virtual laboratory" are supposed to be directly involved in the following activities:

· elaboration of proposals and plans related to the project;

· exchange of information in the course of project’s preparation and implementation;

· development of computer programs and analysis of results obtained in the course of the project;

· preparation of reports and publications;

· audio and video conferences to be conducted with the help of modern telecom technologies via the Internet; and

· dissemination of information worldwide using their connections with researchers working in related fields.

Foreign participants of the project possess most comprehensive geophysical and geological databases which will serve as excellent material for applying mathematical methods developed within the framework of the project. This will lead to the elaboration of new methods of interpretation and modeling of geodynamic and geotectonic data. Since 1995, a considerable part of joint research projects between Institute of Physics of the Earth (Russia), National Geophysical Data Center (USA), Institute of Physics of the Earth of Paris (France) and Department of Engineering Topography and Cartography of the Polytechnic University of Madrid (Spain) has been conducted with the use of integrated methods of data transfer and processing. In other words, said institutes have already begun to establish a “virtual laboratory.”


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