On solving reverse problems of geophysics applying the methods of the theory of dynamic systems

Authors

  • I. E. Stepanova Shmidt Institute of Physics of the Earth, RAS, Russian Federation
  • D. N. Rayevsky Shmidt Institute of Physics of the Earth, RAS, Russian Federation

DOI:

https://doi.org/10.24028/gzh.0203-3100.v36i3.2014.116058

Keywords:

regularization, dynamic system, Toda chains, conform reflection, moments of the area

Abstract

Methods of solving the reverse problems of geophysics on discovery of the forms of anomalyforming bodies by the study of solving nonlinear differential equation, which is transformed into infinite chain of linear differential equations - the so-called chain of Toda hierarchies. Infinite system of linear differential equations is in its turn closely tied with geometric parameters of the area sought for - its moments. Moments of the area in three-dimensional space determine reflection of some canonical area upon some unknown source of anomalous field, which can be found by minimization of some regularizing functional. Examples of solving reverse problems of ore type - when the source of gravity field is limited in space and has a stellar property in relation to some of its interior point are presented.

References

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Published

2014-06-01

How to Cite

Stepanova, I. E., & Rayevsky, D. N. (2014). On solving reverse problems of geophysics applying the methods of the theory of dynamic systems. Geofizicheskiy Zhurnal, 36(3), 118–131. https://doi.org/10.24028/gzh.0203-3100.v36i3.2014.116058

Issue

Vol. 36 No. 3 (2014)

Section

Articles

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