Institute of Computational Mathematics and Mathematical Geophysics

International Conference on Mathematical Methods in Geophysics «MMG-2003»

Akademgorodok, Novosibirsk, Russia, October 8-12, 2003

Abstracts

Mathematical problems in geophysical investigations of solid Earth

Procedure for the solution of the overdetermined systems of the linear equations

Dmitriev I.V.

V.I. Il'ichev Pacific Oceanological Institute
FEB RAS (Vladivostok)

The solution of many tasks of mathematical geophysics are connected to the solution of the overdetermined systems of the linear algebraic equations of a kind::

F=AZ+D

where Z is a required matrix by dimension (M, M); A, F - a matrixes by dimension (M, N) containing results of measurements of geophysical fields (N>> M); D - a matrix by dimension (M, N) being an additive component, which can be implied as “noise in a measured field ”. The overwhelming majority of the procedures used for the solution of the specified system are based on optimization of deviations [F-AZ]. Calculation of optimum value of the sum of root mean squares of deviations is ordinarily made.

In the submitted work other approach is considered. It is based on calculation of set V containing allowable values of required parameter Z. The way of construction of set depends on the structure of noise D. Value Z and reliability of the received decision are estimated on the basis of statistical characteristics of set V.

The results of successful realization of the suggested procedure for calculation of an impedance tensor of magnetotelluric sounding and for localization of a body of known geometry on a basis of gravimetry and magnetometry are presented.

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