RUSSIAN JOURNAL OF EARTH SCIENCES VOL. 9, ES1001, doi:10.2205/2007ES000217, 2007
[182] To sum up, the following seven results of this work are most significant.
[183] (1) Undoubtedly, the most important result is the substantiation of the concept according to which three epochs are distinguished in the evolution of Earth sciences and the third epoch of geophysics and geoinformatics started to develop in 1995.
[184] (2) The paper described the subject and method of the new science of geoinformatics.
[185] (3) A new method is described for the representation of geoinformation given at the Earth's surface; in terms of this method, the information is represented through linear analytical approximations, based on the treatment of functions defined at the Earth's surface as the limiting values of functions harmonic in the exterior of the Earth.
[186] (4) A new method is proposed for the description of the Earth's interiors in the form of linear analytical approximations of surfaces of geological bodies and faults.
[187] (5) The paper presented the main concepts of a basically new theory of interpretation of potential fields (gravity and magnetic anomalies) that defines the third paradigm of the potential field interpretation.
[188] (6) Two main techniques of reducing gravity problems to the solution of a system of linear analytical equations (SLAE) on the basis of
[189] (a) the method of linear integral representations (in several variants) proposed by the author, and
[190] (b) a finite element description of a volume of the geological medium under study.
[191] We should emphasize that gravity inversion problems are also reduced the SLAE solution.
[192] (7) The very important result of this paper is a fairly detailed description of the basically new theory of finding approximate solutions x to the SLAE
![]() | (3.1) |
and two new methods of determination of the vector x with reference to the case
![]() | (3.2) |
where d2 min and d2 max are the constants in the inequalities
![]() | (3.3) |
[193] Both methods are based on
[194] (i) the formulation of new constrained extremal problems, and
[195] (ii) the reduction of these problems to SLAEs of a new type, namely, to extended SLAEs of second kind.
[196] However, it is clear that a great deal of effort must be made to develop computer technologies implementing all theoretical ideas proposed in the paper and to test these technologies in a large number of model experiments and on real data.
Citation: 2007), Change of epochs in Earth sciences, Russ. J. Earth Sci., 9, ES1001, doi:10.2205/2007ES000217.
Copyright 2007 by the Russian Journal of Earth Sciences (Powered by TeXWeb (Win32, v.2.0).