de RADU BOTEZATU
Universitatea din Bucuresti
ON THE CONTENT AND SIGNIFICANCE OF SOME MATHEMATICAL MODELS
OF GRAVITY AND MAGNETIC ANOMALIES
(Abstract)
There are shown and discussed the content and the physical and geological
significance of four analytical models with a view to approximating along a
profile the gravity and magnetic anomalies, with different mathematical structure,
namely: a polynomial of powers of the distances (1), development in Maclaurin
(6) or Taylor (7) series, nonharmonical complex function (9) and Miron Nicolescu's
relationship based on the structure theorem of the nearly-periodical (presque–périodiques)
polyharmonical functions (12). The graphical form of the polynomial components
of the first three models are shown in figures 2, 4, 6 and 8 for some gravity
and magnetic anomalies mapped in Romania. It is obvious that such analytical
models have only a formal character, their use being advantageous in the processing
of the anomalies but not furnishing supplementary information on the hidden
geological structures producing anomalies.
The conclusion is that a mathematical model with simulation property, that
in a general form must have the structure of the relationship (13), respectively
a polynomial with terms representing harmonical functions of the gravity or
magnetic effects type, is the only one that can be efficient in the analysis
of such anomalies, that is the establishment of the number of anomalous sources
which actually take part in the creation of the cumulated anomaly and an accurate
determination of the form and intensity of each individual anomaly produced
by these anomalous sources.