Reconstructing the parameters of geofields taking measurement noise into account. Part I. Techniques for smoothing, filtration, and regularization

Various methods of interpolation (approximation, smoothing, and filtering types) which take measurement noise into account (piecewise polynomial approximation, smoothing splines, kriging, filters, etc.) are analyzed. It is found that regularization methods are used in all of them. The advantages and disadvantages of these methods are pointed out and prospects for the use of program packages by nonspecialists in mathematics and information technology are examined. Recommendations regarding the proper choice of estimation techniques, quality criteria, and parameters for monitoring them are made in the case where geofields are to be approximated and modelled.