MODELING, REPRODUCTION, AND MAPPING OF GEOFIELDS WITH AND WITHOUT MEASUREMENT NOISE. PART 6. PIECEWISE POLYNOMIAL APPROXIMATIONS, STATISTICAL DESIGN OF EXPERIMENTS, AND THE CONSTRUCTION OF CONTOUR MAPS

摘要

Spline, finite element, and piecewise polynomial fits of the boundaries of geofields with automatic matching are examined. The unknown coefficients of the approximating polynomials are estimated using measurements of their input and output coordinates in the presence of measurement noise. A new method for constructing contour maps is developed on the basis of the fundamental “recurrence” theorem of Poincare. The capabilities of this method for constructing contours are examined.