A technique for interpolation and smoothing of mass-size-density data

An interpolation and smoothing technique has been developed for observed (analytic or experimental) mass-size-density data defined over a given domain having a reduced number of contiguous size and density intervals. The domain for interpolation employs a larger number of subintervals of the domain of the observed data. The technique imposes mass and attribute mass conservation between the observed and estimated (interpolated and smoothed) data. The proposed technique is an extension of an existing technique developed for interpolating and smoothing mass density or attribute content-density data by utilizing minimization of absolute differentials (incremental specific mass differentials and incremental attribute content differentials). In the proposed technique, several minimization objective functions comprising least relative differential (normalized differentials) squares and two associated special cases are proposed. The associated special cases are introduced to demonstrate the deviation of their results from the normalized differentials results. The present interpolation approach is fundamentally different from existing techniques inasmuch as the interpolation problem is carried out as two-dimensional problem rather than interpolating through a single dimension, and the resulting estimates are used to interpolate through the second dimension. Several data sets are used to demonstrate the main features of the proposed technique. Crown Copyright (C) 2003 Published by Elsevier Science B.V. All rights reserved.