METHOD OF INTERPOLATION BETWEEN A PLURALITY OF OBSERVED TENSORS

摘要

A method of interpolation between a plurality of field gradient tensors including the steps of: accessing a plurality of field gradient data; formatting said plurality of field gradient data into 3-dimensional tensors of rank 2; determining a rotational matrix and a structural matrix for each tensor; interpolating said structural matrices; detecting errors in the raw data only apparent using the rotational component. interpolating said rotational matrices as quaternions on the surface of a unit 4-sphere; reconstructing said structural matrices and said rotational matrices to yield field gradient tensors at the interpolation points, wherein the interpolation is between two said field gradient tensors, the field gradient tensors being expressed as 3x3 matrices of values, each resolved into a rotational matrix and a structural matrix with three diagonal components.