Сравнительная оценка объемов данных, необходимых для вычисления значений геофизических параметров с помощью ортогональных функций и сеток на локальных участках земной поверхности

Abstract

Two approaches to calculating geophysical parameters at arbitrarily specified points on local areas of the Earth`s surface are considered. They are based on orthogonal function and regular meshing methods. The problem of finding the relationship of the series terms number with the grid’s step is solved. It takes into account the spatial variability of the geophysical parameter, the required accuracy of its deducing at any point and the characteristics of the errors for the available measurement data. The solution of the problem is found based on the two-step generalized least squares method (the generalized instrumental variables estimator) and the one of canonical decomposition of a vector random function. It enabled rationalizing the choice one of those approaches as to the data volume amount needed to calculate the values of geophysical parameters at any specified point. An example of estimating the amount of the data required to calculate the values of the gravity anomaly at arbitrarily specified points on a local area is given. It takes into account the increased demands for accuracy and spatial resolution of geophysical parameters. The example shows that the use of orthogonal functions approach is more preferable in the view of the required data amount.