Empirical Earth Rotation Model: a Consistent Way to Evaluate Earth Orientation Parameters
It is customary to perform analysis of the Earth’s rotation in two steps: first, to present results of estimation of the Earth orientation parameters in the form of time series based on a simplified model of variations of the Earth’s rotation for a short period of time, and then to process this time series of adjustmentsby applying smoothing, re-sampling and other numerical algorithms. This approach suffers from self-inconsistency: the total set of Earth orientation parameters depends on a subjective choice of the apriori Earth orientation model, crosscorrelations between points of the time series are lost, and results of an operational analysis per se have a limited use for end users. Here, an alternative approach of direct estimation of the coefficients of expansion of Euler angle perturbations into basis functions is developed. These coefficients describe the Earth’s rotation over the entire period of observations and are evaluated simultaneously with stationpositions, source coordinates and other parameters in a single LSQ solution. In the framework of this approach considerably larger errors in apriori EOP model are tolerated. This approachgives a significant conceptual simplification of representation and estimation of the Earth’s rotation.
Approximation by Spline Functions
Splines play an important role in applied mathematics since they possess high flexibility to approximate efficiently, even nonsmooth functions which are given explicitly or only implicitly, e.g. by differential equations. The aim of this book is to analyse in a unified approach basic theoretical and numerical aspects of interpolation and best approximation by splines in one variable. The first part on "spaces of"" " "polynomials" serves as a basis for investigating the more complex structure of spline spaces. Given in the appendix are brief introductions to the theory of splines with "free knots" (an algorithm is described in the main part), to "splines in"" " "two variables" and to "spline " "collocation for differential equations."A large number of new results presented here cannot be found in earlier books on splines. Researchers will find several references to recent developments. The book is an indispensable aid for graduate courses on splines or approximation theory. Students with a basic knowledge of analysis and linear algebra will be able to read the text. Engineers will find various pactical interpolation and approximation methods.
A geomagnetic field spectrum
Selected MAGSAT data are used to derive a spherical harmonic model of the earth’s internal magnetic field of degree and order 23. The power spectrum, with terms of the form (Mauersberger, 1956; Lowes, 1974): 
 
Rn=(n+1)∑m=0n((gnm)2+(hnm)2), 
 
is computed. It exhibits a distinct change of slope at about n = 14 which is interpreted to mean that the field from the core dominates for n ⩽ 13 and the field from the crust for n ⩾ 15. The two portions of the spectrum are well represented by: Rn = 1.349 × 109 (0.270)n (nT)² for the core and Rn = 37.1 (0.974)n (nT)² for the crust. These representations can be used to establish order of magnitude inaccuracies in core field models due to crustal fields and due to inability to “observe” the core field wavelengths beyond n = 13 which are totally obscured by the crustal field.