VALIDITY OF TOPOGRAPHY REPRESENTATION BY TRUNCATED SERIES OF SURFACE HARMONICS

In a series of papers published in Icarus, Dr. C. L. Goudas has reported on the harmonic analysis of lunar topography. In his studies, the lunar topography was represented by a finite uneven distribution of elevations. For each sample of elevations he applied the unweighted least-squares method in estimating the best-fitting coefficients for a truncated series of surface spherical harmonics. This paper is concerned with the ambiguities of such estimates. The effects of changing the evenness and density of the sample of points on the estimated coefficients are shown by analyzing the correlations among the estimated coefficients, the degree of fit of the derived function, and the results of the orthogonality test. © 1969.