Book Review: Spatial Statistics: Methodological Aspects and Applications. By Marc Moore (ed.). Lecture Notes in Statistics 159. Springer,New York, 2001, 282 p., $69.95 (U.S.), paperback,ISBN 0-387-95240-3

Mathematical Geosciences -     

Book Review: Spatial Statistics for Remote Sensing. By Alfred Stein,Freek Van Der Meer,and Ben Gorte. Kluwer Academic Publishers,Dordrecht, The Netherlands, 1999, 284 p., $135 (U.S.), ISBN 0-7923-5958-X paperback

Mathematical Geosciences -     

Martian Topography: Scaling, Craters, and High-Order Statistics

The high-order structure functions of Mars topography reveal three specific ranges of scales: (1) scaling range at small scales where the structure functions exhibit scaling behavior; (2) transition range where the structure functions continue to grow but do not reveal scaling; and (3) saturation range at large scales where the structure functions saturate. The scaling and saturation ranges are explored in detail in respect to scaling and intermittency. Analysis of the Mars Orbiter Laser Altimeter (MOLA) data and computer simulations suggest that there are two potential contributors to the small-scale scaling: (i) scale-invariant surface formation; and (ii) effects of discrete morphological forms such as craters. The crater effect also provides an explanation for the large-scale intermittency revealed using the normalized structure functions within the saturation range, which cannot be explained by the ‘scale-invariant’ concept. Overall, the obtained results suggest that the “crater” contribution to the structure function behavior often dominates over the effect of the scale-invariant surface formation.     

Book Review: Symmetry Methods for Differential Equations: A Beginner's Guide. By Peter E. Hydon,Cambridge University Press,Cambridge, 2000, 213 p. +xi, $74.95 (hardback) ISBN 0-521-49703-5, $29.95 (paperback) ISBN 0-521-49786-8

Mathematical Geosciences -