HR: 08:00h
AN: NG41A-01    [PDF]
TI: Deriving Spatiotemporal Fractal And Wavelet Models In Terms Of The Generalized Random Field Theory
AU: * Christakos, G
EM: george_christakos@unc.edu
AF: Center for the Advanced Study of the Environment (CASE), Department of Environmental Science and Engineering, University of North Carolina-Chapel Hill, 111 Rosenau Hall, CB\# 7431, Chapel Hill, NC 27599-7431 United States
AB: A powerful unified framework is suggested in terms of generalized spatiotemporal random fields (GS/TRF), which can derive well-known models as its special cases, including fractal, wavelet and heterogeneous random field models. It is worth-noticing that the development of the GS/TRF theory precedes that of its special cases above. A G-S/TRF is typically defined in terms of a functional involving a so-called test function belonging to a space D. The choice of D is made on the basis of the physics of the atmospheric situation and the goals of the analysis. Very rich classes of moments across space and time are derived by means of the corresponding GS/TRF functionals. By properly selecting the test functions, space-time heterogeneous models are generated, termed GS/TRF-n/m, where n and m are the corresponding spatial and temporal orders of heterogeneity, respectively. Well-known fractal random fields are readily obtained from the GS/TRF-n/m which, in addition, can lead to new and richer fractal representations in space-time. By assuming test functions having properties useful in the study of important field characteristics (multiscale features, singularities caused by physical laws, sharp variations etc.), continuous space-time wavelets are derived which have a wide range of earth science and image processing applications.
DE: 1869 Stochastic processes
DE: 3210 Modeling
DE: 3250 Fractals and multifractals
DE: 3367 Theoretical modeling
DE: 4203 Analytical modeling
SC: Nonlinear Geophysics [NG]
MN: 2003 Fall Meeting