Statistics – Computation
Scientific paper
Dec 2003
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2003dps....35.2011m&link_type=abstract
American Astronomical Society, DPS meeting #35, #20.11; Bulletin of the American Astronomical Society, Vol. 35, p.1485
Statistics
Computation
Scientific paper
A combined analytical and numerical simulation approach is used to investigate the first, second, and fourth statistical averages of the signal observed during a ring occultation experiment. The rings are modeled as a randomly blocked diffraction screen. The field behind the screen (the rings) assumes binary values: zero if located in the shadow area cast by ring particles and the full incident field otherwise. The stochastic geometry of the union of shadow areas cast behind the rings defines a so-called Boolean model. Either the random wavefront formed behind the screen or it's statistical averages can be propagated to an observer (a detector) some distance away from the diffraction screen. The parabolic approximation of the wave equation is used to model near-forward diffraction effects over the free-space path from the ring plane to the observation plane. The first and second moments were previously shown to correspond to the well-known coherent and scattered signal components observed during radio occultation experiments. Of particular interest here is the fourth moment of the random field at the observer, which determines the intensity scintillation index. Numerical simulations are used to investigate its behavior as a function of relevant model parameters, in particular, the ring particle radius and the Fresnel scale of observation. A monodispersion of ring particles is assumed to keep the model as simple as possible so as to investigate conditions under which the particle size may be recoverable from the intensity scintillation measurements. The model is also idealized to one-dimensional diffraction screen in order to speed up the computations; however, simulations of the more realistic two-dimensional diffraction screen models are also carried out.
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