The opposition effect and the quasi-fractal structure of regolith: I. Theory

We present a new heuristic model combining the coherent-backscatter and sha dow-hiding opposition effects. The model considers the aggregate structure of regolith in a realistic way and accounts for the fractal architecture of planetary surfaces both on microscopic particulate and macroscopic, textur ally faceted size scales. It describes how the shadow-hiding opposition eff ect is manifested in a fractally arranged surface, the important contributi on of incoherent, multiply scattered light among small scatterers within a surface composed of aggregate grains and its amplification by backscatter i nterference. We provide a general theoretical model as well as a preliminar y, simple analytical approximation that is suitable for investigating the o pposition behavior of planet, satellite, and asteroid surfaces. The analyti cal approximation utilizes only four model parameters; omega (0), the avera ge, single-scattering albedo of elemental scatterers that are the building blocks of aggregates, h, Hapke's (1986, Icarus 67, 264-280) angular-width p arameter for the shadow-hiding opposition effect, L, the diffusion scale le ngth of light through the regolith, and q, a structural parameter that char acterizes the relative size and complexity of aggregate particles. Our mode l explains the simultaneous occurrence of the coherent-backscatter enhancem ent and shadow-hiding in moderate to low albedo soils in addition to the do minance of coherent-backscatter in bright soils. It predicts that coherent backscatter and shadow-hiding can occur at a variety of size scales within the regolith. Individual regolith particles can exhibit their own oppositio n effects which are convolved with the contribution that arises from their packing within the planetary surface. The size domains over which coherent- backscatter and shadow-hiding, respectively, each have their most pronounce d effect is strongly controlled by the albedo of internal scatterers and th e number of hierarchical generations of aggregates required to characterize the particulate-scale behavior of the regolith surface, (C) 2001 Academic Press.