We investigate the terahertz (THz) scattering and emission properties of lunar regolith by modeling it as a random medium with rough top and bottom boundaries and a host medium situated beneath. The total scattering and emission arise from three sources: the rough boundaries, the volume, and the interactions between the boundaries and the volume. To account for these sources, we model their respective phase matrices and apply the matrix doubling approach to couple these phase matrices to compute the total emission. The model is then used to explore insights into lunar regolith scattering and emission processes. The simulations reveal that surface roughness is the primary contributor to total scattering, while dielectric contrasts between the volume and the boundaries dominate total emission. The THz emissivity is highly sensitive to the regolith dielectric constant, particularly its imaginary part, making it a promising alternative for identifying previously undetected water ice in the lunar polar regions. The THz emissivity model developed in this study can be readily applied to invert the surface parameters of lunar regolith using THz observations.
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