Dielectric properties of the Martian south polar layered deposits: MARSIS data inversion using Bayesian inference and genetic algorithm

Abstract

[1] Mars Advanced Radar for Subsurface and Ionosphere Sounding (MARSIS) has offered abundant data, which have been used to estimate dielectric properties of the south polar layered deposits (SPLD) of Mars. This paper presents a new way to invert the data to estimate the dielectric properties of the SPLD. A total of 4364 measurements were analyzed. The received radar signals are controlled by the physical properties of the SPLD and its basal layer and in addition by a number of factors including the transmitted wave properties, the satellite height, and the atmosphere/ionosphere environments. The received signals may also be influenced by surface clutter. Most of these factors are variable. This complexity causes the inversion to be difficult. To carry out the inversion, it is therefore essential to define a reasonably simple model for the physics of the surface/ subsurface layers where the radar signal is reflected. The top and bottom interfaces of the SPLD are observed by MARSIS as two reflection peaks of the radar signals. The intensity ratio between the two reflection peaks is observed to be a function of the time difference separating the two peaks. By modeling this dependency, the influences of the satellite position and the atmosphere/ionosphere environments are canceled. This is a major step toward carrying out the inversion. Nevertheless, the inverse problem remains ill-posed and highly nonlinear. Bayesian inference is employed to deal with the ill-posed aspect of the inversion, and genetic algorithm is introduced to deal with the nonlinearity. It is concluded that the most probable value of the relative dielectric constant of the SPLD lies in 3.0-5.0, conductivity 1.0-2.0 Â 10 À6 S/m, and the relative dielectric constant of the basal layer is 7.5-8.5 (The basal layer conductivity is assumed to be 1.0 Â 10 À7 S/m.) These results support a suggestion that the SPLD are water ice/dust mixtures with dust content varying from 0 to more than 75%.

Mars Advanced Radar for Subsurface and Ionospheric Sounding (MARSIS) after nine years of operation: A summary

“…Also in this case, modelling assumed a plane electromagnetic wave propagating normally through three homogeneous non-magnetic layers. In their analysis, Zhang et al (2008) found a large sensitivity of the solution to small changes in initial conditions, making this an ill-posed problem. It was found that the most probable value of the relative dielectric constant of the SPLD lay between 3.0 and 5.0, and that the relative dielectric constant of the basal layer was between 7.5 and 8.5, a value typical of basalts.…”

“…The ratio between subsurface and surface reflections over a portion of the SPLD was used also by Zhang et al (2008) to develop a different approach to inversion, based on Bayesian inference. Through the parametric forward modelling of propagation through the SPLD and the derivation of the statistical distribution of subsurface-to-surface echo power ratio, they applied a genetic algorithm to estimate the most likely set of physical parameters producing the observed echoes.…”

Permittivity estimation of layers beneath the northern polar layered deposits, Mars

“…[6] Determination of subsurface dielectric permittivity through the inversion of the radar echo is an approach to determine subsurface composition and has been used for MARSIS observations in a limited number of cases [e.g., Picardi et al, 2008;Zhang et al, 2008]. We present a somewhat simplified inversion method to find the dielectric properties at the base of the North PLD's.…”

A simple inversion model for the estimation of subsurface features of Mars poles

“…Such an ill-posed inverse problem has been solved for MARSIS observations in a limited number of cases [10] [11]. In this work, we present a simple inversion method and demonstrate its effectiveness in the investigation of the dielectric properties at the base of the South PLD's.…”