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

[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 × 10−6 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 × 10−7 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%.

[1]  H. Engl,et al.  Regularization of Inverse Problems , 1996 .

[2]  A. Devaney,et al.  Nonuniqueness in inverse source and scattering problems , 1982 .

[3]  Top layers charaterization of the Martian surface: Permittivity estimation based on geomorphology analysis , 2006 .

[4]  R. Parker.  Understanding Inverse Theory , 1977 .

[5]  A. Tarantola.  Inverse problem theory : methods for data fitting and model parameter estimation , 1987 .

[6]  R. Jordan,et al.  Impact of Mars ionosphere on orbital radar sounder operation and data processing , 2003 .

[7]  John H. Holland,et al.  Adaptation in Natural and Artificial Systems: An Introductory Analysis with Applications to Biology, Control, and Artificial Intelligence , 1992 .

[8]  Y. Ilyushin.  Martian northern polar cap: Layering and possible implications for radar sounding , 2004 .

[9]  Subsurface radar sounding of the martian polar cap: radiative transfer approach , 2005 .

[10]  John H. Holland,et al.  Adaptation in Natural and Artificial Systems: An Introductory Analysis with Applications to Biology, Control, and Artificial Intelligence , 1992 .

[11]  Philippe Paillou,et al.  On Water Detection in the Martian Subsurface Using Sounding Radar , 2001 .

[12]  F Forget,et al.  The state and future of Mars polar science and exploration. , 2000, Icarus.

[13]  R. Morris,et al.  ON THE DIELECTRIC PROPERTIES OF DUST AND ICE-DUST MIXTURES: EXPERIMENTAL CHARACTERIZATION OF THE MARTIAN POLAR LAYERED DEPOSITS ANALOG MATERIALS , 2007 .

[14]  W. Kofman,et al.  Mapping of overspread targets in radar astronomy , 1991 .

[15]  M. Malin,et al.  Mars Global Surveyor Mars Orbiter Camera: Interplanetary cruise through primary mission , 2001 .

[16]  P. Drossart,et al.  Perennial water ice identified in the south polar cap of Mars , 2004, Nature.

[17]  D. E. Goldberg,et al.  Genetic Algorithms in Search , 1989 .

[18]  R. Knight,et al.  The dielectric constant of sandstones, 60 kHz to 4 MHz , 1987 .

[19]  L. Carin,et al.  Inverse scattering with sparse Bayesian vector regression , 2004 .

[20]  Distortion of radar pulses by the Martian ionosphere , 2003 .

[21]  Roberto Orosei,et al.  Subsurface Radar Sounding of the South Polar Layered Deposits of Mars , 2007, Science.

[22]  T. Loredo.  Promise of Bayesian Inference for Astrophysics , 1992 .

[23]  Goldberg,et al.  Genetic algorithms , 1993, Robust Control Systems with Genetic Algorithms.

[24]  P. Christensen,et al.  Exposed Water Ice Discovered near the South Pole of Mars , 2002, Science.

[25]  Roberto Orosei,et al.  Performance and surface scattering models for the Mars Advanced Radar for Subsurface and Ionosphere Sounding (MARSIS) , 2003 .

[26]  N. A. Armand,et al.  The “long wavelength radar” on the Mars-94 orbiter , 1995 .

[27]  Roberto Orosei,et al.  Radar Soundings of the Subsurface of Mars , 2005, Science.

[28]  A. Devaney,et al.  Comments on "Nonuniqueness in inverse source and scattering problems" , 1982 .

[29]  F. N. Frenkiel,et al.  Waves In Layered Media , 1960 .