Reference Model for Radar Performance Assessment

1. Reference Model for Radar Performance Assessment

2. Premises • Preliminary modeling for the system concept definition of SHARAD was performed by making use of previous material originally produced for MARSIS • In the report by FORSE it is stated that SHARAD “can probably detect liquid water and ice to depths of about 100 meters in the Mars subsurface”, yet it is acknowledged that “the ability of SHARAD to achieve the science objectives will be largely dependent on the electrical properties, both permittivity and permeability, of the soil, degree of scattering off the surface and volumetric debris, and the stratigraphical layering of the subsurface. Due to a high level of uncertainty in the above parameters, it is possible, given the appropriate subsurface model, to predict both success and failure, with the median of partial success indicating ambiguous detection of some of the subsurface layers.” • The present work improves on some aspects of E.M. modeling by reviewing previous assumptions and by including the latest data from Mars Global Surveyor

3. Factors affecting propagation • Ionosphere • Dispersion and attenuation • Faraday rotation • Surface geometry • Topography • Rock size distribution • Surface and subsurface composition • Dielectric properties • Magnetic properties • Subsurface structure • Layering • Porosity • Volumetric scattering

4. Ionosphere • The effect of the Martian ionosphere on the capability of SHARAD to achieve its goals is minor, if not negligible • In fact, SHARAD will be operating at frequencies which are at least twice the peak plasma frequency on the day side, and about an order of magnitude above the highest values of the plasma frequency measured on the night side • At those frequencies, Faraday rotation should be a minor effect, according to studies performed for MARSIS (Safaeinili, 2001) • As far as the ionosphere is concerned, SHARAD will thus be equally capable of operating on the day and night sides of Mars

5. Parameters for surface clutter characterization • Surface echoes from off-nadir portion of the surface can mask subsurface echoes from nadir if both reach the receiver at the same time • Scattering models from natural terrain make use of statistical parameters, namely the r.m.s. height and the r.m.s. slope, to describe the topography • These parameters are scale-dependent, e.g. the r.m.s. slope depends on the horizontal distance of the points between which slope is measured • Scaling of these parameters between the available data sets (i.e. MOLA altimetry, at 300 m spacing) and the wavelengths of interest (tens of meters) requires hypotheses on the scaling behavior of topographic parameters

6. Method • MOLA topographic profiles, approximately 30 km long, with points spaced 300 m apart • Profile is de-trended to filter out contributions to the topography from larger structures • r.m.s height and point-to-point r.m.s. slope are computed for the profile • We assume that the topography is self-affine, i.e. its statistical parameters change with scale • The scaling behaviour of the topography is described by the Hurst exponent H: 0H 1

7. Method (cont’d) • H=0 means stationary profile, while H=1 means fractal profile (self-similar) • We make use of the r.m.s. deviation: xz(x)-z(x+x)]21/2 • For a stationary surface, , is a constant • For a self-affine surface: (x)=(x0) (x/x0)H • Fitting a straight line to a logarithmic plot of  as a function of lag distance provides the Hurst exponent

8. But is Mars self-affine? • Mostly yes, at the scales of interest for this work

9. But is Mars self-affine? (cont’d) • Sometimes, however, the behaviour of the profiles is more complex

13. The Scaling Problem

14. The Scaling Problem (cont’d)

15. Test Areas

16. Results

17. Rock size distribution at the surface • The size-frequency distribution of rocks on Mars has been determined directly only at the Viking and Pathfinder landing sites • The Viking infrared thermal mapper (IRTM) observations have been used to determine the surface rock abundance on Mars (Christensen, 1986) • Rock abundances calculated in this fashion indicate an unimodal Poisson distribution over the planet with minimum abundances of 1 %, maximum abundances of 30 % and a mode of about 6 % • The Viking landing sites and the Mars Pathfinder landing site show rock size-frequency distributions that can be fit by equations of the form: Fk(D) = k exp [-q(k) D], where Fk(D) is the cumulative fractional area covered by rocks of diameter D or larger, k is the total area covered by all rocks, and q(k) = 1.79 + .152/k (Golombek and Rapp, 1997)

18. Rock size distribution at the surface (cont’d) • In the approximation that electromagnetic scattering is caused only by (supposedly spherical) rocks whose circumference is equal or greater than the wavelength, we need to compute the values of F for D = /, where  is the wavelength of the radiation • For k=30% and =10 m, Fk(D) = 2.0·10-4 • A survey of 25,000 high-resolution MOC images (Golombek, 2001) revealed roughly 25 (~0.1% of the total) with fields of hundred to thousands of boulders, typically at the base of scarps or around fresh craters

19. Global composition of Mars’ surface • Available data allow a broad characterization of the Martian surface composition • Thermal Emission Spectrometer (TES) data from the Mars Global Surveyor (MGS) identify two main surface spectral signatures from low-albedo regions • The two compositions are a basaltic composition dominated by plagioclase feldspar and clinopyroxene, and an andesitic composition dominated by plagioclase feldspar and volcanic glass • The distribution of the two compositions is split roughly along the planetary dichotomy: the basaltic composition is confined to older surfaces, and the more silicic composition is concentrated in the younger northern plains

20. Dielectric properties • Using data in the literature on the complex dielectric constants of the above-mentioned rocks, the following values are proposed for the previously discussed test areas  tan  Vastitas Borealis 5-7 0.004-0.01 Utopia Planitia 5-7 0.004-0.01 Amazonis Planitia 5-7 0.004-0.01 Noachis Terra 7-9 0.01-0.03 Terra Tyrrhena 7-9 0.01-0.03 Hellas Planitia 5-9 0.004-0.03

21. Magnetic properties

22. Layering • Evidence for layering from MOC images • Observed layers are tens to hundreds of meters thick • Origin and extent of observed layering still open to debate • Layering as a limiting factor to penetration is currently neglected • Characterization of subsurface layering is a scientific target in itself: more careful modeling will be required

23. Porosity • Terrestrial analogues could provide an indication, but several factors need to be accounted for (differences in the kind of volcanism, lower gravity, etc.) • A value of surface porosity of 50 % is consistent with estimates of the bulk porosity of Martian soil as analysed by the Viking Landers, but a surface porosity this large requires that the regolith has undergone a significant degree of weathering • We set 20 % as a lower bound for the porosity in our computations: lower values would hardly produce a significant dielectric contrast between empty and ice- or water-filled porous material

24. Volumetric scattering • Since the extinction efficiency of spheres in the optical region (i.e. when  D > ) is approximately 2, we can approximate the fraction of energy lost by a plane wave crossing an unit volume of the Martian regolith as twice the cross-section of rocks for which  D >  in the unit volume • To compute this fraction we need to know the number of subsurface rocks per unit volume per unit diameter interval, which is often inferred by assuming that the upper surface layer is “well mixed”, that is that the surface area rock coverage can be equated to the fraction of volume occupied by rocks (Rosiwal's principle) • Using the surface rock size distribution, for k=30% and =3.3 m (30 MHz wavelength in a medium with =9), Fk(D) = 2.6·10-2 • This translates into a worst-case cross-section per unit volume of about 3.7·10-2 • If k=6% (the mode of the rock abundance distribution), the worst-case cross-section per unit volume becomes 8.6 ·10-4