Resolving topographic detail on Venus by modeling complex Magellan altimetry echoes

Abstract

Magellan's altimeter is providing some of the finest resolution topography of Venus achieved to date. Nevertheless, efforts continue to improve the topographic resolution whenever possible. One effort to this end is stereoscopic imaging, which provides topography at scales similar to that of the synthetic aperture radar (SAR). However, this technique requires two SAR images of the same site to be obtained and limits the utility of this method. In this paper, we present another method to resolve topographic features at scales smaller than that of an altimeter footprint, which is more globally applicable than the stereoscopic approach. Each pulse which is transmitted by Magellan's altimeter scatters from the planet and echoes to the receiver, delayed based on the distance between the spacecraft and each surface element. As resolved in time, each element of an altimetry echo represents the sum of all points on the surface which are equidistant from the spacecraft. Thus, individual returns, as a function of time, create an echo profile which may be used to derive properties of the surface, such as the scattering law or, in this case, the topography within the footprint. The Magellan project has derived some of this information by fitting model templates to radar echo profiles. The templates are calculated based on Hagfor's Law, which assumes a smooth, gently undulating surface. In most regions these templates provide a reasonable fit to the observed echo profile; however, in some cases the surface departs from these simple assumptions and more complex profiles are observed. Specifically, we note that sub-footprint topographic relief apparently has a strong effect on the shape of the echo profile. To demonstrate the effects of sub-resolution relief on echo profiles, we have calculated the echo shapes from a wide range of simple topographic models. At this point, our topographic models have emphasized surfaces where only two dominant elevations are contained within a footprint, such as graben, ridges, crater rims, and central features in impact craters