Imaging targets embedded in a lossy half space with synthetic aperture radar

This paper addresses theoretical aspects of forming images from an airborne synthetic aperture radar (SAR) of targets buried below the Earth´s surface. Soil is generally a lossy, dispersive medium, with wide ranging variability in these attributes depending on soil type, moisture content, and a host of other physical properties. Focussing a SAR subsurface image presents new dimensions of complexity relative to its surface-image counterpart, even when the soil´s properties are known. This paper treats the soil as a lossy, dispersive half space, and presents a practical model for the radar echo-delay time to point scatterers within it. This model is then used to illustrate effects of refraction, dispersion, and attenuation on a SAR´s phase histories, and the resulting image. Various data collection geometries and processing strategies are examined for both two-dimensional and three-dimensional SAR images. The conclusions from this work are that (1) focussing a SAR image must generally take into account both refraction and dispersion, (2) resolving targets at different depths in lossy soils requires perhaps unprecedented sidelobe attenuation, that for some soils may only be achievable with specialized window functions, (3) the impulse response of the soil itself places a practical limit on the usable bandwidth of the radar, and (4) dynamic ranges and sensitivities will need to be orders of magnitude greater than typical surface-imaging SARs, leading to significant impact on SAR parameters, for example compressing the usable range of pulse repetition frequencies (PRFs)