Investigation on the Coherent Component of SHARAD Surface Echo and Surface Roughness: Scaling Behavior and Influence of Hurst Exponent

The radar surface echo can be separated into coherent and incoherent components by statistical approaches, and the coherent component can be described by a backscattering model related to the RMS height. According to backscattering models for fractal surfaces, the coherent power in decibels decreases with RMS height on a scale independent of the wavelength at a rate depending on the Hurst exponent and the roughness scale. We extract the coherent power in four research areas by fitting the amplitude distribution of the Martian surface echoes recorded by the SHARAD radar, and compare the coherent power with the RMS height derived from pulse width of the MOLA laser altimeter. Scatter plots of squared MOLA-derived RMS height-coherent power are drawn to estimate the rates of coherent power fall-off by linear fitting, and the fitting power fall-off rates are compared to the Hurst exponents derived from digital terrain models in those areas. The fitting rates decrease with the Hurst exponent, similar to the theoretical rates. However, the fitting rates decrease with the Hurst exponent more sharply than the theoretical prediction. We explain the mismatch with a linear assumption between different roughness parameters, which helps to estimate the Hurst exponent, and a significant discrepancy between the wavelength and the roughness scale might influence the estimation results due to the scaling dependence of the Hurst exponent. This paper offers an opportunity to learn about the Hurst exponent at a tens-of-meter scale.