Power Spectrum of Martian Topography from MOLA

The plot above shows a topographic power spectrum of Mars from MOLA. The figure represents the topographic variance determined from a 720th degree and order spherical harmonic expansion of a high-resolution MOLA global topographic grid. The spectrum is plotted in log-log space. Note that the power follows an approximate straight line, which indicates that topography on Mars displays fractal properties. Mars is not unique in this regard, as other planetary surfaces measured by altimeters (Earth, Venus and the Moon) also are of a fractal nature. This means that topography is scale-invariant. This property is important because (among other things) knowing this, it is possible to extrapolate to higher degrees and orders (shorter wavelengths) and estimate the statistical variance of topography at scales of interest, such as with regard to future Mars landers. The equation on the plot is the power law for Martian topography. (Credit: MOLA Science Team)

Reference for the MOLA topographic power law and spectrum:
Smith, D.E., Zuber, M.T., H.V. Frey, J.B. Garvin, J.W. Head, D.O. Muhleman, G.H. Pettengill, R.J. Phillips, S.C. Solomon, H.J. Zwally, W.B. Banerdt, T.C. Duxbufy, M.P. Golombek, F.G. Lemoine, G.A. Neumann, D.D. Rowlands, O. Aharonson, P.G. Ford, A.B. Ivanov, P.J. McGovern, J.B. Abshire, R.S. Afzal, and X. Sun, Mars Orbiter Laser Altimeter (MOLA): Experiment summary after the first year of global mapping of Mars, submitted to J. Geophys. Res., 2000.

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Direct inquiries to: dsmith@tharsis.gsfc.nasa.gov