The volcano Olympus Mons on Mars is the largest mountain in the solar system, standing more than twice as high as Mt Everest. On the northern flank there is an extensive field of fractured lava. Does this lava field exhibit scaling? Or is it just a random field with no pattern at all?
The plot below shows a profile of Olympus Mons taken by Mars Orbiter Laser Altimeter (MOLA) during a hiatus in aero-braking when it first entered Marsí atmosphere in 1997.
To investigate the presence of scaling, we have taken the topography of the fractured lava and fitted a 4th order polynomial to it to remove the background topography; then we have decomposed it using continuous wavelets. Wavelet analysis is a method of dealing with signals that are known as non-stationary or quasi-periodic, which means that they have no regularity to them (or equivalently, the standard deviation of the signal varies depending upon the length and position of the sampling window).
The lower plot shows the topography after the background topography has been removed. The upper plot is a contour map of energy as a function of distance and scale: the brighter the colour, the higher the energy. Low energy corresponding to random noise is submerged into the black background, but high energy appears as a series of horn-like structures, indicating there is weak self-similarity, with preferred scales of about 25 km and about 100 km. These scales probably relate to lava of different compositions overlaying each other, having flowed with different speeds depending on their viscosity.
Continuous wavelet analysis is used to discern underlying patterns in a signal. Orthogonal wavelets, on the other hand, are used to split a non-stationary signal into its constituent parts, as shown in the analysis of the Peru tsunami.
Last Updated: 17 November 2003
For more information contact: firstname.lastname@example.org