# LRO LOLA Roughness Map Extra – Hurst Exponents (RMHE)

### RMHE – Roughness Map Extra – Hurst Exponents

**Instrument:** Lunar Orbiter Laser Altimeter

**PDS Data Set ID:** LRO-L-LOLA-8-GDR-V1.0

For more information about LOLA RDR and derived products, see the RDR Product SIS.

For more information about all LOLA products, see the LOLA Archive Volume SIS.

The Lunar Orbiter Laser Altimeter (LOLA) Roughness Map Extra – Hurst Exponents (RMHE) data product is a map of the Hurst exponent of the Moon based on altimetry data acquired by the LOLA instrument. The value of the Hurst exponent is calculated in 1-degree windows spaced 0.25 degrees apart along track, from RMS slopes over the baseline range from 57 m to 2.7 km. The Hurst exponent represents the slope of the best-fit line to a plot of log[v(dx)] vs. log(dx), where v(dx) is the RSM deviation and dx is the baseline (the deviogram). Slopes at the 1-degree (30 km) baseline are removed to eliminate bias on the order of the window size. Many deviograms experience a breakover point marking a transition from one Hurst exponent to another. For each data point, the linear fit to the deviogram spans the baseline range from 57 m to the breakover point, if it exists. Although the baseline range used in this method varies over the surface, it avoids including fits to nonlinear sections of each deviogram and thus presents a more accurate estimate of the Hurst exponent at the smallest available scales.

Hurst exponent values are then interpolated at a resolution of 8 pix/deg by 8 pix/deg and projected using a simple cylindrical projection with the Generic Mapping Tool’s programs ‘surface’ and ‘grdimage’. The LOLA Laser 1 and 2 data through mission phase LRO_NO_13 are the source for this data set. The map is in the form of a binary table with one row for each 0.125 degrees of latitude. The label describes an IMG file in the form of a binary resampling with pixel registration.

The LOLA RMHE data product is named HE_8.IMG, with its corresponding label file. The JPEG2000 version of the product is named HE_8.JP2, with its corresponding label file.

### In ODE, both versions of the RMHE product have the following product ID:

HE_8