Accurate description of the topography of rock surfaces is essential because surface roughness affects frictional strength, the flow of fluids in joints and fractures, the seismic behavior of faults, and the formation of gouge and breccia in fault zones. Real rock surfaces can be described using self-similar and self-affine fractal models of surface roughness. If a surface is self-similar, a small portion of the surface, when magnified isotropically, will appear statistically identical to the entire surface. If a surface is self-affine, a magnified portion of the surface will only appear statistically identical to the entire surface ff different magnifications are used for the directions parallel and perpendicular to the surface. At least two parameters are required to describe a fractal model; one parameter typically describes how roughness changes with scale, while the other spedties the variance or surface slope at a reference scale. The divider method and the spectral method are in common use to determine the best fit fractal model from surface profile data. Power spectra from self-similar surfaces have slopes of -3 on log-log plots of power spectral density versus spatial frequency, while spectra from self-affine surfaces have slopes other than -3. Power spectra can be interpreted with greater facility if dimensionless amplitude to wavelength ratios are contoured on plots of power spectral density versus frequency. The topography of many natural rock surfaces, including both fractures and faults, is approximately self-similar within the 6.5 order of magnitude wide wavelength band of 10 prn to 40 m.Within smaller wavelength bands, natural rock surfaces may exhibit self-affine behavior.

The roughness of fault surfaces is important in the mechanics of fault slip and could play a role in determining whether sliding occurs via earthquakes or fault creep. We have made preliminary measurements of the power spectral density of several fault surfaces over the wavelength range from 10 -5 to 1 m. using field and laboratory scale profilimeters.

In many natural fault systems, the thickness of gouge and breccia increases approximately linearly with displacement. In contrast, many experimental faults show non linear thickness/displacement relationships. The linear relationship for natural faults has been explained in the past using engineering models for adhesive or abrasive wear. Non linear relationships for experimental faults have not been explained. A model for wear during brittle faulting which considers the scaling of surface roughness can successfully describe the difference between wear on experimental faults and wear on natural faults. We suggest the linear relationship for natural faults results from the approximately self‐similar roughness of the fault surfaces. Experimental faults do not generally follow linear relationships because the roughness of ground surfaces normally used in experimental studies scales differently than the roughness of natural rock surfaces. A simple model which assumes that the volume of wear material created is proportional to the volume of mismatch between the surfaces can explain the differences between wear on experimental faults and wear on natural faults. For ground surfaces of experimental samples, the volume of mismatch is independent of the total slip because at the largest scales these surfaces are flat. In contrast, for natural, self‐similar surfaces the volume of mismatch increases with slip, because slip isolates larger and larger asperities from their original positions in the opposite surface. Natural and experimental faults evolve differently because of the difference in scaling of their respective surface roughnesses.

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