NORMAL FAULTING AND THE TOPOGRAPHIC ROUGHNESS OF MIDOCEAN RIDGE FLANKS

The ocean floor on the flanks of mid-ocean ridges is covered by abyssa l hills, topographic features elongated perpendicularly to the directi on of relative plate motion. These topographic features are interprete d as normal fault blocks and/or volcanic constructions that originated near the ridge axis and were later rafted onto the ridge flanks by se afloor spreading. The purpose of this paper is to quantify the topogra phic roughness of a profile perpendicular to the strike of a number of normal faults, given a fault population and a mechanical model for th e response of the lithosphere to faulting. We obtain expressions for t he variation in root-mean-square roughness with profile length and for the power spectral density of a profile given three parameters: a fau lt density (number of faults per unit length crossed by the profile), an average squared fault scarp height, and a characteristic length of flexure. To keep matters simple, we make a number of assumptions and a pproximations, namely, that the lithosphere behaves as an elastic plat e, that faults have an infinite length and a vertical dip, that the re sponse of topography to a number of faults is simply the sum of the re sponses to each fault, and that faults have random locations and scarp heights independently chosen from some statistical distribution. The theory predicts that the roughness-length relationship/power spectral density should follow power laws for scales/wavelengths less than a ch aracteristic scale proportional to the length scale of flexure. We com pare the predictions of the theory with actual measurements of mid-oce an ridge flank roughness, and find good first-order agreement. In part icular, we use independent estimates of fault densities, average squar ed fault scarp heights, and flexural length scales to predict the topo graphic roughness of the East Pacific Rise, and we find that normal fa ulting can explain all the observed topographic roughness. Nevertheles s, there are some differences between predictions and observations. Th ese differences are likely to be due to processes other than faulting that create topographic relief (e.g., volcanism) and to spatial correl ations of fault scarp heights. Despite these shortcomings, the approac h presented here provides a first step in understanding the topographi c roughness signal by quantifying the contribution of the geological p rocesses that generate surface relief.