JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 98, NO. B10, PAGES 17,921-17,939, OCTOBER 10, 1993 Normal Faulting and the TopographicRoughness of Mid-Ocean Ridge Flanks ALBERTO MALINVERNO 1 AND PATIENCE A. COWIE 2 Lamont-Doherty Earth Observatory, Palisades,New York The oceanfloor on the flanks of mid-oceanridgesis covered by abyssal hills, topographic features elongatedperpendicularlyto the direction of relative plate motion. These topographicfeatures are interpreted as normalfault blocks and/or volcanic constructions that originated near the ridge axis and were later rafted onto the ridge flanks by seafloor spreading. The purpose of this paper is to quantify the topographicroughness of a profile perpendicularto the strike of a number of normal faults, givena fault population and a mechanical modelfor the response of the lithosphere to faulting. We obtain expressions for the variation in root-mean-square roughness with profile length and for the power spectral density of a profile given threeparameters: a fault density (number of faultsper unit lengthcrossed by the profile),an average squared fault scarp height,and a characteristic lengthof flexure. To keep matters simple, we make a number of assumptions and approximations,namely, that the lithospherebehavesas an elastic plate, that faults have an infinite length and a vertical dip, that the response of topography to a number of faults is simply the sum of the responses to each fault, and that faults have random locations and scarpheightsindependently chosen from some statisticaldistribution. The theory predicts that the roughness-length relationship/power spectral density should follow power laws for scales/wavelengths less than a characteristic scale proportional to the length scale of flexure. We compare the predictions of the theory with actual measurements of mid- ocean ridge flank roughness, and find good first-order agreement. In particular, we use independent estimates of fault densities,averagesquaredfault scarp heights, and flexural length scales to predict the topographic roughness of the East Pacific Rise, and we find that normal faulting can explain all the observedtopographic roughness. Nevertheless, there are some differences between predictions and observations. These differences are likely to be due to processes other than faulting that create topographic relief (e.g., volcanism) and to spatialcorrelations of fault scarp heights.Despite these shortcomings, the approach presentedhere provides a first step in understanding the topographic roughness signal by quantifying the contribution of the geological processes that generate surface relief. INTRODUCTION Surface topography has always been an important clue to un- derstanding the Earth'sstructure. The large-scale morphologi- cal features of the ocean floor, namely,mid-ocean ridges, frac- ture zones, and deep trenches, provided essential constraints to the formulation of the plate tectonicshypothesis in the 1960s [Menard, 1986]. Topographic features near theridge axes (i.e., axial depressions and highs, transform valleys, overlapping spreading centers, etc.) have received a great dealof attention, as the surface morphology was used to drawinferences on deep- seated tectonic processes [Sleep and Biehler,1970;Lonsdale, 1977; Tapponnier and Francheteau, 1978; Macdonald, 1982; Madsen et al., 1984; Macdonald et al., 1988]. The deepening of the ocean floor as it is transported awayfrom ridgeaxesby seafloor spreading has been interpreted asthe isostatic response to the cooling of theoceanic lithosphere [Parker andOldenburg, 1973; Davis and Lister, 1974; Parsons and $clater, 1977]. Superimposed on theserelatively well understood compo- raphythat remains once a large-scale trendhas been subtracted fromthe observed topography.) The topographic features mak- ingup thisroughness, termed "abyssal hills," areelongated in a direction perpendicular to plate motion, are hundreds of meters to several tensof kilometers in length,and are tensto hundreds of meters high. Abyssal hills havebeeninterpreted as volcanic edifices or fault blocks that were formed in the immediate vicin- ity of ridge axes and were later rafted onto theridge flanks [Di- etz, 1961;Le Pichon,1969;Larson., 1971;Rea, 1975;Harrison and $tieltjes, 1977; Lonsdale, 1977; Macdonald and Atwater, 1978;Laughton and Searle, 1979;Lewis, 1979;Macdonald and Luyendyk, 1985; Kappel and Ryan, 1986; Pockalny et al., 1988]. A number of studies showthat the overallamplitude of abyssal hills is inversely proportional to the spreading rate [Menard, 1967; Hayes andKane,1991a; Malinverno, 1991a; Goff,1992] and is influenced by ridge axis discontinuities [Goff,1991;Goff et al., 1991]. Ridge flank roughness is therefore clearly related to the tectonic and volcanic processes active at ridge axis and nents of ocean floor topography is an ubiquitous, disordered provides aunique record of these processes in time. The funda- roughness. (Following Gilbert and Malinverno [1988] and Goff mental question remains: beyond the observable correlations, and Jordan. [1988], we define "roughness" as the residual topog- what (if anything) is topographic roughness telling us about •Now at Schlumberger-Doll Research, Ridgefield, Connecticut. 2Now atDepartment of Geology and Geophysics, Edinburgh Uni- versity, Edinburgh, Scotland. Copyright 1993 by the American Geophysical Union. Papernumber 93JB01571. 0148-0227/93/93JB-01571505.00 the processes that shape the ocean floor and about the deep structure at mid-ocean ridgeaxes? In other words, how can we decode ridge flankroughness to obtain information onridge axis processes? This paperinvestigates these questions by obtain- ing some first-order relationships between a geological process, namely, normalfaultingof an elastic lithosphere, and the to- pographic roughness that thisprocess generates. The approach we take differs from most other studiesof abyssalhills, as we do not attempt to draw insightfrom the detailedexamination 17,921