ALBERT

Description: The scaling properties of synthetic topographic surfaces and digital elevation models (DEMs) of topography are examined by analyzing their 'structure functions,' i.e., the qth order powers of the absolute elevation differences: delta h(sub q) (l) = E((absolute value of h(x + l) - h(x))(exp q)). We find that the relation delta h(sub 1 l) approximately equal cl(exp H) describes well the scaling behavior of natural topographic surfaces, as represented by DEMs gridded at 3 arc sec. Average values of the scaling exponent H between approximately 0.5 and 0.7 characterize DEMs from Ethiopia, Saudi Arabia, and Somalia over 3 orders of magnitude range in length scale l (approximately 0.1-150 km). Differences in appparent topographic roughness among the three areas most likely reflect differences in the amplitude factor c. Separate determination of scaling properties in the x and y coordinate directions allows us to assess whether scaling exponents are azimuthally dependent (anisotropic) or whether they are isotropic while the surface itself is anisotropic over a restricted range of length scale. We explore ways to determine whether topographic surfaces are characterized by simple or multiscaling properties.

Description: This paper presents a final technical report on a dedicated environmental remote sensing facility for the Columbia Earth Institute. The above-referenced award enabled the Lamont-Doherty Earth Observatory to establish a state-of-the-art remote sensing image analysis and data visualization facility to serve the research and educational needs of students and staff at Lamont and the Columbia Earth Institute.

Description: One- and two-dimensional models for the deformation by horizontal compression of an elastic plate containing a preexisting deflection were developed and analyzed in order to explain why the compressionally deformed oceanic lithosphere in the Central Indian-Ocean basin is not located where maximum levels of compressive stress in the Indo-Australian plate were predicted by Cloetingh and Wortel (1985, 1986). It is concluded from the results that the location of the deformed region is controlled by an earlier lithospheric deformation that is attributed to the emplacement of the Afanazy-Nikitin seamount group in Late Cretaceous or early Tertiary time.

Description: Many rifted or passive continental margins feature a seaward-facing erosional escarpment which abruptly demarcates deeply weathered, low relief, interior uplands from a deeply incised, high relief coastal zone. It is generally accepted that these escarpments originate at the time of continental rifting and propagate inland through the elevated rift flank topography at rates on the order of 1 km/Myr over the course of a margin's history. Considering the length of passive margins worldwide and an average rift flank plateau height of several hundred meters, it is clear that sediment eroded from passive margins is an important component of the mass flux from continents to oceans through geologic time. The overall goal of the research reported here is to develop a quantitative understanding of the kinematics of escarpment propagation across passive margins and the underlying geological processes responsible for this behavior. Plateau-bounding escarpments in general exhibit two basic forms depending on the direction of surface water drainage on the plateau interior relative to the escarpment. Where surface water flows away from the escarpment, the escarpment takes the form of subdued embayments and promontories, such that its overall trend remains fairly straight as it evolves with time. Where upland streams flow across the escarpment, it takes the form of dramatic, narrow gorges whose heads appear to propagate up the plateau drainage systems as large-scale knickpoints. From work on the Colorado Plateau, Schmidt (1987) noted that the Colorado River is located much closer to the Grand Canyon's south rim, a drainage divide escarpment, than to the north rim, which is a gorge-like escarpment. The main implication is that the gorge-like form might be associated with higher long-term average erosion rates compared to the drainage divide escarpment type.