A linear inverse method to reconstruct paleo-topography
2019
Fox, Matthew
Landscape evolution provides insight into the tectonic and erosional processes that have shaped the topography observed today. However, in many cases, an estimate of an earlier topography is required to make first-order interpretations about volumes of sediment eroded or depths of fluvial incision, or to serve as an initial condition in landscape evolution models. This paper presents a means to reconstruct paleo-topography in two dimensions in areas that have experienced an increase in incision using available topographic remnants, or areas of low erosion rate. The approach is based on an analytical solution to the steady state stream power model in which a single elevation within the drainage network is a function of the integrated channel steepness and the normalized landscape response time, or χ, values. The branching structure of a drainage network provides redundant information that can be exploited to infer spatial variations in channel steepness and a base level parameter. A single elevation pixel can be written as a sum of channel steepness multiplied by Δχ values, and a set of elevation pixels can be combined as a system of equations. In order to improve efficiency, channel steepness is parameterized using pixels of constant values. By incorporating smoothness constraints on the channel steepness pixels using a Laplacian operator, a stable solution to the inverse problem can be obtained to infer the channel steepness values in space, a base level parameter and, in turn, paleo-topography. This approach is explored with examples from the Inyo Mountain Range, USA, Grand Canyon, USA and the Karrat Region in Western Greenland.
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