Inversion of Landscape Features for Deformation Patterns using Landscape Evolution Models: An Example from the Eastern Alps

Topography in tectonically active regions can provide a record of the history of uplift and, while less studied, horizontal motions as well. Stream channel geometry, especially, has been shown to be sensitive to tectonically driven rock displacement, which is often reflected in spatial variations of the normalized channel steepness index (K_sn). Numerical landscape evolution models can be used to model the effects of tectonics on the topography. This raises the possibility of using landscape evolution models to solve an inverse problem, in which rates and spatial patterns of uplift and advection are quantified based on observed features of a landscape. Similar methods have been developed previously, but they have mostly been focused on uplift only and/or on the inversion of one-dimensional, longitudinal stream profiles rather than two-dimensional landscapes. In this study, we introduce a new approach to invert for both vertical and horizontal kinematics from present-day topography. We use as data the average elevation and average K_sn calculated in a moving window along a profile across-strike of the orogen, and we search for landscape evolution models that can reproduce these features. To fit models to data we use ensemble Kalman inversion: an efficient, ensemble-based, gradient-free data inversion method that can handle large numbers of free parameters and can quantify uncertainty in the results. We first demonstrate our method using a synthetic model, inspired by the Eastern Alps, and we then apply it to a real-world profile, the TRANSALP geophysical transect. With the synthetic model, we show that our method can accurately recover magnitudes and changes in uplift and advection rates in both space and time. In addition, we test synthetic models with a short-time, low-amplitude (0.1-1 mm/yr), long-wavelength surface uplift superimposed on fault-related kinematics, which represents the effects of mantle processes or isostatic responses. We find that this uplift pulse can be identified if the event occurred within the past ~5 Ma but becomes increasingly difficult to detect as it is moved back in time, although the specific time limits will likely vary with the parameters of the erosion model. Applying the method to the real-world data, we see evidence of a short-wavelength pulse of uplift in the Tauern region, approximately consistent in time and space with other evidence for the exhumation of the Tauern Window. We do not detect evidence of a hypothesized longer wavelength surface uplift, implying that if any such event occurred it must have been sufficiently far back in time that its topographic record has been erased. In summary, our work provides a new method for interpreting tectonics from topography and demonstrates that it can constrain location and magnitude of rock displacement.