A new method to restore tectonically beheaded stream networks

Drainage capture and beheading represent extreme cases of divide mobility, during which large parts of drainage areas are suddenly gained or lost. Though these events may occur in any environment, some of them are directly controlled by displacement on dip-slip faults. In such a case, topographic barriers built through vertical tectonic displacements result in breaking across-fault hydrological connections. Beheaded valleys represent the end-product of this process and can theoretically be used as strain markers that record cumulative displacement on the causative fault. In practice, it is however difficult to derive robust displacement estimates from beheaded valleys because the pre-deformation geometry is generally unknown. This difficulty is usually tackled by introducing two main assumptions: (1) the stream profile was at steady-state at the time of beheading, and (2) the beheading event did not significantly modify the upstream profile. These two assumptions allow constraining the pre-deformation profile by propagating the upstream “undeformed” profile in the downstream direction. We here propose a new approach which offers an opportunity to get rid of the latter assumption, provided that the former is true.

We first present theoretical expectations for the topographic encoding of dip-slip-faulting-induced beheading in chi-transformed coordinates (chi = along-stream distance normalized by the drainage area) as a function of drained catchment loss and post-beheading vertical uplift. In chi-elevation plots, we define “co-tectonic lines” that connect pairs of points located at the same distance from the fault but along distinct downward-branching beheaded channels. The orientation of these lines is insensitive to tectonic displacement, and becomes increasingly tangent to the pre-deformation steady-state profile as catchment loss corrections applied to chi approach the actual values. We then define a two-fold strategy to retrieve the initial unstrained geometry: (1) analyze the distribution of co-tectonic lines for a range of catchment loss solutions, and (2) evaluate the consistency of these distributions with respect to steady-state conditions. We employ this strategy on a fossilized beheaded stream network which formed in response to slip on normal faults of the Wadi al-Akhdar Graben (WAG, NW Saudi Arabia). This natural prototype is ideal to test the method because pre-deformation catchment geometries can be readily quantified in the landscape due to the local arid low-erosion conditions. Forward modeling of the beheaded stream profiles of the WAG well predicts the drained catchment loss quantified independently (at the 90% confidence level), and provides pre-deformation profiles that reduce the quantified cumulative uplift by ~30% relative to the standard method. These results show that working on chi-transformed profiles represents a promising way to reduce the uncertainties associated to the restoration of tectonically beheaded valleys.