Theory connecting non-local sediment transport, earth surface roughness, and the Sadler effect

Earth surface evolution, like many natural phenomena typified by fluctuations on a widerange of scales and deterministic smoothing, results in a statistically rough surface. We present theorydemonstrating that scaling exponents of topographic and stratigraphic statistics arise from long-timeaveraging of noisy surface evolution rather than specific landscape evolution processes. This isdemonstrated through use of "elastic" Langevin equations that generically describe disturbance froma flat earth surface using a noise term that is smoothed deterministically via sediment transport. Whensmoothing due to transport is a local process, the geologic record self organizes such that a specific Sadlereffect and topographic power spectral density (PSD) emerge. Variations in PSD slope reflect the presenceor absence and character of nonlocality of sediment transport. The range of observed stratigraphic Sadlerslopes captures the same smoothing feature combined with the presence of long-range spatial correlationin topographic disturbance.