Detecting Shredded Signals in a Physical Avalanching Rice Pile

Abstract

<p>Tectonic, climatic, and anthropogenic forcing generate sediment flux signals that propagate across the Earth’s surface. Some of these signals get stored in strata but autogenic processes present in the Earth surface active layer can shred (i.e. degrade) and obscure many signals of environmental change prior to stratigraphic storage. In a landmark paper, Jerolmack and Paola (2010) use a numerical rice pile to show that autogenic events in the system saturate at a timescale <em>T</em><sub>x</sub>, which is noted to scale as <em>L<sup>2</sup>/q<sub>in</sub> </em>and corresponds to a red-to-white noise transition. The conceptual utility of this is that those environmental signals with periods less than <em>T<sub>x</sub></em> will experience shredding (unless signal magnitude overwhelms autogenic processes), while signals with periods greater than <em>T<sub>x</sub></em> would be detectable in the output. However, the relationships between signal shredding, preservation and detection are currently not established using physical experiments. Advancing on this work, we use a physical rice pile and find that power spectra generated from efflux time-series exhibit a tripartite geometry defined by red, white and blue noise. The transition between each regime defines two key autogenic timescales: <em>T<sub>rw</sub> </em>and <em>T<sub>wb</sub>. T<sub>rw </sub></em>is defined by the red-to-white noise transition, setting upper bounds on signal degradation, and represents <em>T<sub>x</sub></em> on the power spectra of Jerolmack and Paola (2010), but does not scale with <em>q<sub>in</sub></em>. Whereas signals greater than <em>T<sub>wb</sub></em>, which scales with <em>q<sub>in</sub></em>,<sub> </sub>are unobscured by autogenic noise and show enhanced detectability in the power spectra. We emphasize that while signals greater than <em>T<sub>rw</sub></em> do not experience degradation, they can still be obscured by autogenic noise, unless signal period is greater than <em>T<sub>wb</sub></em><sub>. </sub>This framework can be used to predict the severity of shredding as signals propagate through the Earth surface active layer, and establish robust confidence limits of signal detectability in landscapes and strata.</p>