Natural sampling and aliasing of marine geochemical signals.

It is well known that the sedimentary rock record is both incomplete and biased by spatially highly variable rates of sedimentation. Without absolute age constraints of sufficient resolution, the temporal correlation of spatially disjunct records is therefore problematic and uncertain, but these effects have rarely been analysed quantitatively using signal processing methods. Here we use a computational process model to illustrate and analyse how spatial and temporal geochemical records can be biased by the inherent, heterogenous processes of marine sedimentation and preservation. This confirms that sedimentary hiatuses can span a substantial proportion of geological time, caused by inherent geological processes. Moreover, even in marine geochemical records that are essentially spatially continuous and complete, the signal is irreversibly disguised in time as lower frequency signals by an aliasing effect. We demonstrate that Nyquist's theorem correctly predicts these biased signatures, proving that aliasing can be caused by cyclical and multiscale relative sea-level changes - a natural sampling effect. Our combined results show that deeper marine records are significantly more likely to provide unaliased environmental signatures. Also, some proxy residence times will be sufficiently long that they average over aliased frequencies, cancelling these in the geochemical record. And field observations of changes in sedimentation rate (such as hiatuses, condensation, or lateral expansion) can be used to infer possible aliasing. Where aliasing by natural sampling occurs, this cannot be undone simply by increasing sample resolution (density): aliasing is caused by an absence of sedimentary record, which by definition cannot be sampled at all. To overcome these issues, we propose that spatially separated aliased records may still be correctly correlated in age, and true geochemical cycles inferred, if a paired-sampling strategy informed by local stratigraphy is adopted. In this, two (or more) closely-spaced samples are analysed at each sampling point instead of only one, after which aliased cycles are inferred from geochemical gradients.