Aliasing of the geologic record and the search for long‐period Milankovitch cycles

Abstract

Aliasing of a time series shifts high‐frequency variance into lower frequencies. It is caused by sampling at an interval too broad to resolve true high‐frequency signals. This effect is well understood in classical time series analysis, where sample intervals are known and constant, but in a geologic context, where sample intervals may vary, aliasing remains poorly known. We address here the aliasing problem relevant to the search for orbital variations recorded in sedimentary sections. Our example is aliasing of the 23,000‐year period orbital precession rhythm which is common in late Quaternary paleoclimatic records. We illustrate three cases of aliasing. First, we sample precession at a constant interval of 25,000 years. This is a typical target for many “high‐resolution” studies of Neogene sections. This sampling interval translates precessional variance into predictable spectral peaks near 400 ka and 100 ka, which could be mistaken for the longer‐period eccentricity rhythms. Second, random variations in the sampling interval around the 25,000‐year target spread the aliased variance over a range of frequencies. This induces either unpredictable long‐period spectral peaks or, in the extreme, a white noise spectrum. In the third case, variations of the sampling interval are autocorrelated. This simulates a section with long‐period variations in sedimentation rate sampled at constant depth intervals. Here the single aliased peaks of case 1 are split into two or more peaks of slightly higher and lower frequencies. In all three cases, for long enough time series, the total variance recorded is the same. We compare these numerical experiments to a Miocene oxygen isotope record from Deep Sea Drilling Project site 577, sampled at ∼25,000‐year intervals. With these data it is impossible to tell whether the long‐period variations are due to the direct effects of eccentricity or the aliased effects of precession. In theory it should be possible to test for eccentricity signals at low resolution by randomizing the sampling intervals. In practice, however, it is only through high‐density sampling that we can define intervals well enough to assess the effects of aliasing.