“Empirical pre‐whitening” spectral analysis detects periodic but inconsistent signals in abyssal hill morphology at the southern East Pacific Rise

The existence, or not, of periodicities in abyssal hill morphology has been vigorously debated in recent publications, and some have hypothesized that such periodicities are evidence of the impact of Milankovitch cycle-caused sea level fluctuations on the volcanic construction process at mid-ocean ridges. Periodicities are detected by the presence of spectral peaks that rise significantly above the random variations of sample power spectra associated with an aperiodic, continuous spectrum process, typically modeled as a band-limited fractal (von Karman model). Here I formulate and test a new algorithm to “empirically pre-whiten” the sample power spectrum which, without needing to model the continuous spectrum, flattens it to a zero-mean process. This greatly simplifies definition of the null hypothesis, and additional modeling approximates standard deviation levels that provide a conservative basis for detecting peaks that may be indicative of periodicity. The algorithm is applied to extensive bathymetric data flanking the southern East Pacific Rise. Significant periodicities are detected on many profiles analyzed, but the periods vary widely, and do not cluster at Milankovitch periods. The most substantial harmonic signals detected exhibit periods ~0.082-0.216 my, with root-mean square (RMS) heights approximately a quarter to a third of the RMS height for the aperiodic signal. It is hypothesized that the dominant aperiodic component of abyssal hills corresponds to morphology constructed by faults that follow a random distribution governed by scaling laws, whereas longer-scale periodic signals are associated with crustal thickness variations controlled internally by variations in melt supply.