Hilbert transform analysis of the Elatina varve record of solar activity

Abstract

A sequence of 1337 annual laminae, or varves, from the late-Precambrian Elatina Formation in South Australia has been subjected to spectral analysis by a simplifying technique of Hilbert transformation previously used successfully on the sunspot number series. In the depth interval between one thin varve and the next, which will be referred to as a varve cycle, there are 12±4 varves of regularly increasing and then diminishing thickness. Also conspicuous is a ‘zig-zag’ effect, an inequality of the thickness of consecutive varve cycles. The analysis confirms the presence of (i) an additive undulation with period of $$T_\text U=350$$ varve yr associated with the zig-zag effect and (ii) non-sinusoidal amplitude modulation with a period of $$T_\text E=314$$ varve yr known as the Elatina Cycle. In each group of about 24 varves, a blunt varve cycle precedes a sharp one when the undulation is positive, and vice versa. This phenomenon may be attributable in part to a non-linear dependence of the geological response, although much of the non-linearity apparently originates in the Sun itself. The non-linear distortion influences (i) the duration of the varve cycle and (ii) the apparent shape of the Elatina Cycle, because of the appearance of second harmonic that both shifts the year of solar minimum and also affects the amplitude at solar maximum. Correction for the year of minimum shows the underlying solar oscillator to have greater frequency stability than is apparent from the 11-yr solar cycle. Re-examination of the sunspot number series confirms that the length of the magnetic, or Hale, cycle also is more consistent than the length of the 11-yr sunspot cycle. Correction for amplitude distortion permits a determination of the shape and spectrum of the Elatina Cycle from the varve data.