Six-Year Torsional Waves in the Core and the Recalibration Interval for Studio Master Clocks: A Response to Gillet et al. (2010)

The length of the day is not constant. Tidal friction lengthens it slowly; the atmosphere and the oceans shift it by fractions of a millisecond from season to season; and on time scales of years to decades it varies with exchanges of angular momentum between the mantle and the liquid core beneath it. A six-year oscillation in the length of the day has been recognised in the geodetic record for some time without an agreed cause. Gillet et al. (2010) have now supplied one. Inverting an ensemble of core-flow models derived from the geomagnetic record, they identified a torsional wave in the core recurring about every six years, with an angular momentum that matches the six-year signal in the length of the day in both phase and amplitude. The wave crosses the core in about four years. Torsional waves are a form of Alfvén wave, carried by the magnetic field that threads the core, and their speed depends on the strength of that field. A four-year crossing implies a field inside the core of a few millitesla, many times stronger than earlier estimates. Ferro Acoustic Labs is not a geophysical laboratory, and this bulletin makes no contribution to the physics of the core. It asks what a six-year beat in the rotation of the Earth means for a device whose task is to keep time.

A studio master clock is a quartz oscillator, a divider chain and a calibration. The calibration is made against a reference at a particular time and place, and from that moment the clock runs on its own until it is next calibrated. The author argued in 2003, in a note on the magnetic equator, that a reference must stay where it is. The same principle applies to a reference in time. A clock calibrated on a planet whose rotation varies is calibrated under the conditions of a particular phase of that variation. If the variation has a six-year period, a clock calibrated at one phase and left alone for three years has run through half a cycle of it. Whether a quartz oscillator should care about the rotation of the planet beneath it is a question this bulletin does not settle. It asks only whether the service records of working studio clocks show any sign that they do.

Fourteen master clocks in recording and mastering facilities were included: five in Quito, within a quarter of a degree of the equator; five in Bogotá, at 4.6° N; and four in Lima, at 12.0° S. All were of professional grade, and all had been recalibrated by the same service workshop, irregularly, at intervals of between one and four years, from 2003 to 2010. The workshop's records give, for each recalibration, the frequency correction that was applied. For each clock, the series of corrections was compared with the six-year component of the length-of-day record over the same period, sampled at the dates of recalibration. Clocks in Bogotá and Lima were treated together as the clocks outside the equatorial band.

For the nine clocks outside the equatorial band, the corrections applied at recalibration followed the six-year length-of-day signal, with a pooled correlation of r = 0.57 across 27 recalibrations. The correlation was present in each city separately. For the five clocks in Quito, the corrections showed no relation to the length-of-day signal (r = 0.06 across 16 recalibrations). They were smaller on average than those of the other clocks and showed only the ordinary ageing of the crystals. The author does not claim that a tenth of a millisecond in the length of the day can move a quartz oscillator by the amounts recorded in the workshop's books. He notes that the corrections have the period of the Earth's rotation signal, that they appear only away from the equator, and that the clocks on the equator were indifferent to it.

Master clocks outside the equatorial band should be recalibrated at least every three years, half the torsional period, so that no clock runs through a full swing of the six-year signal between calibrations. Several clocks in the workshop's records had gone four years between calibrations. The date of the last calibration should be recorded on the clock. Clocks in the equatorial band need be recalibrated only for the ageing of their crystals. Ferro Acoustic Labs will offer recalibration at the equator for clocks from elsewhere, on request, from the beginning of 2011.

This bulletin was issued by Ferro Acoustic Labs, the consultancy and cable workshop Dr. Magnus Ferro ran in Quito before the company that became Equatorial Audio, and is reproduced from the bulletin series. It is the first of his writings addressed to the audio industry and not to geophysicists. Gillet et al. (2010) is real and summarised accurately. The six-year torsional wave and its match to the length-of-day record remain an active subject of research. The three-year interval recommended here was later shortened: Ferro, Magnusson, Tanaka and Flux (2026), considering the long-term lengthening of the day as well as the six-year oscillation, recommended annual recertification of master clocks outside the equatorial band. The service-record study is reproduced as recorded and has not been repeated.