Past exam of the year 2 of the earth sciences (geology) course of the University of Oxford / 2024 / Paper 3 / 8 / a / v / Solution

The source text and its figure are inconsistent here. The plotted low-frequency maximum in W is near $0.0055\mathrm{da}{\mathrm{y}}^{-1}$, rather than the printed $0.055\mathrm{da}{\mathrm{y}}^{-1}$. The original PDF shows that this discrepancy is already present in the examination, rather than introduced by transcription.

Machine 2 records only about half a year. Its first nonzero discrete Fourier transform bin is therefore atThe annual component near $1/365\mathrm{da}{\mathrm{y}}^{-1}$ is below that first bin. The finite window function spreads it through spectral leakage, with a prominent first-bin contribution. This explains the plotted peak without invoking a new physical period.

A literal peak at $0.055\mathrm{da}{\mathrm{y}}^{-1}$ would instead have a period of about $18.2$ days. Neither the two stated model frequencies nor the given sampling schedule identifies such a separate component. The interpretation above treats the printed decimal as an apparent typo; it does not silently change the stated number.