An Improbable Observation of the Diurnal Core Resonance

Abstract

The resonance associated with the ellipticity of the core-mantle boundary is usually measured with observations of either the Earth’s nutations, or of tidal gravity, strain, or tilt. But, improbably, it can also be seen in a dataset collected and processed with older and simpler technologies: the harmonic constants for the ocean tides. One effect of the resonance is to decrease the ratio of the amplitude of the $\mathrm{ P_1}$ constituent to the amplitude of the $\mathrm{ K_1}$ constituent to 0.96 of the ratio in the equilibrium tidal potential. The compilation of ocean-tide harmonic constants prepared by the International Hydrographic Bureau between 1930 and 1980 shows considerable scatter in this ratio; however, if problematic stations and regions are removed, this dataset clearly shows a decreased ratio. While these data apply only a weak constraint to the frequency of the resonance, they also show that the effect could have been observed long before it actually was.

Appendix: Corrections to the IHO Data Bank

The following modifications were made to the values in the IHO Tidal Data Bank prior to the processing described here. The tidal constants were originally published as separate sheets bound into fascicles: sheets 1–1967 are each for individual stations, though only sheets 1–1180 were published. Groups of stations, usually with fewer constituents, were published on sheets 2000–2347 and 3000–3055.

Sheet 167 (Bass Harbour, Malaysia). The data bank value for $\mathrm{ P_1}$ is 0.5 cm; reference to the original published sheet shows that this should be 5.5 cm. (This location was not actually part of the winnowed data because of the ratio of $\mathrm{ P_1}$ to the nonlinear tide $\text {SO}_1$.)

Sheet 169 (Sydney, Australia). The data bank value for $\mathrm{ P_1}$ is 0.5 cm; reference to the original published sheet shows that this should be 4.7 cm.

Sheet 670 (Stockton, California). The data bank value for $\mathrm{ P_1}$ is 2.0 cm; the original published sheet shows a value of 1.999 cm, but this sheet also gives the amplitude in feet (the original units), and this amplitude corresponds to 19.99 cm, so in this case there is a typographical error on the sheet.

Sheet 1445 (Yeosu, Korea). The data bank gives two values for $\text {K}_2$ and none for $\mathrm{ K_1}$; looking at the phase of other diurnal tides it is clear that the first $\text {K}_2$ value should be assigned to $\mathrm{ K_1}$.

Sheet 1780 (Nagapatnam, India). The data bank value for $\mathrm{ K_1}$ is 0.5 cm and for $\mathrm{ P_1}$ is 22.3 cm. I have instead used the values given in Darwin (1888): 6.8 cm for $\mathrm{ K_1}$ and 2.2 cm for $\mathrm{ P_1}$.

Sheet 2313 (Santander, Spain). The data bank and published sheet both give $\mathrm{ P_1}$ an amplitude of 9.0 cm, larger than $\mathrm{ K_1}$ (6.4 cm). The values for $\mathrm{ K_1}$ match a number of global models (EOT11A, FES2004, TPXO7.2ATLAS, GOT4P7), which is to be expected since this is a harbor open to the ocean. But these models all give values around 2 to 3 cm for $\mathrm{ P_1}$. I have therefore rejected this station.