Calculating Earth–Moon system parameters from sub-yearly tidal deposit records: An example from the carboniferous tradewater formation

Abstract The secular evolution of the Earth–Moon system remains poorly constrained, largely because there are few continuous tidal rhythmite or foreset bundle sequences that preserve deposition over more than several neap–spring tidal cycles. Deposits recording less than one year of deposition do not facilitate direct calculation of past lunar distance directly from Kepler's Laws, but may prove necessary to reconstruct lunar orbital evolution because they are far more common than longer records. A method is demonstrated to make use of shorter tidal deposit sequences by utilizing conservation of angular momentum between the Earth and Moon and estimating the solar component of tidal deposition, while assuming a constant moment of inertia for Earth since the Proterozoic. The precision and accuracy of spectral estimates obtained from short records are considered, as are the limitations of subsequent calculations of Earth–Moon parameters. The Late Carboniferous Abbott sandstone of the Tradewater Formation in the Illinois Basin preserves just over 6 apparently continuous neap–spring cycles in its semidiurnal deposits. The quality of these data, as assessed via sedimentological evidence and statistical time series properties, produces spectral estimates that are likely within at least ± 5% of the actual underlying periodicity (90% accuracy). To test the usefulness of such records, we assessed the possible scenarios of 90% and 95% accuracy. At 90% accuracy, the error bounds on Earth–Moon parameter estimates become rather large and render individual data sets to be of limited use. At 95% accuracy, very general inferences about the evolution of the Earth–Moon system may be made. Calculated mean lunar orbital distance at 315 Ma is 3.798 × 10 8  m with error bounds of − 0.086 × 10 8  m and + 0.046 × 10 8  m. We conclude that short sequences of cyclic tidal deposits offer rather limited resolution of lunar distance estimates. Utilizing multiple sub-yearly data of similar age in ensemble may prove necessary if further investigations of secular changes in Earth–Moon parameters are to proceed.