Reduction of temporal variations in tidal parameters by application of the local response models at globally distributed SG stations

The already 100 years old harmonic analysis of tides is based on the assumption of separable and non-separable contributions depending on the time series length (Rayleigh criterion in tidal analysis). A priori wave groups had to be composed of different harmonics, which leads to an inaccurate (biased) estimate of tidal parameters. An alternative Regularization Approach to Tidal Analysis, RATA, constrains the solution to be close to a reference model what stabilises the linear regression, making wave grouping obsolete. In this way, the resolution power of the harmonic analysis is exploited to a much larger extent, since the risk of over-fitting is strongly reduced.

We used RATA method to analyse data from globally distributed superconducting gravimeters (SGs) and we are able to achieve super resolution that even highly violates the Rayleigh criterion. The results from double-sphere SG instruments give an indication of the minimum error for the accuracy. We estimated local response models for over 10 stations in Europe, which confirms the consistency of the method. The small differences in phases and amplitudes are most likely caused by ocean loading with varying distance to the ocean. The investigation of stations on other continents reveals significant disparities between the observed tidal response (which accounts for the loading signals as well) and the Earth body model assumptions (like Wahr-Dehant-Zschau elastic analysis model).

Temporal variations of tidal parameters, seen in the moving window analysis (MWA), are known for all tidal wave groups at different SG stations around the globe. The amplitude of variations usually is greater than the standard deviation by a factor of 2 (minimum) to 32 (maximum). In our investigation, we approximated the effect of the time-invariant ocean loading and radiation tides in the data by application of the local response models, already estimated with RATA. We repeated the MWA of 12 wave groups composed from summed harmonics. We found that the periodic variations of groups M₂, K₁, µ₂, N₂, L₂, and S₂ are reduced by up to a factor of 9 compared to earlier studies. Some long-period variations previously seen in the M₁, O₁, Q₁, and J₁ groups are captured as well. The previously neglected influence of radiation tides, degree 3 tides, and significant satellite constituents were the main causes of apparent modulations in previous studies. Hence, with the local model correction, a proper investigation of the remaining temporal variations to study instrument stability or time-varying contributions of ocean loading is more applicable.