## Abstract

The presence of undesirable dominating signals in geophysical experimental data is a challenge in many subfields. One remarkable example is surface gravimetry, where frequencies from Earth tides correspond to time-series fluctuations up to a thousand times larger than the phenomena of major interest, such as hydrological gravity effects or co-seismic gravity changes. This work discusses general methods for the removal of unwanted dominating signals by applying them to 8 long-period gravity time-series of the International Geodynamics and Earth Tides Service, equivalent to the acquisition from 8 instruments in 5 locations representative of the network. We compare three different conceptual approaches for tide removal: frequency filtering, physical modelling, and data-based modelling. Each approach reveals a different limitation to be considered depending on the intended application. Vestiges of tides remain in the residues for the modelling procedures, whereas the signal was distorted in different ways by the filtering and data-based procedures. The linear techniques employed were power spectral density, spectrogram, cross-correlation, and classical harmonics decomposition, while the system dynamics was analysed by state-space reconstruction and estimation of the largest Lyapunov exponent. Although the tides could not be completely eliminated, they were sufficiently reduced to allow observation of geophysical events of interest above the 10 nm s−2 level, exemplified by a hydrology-related event of 60 nm s−2. The implementations adopted for each conceptual approach are general, so that their principles could be applied to other kinds of data affected by undesired signals composed mainly by periodic or quasi-periodic components.

Geophysical data may present strong periodic or quasi-periodic components making difficult the observation of the phenomena of interest. For over half a century, techniques have been proposed for removing undesired periodic/quasi-periodic components which are based on improvements or combinations of three procedures: frequency filtering (which might be done in frequency domain or in time-domain), physical modeling (PM) of the phenomena to be removed, and data-based modelling using the signal itself to infer the behaviour of the undesired component. In the case of gravity signals, the phenomena responsible for large periodic/quasi-periodic variations are the Earth tides. For the removal of tides from the gravity signal, there are many software packages available, such as mGlobe,1 based on the physical modelling procedure, or ETERNA,2 BAYTAP,3 and VAV,4 which adopt a mix of frequency filtering and data-based modelling procedures. However, there is still little comparison between the fundamental blocks, i.e., frequency filtering, physical modelling, and data-based modelling, which are the essence of these more sophisticated software. This study analyses the residual signal after tidal filtering by each of these three methods. As expected, the least-squares data-based modelling produced the residuals with smallest amplitude, which partly justifies its wide adoption by the geophysical community. However, our paper shows that the physical modelling, usually neglected, better preserves the underlying system dynamics.

Geophysical data may present strong periodic or quasi-periodic components making difficult the observation of the phenomena of interest. For over half a century, techniques have been proposed for removing undesired periodic/quasi-periodic components which are based on improvements or combinations of three procedures: frequency filtering (which might be done in frequency domain or in time-domain), physical modeling (PM) of the phenomena to be removed, and data-based modelling using the signal itself to infer the behaviour of the undesired component. In the case of gravity signals, the phenomena responsible for large periodic/quasi-periodic variations are the Earth tides. For the removal of tides from the gravity signal, there are many software packages available, such as mGlobe,1 based on the physical modelling procedure, or ETERNA,2 BAYTAP,3 and VAV,4 which adopt a mix of frequency filtering and data-based modelling procedures. However, there is still little comparison between the fundamental blocks, i.e., frequency filtering, physical modelling, and data-based modelling, which are the essence of these more sophisticated software. This study analyses the residual signal after tidal filtering by each of these three methods. As expected, the least-squares data-based modelling produced the residuals with smallest amplitude, which partly justifies its wide adoption by the geophysical community. However, our paper shows that the physical modelling, usually neglected, better preserves the underlying system dynamics.

Original language | English |
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Article number | 103126 |

Pages (from-to) | 1-12 |

Number of pages | 12 |

Journal | Chaos |

Volume | 27 |

Issue number | 10 |

Early online date | 31 Oct 2017 |

DOIs | |

Publication status | Published - Oct 2017 |

### Bibliographical note

We thanks the participants of the 35th General Assembly of the EuropeanSeismological Commission for comments on preliminary results. The authors

are grateful to all IGETS contributors, particularly to the station operators

and to ISDC/GFZ-Potsdam for providing the original gravity data used in this

study. We also thank the developers of ATLANTIDA3.1 and UTide. Part of this

work was performed using the ICSMB High Performance Computing Cluster,

University of Aberdeen. We also thanks M. Thiel and A. Moura for reviewing

a preliminary version and making comments on the methods section and M.A.

Ara´ujo for comments on Lyapunov exponents.

Funding: A. Valencio is supported by CNPq, Brazil [206246/2014-5]; and

received a travel grant from the School of Natural and Computing Sciences,

University of Aberdeen [PO2073498], for a presentation including preliminary

results.

## Keywords

- time-variable gravity
- earth tides
- time-series analysis
- gravity residuals
- tidal filtering