Experimental Non-Fourier analysis of Earth and Ocean Tides.

The authors gratefully acknowledge the support of National Science Foundation, Division of Ocean Sciences, Marine Geology and Geophysics Program Award Number 0957767, Project Title: EAGER: Exploratory research in non-Fourier tidal analysis of hydrothermal time series, under which the experimental method of non-Fourier based analysis of the Earth and ocean tidal content of time series that appears on this site has been realized.

Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views ofthe National Science Foundation.


We carried out a proof-of-concept "Early Concept Grant for Exploratory Research (EAGER)" project to develop and apply new methods to investigate how ocean and earth tides moderate crustal fluid flow within Mid Ocean Ridge systems. The method explored is also equally appropriate to earth tidal analysis of terrestrial geyser, geothermal, hydrothermal and more general hydrologic time series.

NSF  project  OCE 0957767 enabled us to test concepts in non-traditional spectral analysis that ultimately can be used to determine how ocean and earth tides moderate crustal fluid flow. Conventional signal analysis as applied to hydrothermal and related time series is based on application of Fourier analysis, underlying which is the assumption that the time series under study is temporally stationary, i.e. that the section of time series under study represents a periodically repeating process. The reality is that hydrothermal time series are non-stationary, and even tidal variations cannot be extracted reliably using these methods. This problem is not restricted to hydrothermal systems, although our initial focus is in this domain.

We have selected hydrothermal systems as a target area because temporal variations in permeability such as those related to tidal pressure loading of the seafloor or to solid Earth tidal deformations (which are also important for terrestrial hydroogy) likely alter the path of fluid flow and/or the mass flux through the seafloor. We examine this by employing a non-Fourier based tidal analysis method (by fitting forcing functions derived from gravitational potentials based on the actual positions of the Earth, Moon and Sun) well suited to analyzing finite length, noisy and complicated hydrothermal time-series data. We apply this method to hydrothermal/geothermal data sets to isolate the hydrological response to Earth tides unambiguously from the hydrological response to ocean tides, so that unbiased spectral estimates of tidal frequency components and accurate assessment of the phase delay between flow rates, temperatures, compositions and tides can be attained.

Understanding the relationship between Earth and ocean tides and the significant tidal variability observed in many records of vent fluid temperature, flow rate and composition will allow prediction of the amplitude of those variations and the phase relationships (i.e. the time lags) between them. This capability can assist researchers in their efforts to uncover the linkages between deeper physical forcing factors and variability in fluid characteristics. Ultimately, an assessment of how the vent fluid composition, temperature and volume flux changes with time is required to define the range of conditions that vent biotic communities experience over relevant timescales.

Our software product, nfTides (Non-Fourier Tides) provides a state-of-the-art experimental signal analysis capability of wide applicability across the geosciences. This open-source signal analysis modeling toolkit is freely available under the terms of the Gnu GPLv3.0 license. For further information about registering as an NGF user, which among other benefits provides cost-free access to nfTides, please follow the registration information on the NGF Software Portal web page (see links on lefthand sidebar).