Interferometric Water Level Tilt Meter Development in Finland and Comparison with Combined Earth Tide and Ocean Loading Models
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A modern third-generation interferometric water level tilt meter was developed at the Finnish Geodetic Institute in 2000. The tilt meter has absolute scale and can do high-precision tilt measurements on earth tides, ocean tide loading and atmospheric loading. Additionally, it can be applied in various kinds of geodynamic and geophysical research. The principles and results of the historical 100-year-old Michelson–Gale tilt meter, as well as the development of interferometric water tube tilt meters of the Finnish Geodetic Institute, Finland, are reviewed. Modern Earth tide model tilt combined with Schwiderski ocean tide loading model explains the uncertainty in historical tilt observations by Michelson and Gale. Earth tide tilt observations in Lohja2 geodynamic station, southern Finland, are compared with the combined model earth tide and four ocean tide loading models. The observed diurnal and semidiurnal harmonic constituents do not fit well with combined models. The reason could be a result of the improper harmonic modelling of the Baltic Sea tides in those models.
KeywordsInterferometric tilt meter earth tides ocean tide loading
Discussions on the rigidity of the earth were initiated already 150 years ago by Kelvin 1863 (Michelson 1914). The Earth was recognised not only as an elastic body, but also as a plastic yielding “modulus of relaxation”, termed by Maxwell. Plastic yielding is realised by the lag of the distortion relative to the forces producing it (Michelson 1914).
Michelson (1914), Gale (1914) and staff at Yerkes Observatory, Williams Bay, Wisconsin, USA carried out preliminary studies on the earth’s rigidity using east–west and north–south-oriented long water level tilt meters in autumn 1914. The water level tilt meters were installed at a 1.8-m-deep underground at the Yerkes Observatory. The tubes were 150 m long and half filled with water. Detailed descriptions are given in Michelson (1914) and in Gale (1914).
The amplitude ratio of measured tilt vs. calculated model tilt of an absolutely rigid earth gives the rate of deformation. The plastic yielding of the earth is observed from the retardation (lag) of the observed tilt phase to the tidal model tilt of absolutely rigid earth. The observed retardation of the earth tide signal must always be negative, because positive lag is meaningless (Michelson 1914). The mean amplitude ratio between observed east–west (EW) tilt to theoretical one was 0.710 and for north–south (NS) 0.523. The phase lag of total earth tide tilt for EW was −0.059 h and for NS was +0.007 h in the 1914 tilt observations of Michelson (1914) and Gale (1914).1
A similar difference between amplitude ratios in EW and NS directions was also observed earlier by Hecker, and he interpreted the reason to be the difference in earth rigidity (Michelson 1914).
Love and Schweydar (Michelson 1914, p. 124) had the opinion that the difference is attributed to the effect of ocean tides, and it causes differences in ratios of observed amplitudes and phases to theoretical.
The next step was a modern, redesigned, computer-controlled version of the laser interferometric water level tilt meter, installed at the same place as the NS-oriented instrument of the FGI (Ruotsalainen 2001). Construction details and earth tide analysis results with comparison to OTL models are described in Sect. 4.
2 Predicting Tilt Observations for Michelson–Gale Experiments Using Combined Earth Tide and Ocean Tide Loading Model Tilt
Figure 4 shows that in the NS direction, the diurnal band harmonic amplitudes are quite small. The O1 and K1 wave groups have less than a 3.2 nrad tilt. The major energy NS direction is located in the semidiurnal wave band. The NS diurnal tilt harmonics have negative phase lags, but semidiurnal positive lags according to Schwiderski’s OTL model. These explain the difficulties of amplitude and phase determinations 100 years ago. Love and Schweydar were right in their interpretation.
The only positive phase lag of predicted tilt in the EW direction exists in wave group N2. All others have negative lags.
3 Reanalysis of the Earth Tide Tilt of the FGI Tilt Meters 1977–1993
The EWWT- and NSWT-tilt meter data were reanalysed by ETERNA 3.4 Earth tide analysis program (Wenzel 1996) and the newest version ET34-ANA-V52, developed by Schüller (2016). The OTL values based on Schwiderski (1980), TPXO7.0 (Egbert and Erofeeva 2002) and CSR4.0 (Eanes 1994) ocean tide models were determined using the NLOADF program by Agnew (1997). FES2004 (Lyard et al. 2006) OTL values were obtained using the OTL provided by Bos and Scherneck (2014) (http://holt.oso.chalmers.se/loading/). The phase lags in the OTL provider is relative to Greenwich meridian and lags positive. They must be converted from Greenwich meridian to local with sign convention using the formula by Agnew (2009).
In the NS orientation, all OTL models deviate from observations, and the reason can be partly the improperly modelled Baltic Sea loading and partly the Norwegian Sea/Arctic Sea OTL modelling.
4 Modernisation of the FGI Water Level Tilt Meter
5 Recordings and Analysis of the Earth Tide
Very small differences exist in earth tide analysis results between the old NSWT and new NSiWT water level tilt meters. The largest deviation between amplitude factors is 0.0315 in the O1 wave group, and other deviations are considerably smaller. In the tidal phase, the largest deviation is 6.10° in wave group Q1. In other wave group phases, they are within ±2.15°.
The deviation in phase of the wave group Q1 between instruments can be explained by the loading effect of the seiche oscillation phenomenon of the Baltic Sea. The oscillation of 26.2 h in the Gulf of Finland was determined by Lisitzin (1959), and this non-tidal period is harmfully located inside wave group Q1 in the tidal frequency band. The phases of seiche oscillations frequencies are mainly wind generated; therefore, they strongly disturb both the earth tide tilt and the Baltic Sea tidal wave signals (Witting 1911) and their loading tilt at Lohja (Ruotsalainen et al. 2015, p. 160).
In the semidiurnal band, both in NSWT and NSiWT, the M2 amplitude factor diminishing to 0.56 can be recognised and none of the OTL models can correct the tilt to fit the earth tide model tilt. Amplitudes are of a preferable size, but the phases are not fitting? The Baltic Sea and atmospheric tidal loading harmonic presentations need to be taken into more careful consideration and combined for modelling.
The broad band of other geophysical phenomena (Ruotsalainen 2012) has been recorded since 2008, when the 50.4-m-long NSiWT instrument was set up as operational in the Lohja2 geodynamic station. These include Baltic Sea non-tidal loading and atmospheric loading (Ruotsalainen et al. 2015), free oscillations of the earth after great earthquakes (Ruotsalainen 2012), microseism and secular tilt recordings.
The semidiurnal earth tide tilt predictions in the NS direction using combined earth model tilt and Schwiderski OTL model tilt show positive lags and predicted diurnal amplitudes with negative lags smaller than 3 nrad in the NS direction for Yerkes observatory. The semidiurnal band in the NS tilt recording has a leading role, instead of diurnal, and this explains the uncertainty in the interpretation of the earth tide analysis of the Yerkes tilt observations 100 year ago.
The earth tide analysis of the tilt recordings between the old NSWT and new NSiWT tilt meters of the FGI has no significant differences. However, there are differences in ocean tide loading models compared to the tilt observations in the Lohja2 station. The best OTLs fit the earth tide model tilt in the semidiurnal EWWT tilt observation. The core–mantle resonances exist clearly in all three observation data sets.
OTL models do not explain the amplitude diminishing (0.6948 to >0.56) of M2 wave groups in NSWT and NSiWT tilt meter data in the NS direction. Baltic Sea and atmospheric loading harmonic modellings are the next steps in giving information on the deviating features of OTL models.
A modern NSiWT fluid level tilt meter is suitable for geodynamic and geophysical studies with an absolute scale.
A sign deviation exists in the observed phase of the north–south and east–west tilt meter results between pages 111 and 122 in Michelson’s original paper 1914.
Agnew’s SPOTL program was used for computing ocean tidal loading. The ocean tide loading provider, developed by Bos and Scherneck, was also used for determination of OTL tilt. The modern version of the program ET34-ANA-V52 of the original ETERNA 3.4 program by Wenzel, developed further by Schüller, was used for the earth tide analysis. All of the above programs and data obtained are kindly acknowledged. Thanks go to two anonymous referees on their critical comments of the manuscript. The permission to reproduce material from The Astrophysical Journal, volumes 39 and 50, on behalf of the AAS by IOP Publishing, is kindly acknowledged.
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