**http://www-gik.bau-verm.uni-karlsruhe.de/~iagetc/eterna33.htm, Last
update: 1997 August 27**

**An earlier version of this paper has been published
in Bulletin d'Informations Marees Terrestres, vol. 124, 9425-9439, Bruxelles
1996.**

EARTH TIDE DATA PROCESSING PACKAGE

ETERNA 3.30

by Hans-Georg Wenzel,

Black Forest Observatory Schiltach,

Heubach 206, D-77709 WOLFACH.

e-mail: wenzel@gik.bau-verm.uni-karlsruhe.de

The new version 3.30 of the earth tide data processing
package **ETERNA** is
available since October 1st, 1996. The earth tide processing package **ETERNA**
version 3.30 allows the recording, preprocessing and analysis of earth
tide observations under operating system **MS-DOS**
on an IBM-AT compatible personal computer 80386/387 upwards. The **new
standard format** for the storage and exchange
of high rate or high resolution earth tide data (Wenzel 1995) is used in
all parts of the ETERNA 3.30 package. Compared to previous versions, we
have included into the earth tide analysis package ETERNA (Wenzel 1994b,c)
the most accurate **tidal potential catalogue
by Hartmannn and Wenzel (1995a,b)**. In
all programs, the **DUT1 correction**
due to the Earth's variable rotation has been implemented using DUT1 values
provided by the International Earth Rotation Service (IERS). Together with
the Hartmann and Wenzel (1995a,b) tidal potential catalogue, this upgrade
enables the preprocessing and analysis of earth tide observations and the
prediction of earth tide signals with a **model
accuracy better than 1 ngal** (1 ngal =
0.01 nm/s²).

Several parts of the ETERNA earth tide analysis package have been rewritten and several other pieces have been added. For the computation of tidal signals, we have implemented recursion formulas which reduce the total computation time for some data sets down to 35% compared to previous versions without loss of accuracy. The computation of gravity variation due to polar motion and due to length of day variation from IERS data are implemented in the programs. The ETERNA package has benn given a new and better structure, and several programs have been renamed (e.g. the former program ETERNA has been renamed to ANALYZE, the former program ETGTAB has been renamed to PREDICT, the former program PRETERNA has been splitted into programs DETIDE, DESPIKE and DECIMATE). The program LOAD89 (provided by O. Francis) has been included, which enables the computation of ocean loading effects from different ocean tide models (Schwiderski 1980, CSR3.20, FES952). An on-line manual with search and export functions is provided to assist the user by his operations. We believe that a substantial improvement with respect to accuracy, flexibility and operational comfort has been achieved compared to previous versions of the package. ETERNA 3.30 is currently the only earth tide data processing package beeing able to process earth tide observations with a model accuracy better than 1 ngal.

The ETERNA 3.30 package is installed by an automatic
installation procedure within several directories (Table 1, Fig. 1).
It contains 21 programs (with 38 515 program records in total) and covers
together with the necessary data files 180 MByte. Thus, the ETERNA 3.30
package is provided to the user on **CD-rom**.

01 | ANALYZE.FOR |
Analysis or earth tide observations |

02 | BENCHMAR.FOR |
Comparison of model tides with benchmark series |

03 | DECIMATE.FOR |
Decimation of earth tide observations |

04 | DESPIKE.FOR |
Despiking of earth tide observations |

05 | DETIDE.FOR |
Calibration and detiding of earth tide observations |

06 | ETSTEP.FOR |
Eavluation of recorded step response |

07 | IERS.FOR |
Transformation of earth rotation and polar motion data |

08 | INSTALCD.FOR |
Installation of the ETERNA 3.30 package from CD-rom |

09 | HELPME33.FOR |
On-line manual of the ETERNA 3.30 package |

10 | LOAD89.FOR |
Ocean tide loading computation |

11 | PREDICT.FOR |
Computation of synthetic model tides |

12 | PREGRED.CPP |
Graphical editing of earth tide observations |

13 | PREPLOT.BAS |
Visualization of earth tide observations |

14 | PRINTGL.EXE |
hard copy for HPGL-files |

15 | PLOTDATA.FOR |
Plot of earth tide observations |

16 | PLOTFIL.FOR |
Plot of numerical filter gain |

17 | PLOTSPEC.FOR |
Plot of spectra of earth tide residuals |

18 | PLOTHIST.FOR |
Plot of histograms of earth tide residuals |

19 | RECTIDE.BAS |
Digital recording of earth tide signals |

20 | TRANS.FOR |
Transformation from International Format into PRETERNA Format |

21 | WPAREX.FOR |
Interpolation of synthetic gravity tide parameters from global grid |

Fig. 1: Directories of earth tide data processing package ETERNA version
3.30

Digitital earth tide **data
acquisition** can be carried out with program
**RECTIDE**
(in MS-QuickBasic), which allows the sampling of data from different sensors
at 1 s or 5 s interval. After on-line subtraction of on-line computed model
tides from the data, the residuals are displayed on the colour screen of
the PC. The sampled data are numerically filtered using a symmetrical FIR
lowpass filter with zero phase shift; the filtered data are decimated to
1 min interval and the decimated data are stored on hard disk.

The** preprocessing
**of high rate earth tide data and meteorological
data can be carried out with programs **DECIMATE,
DETIDE, DESPIKE** (in Fortran 77/90) and
**PREGRED**
(in Visual C++). The data preprocessing is carried out using a **remove-restore
technique**: At first all well-known signals
(e.g. computed model tides and computed air pressure influence) are removed
with program **DETIDE**.
The graphical editor **PREGRED**
(Vetter and Wenzel 1995) is a very comfortable tool to delete corrupted
parts of the data, to correct steps and to interpolate gaps under graphical
control of the operator. With program **DESPIKE**,
the residual signal (the earth tide sensors drift) is automatically cleaned
(destepped, despiked, and degapped) and the known signals are added back
to the cleaned residual signal. The corrected samples at high rate are
finally numerically filtered and decimated using program **DECIMATE**.
For the data preprocessing may be used

- up to 500 data sets within one batch run,
- up to 300 data blocks for each data set,
- as observations: Tidal potential, gravity tides, tilt tides, vertical displacements, horizontal displacements, vertical strain, horizontal strain, areal strain, shear strain, volume strain and ocean tides,
- seven different tidal potential catalogues (Doodson 1921, Cartwright et al. 1971, 1973, Büllesfeld 1985, Tamura 1987, Xi 1989, Roosbeek 1996 and Hartmann and Wenzel 1995,
- up to 85 wavegroups,
- up to 8 additional meteorological parameters.

The **analysis of
earth tide observations** can be carried
out with program **ANALYZE**
(in Fortran 77/90), using the least squares adjustment procedure with multi
channel input to derive tidal parameters, pole tide parameters and meteorological
regression parameters. The spectrum of the residuals is used to derive
standard deviations of the adjusted parameters. The mathematical model
of of the **ANALYZE**
earth tide analysis program has been developed by Chojnicki (1973) and
modified and completed by Schüller (1976, 1977a, 1977b, 1978, 1986)
and Wenzel (1976a, 1976b, 1977, 1994a, 1994b). With **ANALYZE**
version 3.30 may be used

- up to 500 different data sets within one batch run,
- up to 300 data blocks for each data set,
- up to 85 wave groups,
- up to 175 unknown parameters,
- unlimited number of observations within each data block,
- data sampling interval from 1 s to 1 h,
- as observations: Tidal potential, gravity tides, tilt tides, vertical displacements, horizontal displacements, vertical strain, horizontal strain, areal strain, shear strain, volume strain and ocean tides,
- seven different tidal potential catalogues (Doodson 1921, Cartwright et al. 1971, 1973, Büllesfeld 1985, Tamura 1987, Xi 1989, Roosbeek 1996 and Hartmann and Wenzel 1995),
- up to 8 meteorological parameters,
- correction of gravity pole tides with a priori pole tide parameters,
- correction of gravity variation due to length of day variation,
- adjustment of pole tide regresssion parameters,
- either highpass filtering of the observations or drift modelling,
- in case of highpass filtering: Different symmetric numerical FIR filters of different length and quality are available,
- in case of drift modelling: Tschebyscheff polynomials of individual degree per observation block may be adjusted,
- unity window or Hann-window may be applied for the weights of the least squares adjustment,
- error estimation by least squares adjustment or by Fouriuer spectrum of residuals.

The **prediction of earth tide signals** can
be carried out with program **PREDICT **(in
Fortran 77/90), using the same parameter model as in program **ANALYZE.**
With **PREDICT**
version 3.30 may be used

- up to 85 wave groups,
- as signal: Tidal potential, gravity tides, tilt tides, vertical displacements, horizontal displacements, vertical strain, horizontal strain, areal strain, shear strain, volume strain and ocean tides,
- seven different tidal potential catalogues (Doodson 1921, Cartwright et al. 1971, 1973, Büllesfeld 1985, Tamura 1987, Xi 1989, Roosbeek 1996 and Hartmann and Wenzel 1995),
- gravity pole tides,
- gravity variation due to length of day variation.

The computation of **ocean
tide loading effects** can be carried out
with program **LOAD89**
(in Fortran 77/90), using different ocean tide models (Schwiderski 1980,
CSR3.0, FES952) and Green's functions for the PREM earth model.

Within 1995, a new tidal potential catalogue (Hartmann and Wenzel 1995a,
1995b) became available, which allows the computation of earth tide signals
with an **accuracy better than 1 ngal**,
as has been verified by comparison with different benchmark gravity tide
series (Wenzel 1996). Therefore, the Hartmann and Wenzel (1995) tidal potential
catalogue using in total 12935 tidal waves has been implemented into the
ETERNA package version 3.30. This tidal potential catalogue includes the
potential due to the Moon up to degree 6, to the Sun up to degree 3, to
the planets Mercury, Venus, Mars, Jupiter and Saturn to degree 2, and the
potential due to the Earth's flattening by the Moon and by the Sun. The
errors of gravity tides computed from the Hartmann and Wenzel (1995) tidal
potential catalogue are 1.4 pm/s² rms and 10.4 pm/s² at maximum
(1 pm/s² = 0.001 nm/s² = 0.1 ngal), as has been verified by comparison
with several different benchmark gravity tide series (Wenzel 1996).

Because the computation of tides using the full 12935 tidal waves of
the Hartmann and Wenzel (1995) tidal potential catalogue is rather time
comsuming and may often be unnecessary compared to the accuracy of the
data, a truncation parameter may be used to truncate the tidal potential
catalog at some amplitude threshold, which degrades the accuracy of the
computed tides but saves computation time. Due to the truncation option,
there is in principle no need to use other tidal potential catalogues,
even if very rough tidal computations shall be carried out. Nevertheless,
we have made available with ETERNA 3.30 **seven
different tidal potential catalogues **for comparison purpose.
Because the Hartmann and Wenzel (1995) tidal potential catalogue uses a
straightforward and simple normalization beeing different from the complicated
Doodson (1921) normalization, the tidal potential catalogues of Doodson
(1921), Cartwright et al. (1971, 1973), Büllesfeld (1985), Tamura
(1987), Xi (1989) and Roosbeek (1996) have been transformed into the Hartmann
and Wenzel (1995) normalization. Resulting from intensive accuracy tests,
the astronomical arguments given by Tamura (1987) are used for the tidal
potential catalogues of Doodson (1921), Cartwright et al. (1971,1973),
Büllesfeld (1985), Tamura (1987) and Xi (1989). For Roosbeek (1996)
and Hartmann and Wenzel (1995), the astronomical arguments given by Hartmann
and Wenzel (1995) are used.

Because the astronomical arguments are computed by polynomials of up
to degree 4, it is necessary to recompute the phases of the tidal waves
from the astronomical arguments at monthly interval in order to achieve
the desired accuracy for the computation of the tidal signals. For the
computation of the tidal signals we have implemented recursion formulas
which reduce the total computation time of programs **ANALYZE**,
**DETIDE** and **PREDICT**
for some data sets down to 35% compared to previous versions without loss
of accuracy.

Within ETERNA 3.30, the time scale of the observations (or predicted
signals) is assumed to be **UTC **(Universal
Time Coordinated), which is distributed by radio transmitters and by GPS
(Global Positioning System). For the accurate computation of tides, the
time scales **UT1 **(Universal
Time no. 1, describes the rotation of the
Earth) and **TDB **(Dynamical Barycentric
Time, used to describe the positions of the celestial bodies) have to be
made available. Within ETERNA 3.30 we have implemented for the first time
for tidal computations the correction **DUT1 = UT1
- UTC**, which is interpolated from daily tabulated values of
DUT1 provided by the International Earth Rotation Service IERS. The difference**
DDT = TDT** **- UTC**, which
is constant for several months or years, is also taken from a table. The
difference **TDB - TDT** (a few msec only)
is computed from a closed formula. The neglection of the DUT1 correction
can reach 0.1 nm/s² at maximum for gravity tides (see Fig. 6, 7).

The accuracy of the tidal potential catalogue by Hartmann and Wenzel
(1995) has been estimated by comparison with several gravity tide benchmark
series (Wenzel 1996). We have used here a gravity tide benchmark series
called BFDE403F (which is supplied with the ETERNA 3.30 package) computed
from the most recent and most accurate **DE403/LE403**
ephemerides (Standish et al. 1995) to verify the accuracy of the model
tide computation within ETERNA 3.30. The series BFDE403F consists of hourly
gravity tides for a rigid model Earth computed directly from the ephemerides
of the Moon, Sun, Mercury, Venus, Mars, Jupiter and Saturn at station BFO
Schiltach (48.3306 deg N latitude, 8.3300 deg E longitude, 589 m elevation)
between January 1st 1987 and December 31st 1994. This benchmark series
has been computed for the UTC time scale and has included the corrections
DUT1 and DDT. The accuracy of the BFDE403F benchmark gravity tide series
itself is estimated to be better than 1 pm/s² = 0.001 nm/s².
In Fig. 2 and 4 are given residuals of the earth tide analysis from program
ANALYZE for the benchmark gravity tide series when using the tidal potential
catalogues of Tamura (1987) and Hartmann and Wenzel (1995); in Fig. 3 and
5 are given the corresponding Fourier amplitude spectra. One has to have
in mind that the residuals of the least squares adjustment always underestimate
the errors because the parameters determined by least squares adjustment
absorb to a certain extend the errors. We can see maximum errors of 0.5
nm/s² and 0.012 nm/s² resp. in time domain and 0.015 nm/s²
and 0.0005 nm/s² resp. in frequency domain for the tidal potential
catalogues of Tamura (1987) and Hartmann and Wenzel (1995) resp. In Tab.
2 is given the last page from program ANALYZE for the benchmark gravity
tide series when using the full Hartmann and Wenzel (1995) tidal potential
catalogue. The maximum error of the adjusted tidal parameters is 0.00012
and 0.0174 degree for the very small wave M4. In Fig. 6 and 7 are given
the residuals and their Fourier amplitude spectrum for the benchmark gravity
tide series BFDE403F when using the Hartmann and Wenzel (1995) tidal potential
catalogue but neglecting the DUT1 correction within program ANALYZE. We
can see that the DUT1 correction can amount up to 0.1 nm/s² in time
domain and up to 0.005 nm/s² in frequency domain.

Fig. 2: Residuals of earth tide analysis with program ANALYZE for benchmark gravity tide series BFDE403F when using the Tamura (1987) tidal potential catalogue; DUT1 corrected.

Fig. 3: Amplitude spectrum of rssiduals of earth tide analysis with program ANALYZE for benchmark gravity tide series BFDE403F when using the Tamura (1987) tidal potential catalogue; DUT1 corrected.

Fig. 4: Residuals of earth tide analysis with program ANALYZE for benchmark
gravity tide series BFDE403F when using the Hartmann and Wenzel (1995)
tidal potential catalogue; DUT1 corrected.

Fig. 5: Amplitude spectrum of residuals of earth tide analysis with program
ANALYZE for benchmark gravity tide series BFDE403F when using the Hartmann
and Wenzel (1995) tidal potential catalogue; DUT1 corrected.

Fig. 6: Residuals of earth tide analysis with program ANALYZE for benchmark
gravity tide series BFDE403F when using the Hartmann and Wenzel (1995)
tidal potential catalogue; DUT1 not corrected.

Fig. 7: Amplitude spectrum of residuals of earth tide analysis with program
ANALYZE for benchmark gravity tide series BFDE403F when using the Hartmann
and Wenzel (1995) tidal potential catalogue; DUT1 not corrected.

Program ANALYZE, version 3.30 960908 File: bfde403f #################################################################### # Gravimetric Earth tide station BFO Schiltach Germany. # # Black Forest Observatory, Geodetic and Geophysical Institutes, # # Universities Karlsruhe and Stuttgart, Germany. # # 48.3306N 8.3300E H589M gravity, # # Hourly gravity tides due to the Moon, the Sun, the Mercury, # # the Venus, the Mars, the Jupiter and the Saturn for a rigid # # Earth model computed from DE403 ephemerides using program # # DE403T.FOR for station BFO Schiltach, including earth flattening # # effects. All waves with amplitude factor 1.000, phase lead 0.00 # # deg. Time corrections UT1-UTC and TDB-UTC applied. # #################################################################### Latitude: 48.3306 deg, longitude: 8.3300 deg, azimuth: 0.000 deg. Summary of observation data : 19870101 0...19941231230000 Number of recorded days in total : 2922.00 Hartmann+Wenzel (1995) tidal potential used with threshold 0.10E-10 Rigid Earth model used. Inertial correction not applied UNITY window used for least squares adjustment. Numerical filter is no filter with 1 coefficients. Spectral condition number of normal equations: 153.754 Estimation of noise by FOURIER-spectrum of residuals 0.1 cpd band 0.0000 nm/s**2 1.0 cpd band 0.0000 nm/s**2 2.0 cpd band 0.0000 nm/s**2 3.0 cpd band 0.0000 nm/s**2 4.0 cpd band 0.0000 nm/s**2 white noise 0.0000 nm/s**2 adjusted tidal parameters : from to wave ampl. ampl.fac. stdv. ph. lead stdv. [cpd] [cpd] [nm/s**2 ] [deg] [deg] 0.000133 0.004107 SA 18.0753 1.00001 0.00139 0.0004 0.0850 0.004108 0.020884 SSA 20.0570 1.00000 0.00001 0.0000 0.0004 0.020885 0.054747 MM 22.7684 1.00000 0.00000 -0.0001 0.0001 0.054748 0.091348 MF 43.1106 1.00000 0.00000 0.0000 0.0000 0.091349 0.501369 MTM 8.2543 1.00000 0.00000 -0.0001 0.0000 0.501370 0.911390 Q1 59.1071 1.00000 0.00000 0.0001 0.0000 0.911391 0.947991 O1 308.7114 1.00000 0.00000 0.0000 0.0000 0.947992 0.981854 M1 24.2657 0.99999 0.00000 0.0000 0.0001 0.981855 0.998631 P1 143.6185 1.00000 0.00000 0.0000 0.0000 0.998632 1.001369 S1 3.3961 1.00002 0.00001 -0.0021 0.0008 1.001370 1.004107 K1 433.9797 1.00000 0.00000 0.0000 0.0000 1.004108 1.006845 PSI1 3.3977 1.00001 0.00001 0.0002 0.0005 1.006846 1.023622 PHI1 6.1807 1.00000 0.00001 0.0000 0.0003 1.023623 1.057485 J1 24.2748 1.00000 0.00000 -0.0003 0.0001 1.057486 1.470243 OO1 13.2799 1.00000 0.00000 -0.0006 0.0001 1.470244 1.880264 2N2 10.1612 0.99999 0.00000 0.0006 0.0001 1.880265 1.914128 N2 63.6222 1.00000 0.00000 0.0000 0.0000 1.914129 1.950419 M2 332.2900 1.00000 0.00000 0.0000 0.0000 1.950420 1.984282 L2 9.3932 1.00000 0.00000 0.0000 0.0001 1.984283 2.002736 S2 154.5844 1.00000 0.00000 0.0000 0.0000 2.002737 2.451943 K2 42.0094 1.00000 0.00000 -0.0001 0.0000 2.451944 3.381478 M3 4.3445 1.00000 0.00000 -0.0001 0.0000 3.381379 4.347615 M4 0.0527 0.99988 0.00001 -0.0174 0.0006 4.347616 7.000000 M5M6 0.0006 0.99990 0.00090 0.0076 0.0517 Adjusted TSCHEBYSCHEFF polynomial bias parameters : block degree bias stdv. 1 0 203.610176 nm/s**2 0.000024 nm/s**2 1 1 0.002443 nm/s**2 0.000043 nm/s**2 1 2 0.000009 nm/s**2 0.000018 nm/s**2 Standard deviation of weight unit: 0.001 Degree of freedom: 70077 Max. correlation: 0.866 bias 1 1 with Y-wave-SA Standard deviation: 0.001 nm/s**2 Routine GEOEXT. Execution time= 2531.410 sec

The earth tide data processing package ETERNA 3.30 is available to anybody; the package should however not be copied and given to third parties by any user. In order to cover the expenses for copying and distributing the ETERNA 3.30 package, a fee of US $ 300,- has to be charged to university and research institutes. The program files, data files and result files are distributed on one CD-rom together with a manual. All programs can be executed on an IBM-AT compatible personal computer 80386/387 upwards under MS-DOS operating system. Requests for the ETERNA 3.30 package should be submitted to:

- Prof.Dr.-Ing H.-G. Wenzel,

Observatorium Schiltach,

Universität Karlsruhe,

Englerstr. 7,

D-76128 KARLSRUHE,

Germany.

FAX: ++49-721-694552.

e-mail: wenzel@gik.bau-verm.uni-karlsruhe.de

Please use the order form given below for your conveniance.

Order form for the ETERNA 3.30 package
I hereby order the ETERNA 3.30 package for scientific use only
in my university or research ____ I have added an international bank cheque of US
$ 300,- payable to Baden-Württembergische ____ I have transferred US $ 300,- to Baden-Württembergische
Bank Karlsruhe, account no. Name: ____________________________________________________________________ Institute: ____________________________________________________________________ Street: ____________________________________________________________________ City: ____________________________________________________________________ Country: ____________________________________________________________________ Phone: ____________________________________________________________________ FAX: ____________________________________________________________________ e-mail: _____________________________________________________________________ Signature: _______________________________________________________ Please send this form back to: Prof.Dr.-Ing. H.-G. Wenzel, |

The implemenatation of the Hartmann and Wenzel (1995) tidal potential catalogue into the ETERNA 3.30 package was the final stroke under a four years project to improve the accuracy of the available tidal potential catalogues. We have now in our hands several tools to process earth tide data with very low model tide errors below 1 ngal. We believe that a substantial improvement with respect to accuracy, flexibility and operational comfort has been achieved compared to previous versions of the ETERNA package. ETERNA 3.30 is currently the only earth tide data processing package with a model tide accuracy better than 1 ngal.

Data and programs used in the ETERNA 3.30 package have been supplied by O. Francis and F. Roosbeek (Observatoire Royal de Belgique, Bruxelles), T. Hartmann (Institut für Theoretische Astrophysik, Universität Tübingen/Germany), International Earth Rotation Service, Paris/France, B. Richter (Institut für Angewandte Geodäsie, Frankfurt a.M./Germany), E.M. Standish (Jet Propulsion Laboratory, Pasadena/USA), Q. Xi (Center for Analysis and Prediction, State Seismological Bureau, Beijing/China), and Y. Tamura (National Astronomical Observatory, Mizusawa/Japan). This is gratefully acknowledged.

- Büllesfeld, F.-J. (1985): Ein Beitrag zur harmonischen Darstellung des gezeitenerzeugenden Potentials. Deutsche Geodätische Kommission, Reihe C, Heft Nr. 314, München 1985..
- Cartwright, D.E. and A.C. Edden (1973): Corrected tables of tidal harmonics. Geophysical Journal of the Royal Atsronomical Society, vol. 33, 253-264, Oxford 1973.
- Cartwright, D.E. and R.J. Tayler (1971): New computations of the tide generating potential. Geophysical Journal of the Royal Astronomical Society, vol. 23, 45-74, Oxford 1971
- Chojnicki, T. (1973): Ein Verfahren zur Erdgezeitenanalyse in Anlehnung an das Prinzip der kleinsten Quadrate. Mitteilungen aus dem Institut für Theoretische Geodäsie der Universität Bonn Nr. 15, Bonn 1973.
- Doodson, A.T. (1921): The harmonic development of the tide generating potential. Proceedings of the Royal Society (London), Series A 100, 306-328. Reprint in International Hydrographic Revue, vol. 31, No. 1, Monaco 1954.
- Hartmann, T. and H.-G. Wenzel (1995a): The HW95 tidal potential catalogue. Geophysical Research Letters, vol. 22, no. 24, 3553-3556, 1995.
- Hartmann, T. and H.-G. Wenzel (1995b): Catalogue HW95 of the tide generating potential. Bulletin d'Informations Mareés Terrestres, vol. 123, 9278-9301, Bruxelles 1995.
- Roosbeek, F. (1996): RATGP95: An analytical development of the tide generating potential. Paper submitted to Geophysical Journal International.
- Schüller, K. (1976): Ein Beitrag zur Auswertung von Erdgezeitenbeobachtungen. Deutsche Geodätische Kommission, Reihe C, Nr. 227, München 1976.
- Schüller, K. (1977a): Standard tidal analysis and its modification by frequency domain convolution. Proceedings of the 8th International Symposium on Earth Tides, Bonn 1977.
- Schüller, K. (1977b): Tidal analysis by the hybrid least squares frequency domain convolution method. Proceedings 8th International Symposium on Earth Tides, Bonn 1977.
- Schüller, K. (1986): Simultaneous tidal and multi-channel input analysis as implemented in the HYCON-method. Proceedings 10th International Symposium on Earth Tides, 515-520, Madrid 1985. Consejo Superior de Investigaciones Cientificas, Madrid 1986.
- Schwiderski, E. (1980): Ocean tides, part I: Global ocean tidal equations. Part II: A hydrodynamical internpolation model. Marine Geodesy, vol. 3, 161-255, 1980.
- Tamura, Y. (1987): A harmonic development of the tide-generating potential. Bulletin d'Informations Mareés Terrestres, vol. 99, 6813-6855, Bruxelles 1987.
- Vetter, M. and H.-G. Wenzel (1995): PREGRED - an interactive gravphical editor for digitally recorded data. Bulletin d'Informations Mareés Terrestres, vol. 121, 9102-9107, Bruxelles 1995.
- Wenzel, H.-G. (1976a): Some remarks to the analysis method of Chojnicki. Bulletin d'Informations Mareés Terrestres, vol. 73, 4187-4191, Bruxelles 1976.
- Wenzel, H.-G. (1976b): Zur Genauigkeit von gravimetrischen Erdgezeitenbeobachtungen. Wissenschaftliche Arbeiten der Lehrstühle für Geodäsie, Photogrammetrie und Kartographie an der Technischen Universität Hanover Nr. 67, Hannover 1976.
- Wenzel, H.-G. (1977): Estimation of accuracy for the earth tide analysis results. Bulletin d'Informations Mareés Terrestres, vol. 76, 4427-4445, Bruxelles 1977.
- Wenzel, H.-G. (1993): Tidal data processing on a personal computer. Proceedings 12th International Symposium on Earth Tides, 4 - 8 August 1993, 235-244, Beijing 1993.
- Wenzel, H.-G. (1994b): PRETERNA - a preprocessor for digitally recorded tidal data. Bulletin d'Informations Mareés Terrestres, vol. 118, 8722-8734, Bruxelles 1994.
- Wenzel, H.-G. (1994c): Earth tide data processing package ETERNA 3.20. Bulletin d'Informations Mareés Terrestres, vol. 120, 9019-9022, Bruxelles 1994.
- Wenzel, H.-G. (1995): Format and structure for the exchange of high precision tidal data. Bulletin d'Informations Mareés Terrestres, voll 121, 9097-9101, Bruxelles 1995.
- Wenzel, H.-G. (1996a): Accuracy assessment for tidal potential catalogues. Bulletin d'Informations Mareés Terrestres, vol. 124, 9394-9416, Bruxelles 1996.
- Wenzel, H.-G. (1996b): The nanogal software: Earth tide data processing package ETERNA 3.30. Bulletin d'Informations Mareés Terrestres, vol. 124, 9425-9439, Bruxelles 1996.

President IAG Earth Tide Commission

Geodätisches Institut

Universität Karlsruhe

Englerstr. 7

D-76128 KARLSRUHE

Germany

FAX: ++49-721-694552

e-mail: wenzel@gik.bau-verm.uni-karlsruhe.de

URL: http//www-gik.bau-verm.uni-karlsruhe.de/~wenzel/

This page has been established in HTML 3.2 in August 1997 by Hans-Georg Wenzel and is still in progress.