Tsoft: graphical and interactive software for the analysis of time
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1. u7 1 m k 1 p with their es timated error and the residual standard deviation are displayed in the text output window and can be exported in a text file In addition two new channels are created 1 The fit to the objective channel fit 2 The residuals of the fit objective channel minus the fit result resid 9 3 1 Advanced applications of multiple LSQ fits The specific tool dedicated to the computation of the vertical gravity gradient using spring gravimeter measurements is based on the multilinear least squares fit the gravity is the objective channel and the component channel is the levels where measure ments are made It is possible to fit a temporal drift linear quadratic etc as well as height dependence M Van Camp P Vauterin Computers amp Geosciences 31 2005 631 640 639 Start 25 03 1998 O7h00m05s Incr 10 000s x 48701 pts Duration 5 63669 days 25 03 1998 16h18m45 000s 106 75249 nm s IDX_YR 722992 Schiltach E FFT Spectrum Hz ET 19 tide _J j1 Caldata nm s o E Text output Exi Finished reading 48701 da Interval 720 gt 29230 28 Mean value of data points Creating Hanning window 8 di weight 350330860 0000023 F calling FFT 00h00m00s 26 03 98 0h00m00s 0h00m00s 00h0Om00s 27 03 08 28 03 082. fA c etme membach travai S21 MBO303T 04 TSF S21 MB0304T 0 TSF S21 MBO0305T 0 TSF S21 MBO306T OP TSF c etme membach travail S21 tusts tsf H GWRCO21 ST2 5 IERS 4 polar motion acc Ef Theoy 01 01 01 28 10 02 03 TIMESHIFT 30 06 1998 0Oh00m00s 9 9 27 11 02 03 L INSTALL 30 06 1998 00h00m00s Membach GGP 28 12 02 03 COMMENT 30 06 1998 11h00m00s New GGP card 28 01 03 I STEP 27 02 1999 10h00m00s 1 42000e 001 28 01 03 I STEP 06 07 1999 10h00m00s 1 20200e 002 25 02 03 I STEP 07 09 1999 00hS9m00s 1 77000e 002 25 02 03 I STEP 07 10 1999 10h00m00s 1 95100e 001 28 03 03 I STEP 03 07 2000 21h00m00s 4 61000e 001 27 04 03 I STEP 20 09 2000 0Sh00m00s 1 20000e 001 28 05 03 E STEF 14 11 2000 13h00m00s 1 26000e 001 28 05 03 T STEP 13 12 2001 12h00m00s 1 72800e 001 I STEP 26 04 2002 09h00m00s 1 80000e 001 F STEP 20 06 2002 11h00m00s 2 90000e 001 T STEP 22 07 2002 07h50m00s 1 31000e 001 T STEP 30 07 2002 16h00m00s 2 02000e 001 I STEP 15 10 2002 10h00m00s 7 70000e 000 I STEP 07 05 2003 OShO0m00s 2 90000e 001 COMMENT 07 05 2003 12h00m00s LHe filling Fig 4 Instrument database At bottom of window there is a time bar where files and events are marked 9 2 Spectral analysis Tsoft calculates spectra and presents the amplitudes in a linear or logarithmic plot with frequencies in hertz or cycles per day Fig 5 The software uses FFT to calculate the spectrum padding the data with cons
3. eos ELSEVIER Computers amp Geosciences 31 2005 631 640 COMPUTERS GEOSCIENCES www elsevier com locate cageo Tsoft graphical and interactive software for the analysis of time series and Earth tides Michel Van Camp Paul Vauterin Royal Observatory of Belgium Avenue Circulaire 3 BE 1180 Brussels Belgium Received 23 January 2004 received in revised form 22 November 2004 Abstract We present Tsoft a graphical interactive analysis software package originally dedicated to the analysis and processing of gravity time series Tsoft can also be used to process and analyze all sorts of time series like seismic or other environmental signals The Tsoft approach has a number of important advantages in the area of pre treatment of the data correction of artefacts such as spikes and steps because the user can always inspect what happened and intervene manually The graphical environment is also very convenient for the detection isolation and analysis of events e g earthquakes Lastly errors in the analysis path are easily detected because the software shows a graphical representation of the results at each stage of the analysis In this article we describe first the general data structure and the possible data manipulations and computations Then we present the correcting tools dealing with unwanted steps spikes and gaps in raw data Afterwards we describe the module dedicated to the computation of tidal si
4. 2 a linear interpolation is created using the value of P1 at the start of the gap together with the value of P2 at the end of the gap 5 If T 3 a third degree polynomial interpolation is created using the value of P1 at the start of the gap and its first derivative together with the value of P2 at the end of the gap and its first derivative 7 3 Steps detection The algorithm uses the following set of parameters which can be chosen by the user D the minimum deviation W the window size V the exclude window size Suppose that A are the data points i ranging from 0 to n 1 1 At each point p of the curve a multilinear regression is performed using a first degree polynomial and a step function S t S t 0 5 for points to the left of pj and S t 0 5 for the other ones This fit is performed inside a window of 2W 1 points around the point p excluding a small window of 2V 1 points around p This exclusion window is used to disregard intermediate points when a step is occurring rather slowly The regression coefficient of S is stored in a temporary channel B 2 All the zones where B gt D are identified Each zone is enlarged with an envelope of W points because each step causes side lobes in B with negative signs and overlapping zones are merged 3 For each zone a step corrector is created having a step value which is the maximum of B inside that zone 8 Computing tides
5. 29 03 08 Fig 5 Amplitude spectrum and recording of LaCoste Romberg spring gravimeter ET 19 measuring at Black Forest observatory BFO Germany Spectrum calculated on active data only in black inactive data are in grey from 5h50 to 85h after 1998 03 25 Balleny Island Earthquake from Van Camp 1999 only linear or quadratic The text output window gives the gradient at the levels of 65 and 90cm required by absolute gravity measurements Vitush kin et al 2002 if the height dependence is quadratic and statistical information Tsoft also provides a very useful tool the Moving Window Multilinear Least Squares fits Here a window of length moves through the time axis of the data set by successive shifts of length ts tw and ts being chosen by the user A multilinear regression is performed for every window and the coefficients varying in time are available in new channels Moreover the possibility is offered to apply a frequency filter on the data before performing the regressions In many cases the regression coefficient of a component channel is frequency dependent There fore Tsoft provides a frequency dependent multi linear least squares fit The idea is to apply to all channels a set of narrow FFT or LSQ band pass filters over a range of frequencies The different values of the coefficients corresponding to different frequencies then reflect the dependency on the frequency These last two applicati
6. analysis processes or causes a large gap after decimating the data due to the anti aliasing filter Therefore it is usually preferable to correct events by interpolating the data at least for short time periods Tsoft unifies two approaches for the correction of perturbations On the one hand the programme auto matically searches for perturbations in the signal and proposes corrections but on the other hand the user can inspect and modify the proposals before applying them For this purpose Tsoft uses the concept of corrector They can be of four types 1 linear interpolations replacing the data points during a certain time interval by a linear function 2 cubic spline interpolations replacing the data by a third degree polynomial 3 steps using a constant value to all data points after a given moment in time or 4 gaps removing all points during a certain time period In the last case gaps are considered as undetermined values in the data files In the first step Tsoft searches for the irregular events corresponding to the parameters and detection threshold given by the user and it creates a corrector for each event detected The correctors still in an unapplied state can be inspected visually and modified by the user who can also add or delete some and finally instruct Tsoft which ones are to be applied or not The information contained in the correctors is saved as metadata in the file allowing the user to investiga
7. and tidal residuals 8 1 Computing tides The Sun and the Moon exert tidal accelerations with maximal peak to peak amplitudes of 2500 nm s 1 nm s 11Gal This is the most important signal affecting gravity measurements if we exemt transient seismic perturbations The calculation of tidal phenomena requires a representation of the tidal potential which is based on the relative position of the Moon the Sun and the planets Wenzel 1996a As the Earth is not a homogeneous and perfectly rigid body it reacts to the astronomical forcing in a complex way The response of the Earth to this excitation can be separated in deformations the body tides changes in the Earth s orientation in space forced nutation and precession and changes in the Earth s rotation rate Wahr 1981 Some of the most important tidal parameters are the frequency dependent tidal gravimetric factor 6 and the phase lead x In the frequency domain 6 is the transfer function between the tidal force exerted along the perpendicular to the ellipsoid and the tidal gravity changes along the vertical as measured by a gravimeter Dehant et al 1999 It depends on the direct attraction of the celestial bodies on the Earth s deformation and on the con secutive mass redistribution inside the Earth The lead K represents the phase difference between the observed wave and the astronomical wave A perfectly elastic Earth model provides 6 1 16 and x 0 Tidal parameter s
8. cut off frequency and the band width The algorithm includes the following steps 1 the FFT transform of the signal is calculated 2 this transform is multiplied by a given filter response function in the frequency domain 3 the resulting transform is transformed back into the time domain As each point of the filtered signal depends on all points of the filtered channel the results are slightly influenced by the limitations in time of the series and by the presence of gaps Therefore the FFT filter should not be used as anti aliasing filter in the routine decimation of the data but rather as a powerful tool for analysis and investigation of the data M Van Camp P Vauterin Computers amp Geosciences 31 2005 631 640 633 5 2 LSQ filter The principle of the LSQ approach is to find a transfer function which minimizes the total approximation error This error is calculated from the difference between the actual and the desired brick wall filter impulse response in the time domain Bloomfield 1976 Two parameters must be provided the cut off frequency and the number of points of the filter Provided they are carefully chosen the Gibbs s phenomenon affecting the transfer function overshoot and ripples on either side of the cut off frequency can be greatly reduced Because of its very good frequency response properties the LSQ filtering is an appropriate choice as an anti aliasing filter to decimate a signal F
9. oma be SEISMO TSOFT tsoft html possible Different sub windows are also opened when needed Moreover the user can specify active and inactive data using the mouse most of the calculations performed by Tsoft acts only on the active part of the activated channel The results of the calculations can be exported in a text file 4 Operations on channels The user can manipulate the channels easily rename delete create duplicate and assign to a channel the result of arithmetical expressions containing standard operators and functions and wherein the other channels can be operands A channel can contain gaps or missing values and Tsoft has the advantage to handle them in an easy and consistent way the result of operations with these missing or undetermined values is simply undetermined allowing further computa tions without producing errors Beside arithmetical operations Tsoft can also apply time shifts to a channel and compute time integrations and derivatives the results are stored in a new channel 5 Filtering channels FFT LSQ and butterworth filters Tsoft offers one filter applied in the frequency domain Fast Fourier Transform FFT filter and two in the time domain Least Squares LSQ and 2 poles Butter worth filters For all types low pass high pass and band pass filters are available 5 1 FFT filter For the finite impulse response FIR FFT filter the user enters two parameters the
10. 1 Calibrations transfer function instrument oriented data base Tsoft includes a database which simplifies the organization of the different files containing recordings Location Synthetic tide Type B vesuvio Napoli Schiltach B strasbourg bUccle Membach Brenna S WDD Solid Borean Z GWR CO21 Solid OceanLoad Fig 2 Location data base used to calculate synthetic tides Each station is described by a text identification longitude latitude and elevation Right pane of window shows tidal parameter sets that have been inserted for currently selected station here Membach New stations and tidal parameter sets can be created or modified by simple clicking in menu M Van Camp P Vauterin Computers amp Geosciences 31 2005 631 640 637 Start 02 05 2003 23hS9m00s Incr 10 000s x 69120 pts Duration 8 00000 days 04 05 2003 10h58m50 000s 3000 201 82094 nm s 2 t IDX_YR 1066672 DRE ae Membach GWRCO21 M1 Vgrav nm s 2 W2 airpressure hPa H MMS Vgravresid cor nm s 2 Theory WES instrtide_ggp nm s 2 P OOAOOTOO zhOOm00 0OhGOm00 p0m00 06 05 03 06 05 03 07 05 0 07 05 0 F
11. 3 6855 Van Camp M 1999 Measuring seismic normal modes with the GWR C021 superconducting gravimeter Physics of the Earth and Planetary Interiors 116 81 92 Van Camp M Wenzel H G Schott P Vauterin P Francis O 2000 Accurate transfer function determination for superconducting gravimeters Geophysical Research Letters 27 1 37 40 Van Dam T M Francis O 1998 Two years of continuous measurements of tidal and nontidal variations of gravity in Boulder Colorado Geophysical Research Letters 25 3 393 396 Vauterin P 1998 Tsoft graphical and interactive software for the analysis of Earth tides data In Proceedings 13th International Symposium on Earth Tides Observatoire Royal de Belgique Serie Geophysique Brussels pp 447 454 Venedikov A P Arnoso J Vieira R 2001 Program VAV 2000 for tidal analysis of unevenly spaced data with irregular drift Journal of the Geodetic Society of Japan 47 1 281 286 Vetter M Wenzel H G 1995 PREGRED an interactive graphical editor for digitally recorded tidal data Bulletin d Information des Mar es Terrestres 121 9102 9107 Vitushkin L Becker M Jiang Z Francis O van Dam T M Faller J Chartier J M Amalvict M Bonvalot S Debeglia S Desogus S Diament M Dupont F Falk R Gabalda G Gagnon C G L Gattacceca T Germak A Hinderer J Jamet O Jeffries G Kater R Kopaev A Liard J Lindau A Long
12. d helium filling These gravity residuals are calculated from gravity data shown on Fig 3 M Van Camp P Vauterin Computers amp Geosciences 31 2005 631 640 635 5 For each interpolation the maximum deviation from the interpolation dmax is calculated as well as the absolute value of the difference between the start and end points ds If dmax ds lt F the interpolation is rejected because it rather resembles a step 7 2 Gaps detection The algorithm uses the following set of parameters which can be chosen by the user The interpolation type T which can be l straight connection of points using a linear interpolation 2 using a linear interpolation on fitted points 3 using a cubic interpolation on fitted points W the window size d the polynomial degree L the maximum gap length in data points Suppose that A are the data points i ranging from 0 ton 1 1 All the gaps are detected 2 If T 1 the last point before each gap and the first point after it are used to create linear interpolations and the algorithm stops 3 If T gt 1 for each gap two polynomials of degree d are fitted one called P1 on the last W points before and another called P2 on the first W points after the gap If one of the polynomials cannot be fitted e g because the gap occurs at the end of the file it is assumed to have a constant value which is equal to the closest value of the other polynomial 4 If T
13. data are mostly interdependent Tsoft is a powerful tool as it allows general manipulations of the data channels such as the possibility to easily fill a particular channel with a mathematical expression of the other data channels Moreover this software provides a wealth of common signal processing applications as well as advanced ones especially dedicated to gravity data On the other hand Tsoft is also dedicated to the correction of raw data The possibility to intervene manually in an automatic data correction system is a prerequisite for any high quality data processing meth od because there will always be perturbations in complex situations that are not handled correctly by automatic algorithms In Tsoft this manual intervention is as convenient and as flexible as possible Moreover the software allows one to re inspect and re edit the corrections at any time as these are saved together with the data In addition it contains advanced calibration routines which can handle any general time dependent nonlinear calibration factors Acknowledgments We are grateful to Marc Hendrickx for his fruitful comments and suggestions We thank Henri Martin for helping us in the C programming We are indebted to Olivier Francis for his fruitful collaboration concern ing the tidal tools and to the Tsoft users for their numerous suggestions and their patience References Baker T Bos M S 2003 Validating Earth and ocean tide model
14. ets and x can be deduced from observations or numerical models for each frequency of the tidal force Tsoft uses the Tamura 1987 potential catalogue containing 1200 waves and is accurate to a 0 6nm s maximum error in time domain Wenzel 1996b Roosbeek 1996 This widely fulfils the accuracy requirements to correct gravity measurements even from superconducting gravimeters Francis 1997 Van 636 M Van Camp P Vauterin Computers amp Geosciences 31 2005 631 640 Dam and Francis 1998 For a given location Tsoft can compute the time series from a tidal parameter set provided either by the user e g after performing a tidal analysis on gravity recordings or by Earth models Tsoft itself can provide accurate frequency dependant tidal parameter sets from the Wahr Dehant latitude dependent model Dehant et al 1999 taking into account the nearly diurnal free wobble the inertial effect the Coriolis force the Earth s flattening and anelasticity The problem is complicated however by the ocean tides which cause additional variations of g at the same frequencies but with different phases than the Earth tide For example this ocean tide attraction and loading effect reaches several Gal in amplitude for the M2 semi diurnal wave in Western Europe Accurate models provide now specific tidal parameter sets corresponding to the ocean tides effect In the near future we plan to include a tool in Tsoft that will calculate these
15. gnals Lastly we give an overview of the most used computing tools like spectral analysis and multilinear least squares fit 2004 Elsevier Ltd All rights reserved Keywords Time series analysis Signal processing Environmental data Tides Gravity 1 Introduction Since 1997 the Royal Observatory of Belgium has developed a graphical and interactive analysis software package called Tsoft Vauterin 1998 It is dedicated to the analysis of time series with a special stress on some geophysical e g gravity and environmental data Code available from server at http www iamg org CGE ditor index htm or from http www astro oma be SEISMO TSOFT tsoft html Corresponding author Tel 3223730265 fax 322 373 0339 E mail address mvc oma be M Van Camp Applied Maths BVBA Keistraat 120 BE 9830 Sint Martens Latem Belgium The user visualizes the data graphically at each stage of the processing and is therefore able to work in a fully interactive way This methodology supported by the graphic capabil ities of the software makes it possible to detect isolate and analyze special events in the series e g seismic free oscillations in gravity or seismic data It also allows the user to detect possible errors early in the analysis path Tsoft contains a large set of numerical analysis tools like FFT spectrum calculation low high and band pass filters multilinear regressions determination of
16. ig 3 Calculation of gravity residuals shown in Fig 1 Up raw calibrated gravity recording black and synthetic tide signal grey Middle barometric recording Bottom gravity residual obtained by removing from raw data synthetic tidal signal and barometric signal multiplied by a linear admittance factor of 3 3nms 7hPa This value was determined by simultaneously fitting tidal parameters and local air pressure in a least squares adjustment Francis et al 2004 from various instruments as well as some other important parameters such as calibration information The instrument database may contain five different types of information related to an instrument installa tions calibrations time shifts steps and file information Fig 4 Installations contains the instrument and location names the data and the time Calibration allows one to apply time dependent calibration using a nonlinear calibration function Each time an instrument has been calibrated the user can enter its calibration function into the software s data base in the form of a general mathematical expression A cubic spline interpolation between these known points is then applied in order to perform a time dependent calibration of each individual data point Time shift deals with time dependent shifts which may be due to instrumental instabilities or to timing errors e g a drifting clock Whenever the exact shift of an instrument was de
17. ing parameters which can be adjusted by the user D the minimum deviation a spike should have out of the calculation W the window size 3 All the zones on the channel where 4 B gt D are E the spike envelope searched on the signal Each individual zone is F the minimum spike slope ratio enlarged at both edges with a number of points E If two zones turn out to be neighbouring or even Suppose that 4 are the data points i ranging from 0 overlapping they are merged into one single larger to n 1 zone 4 For each zone a linear interpolation corrector is 1 A low pass filter FL is applied to the data points created covering the whole zone using the values of This filter has a total length of 2W 1 and has B at both ends Start 02 05 2003 23h59m00s Incr 10 000s x 69120 pts Duration 8 00000 days 04 05 2003 19h54m20 000s 886 47951 nm s 2 IDX_YR 1069885 Membach GWRCO21 M1 Vorav nm s 2 EM 2 airpressure hPa M4 Vorav resid raw nm s 2 EMH 3 instrtide_gop nm s 2 oonodmoos i 00h00m00s f 00h00m00s 06 05 03 07 05 03 08 05 03 Fig 1 Computer display of GWR C021 gravity residuals and some correctors before grey and after black application of correctors Left cubic spline interpolation applied to remove earthquake effects Middle left and right linear interpolations Middle right corrected step induced by a liqui
18. nction of superconducting gravimeters using step func tions Van Camp et al 2000 Another possibility to investigate the amplitude response is to apply the filter on a Gaussian white noise which can be generated by Tsoft and then to apply the spectral analysis tool 6 Changing data frames The sample frame can be shifted and its sample rate can be changed If the new sampling interval is longer than the original one decimation Tsoft proposes to apply a LSQ filter necessary to avoid aliasing Bloomfield 1976 Another possibility is Cumulative which adds all the data included in the new sampling interval This is useful e g to decimate rainfall data On the other hand if the time interval becomes smaller oversampling a linear or cubic interpolation is used to create new points 7 Correctors Raw time series such as long period seismic or gravity recordings can contain undesired events such as spikes steps or gaps missing data Other events with a geophysical origin such as earthquakes recorded in gravity or long period seismic measurements can also cause severe deviations and saturations of the signal for periods up to a few hours Whether they are due to instrumental problems or have a geophysical origin these events may corrupt further signal analyses More over in most circumstances one cannot just replace the undesired event with missing data A gap even one single value also severely corrupts frequency
19. ons of multi LSQ fits proved to be very useful in gravimetry They can be applied to study the influence of environmental parameters such as the effect of the local air pressure admittance on gravity data and its time or frequency dependence Also the variability of the sensitivity of a gravimeter and its phase lag can be controlled by fitting the observed tide to a synthetic tide and its time derivative 9 4 Other time tools It is possible to calculate the first derivative and time integration of a channel with respect to the time The result is stored in a new channel The Time shift tool shifts the highlighted channel in time over a specified number of seconds The software also calculates the time correlation between two channels using the least squares fit this is useful to search the time delay between two channels One channel is time shifted from to and for each step a correlation coefficient is calculated All these coefficients are plotted in a graph A dialog box prompts for and t 640 M Van Camp P Vauterin Computers amp Geosciences 31 2005 631 640 Finally it is possible to draw a histogram and to obtain the mean the standard deviation and the intervals where 68 95 5 and 99 7 of the results lie 10 Conclusions Tsoft is a graphical and interactive software for the processing of time series like seismic gravity tempera ture pressure or water levels recordings As these environmental
20. or example before the decimation of a 1 min sample interval to a 1 h sample interval a LSQ filter with cut off frequency of 12 cycles per day and window size of 480 points can be applied This filter has a total length of 16h and the frequency response curve deviates in the tidal frequency band by less than 0 05 from unity 5 3 Butterworth filter The Infinite Impulse Response IIR Butterworth filter has an overall monotonic response decreasing smoothly Kulhanek 1976 The amplitude response does not have any ripple either inside or outside the pass band However the causal Butterworth filter has nonlinear phase but does not cause any time delay this is very useful when measuring seismic phase arrival times Scherbaum 2001 but not suitable for tidal analysis as measuring the phases of the different tidal waves is important to evaluate recent Earth models Van Camp et al 2000 Baker and Bos 2003 For this purpose non causal FIR filters are preferred because they do not cause any phase distortions of the signal and produce a constant time shift over the whole frequency band which can be accounted for Designing filters is beyond the scope of Tsoft for detailed studies one should use another software like MATLAB However Tsoft allows the user to check the filter transfer functions easily by creating a step function applying the filter and using the transfer function command the latter was used to determine the transfer fu
21. s using tidal gravity measurements Geophysical Journal International 152 468 485 Bloomfield P 1976 Fourier Analysis of Time Series An Introduction Wiley New York 258pp Dehant V Defraigne P Wahr J M 1999 Tides for a convective Earth Journal of Geophysical Research 104 B1 1035 1058 Francis O 1997 Calibration of the C021 superconducting gravimeter in Membach Belgium using 47 days of absolute gravity measurements International Association of Geo desy Symposia vol 117 Springer Berlin pp 212 219 Francis O Van Camp M van Dam T Warnant R Hendrickx M 2004 Indication of the uplift of the Ardenne in long term gravity variations in Membach Belgium Geophysical Journal International 158 346 352 Harnisch M Harnisch G 1997 Longtime behaviour of superconducting gravimeters derived from observed time series Bulletin d Information des Mar es Terrestres 127 9796 9805 Kulhanek O 1976 Introduction to Digital Filtering in Geophysics Elsevier Amsterdam 168pp Roosbeek F 1996 RATPG95 a harmonic development of the tide generating potential using an analytical method Geophysical Journal International 126 197 204 Scherbaum F 2001 Of Poles and Zeros Fundamentals of Digital Seismology second ed Kluwer Academic Publish ers Dordrecht 265pp Tamura Y 1987 A harmonic development of the tide generating potential Bulletin d Information des Mare es Terrestres 99 681
22. sets using the Schwiderski FES CSR GOT NAO or TPX models Baker and Bos 2003 A location database included in Tsoft can store for each station its location multiple tidal parameter sets as well for solid Earth as for ocean loading Fig 2 8 2 Calculation of tidal residuals Thanks to its ability to compute accurate tides Tsoft is very useful to correct gravity recordings from the tidal B Location database File Location Theotide signal which is useful e g for field gravity measure ments study of the Earth s free oscillations or to apply the remove restore technique In this technique well known signals of large amplitude computed synthetic tide and air pressure effects are first removed from the gravity signal producing a residual signal where very small events at the nm s level steps spikes gaps can easily be isolated and corrected see Section 7 The removed signals are then restored to the cleaned residuals Fig 3 The successive steps of this procedure can be automated within a single script making Tsoft a very powerful tool to compute gravity residuals and clean them The data produced in this way may be used for the study of the residuals such as the long term gravity trend or for Earth tides analyses Notice that Tsoft does not perform any tidal analysis for which one should use specific softwares like ETERNA Wenzel 1996a or VAV 2000 Venedikov et al 2001 9 Computing tools 9
23. tant values up to a power of 2 and using multiple Hanning Parzen or Square window functions Bloomfield 1976 It is also possible to calculate phase and power spectra In addition one can compute a series of spectra corresponding to a series of time windows of duration tw moving successively all over the length of the selected channel with a fixed time shift ts ftw and t being determined by the user The result is a frequency against time array plot where colours represent the amplitude of the frequency and refer to an adjustable scale included in the sub window 9 3 Multilinear least squares fits The aim of this fit is to try to express an objective channel choj as a linear combination of a set of m component channels ch and their power n so that the square of the residuals R t is minimized m n P chopj t gt 5 aychc 5 byt R t j l i l k 0 where che is the jth channel at the power i by default n 1 The drift polynomial eg can be expressed as a linear combination of orthogonal Chebycheff polynomials This alternative returns the same drift result but it is highly recommended for high degrees p gt A4 because it drastically improves the stability of the LSQ fit The users choose the power n for the channel and the degree p and type Chebycheff or not of the polynomial time drift Upon completion of the calculations the correlation matrix the fit coefficients of each component i e a and b i 1
24. te the correction process again and if necessary to re edit the applied corrections in the future The advantage of this method is to offer a fast objective way of processing the data while the user still keeps full control over the adjustments made and can at any moment override them manually This is very important because there will always be strong perturbations in 634 M Van Camp P Vauterin Computers amp Geosciences 31 2005 631 640 complex situations that are not handled correctly by no coefficients that decrease linearly towards the end interactive automated algorithms Vetter and Wenzel e g for W 5 the filter points are 1 25 2 25 3 25 1995 Harnisch and Harnisch 1997 Fig 1 shows an 4 25 5 25 4 25 3 25 2 25 and 1 25 These example of some correctors on the superconducting filtered data points are stored in an intermediate gravimeter GWR C021 recording Francis et al 2004 channel Bj in an un applied then in an applied state 2 For each point i where the absolute value A B gt D A is replaced by B The same filter FL is applied a second time on A and the result is again stored in B This complete manipulation is repeated twice which proved to be sufficient to have a good convergence The reason for this step is that very aberrant points could bias the low pass channel B too much Using this step the spikes are already left 7 1 Spikes detection The detection method uses the follow
25. termined the user can enter the corresponding value in the data base A cubic spline interpolation is applied on these points in order to obtain the phase shifts in between The programme further applies this time dependent shift to the observa tional data points by shifting each point over the appropriate time interval Of course this time shift will in general not be an integer multiple of the sampling interval Therefore a quadratic interpolation is used in order to get values between the sampled points Steps allows one to store the steps that occurred on a data channel by specifying the instrument and measurements the data and the step value Finally File information contains for a given instrument and measurement a list of the relevant data files 638 M Van Camp P Vauterin Computers amp Geosciences 31 2005 631 640 Database oj x File Event f GWRCO21 fy GWRC021 521 ait pressure Se Varav y E a Varav cor 10s nm s 2 3600s nm s 2 A BOs nm s 2 Ha Vgrav resid corr fe Vgrav resid Hraw fa GWRCO021 ST1 c etme membach travai S21 MB0211T0 TSF c etme membach travail S 21 MB0212T0 TSF fl c etme membach travail c etme membach travail H c etme membach travail S21 MBO0301TO TSF S21 MB0302T 04 TSF S21 MB0302T0 TSF Bid c etmc membach travail 521 MBO303T0 TSF H c etme membach travai c etme membach travai E c etme membach travai
26. transfer functions etc Tsoft allows the user to calculate tidal parameters and synthetic tidal signals which is useful for any gravity measurements Lastly Tsoft offers the possibility to write scripts allowing one to automate and speed up routine tasks considerably 0098 3004 see front matter 2004 Elsevier Ltd All rights reserved doi 10 1016 j cageo 2004 11 015 632 M Van Camp P Vauterin Computers amp Geosciences 31 2005 631 640 Tsoft runs on PCs using Windows 95 98 2000 XP or NT This public domain software and its user manual can be downloaded freely from the Royal Observatory web site 2 Data structure and input output To a given data set there corresponds a sample frame which is a series of moments on the time scale beginning at an initial time and regularly spaced by a duration called sample rate Tsoft accepts sample rates from 0 001 s up to 69 years which is also the longest possible data series A Tsoft data set consists of several channels up to several dozens The length of the data set and therefore the number of values per channel is only limited by the memory capacities of the PC The channels are identified and sorted by location instru ment measurement and unit which refer to their data Data sets are mostly loaded from data files but it is also possible to create a data set from scratch specifying its time interval and sample rate This allows theoretical computations and is especiall
27. uevergne L Luck B Maderal N M kinen J Meurers B Mizushima S Mrlina J Newell D Origlia C Pujol E R Reinhold A Richard Ph Robinson I Ruess D Thies S Van Camp M Van Ruymbeke M de Villalta Compagni M F Williams S 2002 Results of the sixth international comparison of absolute gravimeters ICAG 2001 Metrologia 39 407 424 Wahr J 1981 Body tides on an elliptical rotating elastic and oceanless Earth Geophysical Journal of the Royal Astro nomical Society 64 677 703 Wenzel H G 1996a The nanogal software Earth tide data processing package ETERNA 3 30 Bulletin d Information des Mar es Terrestres 124 9425 9439 Wenzel H G 1996b Accuracy assessment for tidal potential catalogues Bulletin d Information des Mar es Terrestres 124 9394 9416
28. y useful to predict synthetic and theoretical Earth tides see Section 8 When loading data sets from files several formats are accepted beside its own Tsoft format TSF files in ASCH Tsoft also accepts several other formats such as GSE a standard format in seismology PR ETERNA so named from the Earth tides analysis software Wenzel 1996a widely used for gravity data and the commercial format EVT the Kinemetrics format for strong motion instruments Tsoft also accepts any ASCII free format It is also possible to append several files each to the others so that the user can gather them to form one data set When saving data sets the Tsoft format is preferred because a lot of metadata is saved over the data values identification of the channels correctors Section 7 However it is also possible to save the data into the PR ETERNA formats in order to ensure compatibility with the ETERNA software Finally one can also export the values of the selected channels only in a file of which the format is currently accepted by many graphical softwares 3 Visualization and general manipulation of files In the Tsoft application window the left pane is devoted to the metadata identification display and selection of channels while the right pane displays the curves corresponding to the data The user may act interactively in both panes and zooming in and out is Royal Observatory of Belgium 2004 http www astro
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