Estimating tides in strainmeter data ( ( )2 ( )2
Contents
1. SPAN 2171 SHIFT 2171 The program stepped through the minimizing algorithm six times Our initial value of DMIN is set to 0 05 in the input05 dat file so the program begins with a D value of 0 2 It reached a minimum value at D 7 0711E 02 and an ABIC value of 3736 17 11 89 ABIC 2 0000E 1 3741 65 ALSQE 3 75324E 3 ALNDN 2 30894E 2 ALNDTD 3 51455E 03 90 ABIC 2 8284E 1 3757 68 ALSQE 2 56940E 3 ALNDN 3 99404E 2 ALNDTD 2 76214E 03 91 ABIC 1 4142E 1 3738 07 ALSQE 5 04583E 3 ALNDN 1 22986E 2 ALNDTD 4 26696E 03 92 ABIC 1 0000E 1 3736 94 ALSQE 6 42014E 3 ALNDN 5 71691E 1 ALNDTD 5 01937E 03 93 ABIC 7 0711E 2 3736 17 ALSQE 7 84571E 3 ALNDN 1 71553E 1 ALNDTD 5 77178E 03 94 ABIC 5 0000E 2 3737 14 ALSQE 9 29865E 3 ALNDN 8 30084E 0 ALNDTD 6 52420E 03 95 96 MINIMUM ABIC 3736 17 ATTAINED AT VMIN 7 0711E 02 SD 1 6197E 01 This output06 dat file contains information on the pressure response coefficient 106 RESPONSE WEIGHTS ASSOCIATED DATASET NO 1 107 LAG 0 108 RESPC 2 57748E 01 109 ERROR 2 24831E 01 This means that at zero lag interval one millibar of pressure change induces a change of 2 57748E 01 2 24831E 01 counts of strain The phase and amplitudes of the tidal groups and the associated uncertainty follow 137 GROUP SYMBOL FACTOR RMSE PHASE RMSE AMPLITUDE RMSE 138 LOCAL LAG NEGATIVE 139 1 1 143 Q1 1 43024 0 16271 171 591 6 519 4 118 0 468 140 2 144 201 O1 1 40260 0 06474 1712. Reference Series 96 8 p 34 Pawlowicz R Beardsley B and Lentz S 2002 Classical tidal harmonic analysis including error estimates in MATLAB using T_TIDE Computers and Geosciences 28 8 929 937 Van Camp M and Vauterin P Tsoft graphical and interactive software for the analysis of time series and Earth tides Computers amp Geosciences 31 5 631 640 2005 Wenzel H G 1996 The nanogal software Earth tide data processing package ETERNA 3 30 Marees Terrestres Bulletin d Informations 124 1996 9425 9439 18 Tamura Y T Sato M Ooe and M Ishiguro 1991 A Procedure for Tidal Analysis with a Bayesian Information Criterion Geophysical Journal International 104 507 516
3. least square adjustment by minimizing equation 2 for a data set of length n n M K 2 n 5 y DJ A C B nS ini d 5 b Xix hz l T D By d 2d d f i 1 m 1 k 0 i l 2 WEIGHT An Annt B B m 2 27 1 54 3 j Vineyard amp S Frolich V wn 2 2 14 Jack Canyon 0 5 4 ES Red Hills l l l 2004 9 16 2004 9 18 2004 9 20 2004 9 22 2004 9 24 2004 9 26 2004 9 28 165 i Atmospheric pressure z 160 E S E o 5 155 _ g a T 150 _ lz 145 i r r r 2004 9 16 2004 9 18 2004 9 20 2004 9 22 2004 9 24 2004 9 26 2004 9 28 2004 9 30 Figure 1 Strain change measured by volumetric dilatometers in Parkfield September 2004 where M is a group number of tidal constituents Cm and Sm are the summation of the cosine and sine parts of each of the constituents in the m th group respectively theoretical values A and Bm are the tidal constants to be determined d is the trend x are associated data b are response weights h is step value and z is a step function whose value is zero until a step occurs and increases by one after a step D and WEIGHT are hyperparameters that are chosen to minimize ABIC BAYTAP G assumes that the trend varies smoothly and is represented by d 2d di2 u where d is the trend at observation point i and d and d are the trend values at the two preceding data points The term u represents a white noi
4. periods shorter than one year Pawlowicz R Beardsley B and Lentz S 2002 e TSOFT A windows based tidal analysis package Van Camp M and Vauterin P 2005 e ETERNA Uses the least squares method to estimate tidal parameters meteorological and hydrological responses Wenzel 1996 Runs on an MS DOS system e BAYTAP G A package that implements Bayesian statistics to estimate tidal parameters and meteorological responses Tamura et al 1991 It is written in FORTRAN77 and runs on most UNIX like systems BAYATP G is widely used in the scientific community and it is the package we will use in this course BAYTAP G In the lecture on earth tides we saw that the tides can be thought of as a series of bands or groups separated by one cycle month BAYTAP G assumes that within one group the phase and amplitude of the individual tides are constant and it is these two terms that we solve for within each group With an increasing number of data points we can resolve more groups of tides and determine a more accurate description of the tidal signal BAYTAP G assumes that a signal y can be decomposed into a tidal signal t a trend term dj perturbation term r and a random noise term e yi t d r e 1 The perturbation term or response term is the change in the signal induced by another force such as atmospheric pressure Tidal parameters the trend response terms and noise are estimated through an iterative method similar to
5. respect to the local potential and error and the amplitude and error The amplitude is in the same units as the input 105 STATION Pinyon Flat 106 LON 116 455 E 107 LAT 33 610 N 108 H 0 00 M 109 INSTRUMENT GTSM 110 AMPLITUDE COUNTS 111 112 PERIOD 1990 1 3 8 8 1990 329 17 8 113 114 AVAILABLE BLOCK LEN 684 684 115 116 ANALYZED BY BAYTAP G VERSION 99 11 15 117 POTENTIAL TAMURA Y 1987 BIM 99 WITH P4 118 CALCULATION NATIONAL ASTRONOMICAL OBSERVATORY MIZUSAWA 119 120 121 GROUP SYMBOL FACTOR RMSE PHASE RMSE AMPLITUDE RMSE 122 LOCAL LAG NEGATIVE 123 1 1 143 Q1 0 57317 0 01601 19 688 1 603 1 597 0 045 124 2 144 201 O1 0 58692 0 00267 16 203 0 261 8 542 0 039 125 3 202 249 M1 0 61817 0 03463 19 629 3 209 0 708 0 040 126 4 250 305 PISIK1 0 54246 0 00188 14 220 0 199 11 104 0 039 127 5 306 345 J1 0 62440 0 03325 3 852 3 051 0 715 0 038 128 6 346 450 OO1 0 68638 0 03416 10 333 2 850 0 430 0 021 129 130 7 451 549 2N2 0 85911 0 04293 25 371 2 869 0 578 0 029 131 8 550 599 N2 0 74344 0 00625 7 941 0 481 3 782 0 032 132 9 600 655 M2 0 63454 0 00107 6 027 0 097 16 860 0 028 133 10 656 681 L2 0 75694 0 04889 13 121 3 696 0 568 0 037 134 11 682 827 S2K2 0 59756 0 00186 7 220 0 179 7 387 0 023 135 136 12 828 909 M3 0 21205 0 08853 38 428 23 930
6. 0 061 0 026 Since the data set is 3 months long and we instructed the program to automatically select the number of tidal groups 12 groups are solved for The M2 and O1 tides are those usually used to calibrate strainmeters as they are the largest tides with periods sufficiently different from 24 hours so as not to be contaminated by thermal or other diurnal non tidal signals The phase of the M2 tide is 6 027 0 097 degrees and the amplitude is 16 860 0 028 counts The factor column contain the relative amplitudes that would be input to Tamura s tidal prediction program BAYTAP G also prints out a useful plot of the power spectrum of the trend We expect that if the tides have been properly estimated then there will be no energy above the background noise at the tidal frequencies This plot provides a quick visual guide as to how well the tides have been determined Time series output file If FILOUT 1 was specified in the input05 dat file then an outputl6 dat will be written The output is decomposed into four parts the tidal component the trend the response if there is associated data and a noise part ORIGINAL DATA TIDAL COMP TREND RESPONSE NOISE In this example the response part is zero as we have no associated data Plot_baytap sh is a simple GMT script that can be used to plot the data It reads the results from the outputl6 dat file and the start times and titles from the input 2 dat file The process of estimating the am
7. 581 2 646 21 093 0 974 141 3 202 249 M1 1 23411 0 12193 169 672 5 660 1 460 0 144 142 4 250 305 PISIK1 1 05665 0 05042 166 463 2 720 22 348 1 066 143 5 306 345 J1 1 10994 0 16200 167 842 8 360 1 313 0 192 144 6 346 450 OO1 1 12289 0 22124 169 405 11 289 0 727 0 143 145 146 7 451 549 2N2 1 40348 0 16807 161 674 6 861 0 895 0 107 147 8 550 599 N2 1 42390 0 06628 160 402 2 666 6 862 0 319 148 9 600 655 M2 1 57712 0 01138 163 686 0 414 39 696 0 286 149 10 656 681 L2 1 60321 0 10609 169 593 3 792 1 141 0 075 150 11 682 827 S2K2 1 57998 0 01844 171 276 0 738 18 502 0 216 151 152 12 828 909 M3 0 63920 0 46740 176 189 41 911 0 171 0 125 The frequency response of the associated data the power spectrum of the trend and a summary of potential outliers follow Most of the data points listed in the summary correspond to missing data points where the trend or response could not be evaluated We can examine the results by plotting the file output16 dat using plot_baytap_dates sh figure 3 There is a small step in the trend on the 30 August This offset corresponds to an instrument reset and an offset correction that was applied during editing A small step still remains in the data set but is only visible once the tides have been removed For this reason the editing process is often an iterative one where one edits the data and estimates th
8. 6 2004 9 18 2004 9 20 2004 9 22 2004 9 24 2004 9 26 2004 9 28 2004 9 30 165 1 f f f 1 Atmospheric pressure A 160 E o 3 155 _ Es g a amp 150 lis 145 2004 9 16 2004 9 18 2004 9 20 2004 9 22 2004 9 24 2004 9 26 2004 9 28 2004 9 30 Figure 4 Strain data from Donnalee with tides and atmospheric pressure response removed The atm response lag is three hours The lower figure shows the atmospheric pressure measured at Donnalee Once the amplitude and phase of the M2 and O1 tides are known a time series correction can be generated using those parameters for any time period and sample interval using the program hartid from the SPOTL package Agnew 1996 Although BAYTAP G solves for at least 12 tidal groups it is best to input just the M2 O1 and N2 parameters if the analysis is based on 3 to 6 months of data If the data set is longer than 6 months then the K1 tide could be included The program then uses spline interpolation to estimate the amplitudes of an additional 116 individual tides 18 long period 51 diurnal and 50 semidiurnal constituents are used in the prediction 15 In theory if the tidal amplitudes and phases have been found for one window of data then they should not change over the lifetime of the instrument A set of M2 and O1 parameters determined from three months of data should be sufficient to predict the tides at a time many years later For laser strainmeters this is the case but it has been found that
9. 82 024 Gals SPAN The number of observations to process in one window SHIFT The number of data points the data window being analyzed is shifted by For example if SPAN 744 and SHIFT 720 the data window will be 744 observations long and overlap by 24 data points If SHIFT is set to zero the trend is not obtained and BAYTAP G processes with the entire data set ignoring the SPAN parameter If the SHIFT is greater than the SPAN the data that are skipped are not used in the analysis DMIN The lower limit of hyperparameter D BAYTAP G searches for the value of D that minimizes the ABIC value The range searched for the D value is DMIN lt D lt 1000 0 The default value is 0 25 LPOUT Tidal analysis output If LPOUT 0 the estimated tidal factors and the frequency response of associated data are printed If LPOUT 1 and SHIFT gt 0 the determined trend and irregular part are also printed If LPOUT 2 then debug information is printed along with the output of LPOUT 1 The default value is 0 FILOUT Tidal calculations output BAYTAP G assumes the input data can be decomposed into four parts the tidal component trend response part if an associated dataset exists and irregular part noise The result of this decomposition is written to an output16 dat file when FILOUT 1 TIMSYS Correction amount by which to adjust time system to UTC For example if the data are observed in UTC TIMSYS 0 0 If the time system is Japanese Standard Time JST TI
10. Estimating tides in strainmeter data Introduction At time periods of days to months earth tides dominate the signal in strain and tiltmeter data In fact the earth tides provide a known strain signal with which to perform an in situ calibration of the instruments However to identify transients in strain data the tidal signal must be removed and the relation between external forces and strain change identified Consider Figure which shows the strain changes recorded by 5 volumetric dilatometers in Parkfield at the time of the M6 0 28 September 2004 Parkfield earthquake We see the tides clearly and we see an apparent change in strain rate that preceded the earthquake by 7 days We can also see however that the strain changes are temporally correlated with the atmospheric pressure Performing a tidal analysis of strain or tilt data is therefore necessary for two reasons the amplitudes and phases of the main tidal constituents can be used to calibrate the instrument and once known the tidal parameters can be used to predict the tides at any time and the tidal signal may be removed from the data To remove the tides we need to identify the phase and amplitude of the main tidal constituents in the time series There are a variety of free software packages that estimate the tides in time series data e PIASD Package for Interactive Analysis of Strain Data Agnew May 2004 e T tide A Matlab program that performs classical harmonic analysis for
11. MSYS 9 0 The difference between ephemeris time dynamic time and universal time is fixed to 51 seconds MAXITR Upper limit of number of iterations to search minimum ABIC The default value is 21 The input data are described on lines 11 to 20 of the above example 11 Beginning date of analysis number of samples and resample interval The FORMAT is as follows YYYY MM DDNNNN SS 315 F5 0 15 F10 0 where YYYY is the year MM the month and DD the day of the month NNNN is the number of samples and S S is the sample interval in hours If the files are type 1 user defined format type the sample interval given here is ignored and the value is defined in the tidal data set input12 dat file Grouping of tidal constituents The number of tidal constituents to be determined by the program is set here If this parameter is zero the number of groups is automatically selected according to the data length as follows Data window days Number of groups 0 to8 3 8 to 16 5 16 to 180 12 180 to 364 14 364 to 2000 15 gt 2000 20 Groups can also be defined manually If the grouping parameter is set to 2 1 1 2 3 4 5 or 6 then 3 5 12 14 15 20 22 and 31 groups are adopted respectively no matter what the data length is However it is advisable to select the number of groups considering the quality and amount of data Tidal data set The input unit number for the tidal dataset format specification and flag to re estimat
12. ND FP OWANADNPWN KE 11 1990 1 1845 2170 3 0 12 0 GROUPING 0 AUTO 2 1 1 6 MANUAL 13 12 1 0 T O UNIT FORMAT STEP TIDAL DATASET 14 9999 TITLE 15 STRAIN TIDE ANALYSIS 16 9999 17 PINYON FLAT CALIFORNIA STATION NAME 18 GLADWIN TENSOR STRAINMETER INSTRUMENT NAME 19 9999 20 COUNTS UNIT OF TIDAL DATA KIND Defines the kind of theoretical tide calculation for analysis 1 Gravity tide micro Gal increase is taken to be positive 2 NS Tilt millisecond of arc Subsiding northern ground taken to be positive For a horizontal pendulum tiltmeter tending the pendulum to the north is positive and for a water tube tiltmeter uplift of water level in the northern pot is positive For water tube tiltmeters the data set must be the difference of water levels between the northern and southern pots 3 EW Tilt millisecond of arc Subsiding eastern ground is taken to be positive There is an optional parameter AZ that allows analysis of the tilt tide in any direction If the direction of tilt is n degrees measured clockwise from north set KIND 2 and AZ n 4 NS Strain 5 EW Strain 6 NE Strain 7 Strain The tide generating potential mean earth radius acceleration due to gravity is used as the theoretical tide where the mean radius is assumed to be 6371023 6 m This value is non dimensional 8 Ocean tide cm uplift is taken to be positive The theoretical value is defined as potential mean gravity where mean gravity is 9
13. al explains all possible processing options and data formats The following examples however summarize the most important options for strain data analysis BAYTAP G requires two input files a file that contains the processing options the input05 dat file and a tidal data set in this case strain Associated data sets e g atmospheric or pore pressure are optional input files Everything input to the program is read in formatted statements This means that you have to be careful that the input files are formatted correctly In both the examples below we will use the user defined format type 1 in the user s manual The strain data should be cleaned before input to BAYTAP G By cleaning we mean obvious outliers steps and periods of noisy data are removed regardless of whether the irregular data are geophysical or instrumental in origin It is also important to remove any steps or outliers in associated data sets if they are going to be used Estimation of the phase and amplitudes of the earth tides for a 3 component tensor strainmeter For this example we will look at the 3 component strain data measured by the Gladwin Tensor Strainmeter at Pinyon Flat Observatory PFO in Southern California A laser strainmeter and three volumetric dilatometers have also been installed at PFO and so the data set proves an interesting one in terms of comparing the measured earth tides with that measured by a co located laser strainmeter and dilatometers and wit
14. celeration due to gravity cm s 3 Date of first observation The format is YYYY MM DD HH HH where YYYY is the year MM is the month DD is the day of the month and HH HH is the hour 4 Number of observations sampling interval units of hours missing data flag The missing data flag must be positive or zero If it is positive data whose absolute values are greater than the missing data flag are ignored If it is zero all observations are used in the analysis 5 Format of input data Describes the format of the data in a FORTRAN77 formatting statement e g 6f12 4 would imply six values per row each twelve characters long with four decimal places 6 Input data The tidal analysis output file The following is a description of the results from BAYTAP G after analyzing the data from gage 3 of the Pinyon Flat tensor strainmeter The tidal results are output to file output06 dat In our example lines 1 to 71 list all the parameter settings data start date and station information You should check these values to make sure that your input files are formatted correctly Note that all the parameter settings are listed If we did not specifically set them then the default values are used where necessary Line 74 contains the date and time of the first and last data points of each window This is another opportunity to check the time interval dates and number of sample has been read in correctly The ABIC trace information follows BAYTAP G va
15. change and strain change to be zero hours A response coefficient will be calculated for each allowable lag if we allow a lag of up to 3 hours BAYTAP G will calculate the response coefficient at 0 1 2 and 3 hours The input file has 2171 observation points and the time series begins on 19 00 1 August 2004 UTC line 13 We specify that the associated data will be in unit 14 line 16 The units of the tidal data set and title of the atmospheric pressure data are stated on lines 23 and 24 respectively The strain input file input12 dat and the pressure input file input 4 dat have exactly the same data formats as described in first example The strain data is in units of counts and the pressure data in units of millibars The header lines of the input 2 dat and input14 dat files have similar information DONNALEE PARKFIELD VOL DILATOMETER 35 94 120 42 568 0 980 122 2004 8 119 0 2171 1 0 99990 D0 1F9 1 4F13 1 AB WN On line 4 the missing data flag is set to 999990 0 any data point with a value greater than this will not be used in the analysis The output files An output06 dat and an output16 dat file are created Looking at the ouput06 dat file we should check that the dates and correct number of samples have been read correctly The following line numbers correspond to the numbers of the lines in the output06 dat file 48 DATE OF THE FIRST DATA 49 YEAR MONTH DAY HOUR DATA COUNT SAMPLING 50 2004 8 1 19 00 2171 1 00 51 52
16. e a step size respectively are specified on this line The unit number corresponds to the input file name of the tidal data set For example 12 would imply the filename of the tidal dataset is input12 dat The format type describes the format of the data it is one of 1 0 or 1 14 16 Title line This will be printed in the output files Descriptive text can be recorded within the next 10 17 18 lines It must be preceded and followed by the term 9999 Station name Instrument name 20 Unit of tidal data Since one of the main reasons we look at the amplitude and phases of the tides is for calibration purposes we input the data in volts or counts as measured by the data logger Then we can relate the amplitude and phase of the tide in counts to that predicted in nanostrain Tidal Data Input file We specified on line 12 of the input05 dat file that the strain data file would be called input12 dat We also specified that the data would be input in a user defined format We will define what the format will be in the input12 dat file The following is an example of an input12 dat file Line Content 1 PINYON FLAT OBSERVATORY GTSM GAUGE 1 2 33 610 116 4550 0 00 982 024 3 1990 1 1 8 45 4 2170 3 0 99990 0 5 6F12 4 6 4565 000 44566 000 44567 000 44568 000 44565 000 44566 000 7 4565 000 44563 000 99999 000 44561 000 44563 000 44564 000 8 1 Title Coordinates of site Latitude and longitude degrees altitude m ac
17. e 16 to the 30 September 2004 You can see that while the shorter term variations in strain caused by the pressure changes are removed from the data there is still a change in trend from the 20 to 22 of September that may be correlated with pressure changes Estimating the pressure response using cross spectral analysis is another way to try and remove this longer term pressure signal 13 DONNALEE PARKFIELD VOL DILATOMETER 7000 6500 ORIGINAL iT Jil Fil ull Wi ili i Hl 15 August 8 p M ll I 22 liiy i y ii i 12 19 September IN i tia l il Hl 12 19 September i 5 mi I 26 17 October lh i 10 24 il ii Ml Hy Hii ny n mM l vill iil nT i wi iil ii hit if i ii i Hl Yi th mi 17 October 10 24 7000 6500 6000 8 15 August 8 15 August 22 22 IRREGULAR 12 19 September 12 19 September 26 17 October 10 24 26 10 17 October 24 HAaAoNLOLNWAH 8 15 August 22 29 5 12 19 September 26 17 October 3 10 24 Figure 3 Three months of data from Donnalee volumetric dilatometer Parkfield Atm lag is zero 14 9000 ORIGINAL 8500 n ke Z so00 L Q O ORIGINAL TIDES 7500 Peel ORIGINAL TIDES ATM PRESSURE RESP 7000 T T T T T I T T T T T T 2004 9 1
18. e tides The raw data should be re edited with the tides removed Once removed better offset corrections are achieved and other smaller offsets may become more easily identified We can examine the effect of increasing the lag time for which we allow an atmospheric pressure response by running BAYTAP G several times each time increasing the LAGP value Table 2 Each time we examine the ABIC value to look for an improvement in fit LAGP ABIC 0 3736 17 1 3609 77 2 3603 08 3 3598 50 RESPO 2 5775E 01 2 248E 01 2 5416E 01 2 203E 01 2 5727E 01 2 3874E 01 2 5763E 01 2 3837E 01 12 RESP1 2 5734E 00 2 2039E 01 2 41325E 00 2 24581E 01 2 73869E 00 2 42023E 01 RESP2 8 12720E 01 2 39591E 01 6 63 186E 01 2 42658E 01 RESP3 8 52815E 01 2 39259E 01 Letting the lag interval be up to 3 hours LAGP 3 gives the lowest ABIC value indicating that allowing a 3 hour lag response gives a better fit to the data Increasing LAGP to 4 results in a larger ABIC value The response coefficient is largest at zero lag and becomes less significant as the lag increases The phase and amplitude of the M2 and O1 tides are not changed outside the RMS error listed in the output The response coefficients although above the stated error are two orders of magnitude less than the response coefficients at zero and 1 hour lags Figure 4 shows the original data minus the tides and the pressure response from the output16 dat file from th
19. e we should begin with a cleaned strain and pressure data set We will look at the strain data from the volumetric dilatometer at Donna Lee from August to October 2004 The data have been cleaned low pass filtered and decimated to 1 hour samples using the methods outlined in Viewing and Editing data The data are then reformatted into BAYTAP G files The BAYATAP G files for Donnalee are in home data baytap_example and called input05 dat donnalee input 2 dat donnalee and input14 dat donnalee Parameter Input File The input05 dat file is similar to the above example This time we include information on an associated data set in this case atmospheric pressure amp PARAM KIND 7 SPAN 2171 SHIFT 2171 DMIN 0 01 LPOUT 0 FILOUT 1 NYDN WN KE 10 8 IAUG 1 9 LAGP 0 10 TIMS YS 0 0D0 11 MAXITR 50 12 amp END 13 2004 08 119 02171 1 0 14 0 GROUPING 0 AUTO 2 1 1 6 MANUAL 15 12 1 0 T O UNIT FORMAT STEP TIDAL DATASET 16 14 1 0 T O UNIT FORMAT STEP ATM DATASET 17 9999 TITLE 18 VOLUMETRIC STRAIN 19 9999 20 DONNALEE PARKFIELD STATION NAME 21 SINGLE CHAMBER VOL DILATOMETER INSTRUMENT NAME 22 9999 23 COUNTS UNIT OF TIDAL DATA 24 ATMOSPHERIC PRESSURE TITLE OF ASSOSIATED DATASET We have set the shift and span to the same value which means the data will be analyzed in one window The IAUG states there is one associated data set atmospheric pressure LAGP sets the allowable time lag between pressure
20. for some dilatometers and GTSMs the tidal parameters are not constant with time Figure 5 shows the change in M2 amplitude at the Coyote dilatometer in the Bay Area The entire data set from the instrument was analyzed in 2 month windows using BAYTAP G and the amplitude and phases plotted There is a clear drift in M2 amplitude with time the reason may be a result of aging cables or electronic drift The implication is that the scale factors at this site will change with time Figure 6 shows that change in phase of the M2 tide as measured by the PFO GTSM While the phases for gages 2 and 3 remain constant with time the gage 1 M2 phase changes by 12 again the implication is that the scale factor will change with time 0 01 gt S oo 0 006 M2 AMP Microstrain 0 004 0 002 1993 0 012 0 01 0 008 O1 AMP Microstrain 0 006 0 004 1993 16 Coyote Hills M2 Amplitude 1995 1997 1999 2001 2003 Year Coyote Hills O1 Amplitude 1995 1997 1999 2001 2003 Year Figure 5 Amplitude and phase of the M2 tide at the Coyote Hills volumetric dilatometer Bay area 17 Pinyon Flat GTSM 5 la N le ete RN pa AA i 5 ae 3 10 l M2 Phase G1_phase_change G3_phase_change 20 1984 1988 1992 1996 2000 2004 Year Figure 6 Change in M2 phase with time at the PFO GTSM References Agnew D C 1996 SPOTL Some Programs for Ocean Tide Loading SIO
21. h theoretical models The instrument was installed in December 1983 and samples at 18 minute intervals The data set consists of 3 months of data measured in 1990 figure 2 The data have had borehole trends removed and have been lowpass filtered and decimated to 3 hour sample intervals The sample data sets are in the data directory home data baytap_examples and are called input05 dat pft input12 dat pftl input12 dat pft2 and input 2 dat pft3 150 100 HH 50 COUNTS a e 100 150 THH F H 200 250 1990 Jan 1 1990 Feb 1 1990 Mar 1 1990 Apr 1 Date Figure 2 Three months of data from Pinyon Flat GTSM The data are edited and have had the borehole trends removed Parameter Input File The input05 dat file defines the period of data being analyzed and contains all the parameter settings used by the program All processing parameters must be placed between amp PARAM and amp END Example of input05 dat file Line amp PARAM KIND 7 SPAN 1780 SHIFT 1780 DMIN 1 LPOUT 0 FILOUT 1 TIMSYS 0 0D0 MAXITR 21 0 amp E
22. plitude and phase of the M2 and O1 tides is repeated for each gauge The final results are a set of 12 observations the phase and amplitude of the M2 and O1 tides for three gauges The results from this analysis are summarized in Table 1 Table 1 Phase degrees and amplitude counts of the M2 and O1 tides on each of the PFO tensor strainmeter M2 phase M2 amp O1 phase O1 amp Gagel 69 633 0 440 5 209 0 040 8 464 0 889 8 045 0 125 Gage2 1 443 0 258 26 449 0 119 14 189 3 432 5 754 0 345 Gage3 6 027 0 095 16 860 0 028 16 203 0 270 8 542 0 040 When we use these parameters for calibration it is often more useful if they are described as real and imaginary numbers rather than the amplitudes and phases If a signal is expressed in terms of amplitude R and phase theta then the real component is computed using R cos theta and the imaginary component computed using R sin theta Estimating the relation between atmospheric pressure and strain change BAYTAP G can be used to estimate the linear relation between strain change and changes in pressure In this example we will look at how to estimate a linear relation between atmospheric pressure and volumetric strainmeters using BAYTAP G Volumetric dilatometers consist of fluid filled chambers that are several feet long and thus are much more sensitive to changes in vertical strain than Gladwin Tensor Strainmeters where each cell is 17 cm tall As for the above exampl
23. ries the parameter D to try and attain a minimum value for the ABIC value The program starts with a D value that is four times DMIN and iterates until it reaches a minimum If the minimum value is not reached and BAYTAP reaches the DMIN value then a warning message is generated and the program continues using the DMIN value in the input05 dat file In this example we set DMIN to be 0 5 the program therefore begins with a D value of 4 0 78 ABIC 4 0000E 00 132 95 ALSQE 5 87259E 02 ALNDN 1 28587E 03 ALNDTD 9 27765E 02 TIABIC S 6569E 00 197 58 ALSQE 4 44761E 02 ALNDN 1 48399E 03 ALNDTD 1 16482E 03 80 ABIC 2 8284E 00 88 02 ALSQE 7 25021E 02 ALNDN 1 09523E 03 ALNDTD 6 90709E 02 81 ABIC 2 0000E 00 59 18 ALSQE 8 64761E 02 ALNDN 9 13621E 02 ALNDTD 4 53652E 02 82 ABIC 1 4142E 00 45 02 ALSQE 1 01195E 03 ALNDN 7 43084E 02 ALNDTD 2 16596E 02 83 ABIC 1 0000E 00 46 77 ALSQE 1 17073E 03 ALNDN 5 86288E 02 ALNDTD 2 04605E 01 84 85 MINIMUM ABIC 45 02 ATTAINED AT VMIN 1 4142E 00 SD 4 7724E 01 The program iterates six times before finding that a DMIN of 1 4142 gives the best ABIC value of 45 02 There is some trial and error here in choosing an initial DMIN value and making sure that you have set the number of iterations MAXITR large enough The station information data window information and tidal values are printed between lines 105 and 136 For each tidal group the print out shows the tidal group name a tidal factor and error the phase with
24. se component The program varies D and each time computes the Akaike Bayesian Information Criterion ABIC value The best set of tidal parameters trend values and response coefficients are found when the ABIC value is minimized The user can control how many iterations are stepped through and place constraints on minimum values of D The program will stop when the minimum ABIC is reached The following notes illustrate how to use BAYTAP G to estimate the phase and amplitudes of the main tidal constituents in strain or tidal data These constituents can be to generate a time series correction to remove the tidal signal from the dataset They can also be used to calibrate the instrument by comparing the observed phase and amplitude with that predicted by theory We will work through two examples 1 We will estimate the tides in data from a Gladwin tensor strainmeter and form a set of amplitudes and phases of the M2 and O1 tides as measured by each gage 2 We will estimate the tidal parameters for the M2 and O1 tides as measured by a volumetric dilatometer and also estimate the atmospheric pressure response Installing and running BAYTAP G BAYTAP G is written in FORTRAN77 It is available as a tar file from the National Astronomical Observatory Mizusawa Japan via anonymous ftp The recommended reference is Tamura et al 1991 Since the program does not produce any graphics it is easily installed and compiled using f77 or g77 The BAYTAP G manu
Download Pdf Manuals
Related Search