Briefing of analyze_tseri package
   GPS derived time series analysis is an important complement of the global network analysis. Time series analysis studies the time series of each individual site. The advantages of time series analysis are:
    1. It is much efficient than the global analysis.
    2. It is easy to detect outliers.
    3. Any misfit of one time series (for example: any local effect at one site) will not affect the estimates of other sites.
   Although such an analysis neglects the correlations between different sites so that it is not theoretically optimal. However, Zhang [1996] had showed that these correlations are small, such a neglection only imposes very minor impact on the solutions.
   This time series analysis approach gains great success in the deformation field analysis, in particular for the coseismic field, seasonal deformation field and postseismic deformation field. The example of seasonal deformation analysis can be found in Dong et al., 2002.
   The utility analyze_tseri was designed to perform site position time series analysis. It estimates constant offset, velocity, (also quadratic and cubic terms, if specified), jumps, seasonal variations, non-linear variation (exponential decay and logarithmic decay), and any user defined non-linear periodic variations. It can also model any shape of periodic pattern and its modulation (this part is not open to public yet). This utility considers the correlation between east, north and up components of the station time series. It is also able to set constraints, accept multiple velocities and any user defined periodic variations.

   Our analyze_tseri is different from the conventional time series analysis software package in two places. First, it has the option to consider the correlations between east, north and vertical components, or to neglect the correlations among the components. The later option is equivalent to the conventional time series analysis package. Second, it estimates the jump parameters not the same as conventional simultaneous least squares approach. For the conventional least squares adjustment, the solutions will minimumize the sum of weighted postfit residual squares. Thus, any unmodeled variations, such as non-linear undulations, will affect the estimated parameters in particular the jump parameters.
   Unlike the other parameters, the jump parameters are mostly sensitive to the nearby data points around the jump epoch. We do not want the unmodeled variations of remote data points to distort the estimation of jump parameters. In particular, the coseismic jump parameters are very important to the inverse of the fault source mechanism. Any small inaccuracy in the estimated jump parameters will change the inferred fault parameters significantly. Our analyze_tseri first uses the short span (user defined, the default is 0.1 year) data around the jump epoch to estimate the jump parameters (together with one bias and two velocity parameters). Then using the estimated jump parameter values to replace the original apriori values of the jump parameters. Also, the program will re-set the apriori constraints of the jump parameters using factor*sigma (formal uncertainty) of the estimated jump parameters. Here the factor is user defined, its default value is 0.2 (20%). However, if there is strong post-seismic deformation, the co-seismic jump value can not be estimated accurately using short interval data. Unility analyze_tseri will not use the short interval to estimate the jump parameter if the post-seismic parameter is also estimated. In the next step the analyze_tseri starts to perform global simultaneous least squares adjustment. Such an approach makes the estimated jump parameters much consistent with the jump offsets in the time series. Sometimes there is a big gap around the jump epoch and there is no enough data points within the short span specified by the users, in this case the analyze_tseri will use the conventional way to estimate this jump parameter and give a warning to the user.
   The interval of estimating jump parameter should be set properly. The best way is to set the interval jump by jump. Unfortunately, current analyze_tseri only allows the same interval and constraint factor for all jumps. If different jumps require different estimating intervals or constraints, the users have to set several runs to analyze the time series. If the interval is too small, the estimates might be biased by the postseismic transcients. If the interval is too large, the estimates might also be biased by the postseismic relaxation. Based on our experiences, for the daily solutions the interval of 0.1-0.2 year should be good.
   Thus, if we use short interval to estimate the jumps, the apriori value and constraint for this jump parameter are actuary not used. But sometimes we already know the apriori value of the jump very well. We want to tightly constrain the jump parameter to the apriori value rather than re-estimate the jump value. The analyze-tseri sets a criterion: if the constraint is less than 0.2 mm, the program will not re-estimate the jump and use the apriori and constraint values in the global least square adjustment.

   Our analyze_tseri also sets some parameter control. If the effective span of the time series is less than 1.5 year, the program will not estimate annual terms even if these parameters exist in the parameter file. if the effective span is less than 0.9 year, the program will not estimate the semi-annual terms.
   For many theoretical studies and operational usages, the users want to separate the seasonal signals from the long period and secular motions. In many station time series, the seasonal patterns are not exactly sinusoidal. Futhermore, the amplitudes of the seasonal pattern are also variable. To separate such seasonal patterns thouroughly, analyze_tseri is also able to estimate periodic Spline functions and polynomial amplitude modulation functions. (Note: this part is not open to public yet).
   Currently, analyze_tseri accepts multiple input data formats, for example QOCA map file format, SOPAC neu file format, GIPSY stacov format (not finished yet), st_filter site_xyz and site_enu format, GIPSY point positioning site N, E, U file format etc. Note, the default QOCA map file only contains residuals. If we want to analysis the secular motion of the network, users should run QOCA separate mode to output full time-dependent site position variations (including the secular motion) rather than the residual motion. Because the default map file output is the de-trened position adjustment.
   To get the secular motion in the separate mode map file, user should specify his request in the qoca driver file by adding a tag 'velocity' in the command line:

  mapping file:      separate_mode.map   velocity
   Here we discuss the application in post-seismic deformation field analysis as an example.
   The signal of the postseismic deformation is much smaller than the signal of the coseismic deformation. Furthermore, the mechanisms of the postseismic deformation are much complicated than the coseismic deformation, which lead to multiple spacial wavelengths and multiple temporal periods coexisting in the postseismic deformation field. Currently, only a few simplified models are used to quantify the post-seismic deformation field. Two common used models are exponential decay model and logarithmic decay model, both are non-linear models. Based on our experiments, the geodetic data have very weak resolution power to estimate the characteristic time parameters in the two non-linear models. So that QOCA utility implements the two models, but only estimates the amplitudes. That means the characteristic time (tau) must be determined in advance from external knowledge.
   At the current stage, the mismodeling of the postseismic deformation seems much more serious than the neglecting the correlation between each time series. So that QOCA utilizes the time series analysis to estimate the postseismic deformation field. The first step is to run QOCA separate mode to create the time series outputs which are stored in the output map file (see the basic class about the separate mode setup and example files). In order to minimize the influences from other deformation features such as secular and episodic deformations, the dejump option in the qoca driver file should be turned on. When the djump option is turned on, the secular and episodic displacements will be removed from the output map file (the unmodeled secular and episodic residuals might remain in the time series). The resultant qoca separate mode output map file will be the input file of the next step. For the purpose of postseismic deformation reasearch, the qob files before the earthquake are not necessary. In most case, only the qob files after the earthquake are used in the qoca separate mode run.
   The runstring of analyze_tseri is:
     analyze_tseri <driver file>
   In the driver file, the followings are currently used commands:
 apriori value file: the same used in qoca run.  
 input list file: the list of QOCA separate mode output map files. 
       The first line has two entries. The first entry is the number of files. The second 
           entry is the file format type. For example, type = 1 means QOCA map format, type = 2 is 
           the SOPAC neu format. (See detailed type list in the following section) If the second 
           entry is missing, the default type is 1.   
       The rest lines are map file names. 
 sit_list file: site name file (see example in above frame).
       The format of site_list file is simple (see example in above frame).  The first 
       line is the number of sites.  The rest lines are site names. 
 est_parameter file: estimate parameter file (see example in above frame).
       Note that the site number in the site_list file is not necessarily the same as the 
       site number in the estimate parameter file.  The site number in the site_list file 
       can be only a subset of the sites in the estimate parameter file.  
       In the parameter file, every estimated parameter has start epoch and end epoch. Such a 
       structure allows multiple velocities (cover different spans) for the same station. 
       For the jump parameters, if the parameter spans are not overlaped, the jump parameter
       represents box function. If the jump parameter spans are overlated, the jump parameter
       represents step function. 
       There is a special "site name": "all_site". If the "all_site" is used as a site name, then
       the parameters are related to all sites in the site_list file. Such a special site name 
       gives the users much conveniences. To use this special site name, the user should note the
       following two things. First, this special site should appear before any individual site.
       That means this site should be at the top of the parameter file. Second, when this special
       site name is used, the individual site can not assign redundant parameters. Because the 
       analyze_tseri utility will append the parameter list, not overwrite the parameter list.
       Since analyze_tseri usually deals with residual time series, the apriori value (unit: mm and
       mm/year for coordinate and velocity) is usually related to residuals, i.e the correction to 
       the nominal value. If there is no information about the correction value to the nominal 
       value, we usually assign zero apriori value. It is time-consuming to manually type apriori 
       velocities for every site. The utility analyze_tseri accepts a special apriori velocity 
       value to make the user's life much easier. If the velocity apriori value is 9999.0, that 
       means we use the nominal velocity values from the network file as the apriori velocity 
       values. The software code will automatically check the network file to get the nominal 
       valocity value for the stations. 
 residual file: output residual file name.
 res_option: residual output option. 
       If the option is empty, that means output original time series and 
              hence the residual file is ignored.
       The option is a bit map integer.
       if bit(1) = 1 (number 1): the bias term is removed in residuals
       if bit(2) = 1 (number 2): the secular motion is removed in residuals
       if bit(3) = 1 (number 4): the annual terms are removed in residuals
       if bit(4) = 1 (number 8): the semi-annual terms are removed in residuals
       if bit(5) = 1 (number 16): the jump terms are removed in residuals
       if bit(6) = 1 (number 32): the user defined harmonic terms are removed in residuals
       if bit(7) = 1 (number 64): the Spline function terms are removed in residuals
       if bit(8) = 1 (number 128): the global quadratic terms are removed in residuals
       if bit(9) = 1 (number 256): the global cubic terms are removed in residuals
       if bit(10) = 1 (number 512): the modulation terms are removed in residuals
       if bit(11) = 1 (number 1024): the postseismic decay terms are removed in residuals
       if bit(12) = 1 (number 2048): the local polynomial terms are removed in residuals
       For example, if the res_option = 29, that means the bias, jump, annual and semi-annual 
           terms are removed. The residuals contain the other terms, including 
           velocity (secular motion) term. 
specific term output file: output time series with specified terms. specific term_option: option to select the specific terms. If the option is empty, that means output nothing. The option is a bit map integer. if bit(1) = 1 (number 1): the bias term is included in the output terms. if bit(2) = 1 (number 2): the secular motion is included in the output terms. if bit(3) = 1 (number 4): the annual terms are included in the output terms. if bit(4) = 1 (number 8): the semi-annual terms are included in the output terms. if bit(5) = 1 (number 16): the jump terms are included in the output terms. if bit(6) = 1 (number 32): the user defined harmonic terms are included in the output terms. if bit(7) = 1 (number 64): the Spline function terms are included in the output terms. if bit(8) = 1 (number 128): the global quadratic terms are included in the output terms. if bit(9) = 1 (number 256): the global cubic terms are included in the output terms. if bit(10) = 1 (number 512): the modulation terms are included in the output terms. if bit(11) = 1 (number 1024): the postseismic decay terms are included in the output terms. if bit(12) = 1 (number 2048): the local polynomial terms are included in the output terms. For example, if the res_option = 29, that means the bias, jump, annual and semi-annual terms are included in the specific output file.
resi_file2: output second residual file name. User can use this file to generate another residual file with different option. The format of the second residual file is different from the first residual file. It allows several (up to 3) residual options and output corresponding residuals. res2_option: residual output option for second residual file. The option index is the same as res_option. However, it allows several (up to 3) different option indexes (separated by space). mdl2_out file: output second modeled time series. Similar to the second residual file, the second model file allows several (up to 3) model options. mdl2_option: option to select specific terms for second model file. The option index is the same as term_option. However, it allows several (up to 3) options.
omitted_span file: (input) file name This file specifies which station and which span data should be discarded. If this line is missing or the file name is missing, the default is no omitted data. cme_correction file: (input) two file names The first file is the spatial eigenvector file. The second file is the principal component file. Both files are pca (another QOCA utility package) program output files. This option asks the analyze_tseri program to perform regional filtering. enu_correlation usage: yes (use enu correlation), no (do not use enu correlation). The QOCA map file format includes the correlation between east, north, up components. Users can choose if using the correlation or not. If yes, analyze_tseri will adjust east, north and up parameters together using the enu subcovariance with the correlation. If no, the analyze_tseri will adjust east, north, up parameters independently. This case (choose 'no') is equivalent to conventional single component time series analysis. The default is 'yes'. color_noise analysis model: use color noise model to re-estimate sigmas. Currently only model=2 is implemented, which is flick noise + white noise model. We adopt Williams' algorithm to calculate the sigmas. If this option is not activated, analyze_tseri still uses scatters to re-scale the formal uncertainties. jump_day solution removal: yes (do not use the solution in the jump occurance day), no (still use the daily solution of the jump occurance day). In most cases, the earthquake jump occured in the middle of the day, so that the daily solution at this day is a mixture of jump and no jump parts. This daily solution is very hard to be modeled accurately. We usually select "yes" and do not use this daily solution (for this site). otide_load correction: option (if ocean tide load should be corrected) If we put the ocean tide load correction file name, that means the ocean load effects should be corrected. The file format is the same as QOCA used. In this case, another option should be filled: otide_select: select ocean tide name for the correction The 11 tides are: M2 S2 N2 K2 K1 O1 P1 Q1 MF MM SSA The format of the option is (11i2), where 1 means yes and 0 means no. cutoff criterion: unit: year, give a numerical number, for example 2.5 means 2.5 years. It the data span of this site is less than 2.5 years, this site will be neglected. Such a criterion is necessary to avoid weak site, in particular for velocity and seasonal term estimates. adjust_allsite option: yes or no If the option is 'yes', the utility will analyze all stations listed in the site list file. If this station is not found in the apriori file, the utility will use the first data record as the apriori value of this station. This option is very useful, when we want to use the data to adjust station coordinates and velocities, then use the solutions to update the pariori file. The default option is 'no'. oneline_netformat option: yes or no If the option is 'yes', the utility will output one line "lsq_coor" in the output file, which contains site coordinate, velocity and reference epoch in the apriori file format. Thus these lines can be used directly to update the apriori file using the net_update utility. The default option is 'no'. span and sigma factor to estimate jump apr value: unit: year, real value. This is one-side span. The analyze_tseri program will check if there are effective jump parameters. If the answer is yes, the program will use the data within the span around the jump epoch to estimate the apriori value of the jump parameter. Then reset the apriori value of the jump parameter using the estimated value and reset the jump parameter constraint using the formal sigma*factor value. The default span value is 0.1 year. The default sigma factor is 0.2 (20%). weak_obs (big sigma) criteria: give criteria based on the formal errors. If at one epoch, the formal sigmas of one site are bigger than the specified criteria, the solution of this site at this epoch will be ignored. This command provides another way to avoid weak solutions to contaminate the time series analysis. The unit is mm. The order is e, n, up. outlier (big o-c) criteria mm: give criteria based on the postfit residuals. If at one epoch, the residuals of one site are bigger than the specified criteria, the solution of this site at this epoch will be ignored. This command prevents outliers from contaminating the time series analysis results. The order is e, n, up. very bad_observation criteria mm: If the data have very bad observations, the initial adjustments will be biased. Then the residuals are not accurate and some innocent observations will be considered as outliers. To avoid this case, we set bad_obs to remove very bad observations before the adjusting. The default is 3000000 mm. The order is e, n, up. t_interval: give the start and end epoch for the time series analysis. It this command is ignored, the default action is to use the whole time series. atmos_load correction file: give list of atmospheric load files. The first line of the list file is the load file number. The rest lines are load file names. The load files are generated by mload. moisture_load correction file: give list of soil moisture load files. The first line of the list file is the load file number. The rest lines are load file names. Each line has two load files, one is 0-10 cm load, another one is 10-200 cm load. The load files are generated by mload. snow_load correction file: give list of snow load files. The first line of the list file is the load file number. The rest lines are load file names. The load files are generated by mload. ocean_load correction file: give list of ocean load files. The first line of the list file is the load file number. The rest lines are load file names. The load files are generated by mload from ECCO model.
parameter file
   The format of the estimate parameter file is as followings:
   The first line is the number of sites.
   From the second line are the parameter blocks for each site.
   In each block, the first line is the site name and the number of estimate parameters for this site. The remaining lines in the block are parameter lines. In each parameter line, the first entry is the estimated parameter index, the second entry is the apriori value for this parameter, the third entry is the apriori constraint (sigma) for this parameter, and the next two entries are parameter-dependent usage.
For coordinates the fourth entry is the reference epoch. The fifth entry is not used.
For velocity and jump parameters, the last two entries stand for start and end epochs. That means we can assign multiple velocities for the same station with different intervals. For the jump parameters, the interval can either overlap or no overlap. For example, if the vertical time series are as followings:
  xxxxxxxxxxxxxxxxxxx                                                   (h1)
                     xxxxxxxxxxxxxxxxxx                                 (h2)

                                       xxxxxxxxxxxxxxxxxxxxxx           (h3)
                    t1                t2                    t3
We can set two jump parameters in two ways.
In the first way, 
  9  0.0  50.0   t1   t2
  9  0.0  50.0   t2   t3
Then the estimated jump parameters will be (h2-h1) and (h3-h1).
In the sercond way,
  9  0.0  50.0   t1   t3
  9  0.0  50.0   t2   t3
Then the estimated jump parameters will be (h2-h1) and (h3-h2).
If the time series are as followings:
  xxxxxxxxxxxxxxxxxxxxxx                     xxxxxxxxxxxxxxxxxxxxxxx

                        xxxxxxxxxxxxxxxxxxxxx
                       t1                   t2
We need only one jump parameter:
  9  0.0  50.0  t1  t2
Here, we can see the advantage of box function over the step function. If we want to use the 
conventional step function to estimate the above jump, we have to set two jump parameters:
  9  0.0  50.0  t1
  9  0.0  50.0  t2
Then we have to impose a constraint jump2 = -jump1 to get the final estimate.
It is easy to see that the step function is a special case of the box function. If we 
set a very large value for t2, the box function is equivalent to the step function.
For the exponential or logarithmic decay parameters, the first epoch represents the start epoch, the second epoch is the characteristic decay time tau. Both are in unit of year.
For the harmonic (including seasonal and user defined terms) parameters, the first epoch is the period (in this case the unit is day, not year), the second epoch is the reference epoch in unit of year.
For quadratic and cubic terms, the last two entries represent the start and end epochs.
   Although there are many parameter indexes, not all parameters can be estimated simultaneously. We can only choose either exponential decay model or logarithmic decay model, not both. Within a short period (~2-3 characteristic time), there is no significant difference between the two models. They can be distinguished only with long span and adequate measurements. The logarithmic decay model is commonly attributed to the continuous fault rupture mechanism, while the exponential decay model is often related to the viscoelastic relaxation mechanism. Unlike the conventional definition of amplitede, the amplitudes for both exponential decay or logarithmic decay are not necessarily to be positive values. Please do not be surprised why the apriori and estimated amplitude parameters (for east, north and vertical components) could be negative values.
   Since the GPS measurements have very poor resolving power for the characteristic decay time tau, analyze_tseri does not estimate tau using the GPS data. The users must assign the tau values (unit: year) from external knowledge.
   The postseismic decay parameters are highly correlated with the velocity and seasonal parameters. When the measurement number and the data span are limited, it is recommended not to estimate the velocity and the seasonal parameters together with the postseismic deformation parameters. Sometimes you can estimate the velocity and seasonal parameters with tight constraints. The characteristic decay time (tau) is a non-linear parameter in general. To use the linear estimator to estimate tau, the linear region is very limited. Based on our experiences, the GPS data have very weak resolution to solve tau. So that we decide that analyze_tseri does not estimate tau (estimate the amplitude only) to avoid potential confusing.

data list file:

The format of the data list file is as followings:
  567  1
dir/first_file.map
dir/second_file.map
dir/third_file.map
.......
  
  The first line specifies data file number and data file type.
From the second line, each line has one data file name.
  Current analyze_tseri accepts the following data file types:
  1 = QOCA map file
  2 = SOPAC neu file
  3 = GIPSY stacov file (not finished yet)
  4 = st_filter site_xyz output record
  5 = st_filter site_enu output record
  6 = Japan station position file
  7 = point positioning station component file
  8 = REASoN web service output xyz file
  9 = REASoN neu tar file
  10 = REASoN xyz tar file
The default file type is 1 (QOCA map file).
output file:
   The output file contains the parameter estimate information for each time series. The first two lines are:
*    obs     para     dof           chi2        nrms       wrms        power(pre)      power(post)
   10254      44  10210.375     162033.421     3.9837     4.2085    259246151.603       383941.624
The eight entries represent the quasi-observation number, estimated parameter number, degrees of freedom, chi square, normalized rms (unitless), weighted rms (weighted mean scatters, unit: mm), sum of scatter squares (unit: mm**2) for prefit, sum of scatter squares (unit: mm**2) for postfit.
   The next two (or three) lines are:
* enu nrms, wrms(weighted mean scatter):    4.278    4.625    2.814    3.789    4.080    7.865  0011_GPS
* removed outliers (not in the obs):     1 =     3 obs
* the formal uncertainty is not rescaled by the scatters, but one_line velo uses scaled sigmas
The first line specifies the nrms (unitless) for east, north, up components, and the wrms (unit: mm) for east, north and up components.
   The ten entries of the remaining lines represent parameter name, longitude, latitude, apriori value, estimated adjustment, total estimated parameter value, formal error (sigma), resolution, site name, and reference epoch respectively. For the user assigned harmonic parameters, the tenth entry represents the period of the harmonics (unit: day). There are several lines collecting the estimated parameter information together for easy use. For example, the "lsq_velo" line puts the east, north and vetical velocity estimates and their covariance matrix information in one line. Note: in "lsq_velo" line, the uncertainties are rescaled by the nrms to reflect the realistic uncertainties.
   The following lines are an example of the output solutions:
* General statistics for site 0011_GPS
*    obs     para     dof           chi2        nrms       wrms        power(pre)      power(post)
   10254      44  10210.375     162033.421     3.9837     4.2085    259246151.603       383941.624
* enu nrms, wrms(weighted mean scatter):    4.278    4.625    2.814    3.789    4.080    7.865  0011_GPS
* removed outliers (not in the obs):     1 =     3 obs
* the formal uncertainty is not rescaled by the scatters, but one_line velo uses scaled sigmas
*  para      lon      lat         apr          adj          tot          sig      reso      site      epoch
EST_BIAS  143.4592  43.0286       0.0000     -52.6143     -52.6143       0.0234   1.0000  0011_GPS  2000.0000 2200.0000
NOR_BIAS  143.4592  43.0286       0.0000     158.8382     158.8382       0.0231   1.0000  0011_GPS  2000.0000 2200.0000
VER_BIAS  143.4592  43.0286       0.0000     195.5079     195.5079       0.0799   1.0000  0011_GPS  2000.0000 2200.0000
EST_VELO  143.4592  43.0286       0.0000     -10.2701     -10.2701       0.0118   1.0000  0011_GPS  1990.0000 2009.0000
NOR_VELO  143.4592  43.0286       0.0000      -2.4767      -2.4767       0.0117   1.0000  0011_GPS  1990.0000 2009.0000
VER_VELO  143.4592  43.0286       0.0000      -4.6125      -4.6125       0.0402   1.0000  0011_GPS  1990.0000 2009.0000
lsq_velo  143.4592  43.0286  -10.270   -2.477    0.050    0.054  0.0000   -4.613    0.113  0.0000  0.0000  0011_GPS 1990.0000 2009.0000
lsq_coor 0011_GPS            N43  1 43.069879 E143 27 33.219728     60.96921 -0.0103 -0.0025 -0.0046 2000.0000 1900.0000 2500.0000
E_ANN_AM  143.4592  43.0286       0.0000       0.6086       0.6086       0.0241   0.9999  0011_GPS   365.2500 2000.0000
E_ANN_PH  143.4592  43.0286       0.0000      93.2081      93.2081       2.2186   1.0000  0011_GPS   365.2500 2000.0000
e_ann_sc  143.4592  43.0286      -0.0341       0.6077       0.0237       0.0242   0.0771  0011_GPS
N_ANN_AM  143.4592  43.0286       0.0000       0.4793       0.4793       0.0232   0.9999  0011_GPS   365.2500 2000.0000
N_ANN_PH  143.4592  43.0286       0.0000      66.7678      66.7678       2.8521   1.0000  0011_GPS   365.2500 2000.0000
n_ann_sc  143.4592  43.0286       0.1891       0.4404       0.0234       0.0225   0.0704  0011_GPS
U_ANN_AM  143.4592  43.0286       0.0000       6.6767       6.6767       0.0741   0.9993  0011_GPS   365.2500 2000.0000
U_ANN_PH  143.4592  43.0286       0.0000     249.8776     249.8776       0.6692   0.9998  0011_GPS   365.2500 2000.0000
u_ann_sc  143.4592  43.0286      -2.2970      -6.2692       0.0768       0.0716   0.0757  0011_GPS
E_SEM_AM  143.4592  43.0286       0.0000       0.8949       0.8949       0.0221   0.9999  0011_GPS   182.6250 2000.0000
E_SEM_PH  143.4592  43.0286       0.0000     109.9202     109.9202       1.3828   1.0000  0011_GPS   182.6250 2000.0000
e_sem_sc  143.4592  43.0286      -0.3049       0.8414       0.0218       0.0224   0.0426  0011_GPS
N_SEM_AM  143.4592  43.0286       0.0000       0.8900       0.8900       0.0216   0.9999  0011_GPS   182.6250 2000.0000
N_SEM_PH  143.4592  43.0286       0.0000     306.4364     306.4364       1.3839   1.0000  0011_GPS   182.6250 2000.0000
n_sem_sc  143.4592  43.0286       0.5286      -0.7160       0.0217       0.0221   0.0323  0011_GPS
U_SEM_AM  143.4592  43.0286       0.0000       0.7878       0.7878       0.0691   0.9995  0011_GPS   182.6250 2000.0000
U_SEM_PH  143.4592  43.0286       0.0000     121.8763     121.8763       5.0127   0.9998  0011_GPS   182.6250 2000.0000
u_sem_sc  143.4592  43.0286      -0.4160       0.6690       0.0699       0.0702   0.0343  0011_GPS
EST_JUMP  143.4592  43.0286       3.3053      -3.6234      -0.3182       0.0937   0.9943  0011_GPS  2003.1781 2200.0000
EST_JUMP  143.4592  43.0286      -8.8025       0.4232      -8.3793       0.0886   0.9968  0011_GPS  2002.8719 2200.0000
NOR_JUMP  143.4592  43.0286      10.3522       3.4804      13.8326       0.0641   0.9984  0011_GPS  2002.8719 2200.0000
VER_JUMP  143.4592  43.0286     -61.3738      -1.9240     -63.2977       0.2099   0.9984  0011_GPS  2002.8719 2200.0000
EST_JUMP  143.4592  43.0286     244.9460     -12.2719     232.6741       0.3866   0.8951  0011_GPS  2003.7344 2200.0000
NOR_JUMP  143.4592  43.0286    -355.8597      11.6124    -344.2473       0.3794   0.8938  0011_GPS  2003.7344 2200.0000
VER_JUMP  143.4592  43.0286     -95.6338       5.1232     -90.5106       1.1366   0.8946  0011_GPS  2003.7344 2200.0000
EST_JUMP  143.4592  43.0286       0.0000       3.7701       3.7701       0.5433   1.0000  0011_GPS  2003.7452 2200.0000
NOR_JUMP  143.4592  43.0286       0.0000      -6.6657      -6.6657       0.5315   1.0000  0011_GPS  2003.7452 2200.0000
VER_JUMP  143.4592  43.0286       0.0000     -35.1886     -35.1886       1.5996   0.9997  0011_GPS  2003.7452 2200.0000
E_LOG_AM  143.4592  43.0286       0.0000      63.0576      63.0576       2.5460   0.9994  0011_GPS  2003.7452 0.1000
N_LOG_AM  143.4592  43.0286       0.0000     -36.1936     -36.1936       2.4860   0.9994  0011_GPS  2003.7452 0.1000
U_LOG_AM  143.4592  43.0286       0.0000     231.9992     231.9992       7.5361   0.9943  0011_GPS  2003.7452 0.1000
EST_JUMP  143.4592  43.0286       0.0000       3.2641       3.2641       0.2958   1.0000  0011_GPS  2003.7699 2200.0000
NOR_JUMP  143.4592  43.0286       0.0000      -8.0911      -8.0911       0.2888   1.0000  0011_GPS  2003.7699 2200.0000
VER_JUMP  143.4592  43.0286       0.0000     -15.0394     -15.0394       0.8709   0.9999  0011_GPS  2003.7699 2200.0000
E_LOG_AM  143.4592  43.0286       0.0000     -37.8265     -37.8265       2.3913   0.9994  0011_GPS  2003.7700 0.1000
N_LOG_AM  143.4592  43.0286       0.0000       9.7727       9.7727       2.3345   0.9995  0011_GPS  2003.7700 0.1000
U_LOG_AM  143.4592  43.0286       0.0000    -204.9520    -204.9520       7.0765   0.9950  0011_GPS  2003.7700 0.1000
EST_JUMP  143.4592  43.0286       0.0000       9.3136       9.3136       0.1225   1.0000  0011_GPS  2004.9098 2200.0000
NOR_JUMP  143.4592  43.0286       0.0000       0.8801       0.8801       0.1223   1.0000  0011_GPS  2004.9098 2200.0000
VER_JUMP  143.4592  43.0286       0.0000      -2.6992      -2.6992       0.5337   1.0000  0011_GPS  2004.9098 2200.0000
E_LOG_AM  143.4592  43.0286       0.0000       4.8239       4.8239       0.0655   1.0000  0011_GPS  2004.9100 0.1000
N_LOG_AM  143.4592  43.0286       0.0000      -3.6355      -3.6355       0.0658   1.0000  0011_GPS  2004.9100 0.1000
U_LOG_AM  143.4592  43.0286       0.0000      -2.9083      -2.9083       0.2253   1.0000  0011_GPS  2004.9100 0.1000
VER_JUMP  143.4592  43.0286      -8.0666       2.3965      -5.6700       0.5988   0.9690  0011_GPS  2004.9583 2200.0000
The output file has a key-word oriented structure. Please look at the template to get some impression. Users can use "grep" to extract the desired information from the output file. For example, if you want to get the east component velocity estimate, you can type
  grep "EST_VELO" [analyze_tseri output file] | cut -c9-
to get the information. The definitions of the key-word are:
 EST_BIAS: bias term of the east component
 NOR_BIAS: bias term of the north component
 VER_BIAS: bias term of the vertical component
 EST_VELO: velocity term of the east component
 NOR_VELO: velocity term of the north component
 VER_VELO: velocity term of the vertical component
 lsq_velo: velocity terms of this site, the same format as the map file.
  long,lat,vel(e),vel(n),sig(ve),sig(vn),corr(en),vel(up),sig(vu),corr(ve),corr(vn),site
 lsq_coor: both coordinate and velocity terms of this site, the same format as the apr file.
 EST_JUMP: jump term of the east component
 NOR_JUMP: jump term of the north component
 VER_JUMP: jump term of the vertical component
 E_LOG_AM: logarithmic decay amplitude term of the east component
 N_LOG_AM: logarithmic decay amplitude term of the north component
 U_LOG_AM: logarithmic decay amplitude term of the vertical component
 E_ANN_AM: annual amplitude of the east component
 E_ANN_PH: annual phase of the east component
 e_ann_sc: horizontal annual components of the east component.
  long,lat,annu(sine),annu(cosine),sig(sine),sig(cosine),corr,site
 N_ANN_AM: annual amplitude of the north component
 N_ANN_PH: annual phase of the north component
 n_ann_sc: horizontal annual components of the north component.
  long,lat,annu(sine),annu(cosine),sig(sine),sig(cosine),corr,site
 U_ANN_AM: annual amplitude of the vertical component
 U_ANN_PH: annual phase of the vertical component
 u_ann_sc: horizontal annual components of the vertical component.
  long,lat,annu(sine),annu(cosine),sig(sine),sig(cosine),corr,site
Change the "ANN" of the key-word to "SEM", these keywords represent the corresponding
estimates of the semiannual terms.
Change the "ANN" of the key-word to "HAR", these keywords represent the corresponding
estimates of the user defined harminic terms.
Change the "LOG" of the key-word to "EXP", these keywords represent the 
exponential decay amplitude estimate.