PyGeoNS (pronounced like the bird) is a suite of command line functions that are used to identify transient strain in GNSS data. This analysis is performed in a Bayesian framework, using Gaussian process regression, and thus the results have well-quantified and meaningful uncertainties. Gaussian process regression is not robust against outliers, which is a common defect in GNSS data. Thus, PyGeoNS provides a function for detecting outliers as a pre-processing step. The outlier detection algorithm flags data which are spatially or temporally anomalous. PyGeoNS also provides a function for interactively removing data defects. Lastly, PyGeoNS provides functions to interactively view the data and results.

Gaussian process regression requires solving a system of equations where the number of unknowns is equal to the number of observations. Assuming that a high-end desktop computer is being used, this means that datasets will be limited to several dozen stations and a few years of daily observations. This limitation can be alleviated to some extent by using a compact prior covariance function.

PyGeoNS calculates strain on a transverse-mercator projection. It is assumed that the stations cover a sufficiently small area that such a projection is appropriate.

If you want to use Gaussian process regression to analyze your data, but PyGeoNS is too rigid for your needs, then consider working directly with the RBF python package (www.github.com/treverhines/RBF).

PyGeoNS runs in Python 2.7 and it requires older versions of the packages basemap and matplotlib. I recommend installing PyGeoNS in its own conda environment to avoid package conflicts. Assuming that conda is installed (www.continuum.io/downloads), you can install PyGeoNS by following these steps:

Create and activate a new conda environment called pygeons-env which uses Python 2.7 and contains the default anaconda packages.

$ conda create -n pygeons-env anaconda python=2.7
$ source activate pygeons-env 

Install additional required packages. Note that these are not the lastest versions of basemap and matplotlib.

$ conda install basemap=1.0.7
$ conda install matplotlib=2.1.2
$ conda install scikit-sparse=0.4.4 -c conda-forge

Create a new directory where we will install PyGeoNS and RBF

$ mkdir pygeons_packages
$ cd pygeons_packages

Clone and install the last compatible version of RBF

$ git clone --single-branch --branch=2019.04.28 --depth=1 http://www.github.com/treverhines/RBF.git
$ cd RBF
$ python setup.py install
$ cd ..

Clone and install PyGeoNS

$ git clone http://www.github.com/treverhines/PyGeoNS.git
$ cd PyGeoNS
$ python setup.py install

We can verify that PyGeoNS was installed successfully by running one of its demos. This should compute and display transient strain from a slow slip event in the Pacific Northwest.

$ cd demo/demo2
$ bash run.sh

I am currently working on updating PyGeoNS so that it runs in Python 3, and has cartopy, rather than basemap, as a a dependency. This version of PyGeoNS is on the branch py3 and it should be compatible with the latest versions of each of its dependencies.

PyGeoNS contains the following subcommands. Call these functions with a -h flag to see more information.

• pygeons toh5 : Converts data from a text file to an HDF5 file.
• pygeons totext : Converts data from an HDF5 file to a text file.
• pygeons crop : Spatially and temporally crops an HDF5 data file.
• pygeons merge : Combines multiple HDF5 data files.
• pygeons info : Displays metadata for an HDF5 data file.
• pygeons vector-view : Interactively view a data file or multiple data files.
• pygeons strain-view : Interactively view strain from the deformation gradients returned by pygeons strain.
• pygeons reml : Estimates hyperparameters with the restricted maximum likelihood (REML) method.
• pygeons strain : Conditions a Gaussian process with displacements to form a posterior estimate of transient displacements. The posterior is spatially and temporally differentiated to form the transient velocity gradients.
• pygeons fit : Fits a Gaussian process to the displacements. This is used to judge whether a Gaussian process model is appropriate.
• pygeons clean : Interactively remove jumps and outliers in a data file.
• pygeons autoclean : Automatically removes outliers in displacements.

This demonstration walks through the script demo/demo2/run.sh, which estimates transient strain resulting from a slow slip event in Washington. First, navigate to the directory demo/demo2.

$ cd demo/demo2

You will find urls.txt which contains urls pointing to the GNSS data that we will use. Lets download the data and save it in the directory work/csv

$ mkdir -p work/csv
$ for i in `cat urls.txt`
    do
    wget -P 'work/csv' $i
    done

Next we merge each data file into one data file that PyGeoNS can read. This just requires concatenating the files with a *** delimiter.

$ sed -s '$a***' work/csv/* | sed '$d' > work/data.csv

Now we are ready to use PyGeoNS. We convert the csv file to an HDF5 file, which is more efficient for i/o.

$ pygeons toh5 'work/data.csv' \
               --file-type 'pbocsv' 

This will generate a file work/data.h5. We can now interactively view the data file with

$ pygeons vector-view 'work/data.h5' \
                      --no-show-vertical \
                      -v

The -v flag increased the verbosity and caused instructions for the interactive viewer to be printed to the screen. Use the arrow keys to view different stations and times. To keep this demonstration tractable, we crop the dataset down so that it only spans two years.

$ pygeons crop 'work/data.h5' \
               --start-date '2015-05-01' \
               --stop-date '2017-05-01'

This produces the file work/data.crop.h5. Next we automatically identify and remove outliers in the dataset with the command pygeons autoclean. There are several arguments to this function that should be tweaked, but we will just use the defaults for now.

$ pygeons autoclean 'work/data.crop.h5' -vv

This function will take a few minutes to run. The verbosity has been increased so that we can see its progress. We can compare the dataset before and after cleaning by using pygeons vector-view again.

$ pygeons vector-view 'work/data.crop.h5' 'work/data.crop.autoclean.h5' \
                      --no-show-vertical 

We now estimate transient strain from the cleaned GNSS data. Since PyGeoNS performs Bayesian analysis, we must specify a prior for transient displacements and a noise model. Our prior is a Gaussian process with temporal covariance described by a Wendland function and spatial covariance described by a squared exponential. We also specify three hyperparameters for the prior. The first describes the standard deviation of our prior (in mm), the second is a time-scale parameter (in yr), and the third is a length-scale parameter (in km). The noise in our data consists of white noise (which we do not need to specify) and a linear trend that is unique for each station. This linear trend is secular tectonic deformation, which we are not interested in for this demonstration. See Network and Station Processes for more information on specifying noise and prior models. By default, strains will be estimated at the locations of each station in the dataset and for each day in the dataset. The computation time can be decreased by specifying a smaller range of times and positions to output at. Use the --start-date and --end-date arguments to set the range of output times. Use the --positions or --positions-file to set the output positions.

$ pygeons strain 'work/data.crop.autoclean.h5' \
                 --network-prior-model 'spwen12-se' \
                 --network-prior-params 1.0 0.1 100.0 \
                 --station-noise-model 'linear' \
                 --start-date '2015-10-01' \
                 --stop-date '2016-04-01' \
                 -vv

This returns two files, work/data.crop.autoclean.strain.dudx.h5 and work/data.crop.autoclean.strain.dudy.h5, which are the velocity gradients along the x (east) direction and the y (north) direction, respectively. Use the --no-rate flag to return displacement gradients rather than the velocity gradients. The deformation gradients can be viewed with pygeons vector-view. We can also use the deformation gradients to view strain with pygeons strain-view.

$ pygeons strain-view 'work/data.crop.autoclean.strain.dudx.h5' \
                      'work/data.crop.autoclean.strain.dudy.h5' \
                      --scale 20000.0 \
                      --key-magnitude 1.0 \
                      --key-position 0.15 0.85 \
                      -vv

This will open up an interactive viewer for the estimated strain rates. The following two figures were saved from the interactive strain viewer. The strain glyphs in the map view figure show the normal strain rates for all azimuths. Orange indicates compression and blue indicates extension. The time series figure shows the strain rate components through time at one station. The shaded regions in both figures indicate the 68% confidence interval.

The deformation gradients (or any of the intermediary HDF5 files) can be output to a user-friendly csv file format with the command pygeons totext. The name of the output file (minus the extension) is specified with the --output-stem argument

$ pygeons totext 'work/data.crop.autoclean.strain.dudx.h5' \
                 --output-stem 'dudx'
$ pygeons totext 'work/data.crop.autoclean.strain.dudy.h5' \
                 --output-stem 'dudy'

That completes the demonstration. More detailed information about PyGeoNS can be found below or by calling each PyGeoNS subcommand with the -h flag.

PyGeoNS subcommands mostly read from and write to HDF5 data files. An HDF5 file can be read using, for example, the h5py package in python. Each HDF5 file contain the following entries

• time : Array of unique integers with shape (Nt,). Integer values of modified Julian dates.
• id : Array of unique strings with shape (Nx,). 4-character IDs for each station.
• longitude, latitude : Array of floats with shape (Nx,). Coordinates for each station.
• east, north, vertical : Array of floats with shape (Nt,Nx). These are the data components. The units should be in terms of meters and days and should be consistent with the values specified for space_exponent and time_exponent. For example, if time_exponent is -1 and space_exponent is 1 then the units should be in meters per day. If data is missing for a particular time and station then it should be set to nan.
• east_std_dev, north_std_dev, vertical_std_dev : Array of floats with shape (Nt,Nx). One standard deviation uncertainties for each component of the data. The units should be the same as those used for the data components. If data is missing for a particular time and station then it should be set to inf.
• time_exponent : Integer. This indicates the exponent of the time units for the data. -1 indicates that the data is a rate, -2 indicates an acceleration, etc.
• space_exponent : Integer. Indicates the exponent of the spatial units for the data.

An HDF5 file can be created from a text file of GNSS data with pygeons toh5. This function is currently able to read three text file formats: PBO csv files, PBO pos files, and a csv file format designed for PyGeoNS. To use pygeons toh5, the text files for each station must be concatenated into a single file with delimiter ***. For example, if the data files are in the current directory and contain a .csv extension then they can be concatenated with the following sed incantation

$ sed -s '$a***' *.csv | sed '$d' > data.csv 

Next, call pygeons toh5 with the new file name and specify the file type with --file-type. The file type can be csv, pbocsv, or pbopos.

See www.unavco.org for information on the PBO data file formats. An example of each file format is provided below.

PBO Station Position Time Series.
Format Version, 1.2.0
Reference Frame, NAM08
4-character ID, P403
Station name, FloeQuaryGWA2005
Begin Date, 2005-09-13
End Date, 2017-01-26
Release Date, 2017-01-27
Source file, P403.pbo.nam08.pos
Offset from source file, 48.54 mm North, 60.55 mm East, -5.06 mm Vertical
Reference position, 48.0623223017 North Latitude, -124.1408746693 East Longitude, 284.67725 meters elevation
Date, North (mm), East (mm), Vertical (mm), North Std. Deviation (mm), East Std. Deviation (mm), Vertical Std. Deviation (mm), Quality,  
2005-09-13,0.00, 0.00, 0.00, 4.71, 3.14, 13.2, repro,
2005-09-14,7.43, 8.65, 2.37, 1.85, 1.34, 5.6, repro,
...
2017-01-26,98.68, 132.58, 6.00, 1.93, 1.49, 6.34, rapid,

PBO Station Position Time Series. Reference Frame : NAM08
Format Version: 1.1.0
4-character ID: P403
Station name  : FloeQuaryGWA2005
First Epoch   : 20050913 120000
Last Epoch    : 20170126 120000
Release Date  : 20170127 235743
XYZ Reference position :  -2396874.51122 -3534734.44146  4721722.14918 (NAM08)
NEU Reference position :    48.0623223017  235.8591253307  284.67725 (NAM08/WGS84)
Start Field Description
YYYYMMDD      Year, month, day for the given position epoch
HHMMSS        Hour, minute, second for the given position epoch
JJJJJ.JJJJJ   Modified Julian day for the given position epoch
X             X coordinate, Specified Reference Frame, meters
Y             Y coordinate, Specified Reference Frame, meters
Z             Z coordinate, Specified Reference Frame, meters
Sx            Standard deviation of the X position, meters
Sy            Standard deviation of the Y position, meters
Sz            Standard deviation of the Z position, meters
Rxy           Correlation of the X and Y position
Rxz           Correlation of the X and Z position
Ryz           Correlation of the Y and Z position
Nlat          North latitude, WGS-84 ellipsoid, decimal degrees
Elong         East longitude, WGS-84 ellipsoid, decimal degrees
Height (Up)   Height relative to WGS-84 ellipsoid, m
dN            Difference in North component from NEU reference position, meters
dE            Difference in East component from NEU reference position, meters
du            Difference in vertical component from NEU reference position, meters
Sn            Standard deviation of dN, meters
Se            Standard deviation of dE, meters
Su            Standard deviation of dU, meters
Rne           Correlation of dN and dE
Rnu           Correlation of dN and dU
Reu           Correlation of dEand dU
Soln          "rapid", "final", "suppl/suppf", "campd", or "repro" corresponding to products  generated with rapid or final orbit products, in supplemental processing, campaign data processing or reprocessing
End Field Description
*YYYYMMDD HHMMSS JJJJJ.JJJJ         X             Y             Z            Sx        Sy       Sz     Rxy   Rxz    Ryz            NLat         Elong         Height         dN        dE        dU         Sn       Se       Su      Rne    Rnu    Reu  Soln
 20050913 120000 53626.5000 -2396874.58357 -3534734.44007  4721722.12054  0.00645  0.00812  0.00994  0.811 -0.686 -0.775      48.0623218656  235.8591245168  284.68231    -0.04854  -0.06055   0.00506    0.00471  0.00314  0.01320  0.163 -0.115 -0.095 repro
 20050914 120000 53627.5000 -2396874.57419 -3534734.44167  4721722.12726  0.00261  0.00353  0.00416  0.793 -0.733 -0.788      48.0623219323  235.8591246330  284.68468    -0.04111  -0.05190   0.00743    0.00185  0.00134  0.00560 -0.002 -0.141 -0.016 repro
 ...
 20170126 120000 57779.5000 -2396874.43473 -3534734.45725  4721722.19088  0.00295  0.00382  0.00479  0.797 -0.776 -0.801      48.0623227520  235.8591262989  284.68831     0.05014   0.07203   0.01106    0.00193  0.00149  0.00634 -0.045 -0.073 -0.110 rapid

The PyGeoNS CSV file only contains information that PyGeoNS uses, making it unambigous which fields can influence the results. For example, there is no reference frame information in the PyGeoNS csv format because PyGeoNS does not ever use that information.

4-character id, P403
begin date, 2005-09-13
end date, 2017-01-26
longitude, 235.859125331 E
latitude, 48.0623223017 N
units, meters**1 days**0
date, north, east, vertical, north std. deviation, east std. deviation, vertical std. deviation
2005-09-13, -4.854000e-02, -6.055000e-02, 5.060000e-03, 4.710000e-03, 3.140000e-03, 1.320000e-02
2005-09-14, -4.111000e-02, -5.190000e-02, 7.430000e-03, 1.850000e-03, 1.340000e-03, 5.600000e-03
...
2017-01-26, 5.014000e-02, 7.203000e-02, 1.106000e-02, 1.930000e-03, 1.490000e-03, 6.340000e-03

The subcommands pygeons strain, pygeons autoclean, and pygeons reml require the user to specify Gaussian process models. PyGeoNS distinguishes Gaussian processes as either "network" processes, which are spatially and temporally correlated, or "station" processes, which are only temporally correlated. The processes may contain hyperparameters that the user must also specify. Some of the available processes and their corresponding hyperparameters are documented below

Each network process has zero mean and a covariance function that can be described as

C( (x,t) , (x',t') ) = T(t,t') X(x,x')

where X and T are spatial and temporal covariance functions.

• wen12-se : Temporal covariance is described by a Wendland function,

  T(t,t') = φ² (1 - /τ)₊⁵ (8²/τ² + 5/τ + 1).

  Spatial covariance is described by a squared exponential,

  X(x,x') = exp( -||₂² / (2ℓ²) ).

  Requires three hyperparameters to be specified,

  φ [mm], τ [yr], ℓ [km].

• spwen12-se : Same as wen12-se but covariance matrices are treated as sparse.

• se-se : Temporal covariance is described by a squared exponential,

  T(t,t') = φ² exp( -² / (2τ²) ).

  Spatial covariance is described by a squared exponential,

  X(x,x') = exp( -||₂² / (2ℓ²) ).

  Requires three hyperparameters to be specified,

  φ [mm], τ [yr], ℓ [km].

• ibm-se : Temporal covariance is described by integrated Brownian motion,

  T(t,t') = φ²/2 min(s,s')² ( max(s,s') - min(s,s')/3 ),

  where

  s = t - τ, s' = t' - τ.

  Spatial covariance is described by a squared exponential,

  X(x,x') = exp( -||₂² / (2ℓ²) ).

  Requires three hyperparameters to be specified,

  φ [mm/yr^1.5], τ [mjd], ℓ [km].

• fogm : A Gaussian process with zero mean and covariance described by

  C(t,t') = β²/(2α) exp( -α ).

  Requires two hyperparameters to be specified,

  β [mm/yr^0.5], α [1/yr]

• bm : A Gaussian process with zero mean and covariance described by

  C(t,t') = β² min( t - α , t' - α ).

  Requires two hyperparameters to be specified,

  β [mm/yr^0.5], α [mjd]

• linear : Unconstrained offset and linear trend. Requires no hyperparameters to be specified.
• per : Unconstrained annual and semiannual sinusoids. Requires no hyperparameters to be specified.

pygeons autoclean and pygeons reml require the user to specify some combination of network and station processes to describe the data. Suppose we want to clean the displacements saved in data.h5. We expect that the data consists of a se-se network process with hyperparameters 1.0 mm, 0.1 yr, and 100.0 km. We also expect each station to have an independent offset and linear trend. We can clean the data with the command

$ pygeons autoclean data.h5 \
                    --network-model 'se-se' \
                    --network-params 1.0 0.1 100.0 \
                    --station-model 'linear' \
                    --station-params 

We can also specify multiple network and station processes to combine them. Suppose we also expect periodic deformation and a FOGM process at each station. We can then clean the data with the modified command

$ pygeons autoclean data.h5 \
                    --network-model 'se-se' \
                    --network-params 1.0 0.1 100.0 \
                    --station-model 'linear' 'per' 'fogm' \
                    --station-params 0.5 0.01

pygeons strain also requires the user to distinguish processes as being part of the prior or part of the noise. Hence, the models are specified as --network-prior-model, --network-noise-model, and --station-noise-model. There is no --station-prior-model argument because the prior must be spatially and temporally continuous.

There is absolutely no guarantee that this software is free of bugs. It is recommended that you perform synthetic tests to verify that PyGeoNS is working properly. Please report any issues at www.github.com/treverhines/PyGeoNS/issues.