Coordinate Converter - Using Station Velocity

Methodology

 

In most cases, information about site velocity is not available for the site we wish to make a coordinate conversion of.  Nevertheless, we offer in Coordinate Converter the possibility to estimate a velocity by spatially interpolating the velocities of permanent stations near the site. For now, three networks of permanent sites offering velocity information are used:

Here are the main steps to estimate a site velocity:

1. Choose a maximum distance for interpolation. Only stations within this distance from the site will then be taken into consideration for the calculation.

2. Press the “Search for stations” button. On the velocity map, on the right, all the stations within the specified distance will be shown using red arrows.

    The length and direction of these arrows correspond to the velocity magnitude and direction respectively.

Note that the unselected stations are grayed in the velocity map. You can also have additional information by clicking on one of the arrows:

Step-by-step procedure

 

Once the “Estimate velocity” button is pressed in the main interface, a second window opens, showing the main parameters to be set for velocity interpolation:

Note that the datum and the data source are shown at the bottom. If no stations are shown, it may be due to the following reasons:

·       The nearest stations are farther away than the specified distance. Try a longer distance.

·      There is no data for the selected datum, and the selected region. Try using one of the supported datums. If your site is outside the supported regions, then no interpolation will be possible.

 

 

3. Optionally, unselect stations you want NOT to be used in the interpolation process.

4. Choose the interpolation method (explained on the previous section):

If these values are too high, try reducing the distance or change the interpolation method. You can check the resulting interpolated values by clicking on the black arrow, which represents the site whose velocity is being estimated:

: 3D components of the velocity vector field, each one being modeled as a function of a 2D coordinate (x,y)

 

: 2D coordinates, using a local coordinate system (North, East)

: parameters of the 2D linear function for  to be determined

: parameters of the 2D linear function for  to be determined

: parameters of the 2D linear function for  to be determined

The third method is, in our opinion, the one that should more accurately reflect the velocity vector field but it may not be the best method in all cases. We recommend that you perform a comparative analysis and use your own judgment.

5. Press the “Compute” button.

You should now see the residuals of the estimation process along with the RMS:

Press the “Ok” button to accept the interpolated velocity and this value will be automatically added in the main interface:

You can now proceed to the coordinate conversion process in the main interface.

Where,

1.       Simple mean, weighted by the inverse of the distance

In this case, the mean of the velocities of the nearest stations (within a limit established by the user) is computed. To take into consideration that the velocity of a station is generally more similar to the velocity of the nearest stations, a weighted mean is performed. The weight is inversely proportional to the distance to the station. This method is simple but it ignores any directional gradient that may be present in the velocity vector field.

 

2.       Linear 2D interpolation

In this method a 2D (x,y) linear function is estimated for each of the three components of the velocity vector.  The mathematical function for each component is as follows:

If your site is within one of these networks, then an interpolation is possible. Several methods exist for spatial interpolation of vector quantities (the velocity vectors). Accurately modeling of the phenomena responsible for the velocity of the sites, i.e. tectonic and other geological processes, is a complex task and beyond the scope of this simple coordinate conversion tool. Thus, we limited the velocity estimation to three simple interpolation methods.

· The Unavco network, covering North America, with velocity information using  ITRF2008 (www.unavco.com )

· The National Geodetic Services’ Continuously Operating Reference Stations (CORS), with velocity information using NAD83.

( http://geodesy.noaa.gov/CORS/ )

· The Euref Permanent GNSS Network  (EPN) with velocity information using ETRS89. (http://epncb.oma.be/ )

3.       Linear 2D interpolation, weighted by the inverse of the distance

This is the same case as the previous one, except that, additionally, a weighting scheme is included.

Since there are 3 parameters to be determined for each velocity component, we need at least 3 stations with velocity information near the site. If four or more stations are available, then a least squares adjustment (LSQ) is performed and the rms value of the residuals is calculated.

Article: 000116

Related Products: EZField, EZSurv, EZTag CE, OnPOZ Tools

Last Update: 2016-07-14 18:44:15

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