interpolating sparse arrays - where's the trend?

[Simon Cox]

I have been using s.surf.tps to interpolate through very sparse arrays.
This means that I generally do NOT have data points near to the edge of the
area.  I realise that this means that I am "extrapolating" rather than
interpolating for these parts of the model.  However, I am a bit surprised
at the results:  for example, here is a sketch of an masked area with the
data


<--- 25km -------->
___________________
|                 /
|                /
|               /
|              /                Only 3 data points!
|             /
|            /                  I look at that & see a "trend" with +ve
| x 200     /                   values in the north and -ve values in
|          /                    the south.  However, s.surf.tps processes
|         /                     this and produces a flat, level surface with
|        /                      a +ve anomaly in the middle and a -ve
| -324 x/                       anomaly in the SE, and a (almost) uniform
|      /                        height edge all around.  In other words, in
|-201x/                         the "far field" only the mean level of the
|    /                          data is seen in the interpolated surface,
|   /                           and not the trend.  Is this just a matter of
|  /                            decreasing the tension, or does the tps method
| /                             inevitably fall back the the mean value
|/                              outside the data?

Simon Cox

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Dr Simon Cox                             __  L
CSIRO Exploration & Mining            ,~'  L_|\       Australian
39 Fairway, PO Box 437,            ;-'         \      Geodynamics
Nedlands, WA  6009,  Australia     (            \     Cooperative
      Phone +61 9 389 8421         +    ___     /     Research
      Fax   +61 9 389 1906          L~~'   "\__/      Centre
s.cox at dem.csiro.au                            7
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