Find the Volcano

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Previous Eruption

This is just so that you can see what uncorrupted data might look like. Here was the ground temperature just before an eruption that occured at x=66, y=40:

VolcanoFig0.jpg

The functional form of the measured temperature Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle T} is known to be a 2-dimensional Gaussian, centered on the predicted point of eruption Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle (x_0,y_0)} ,

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle T = T_0 + (T_1-T_0)\exp\left(-\frac{(x-x_0)^2+(y-y_0)^2}{2\lambda^2}\right)}

with unknown parameters Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle T_0, T_1, x_0, y_0, \lambda} that vary with each eruption.

But we only get to measure the temperature around the perimeter of the fenced area (top, bottom, left, right). Here is what its actual values were (blue=top, green=bottom, red=left, black=right):

VolcanoFig1.jpg

Worse yet, there is a lot of measurement noise, in fact, Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \sigma(T) = 30} . So these were the actual measurements of the previous eruption (blue=top, green=bottom, red=left, black=right):

VolcanoFig2.jpg

The Coming New Eruption

Uh-oh, it's about to erupt again, and we need to save the poor residents (but only in the correct village). Where is it going to erupt? The data (blue=top, green=bottom, red=left, black=right) is:

VolcanoFig3.jpg

Or, numerically,

topdata =

        0   48.6345
  10.0000   93.0313
  20.0000  133.1038
  30.0000  147.1216
  40.0000  147.6922
  50.0000  163.8339
  60.0000  168.1475
  70.0000  163.4634
  80.0000  150.7994
  90.0000  141.3370
 100.0000  116.9523

botdata =

        0   54.9420
  10.0000   36.9229
  20.0000   70.5617
  30.0000   30.5953
  40.0000   34.5474
  50.0000   47.0488
  60.0000   11.4761
  70.0000   37.6386
  80.0000   20.1398
  90.0000   22.9232
 100.0000   29.1138

leftdata =

        0   54.9420
  10.0000   -2.9088
  20.0000   39.9287
  30.0000   31.6726
  40.0000   24.5548
  50.0000  105.5842
  60.0000  130.5641
  70.0000  116.5640
  80.0000   24.0367
  90.0000   50.8359
 100.0000   48.6345

rightdata =

        0   29.1138
  10.0000   38.6237
  20.0000   66.5028
  30.0000   45.9631
  40.0000   89.7711
  50.0000   89.2857
  60.0000  106.7689
  70.0000   53.4243
  80.0000  126.1221
  90.0000  104.2912
 100.0000  116.9523

Or, here is a link to a file with all the data as (x,y,T) triplets:

volcanodata.txt

Or, the data repeated here,

        0  100.0000   48.6345
  10.0000  100.0000   93.0313
  20.0000  100.0000  133.1038
  30.0000  100.0000  147.1216
  40.0000  100.0000  147.6922
  50.0000  100.0000  163.8339
  60.0000  100.0000  168.1475
  70.0000  100.0000  163.4634
  80.0000  100.0000  150.7994
  90.0000  100.0000  141.3370
 100.0000  100.0000  116.9523
        0         0   54.9420
  10.0000         0   36.9229
  20.0000         0   70.5617
  30.0000         0   30.5953
  40.0000         0   34.5474
  50.0000         0   47.0488
  60.0000         0   11.4761
  70.0000         0   37.6386
  80.0000         0   20.1398
  90.0000         0   22.9232
 100.0000         0   29.1138
        0         0   54.9420
        0   10.0000   -2.9088
        0   20.0000   39.9287
        0   30.0000   31.6726
        0   40.0000   24.5548
        0   50.0000  105.5842
        0   60.0000  130.5641
        0   70.0000  116.5640
        0   80.0000   24.0367
        0   90.0000   50.8359
        0  100.0000   48.6345
 100.0000         0   29.1138
 100.0000   10.0000   38.6237
 100.0000   20.0000   66.5028
 100.0000   30.0000   45.9631
 100.0000   40.0000   89.7711
 100.0000   50.0000   89.2857
 100.0000   60.0000  106.7689
 100.0000   70.0000   53.4243
 100.0000   80.0000  126.1221
 100.0000   90.0000  104.2912
 100.0000  100.0000  116.9523