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Interpolation[funcvaluelist,Method→"Shepard",(options)] represents a way to perform interpolation according to Shepard's method, when funcvaluelist is a list of scattered control points together with the function values in these points. 
DistanceFunction  Automatic  distance function to use in calculation of the distance matrix and the calculation of the distance from the interpolation point to the control points. Note, that the function here is expected to return the square of the distance  
ShepardPower  6  The weight of each control point is proportional to the distance, taken to the inverse ShepardPower power. 
If the same interpolation should be used in many different points, the function can be precompiled without specifying in which point it will be used. Note, in the plot below, that extrapolation is used along the border of the plot. In the plot below, you might test with different values for the ShepardPower option.
