Accelerometer, Interpolation, Extrapolation and severe edge effects

Hello, I have accelerometer data from 12 stations over an approximately 85x85m grid. I am able to interpolate/extrapolate out to fill my grid, but I am getting severe edge effects. I know for a fact that the ground did not move in such a fashion. Think of it more like a speaker or a piston in a rigid baffle. I am taking the ground motion data and converting it into acoustic pressure. The biggest problem I'm having is the edges. Is there a way to interpolate/extrapolate that pins the edges of my grid to zero so that the edges don't fly around in a very unrealistic fashion? Any help would be greatly appreciated.

Extra information: I have used three different methods for the interpolation/extrapolation and they all pretty much result in the same issue. I first tried griddata alone, this creates a nice interpolation but lacks the extrapolation out to the edges. I then used inpaintnans around griddata to get to the edges. This is where the huge edge effects occur. Finally, I tried Scattered Data Interpolation and Approximation using Radial Base Functions (<http://www.mathworks.com/matlabcentral/fileexchange/10056-scattered-data-interpolation-and-approximation-using-radial-base-functions)>. This produced the best results with the least edge effects, but it is still unrealistic and won't work for my calculations.