Is the Bulls Eye Effect generally caused by a sample point with a high value being too far from other sample points?
Or rather a sample point with a higher value than others close to it?
What exactly causes this?
The bulls eye effect describes concentric areas of the same value around known data points. It's simply an unfortunate artifact of IDW interpolation. The effect gets worse the more isolated your data points are.
IDW suffers from this problem more than other interpolation methods (e.g., Kriging), but to a large extent nearly any interpolation method will give unreliable results if the points are sparse and clustered. Conversely, you'll get good results with a range of methods if your points are dense and uniformly spaced.
If the power is large, in the range of 10 and greater, the IDW approximates a polygonal interpolation method. That is, the closest point's value dominates the calculation summations. When the distance crosses 1/2 the distance to the next closest point the cell values switch to the now closest point. This is the easiest way I know to imprint a polygonal estimation method onto a gridded surface.
Likewise, if the power is 1/10, the farther points have a greater influence than the closest point. (Can't think of a practical use for this)!