A comparison of methods to determine measurement support volumes

We examine methods that can be used to identify the spatial filter function associated with the measurement of quantities on two scales. We divide the methods into two general classes: deconvolution methods and sensitivity-based methods. We briefly describe the two classes of methods, provide examples of each from the literature, and introduce a new sensitivity-based method inspired by Backus-Gilbert model resolution ideas, We compare the approaches by examining the filter function that relates smaller-scale grid block parameters to parameters determined by a Theis model interpretation of drawdown data. In general, we find that sensitivity approaches are easier to implement numerically and are less subject to the problems of identifiability, stability, and uniqueness associated with deconvolution methods.