The data resolution matrix

Since matrix A+ solves the inverse problem Am = d, it is often called the generalized inverse matrix A = A (Menke, 1989). 

VVc can now retros])ediv( ly ask how well (his ostirnate mo fils the observed data d  

If N -- I is an identical matrix, then d — d, and the prediction errors arc zero. In general eases 

From the last foi innla one can see that the predicted value r/ is the wedghted average of the observed data r/,..], (/, and di+. So, the rows of the re.solution matrix N 

Note also that the data resolution matrix is not a function of the data but only of the operator of the forward problem. It can therefore be studied without actually performing the geophysical observations and can therefore be used for planning the field experiment. 

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