Pseudoinverse to nearest-neighbor NMO

Examine the matrix ${\bf N' \, N}$:

 

$${\bf N'\,N} \eq \left[ \begin{array} {cccccccccc} .&.&.&... ...&.&.&.&.&.&.&.&1&. \ .&.&.&.&.&.&.&.&.&1 \end{array} \right]$$ (19)

Any mathematician will say that equation (19) is not invertible because the zeros on the diagonal make it singular. But as a geophysicist, you know better. Our inverse, called a ``pseudoinverse,'' is

$$({\bf N'\,N})^{-1} \eq \left[ \begin{array} {cccccccccc} ... ... &. &. &. &1&. \ .&.&.&.&. &. &. &. &.&1 \end{array} \right]$$ (20)

We could write code for inverse NMO, which is an easy task, or we could try to write code for inverse NMO and stack, which has no clean solution known to me. Instead, we move to other topics.