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Formulation of the problem

We want to solve the deconvolution problem:

 
y = a * x , (8)

y being the data, x the unknowns, a the convolution filter. It can be written in the matricial form A.x=y, with:

\begin{displaymath}
x=(x_1,\ldots,x_{n_x})^T\;,\mbox{\hspace{1.0cm}} y=(y_1,\ldots,y_{n_y})^T\;,\mbox{\hspace{1.0cm}}n_y = n_a + n_x -1\;,\end{displaymath}

 
 \begin{displaymath}
A=\pmatrix{a_1 & & & & \cr
 a_2 &a_1& &0 & \cr
 \vdots&a_2&\...
 ..._{n_a}\cr} \mbox{\hspace{1.5cm} ($n_y\times n_x$\space matrix)}\end{displaymath} (9)

I will consider two kinds of deconvolution:
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Stanford Exploration Project
1/13/1998