Theory

The addition of a second simultaneous linear operator expands the usual linear inversion equations to the slightly more complicated linear operator Claerbout (1999),

$${\bf L}=[{\bf L}_1 \; {\bf L}_2]$$

and a correspondingly longer model vector

$${\bf m}=\left [ \frac{{\bf m}_1}{{\bf m}_2}\right ] \;.$$

This simple introduction leads to the form of the inversion goals used here

$$\begin{eqnarray}[{\bf L}_h {\bf L}_l] \left [ \frac{{\bf m}_h}{{\bf m}_l} \right... ...^2 {\bf I}\left [ \frac{{\bf m}_h}{{\bf m}_l}\right ] & = & 0 \;, \end{eqnarray}$$ (1) (2)

where subscripts h and l refer to the hyperbolic (HRT) and linear (LRT) radon transforms and we add identity operator regularization to provide damping.