Combined LSJIMP Data and Model Residuals  

To effect the final step of LSJIMP, the estimation of the optimal set of $\bold m_{i,k,m}$, we minimize a quadratic objective function which consists of the sum of the weighted $\ell_2$ norms of the data residual [equation ()] and of the three model residuals [equations (), (), and ()]:  

$$\mbox{ \raisebox{-1.0ex}{ $\stackrel{\textstyle \mbox{\LARGE... ...} \Vert^2 \; + \; \epsilon_3^2 \Vert \bold r_m^{[3]} \Vert^2.$$ (12)

$\epsilon_1, \epsilon_2,$ and $\epsilon_3$ are scalars which balance the relative weight of the three model residuals with the data residual. For the large scale problems endemic to seismic imaging, the conjugate gradient method is a logical choice to minimize $Q(\bold m)$.