Least-squares migration/inversion of blended data

LSI in the data space

The data-space LSI minimizes the following objective function:

$$F({\bf m}) = \vert\vert\widetilde{\bf L}{\bf m}-\widetilde{\bf d}_{\rm obs}\vert\vert _2^2+\epsilon\vert\vert{\bf A m}\vert\vert _2^2.$$ (7)

The data-space objective function $F({\bf m})$ can be minimized through gradient-based optimization schemes, which iteratively reconstruct the model parameters. The advantage of this data-space formulation is that it does not require explicitly building the Hessian operator; hence all crosstalk information is captured implicitly. However, the data-space formulation lacks flexibility and can not be implemented in a target-oriented fashion. Its cost is another concern, because each iteration costs about the same as two migrations, making it challenging for large scale applications. The cost can be significantly reduced by using proper preconditioners, which may speed up the convergence considerably.

Least-squares migration/inversion of blended data