Least-squares reverse time migration for the Cascadia ocean-bottom dataset |
In OBS acquisition, pre-stack images are created from data in the common-receiver domain. This intrinsically requires that each trace in the CRG is de-signatured. In RTM, the migration image is a linear operator applied to the recorded data:
(1) |
The difference between mirror imaging and higher-order mirror imaging lies within the incident wavefield, , which is calculated differently to the method described in the previous two sub-sections.
To obtain a better reflectivity image, we go beyond migration by formulating the imaging problem as a least-squares inversion problem. The solution is obtained by minimizing the objective function , which is defined as the least-squares difference between the forward modeled data and the recorded data .
(2) |
(3) |
It is important to point out that the forward modeling operator is the adjoint of the reverse-time migration operator . Even for the case of modeling certain classes of surface-related multiples, the operator is still linear with respect to . This is because simulates only events that would interact with the model space once.
Least-squares reverse time migration for the Cascadia ocean-bottom dataset |