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) |

where is frequency, represents the reflectivity at image point , is the source waveform, and is the Green's function that is the solution to the two-way acoustic constant-density equation. In practice, the Green's function is calculated using a finite-difference time-domain technique, and the multiplication in the frequency domain is replaced by a zero-lag cross-correlation in the time domain.

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) |

In least-squares reverse time migration (LSRTM), the forward modeled data is defined to be the Born approximation of the linearized acoustic wave equation:

(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 |

2011-05-24