Joint imaging with streamer and ocean bottom data |

We pose the imaging problem as an inversion problem by linearizing the wave-equation with respect to our model ( ). Assuming that the earth behaves as a constant-density acoustic isotropic medium, we linearize the wave equation and apply the first-order Born approximation to get the following forward modeling equation:

where represents the forward modeled data, is the temporal frequency, represents the reflectivity at image point , is the source waveform, and is the Green's function of the two-way acoustic constant-density wave equation. Note that is actually dependent. It is important to point out that the adjoint of the forward modeling operator is the migration operator:

(2) |

The inversion problem is defined by minimizing the least-squares difference between the synthetic and the recorded data: One can use various types of propagators to formulate the Green's function. In our study, we use the two-way propagator. In this case, the migration operator is equivalent to reverse time migration (RTM). The inverted image ( ) is better than the migration image in the sense that its forward-modeled data fits the recorded data. Next, we discuss how to apply linearized inversion to jointly image with streamer and OBN data.

Joint imaging with streamer and ocean bottom data |

2012-05-10