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Basics of Seismic Migration

I present the theory of seismic migration. Denote the earth's reflectivity distribution by the vector m, the recorded seismic data by the vector d, and the Born forward modeling operator by L. In this case, d=Lm represents the Born approximation to forward modeling so that migration is defined to be the adjoint operator L^T applied to the data d, that is m_mig = L^Td. I show several interpretations of migration, including "migration image is obtained by smear- ing data along ellipses", "migration image is obtained by summing data along hyperbolas", and "migration is the first iteration of a steepest descent method that minimizes the sum of the squared data residuals". I show how the resolu- tion of a migration image is obtained using ideas borrowed from the generalized Radon transform.

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