Global wave-equation reflection tomography

In tomography it has been recognized that the finiteness of the frequency content of seismic data leads to interference effects in the process of medium reconstruction, that need to be accounted for. Various ways of looking at these effects in the framework of transmission tomography can be found in the literature. Here, we consider single-scattered body waves and develop from our earlier work on inverse scattering a method of wave-equation reflection tomography – which in exploration seismics is identified as a method of wave-equation migration velocity analysis – admitting bandlimited data. In the transition from transmission tomography to reflection tomography the usual cross correlation between modelled and observed data is replaced by modelled annihilators applied to the observed data. Using the generalized screen expansion for one-way wave propagation, we derive the Fréchet or sensitivity kernels and explain how they can be evaluated with an adjoint state method.