  We present the development of extended diffraction tomography, a new approach
to the solution of the linear seismic waveform inversion problem. This method
has several appealing features, such as the use of arbitrary depth-dependent
reference models and the decomposition of the full 2D or 3D inverse problem
into a large number of independent 1D problems. This decomposition makes the
method naturally highly parallelizable. Careful implementation yields
significant robustness with respect to noise. Several synthetic examples are
shown which characterize the benefits of our method and demonstrate the
usefulness of choosing realistic 1D reference media.
