Unfortunately, however, inversion methods can be limited by the accuracy of their forward modeling operators, and most practical implementations of traveltime tomography are based on ray-theory, which assumes a high frequency wave, propagating through a smoothly varying velocity field, perhaps interrupted with a few discrete interfaces. Real world wave-propagation is much more complicated than this, and the failure of ray-based methods to adequately model wave propagation through complex media is fueling interest in ``wave-equation'' migration algorithms that both accurately model finite-frequency effects, and are practical for large 3-D datasets. As a direct consequence, finite-frequency velocity analysis and tomography algorithms are also becoming an important area of research Biondi and Sava (1999); Woodward (1992).
Recent work in the global seismology community Marquering et al. (1998, 1999) is drawing attention to a non-intuitive observation first made by Woodward (1992), that in the weak-scattering limit, finite-frequency traveltimes have zero-sensitivity to velocity perturbations along the geometric ray-path. This short-note aims to explore and explain this non-intuitive observation.