Traveltime sensitivity kernels: Banana-doughnuts or just plain bananas?

Introduction

Estimating an accurate velocity function is one of the most critical steps in building an accurate seismic depth image of the subsurface. In areas with significant structural complexity, one-dimensional updating schemes become unstable, and more robust algorithms are needed. Reflection tomography both in the premigrated (Bishop et al., 1985) and postmigrated domains (Stork, 1992; Kosloff et al., 1996) bring the powerful technologies of geophysical inversion theory to bear on the problem.

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.

Traveltime sensitivity kernels: Banana-doughnuts or just plain bananas?