Gradient Sensitivity Kernels for Structural Analysis

In recent years there has been considerable emphasis on the calculation of sensitivity kernels for Earth structure for different types of seismological information. The basis of such results has been a first order Born approximation in terms of variations in wavespeeds or density. Such a model requires scattering to produce travel time changes, with non-intuitive consequences such as lack of sensitivity along a ray path. A different class of sensitivity kernels can be developed by working with velocity gradients through a integration by parts. The resulting kernels do not depend on localized scattering. In particular they restore the sensitivity near the turning point of a ray that has been successfully employed for many years in seismic interpretation. For a 1-D inversion, such `quelling' is required to remove singularities and there are major benefits in 3-D as well since attention is focused on those regions where there are changes in structure.