Structural sensitivities of finite‐frequency seismic waves: a full‐wave approach

SUMMARY We use the normal‐mode theory to investigate the sensitivities of the delay times of finite‐frequency seismic waves to 3‐D perturbations in wave speeds relative to 1‐D reference models. The normal‐mode theory provides the exact solutions to the wave equation in 1‐D models, thus enabling a full‐wave approach to the wave propagation in the sense that for a given pair of source and receiver, it accounts for all the waves that travel from the source to the receiver following any possible paths, and that it models accurately all the possible wave effects such as diffraction and non‐geometrical propagation. We illustrate the complex picture of finite‐frequency wave propagation using a series of numerical examples of the 3‐D Fréchet kernels for the delay times of different kinds of seismic arrivals. We demonstrate that owing to the accuracy in modelling multipathing and non‐geometrical arrivals, the full‐wave approach provides a practical means to utilize seismic signals that are often discarded in conventional high‐frequency tomography methods, such as the surface reflected phases at regional distances that carry rich information on the structures in the upper‐mantle transition zone. For this reason, tomography resolution in the upper mantle can be greatly improved by using the full‐wave, finite‐frequency Fréchet kernels. Moreover, the full‐wave approach is also well suited for studying structures near other velocity discontinuities such as the core–mantle boundary.