### Joint tomography using three-dimensional sensitivity of finite-frequency body and surface waves

The ultimate goal of seismic tomographic inversions is to provide direct constraints on the physical and chemical states of the solid earth (e.g., temperature, composition, and partial melt). As we try to go beyond identifying “blue” and “red” areas in tomographic images (high and low wavespeeds, respectively), it becomes crucial that we recover the true form and magnitude of velocity anomaly as closely as seismic data permit. For relatively small-scale features, such as mantle plumes, this has been difficult or impossible in conventional tomographic inversions due to a fundamental limitation in ray theory. Ray theory is valid strictly only in the limit of infinite frequency. In ray theory, the travel times of body waves or the phase delays of surface waves are attributed to velocity variations along geometric ray paths. For velocity heterogeneity on scales smaller than the Fresnel zone of seismic waves, ray approximation overestimates travel time shifts and phase delays because it does not account for wavefront healing and other finite-frequency effects of wave diffraction. Consequently, tomographic inversions based on ray theory likely underestimate the magnitude of velocity anomaly.

In this project, we capitalize on the recent advancements in wave propagation theory by developing a tomographic method using the 3D sensitivities of finite-frequency seismic waves across a regional seismic array. In particular we develop a joint P and S body wave tomography for compressional and shear velocities.