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Finite-Frequency Sensitivity Kernels of Head Waves

While in ray theory travel-time anomaly is sensitive only to velocity perturbation along the geometric ray path and the sensitivity is the same along the ray path, head waves with finite frequencies are sensitive to the 3D structure in a complex way. Below the interface, the peak travel-time sensitivity is located near the two piecing points of the geometric ray entering and leaving the interface. The pattern of positive and negative sensitivities approximately matches with the Fresnel zones. Unlike the turning waves, the sensitivity right beneath the interface is non-zero along the source-receiver path. The sensitivity beneath the layer interface is strong at some distance from the ray path, depending on the wavelength and propagation distance. There is a local minimum (zero) in the travel-time sensitivity kernel surrounded by negative sensitivity kernels below the interface. Cossing head wave ray paths do not necessarily sample the same structure beneath the interface. Because the distribution of the sensitivity kernels is a function of wavelength, head waves are dispersive if the velocity structure in the lower layer has a gradient with depth. Thus the finite-frequency head wave kernels may provide a powerful tool to constrain the vertical velocity gradient in the mantle lithosphere and extend the head wave (Pn/Sn) tomography from presently two dimensions to three dimensions.

The traveltime sensitivity kernels for the head wave on the horizontal planes at depths below and above the interface that separates the low and high velocity layers. The green line marks the head wave ray path. The source is located on the left side of this figure. The negative (red colors) and positive (blue colors) values are so defined that a low-velocity anomaly located in the region of the negative kernels results in a travel time delay and the same velocity perturbation in the region of positive kernels leads to an earlier head wave arrival. (upper right) The traveltime sensitivity kernel for the head wave on a vertical profile half way between the source and receiver and perpendicular to the ray path. The dashed line is the layer interface. (lower right) The traveltime sensitivity kernels for the head wave on the vertical profile containing the source and receiver. Zhang et al., GJI, 2007. (pdf)