Hung, Shu-HueiShu-HueiHungDahlen, F. A.F. A.DahlenNolet, GuustGuustNolet2019-07-022019-07-022000-01-010956540Xhttps://scholars.lib.ntu.edu.tw/handle/123456789/4122683-D Born-Fréchet traveltime kernel theory is recast in the context of scalar-wave propagation in a smooth acoustic medium, for simplicity. The predictions of the theory are in excellent agreement with 'ground truth' traveltime shifts, measured by crosscorrelation of heterogeneous-medium and homogeneous-medium synthetic seismograms, computed using a parallelized pseudospectral code. Scattering, wave-front healing and other finite-frequency diffraction effects can give rise to cross-correlation traveltime shifts that are in significant disagreement with geometrical ray theory, whenever the cross-path width of wave-speed heterogeneity is of the same order as the width of the banana-doughnut Predict kernel surrounding the ray. A concentrated off-path slow or fast anomaly can give rise to a larger traveltime shift than one directly on the ray path, by virtue of the hollow-banana character of the kernel. The often intricate 3-D geometry of the sensitivity kernels of P, PP, PcP, PcP2, PcP3, ... and P+pP waves is explored, in a series of colourful cross-sections. The geometries of an absolute PP kernel and a differential PP-P kernel are particularly complicated, because of the minimax nature of the surface-reflected P P wave. The kernel for an overlapping P+pP wave from a shallow-focus source has a banana-doughnut character, like that of an isolated /-wave kernel, even when the teleseismic pulse shape is significantly distorted by the depth phase interference. A numerically economical representation of the 3-D traveltime sensitivity, based upon the paraxial approximation, is in excellent agreement with the 'exact' ray-theoretical Fréchet kernel. © 2000 RAS.Body waves | Fréchet derivatives | Global seismology | Ray theory | Tomography, traveltimejournal article10.1046/j.1365-246X.2000.00072.x2-s2.0-0034104547https://api.elsevier.com/content/abstract/scopus_id/0034104547