Fréchet kernels for finite-frequency traveltimes-II. Examples

Details Fréchet kernels for finite-frequency traveltimes-II. Examples Fréchet kernels for finite-frequency traveltimes-II. Examples

Apr 2000

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2000geoji.141..175h&link_type=abstract

Geophysical Journal International, Volume 141, Issue 1, pp. 175-203.

Astronomy and Astrophysics

Astronomy

92

Body Waves, Fréchet Derivatives, Global Seismology, Ray Theory, Tomography, Traveltime

Scientific paper

3-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 cross-correlation 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 Fréchet 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 PP wave. The kernel for an overlapping P + pP wave from a shallow-focus source has a banana-doughnut character, like that of an isolated P-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.

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