Large-offset P-wave traveltime in layered transversely isotropic media
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Large-offset seismic data processing, imaging, and velocity estimation require an accurate traveltime approximation over a wide range of offsets. In layered transversely isotropic media with a vertical symmetry axis, the accuracy of traditional traveltime approximations is limited to near offsets. We have developed a new traveltime approximation that maintains the accuracy of classic equations around the zero offset and exhibits the correct curvilinear asymptote at infinitely large offsets. Our approximation is based on the conventional acoustic assumption. Its equation incorporates six parameters. To define them, we use the Taylor series expansion of the exact traveltime around the zero offset and a new asymptotic series for the infinite offset. Our asymptotic equation indicates that the traveltime behavior at infinitely large offsets is dominated by the properties of the layer with the maximum horizontal velocity in the sequence. The parameters of our approximation depend on the effective zero-offset traveltime, the normal moveout velocity, the anellipticity, a new large-offset heterogeneity parameter, and the properties of the layer with the maximum horizontal velocity in the sequence. We have applied our traveltime approximation (1) to directly calculate traveltime and ray parameter at given offsets, as analytical forward modeling, and (2) to estimate the first four of the aforementioned parameters for the layers beneath a known high-velocity layer. Our large-offset heterogeneity parameter includes the layering effect on the reflections’ traveltime.