In seismic reflection tomography, the velocity model of the subsurface is updated by back-projecting travel-time residuals along ray-paths. The travel-time residuals are picked from the seismic data itself and the methodology used to gather these picks is a fundamental part of any velocity inversion workflow. In particular, the density at which the residuals are represented in the four-dimensional data space (inline, crossline, offset and depth/time) appears to have a significant effect on the precision of the velocity updates that are output from the tomographic inversion. Utilising dense, hyperbolic- (or parabolic-) fitting means that the residuals are finely sampled in the data space but does not necessarily represent their true values with great accuracy. Dense, non-hyperbolic fitting offers a similarly fine sampling but with greater adherence to the true residual value. These two methodologies have been compared and contrasted on a complex synthetic dataset. It can be seen from this comparison that the dense, non-hyperbolic tomography offers greater potential for resolving small-scale velocity heterogeneities in the Earth.


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