# CRS theory based on a data-driven homeomorphism

Ernesto Bonomi

Journal of Geophysics and Engineering, Volume 14, page 570-585 - 2017

The present article outlines an innovative derivation of the well-known CRS traveltime formula. This is made possible by approximating the isochrones tangent to a small reflecting element embedded in a 3D homogeneous auxiliary medium. The arising paraxial traveltime formula is then parametrised by six attributes, each one characterising geometrically the wavefront of the reference normal-incident ray at the emergence point x0 of the datum plane. For a layered medium, the assignment of the six attributes for each azimuthal direction around x0 describes locally the emerging wavefront and establishes the mapping between reflecting elements of the two media, the auxiliary and the real, which respond, however, with different traveltimes. This 3D homeomorphism provides the time correction that gives rise to the CRS traveltime formula with eight attributes. For time imaging applications, the traveltime profile must be numerically shaped by improving iteratively the value of the eight attributes, so as to intercept, without the need of a velocity model, the largest number of coherent data in the volume of seismic traces gathered in the midpoint-offset domain.

## BibTex references

@Article{Bon17,
author = {Bonomi, E.},
title = {CRS theory based on a data-driven homeomorphism},
journal = {Journal of Geophysics and Engineering},
volume = {14},
pages = {570-585},
year = {2017},
publisher = {IOP Publishing},
keywords = {CRS stacking,data-driven imaging,velocity-independent imaging,seismic processing},
doi = {10.1088/1742-2140/aa61d8},
url = {http://publications.crs4.it/pubdocs/2017/Bon17},
}

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