Seismics and optics: hyperbolae and curvatures

We rederive and generalize hyperbolic moveout formulae for the common-midpo int (CMP) gather and for the zero-offset (ZO) section that can be efficient ly used for macro-model-independent reflection imaging in two-dimensional m edia. The hyperbolic moveout formulae for the common-midpoint gather an obt ained from different Taylor series expansions of a particular parametric mo veout surface defined in the multicoverage data space. Such a moveout surfa ce involves three kinematic wave-field attributes of two hypothetical waves , which have to be determined by a coherency analysis. By using hyperbolic moveout curves in the GRIP gather and in the ZO section one can determine t hese attributes in two steps. The relationships between the local shapes of the interfaces and the attributes of the hypothetical wave-fields attribut es are considered by means of geometrical optics. The determination of thes e attributes allows to perform a macro-model-independent ZO simulation and a subsequent inversion. (C) 1999 Elsevier Science B.V. All rights reserved.