The formulae for the calculation of the Fresnel zones or volumes
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The symmetrized invariant formulae for the calculation of Fresnel zones or volumes are derived. It is assumed that an inhomogeneous medium with curvilinear interfaces is located between the source and/or the receiver and along the central ray within the Fresnel zone or volume. In the vicinity of the zone centre, the medium is considered locally homogeneous. The formula for the leading term of the field of a wave scattered by a bent body immersed in the above-mentioned medium is obtained by the Kirchhoff approximation. With the help of this formula and the expressions for the Fresnel radii for a particular case, the formulae for the Fresnel zones in the general case considered are obtained on the basis of the reciprocity relation. The formulae for the Fresnel zones are used to obtain the expressions for the Fresnel volumes. The physical consequences of the derived formulae with respect to the validity of the ray formulae and the resolution of seismic methods etc. are discussed.
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