Kirchhoff integrals and Fresnel zones

Ludek Klimes


The accuracy and efficiency of the numerical quadrature of the Kirchhoff integrals is studied. The weighting function localizing the Kirchhoff integral is derived. The weighting function minimizes the number of discrete values necessary for the numerical quadrature. The Fresnel zones are then derived as the minimum areas of integration with the specified accuracy. The new, explicit, and very general definition of Fresnel zones is purely local, independent of the reference travel times. The definition of Fresnel zones is expressed in terms of the first and second derivatives of the sum of travel times along the surface of integration. As far as the author can appreciate, the new, quantitative definition of Fresnel zones is conformal with other, usually qualitatively or empirically derived definitions, within the regions of their applicability.


Kirchhoff integral, Fresnel zone, travel time.

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In: Seismic Waves in Complex 3-D Structures, Report 1, pp. 77-84, Dep. Geophys., Charles Univ., Prague, 1994.
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