## Kirchhoff integrals and Fresnel zones

**Ludek Klimes**
### Summary

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.

### Keywords

Kirchhoff integral, Fresnel zone, travel time.

### Whole paper

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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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