The Kirchhoff-Helmholtz Transform Pair

Modeling a reflected wave by the Kirchhoff-Helmholtz integral consists of an integration along the reflector. By<br>this, one sums up the Huygens secondary-source contributions to the wavefield at the observation point. The<br>proposed asymptotic inverse Kirchhoff-Helmholtz integral, by which this modeling process is inverted, works in<br>a completely analogous way. It consists of an integral along the reflection traveltime surface of the reflector.<br>For a point on the reflector, one sums up the reflected-wave contributions present at the respective reflectiontraveltime<br>surface associated with the related source-receiver pair. The new inverse integral reconstructs the<br>Huygens sources along the reflector, providing their positions and amplitudes. In this way, one can devise a new<br>true-amplitude migration algorithm.