Kirchhoff synthetics for seismic reflections and diving waves in two dimensions and application to the D" layer

The Kirchhoff-Helmholtz (KH) integration has been used to model the reflected and the diving waves from an interface with a positive velocity gradient. The modelling is carried out for a spherical boundary and for a sinusoidal topography with a long-scale wavelength.
An artefact, which is a major problem in modelling the seismic response using the KH integration, has been reduced by introducing a Hilbert transform sign manipulation. Cleaner synthetic seismograms with correct amplitudes have been produced by this method. A discretization in larger surface elements has been made possible by introducing a smoothing factor that suppresses the noise that normally follows the constructed signal if a large element size is taken.