Depth migration with Gaussian wave packets based on Poincaré wavelets

Abstract

An approach to depth migration, based on an integral representation of seismic data, that is, wavefields recorded on the boundary, is presented in terms of Poincaré wavelets. Each wavelet is taken as a boundary datum for a high-frequency asymptotic solution of the wave equation. This solution, which we call the quasiphoton or the Gaussian wave packet, decreases in a Gaussian manner away from a point running along a ray that is launched from the surface. The deformation of the propagating packet is taken into account in the migration algorithm. A numerical example of zero-offset migration with synthetic seismograms calculated for the 2-D SEG/EAGE salt model is presented. The result, which uses only 3.9 per cent of the total number of coefficients, is a satisfactory image, with a threshold of 0.75 per cent.