Angle domain common image gathers extracted from reverse time migrated images in isotropic acoustic and elastic media

Abstract

We propose an alternative (new) method to produce common image gathers in the incident-angle domain by calculating wavenumbers directly from the P-wave polarization rather than using the dominant wavenumber, for obtaining the normal to the source wavefront. In isotropic acoustic media, the wave propagation direction can be directly calculated as the spatial gradient direction of the acoustic wavefield, which is parallel to the wavenumber direction (the normal to the wavefront). Instantaneous wavenumber, obtained via a novel Hilbert transform approach, is used to calculate the local normal to the reflectors in a stacked migrated image. The local incident angle is produced as the difference between the propagation direction and the normal to the reflector. By reordering the migrated images (over all common-source gathers) by incident angle, common-image gathers are produced in the incidentangle domain. Pand S-wave separations allow both PP and PS common-image gathers to be calculated in the angle domain. Unlike the space-shift image condition for calculating the common-image gather in the angle domain, we use a crosscorrelation image condition, which is substantially more efficient. The proposed method is a direct method, and the resolution of the local incident angles is higher than those of Fourier transform-based methods. In addition, this method is less dependent on the data quality than the space-shift method. The concepts are successfully implemented and illustrated with 2D synthetic acoustic and elastic examples.