Availability of Fresnel volume migration to one-component seismic reflection data using tau-P transforms

An elastic wave propagates in the spatial volume depending on its wavelength, which is called the Fresnel volume. In the seismic migration, diffracted waves are propagated back to every secondary seismic source, i.e., diffractors or scatterers that represent detailed underground structures. Fresnel volume migration is based on an idea of restricting the aperture in which a migration operator is applied in space and time. The conventional Fresnel volume migration uses the paraxial ray method for a single component data. Schleicher et al. (1997) addressed an important role of the Fresnel zones in the framework of the theory of pre-stack true-amplitude migration and demigration. Luth et al. (2005) extended the method to the three-components (3C) Kirchhoff prestack depth migration in which the migration operator is applied in the Fresnel volume using the measured polarization direction at a 3C receiver to determine the points of possible reflections. In seismic reflection surveys, recorded P- and S- waves could be decomposed into two wavefields. Mikada et al. (2009) worked about the decomposition of seismic wavefield into compressional (P or scalar) and shear (S or vector) wavefields. This method gives us the incident angles of the two waves to receivers. Therefore, it becomes possible to estimate the incident angles and to use the angles in the Fresnel volume migration. In this study, we consider both Fresnel volume migration and Kirchhoff migration for acquired data in our laboratory’s water tank. The tank size is 3m x 2m x 1.5m. The target structure is a pinball describing reflection point whose size is almost negligible compared to the wavelength of acoustic signals. In the acquired shot gather, there is characteristic difference in S/N ratio. When receivers are located in the left side of the pinball target, received data has comparatively small S/N ratio, while received data has high S/N ratio for receivers on the other side. A method using pre-stack depth migration with the aperture restricted to the Fresnel volume is applied to image underground structure after the decomposition of recorded reflection data. For the decomposition, we used the method using tau-P transform. Our result shows that Fresnel volume migration is a better focusing tool than Kirchhoff migration when S/N of acquired data is high. Kirchhoff migration has in general less migration smile than the Fresnel volume migration. Also, at the migrated data by Fresnel volume has also difference in S/N ratio same as acquired data. Left side of the target has little migration smiles, while right side results in much higher migration smiles. This result indicates that the Fresnel volume migration needs a certain critical level of S/N ratio. This is because the estimation of incident angles for defining the Fresnel volume position using tau-P transforms for received data needs higher S/N ratio than Kirchhoff migration.