Resolution conditions of wave equation imaging
Presenter: Haw-Chun Wang Adviser: How-Wei Chen
Abstract
Wave equation migration such as Kirchhoff migration, Reverse Time migration and Least Squares migration, Full Waveform inversion as well as travel-time inversion are common tools to investigate the earth structure in seismic data processing. In spite of their different approach, those methods share a similar imaging condition which is associate with the wave path and dominant frequency band in a homogeneous model. The shape and size of their migration trajectory corresponds to a fat ellipse, with source and receiver as the foci. More rigorously speaking, the fat ellipse is an area within the 1st Fresnel zone as well as the sensitivity kernel. The wave paths from source and receiver to the scatterer point have a residual less than half a waveform and cause constructive interference.
The Born-type modeling and migration approximation is strongly associated with the first Fresnel Zone imaging principle and the source-scatterer-receiver distance. For waveform migration, one of the resolving conditions is affected by the offset-dependent arrivals. The far-offset traces would contribute to better horizontal resolution while near-offset traces provide better vertical resolution. In this research, synthetics from homogeneous model are migrated by Least Square migration. The resolution limits of several common arrivals, such as diving waves, reflected waves and diffracted waves are been discussed from geometrical (ray path) and Born approximation point of view. Also, the formulas for migration-data kernels of each arrivals are also derived, which are applicable to images formed by those wave equation imaging method mentioned in the beginning.
References
Huang, Y., Schuster, G.T., 2014. Resolution limits for wave equation imaging. Journal of Applied Geophysics 107 (2014) 137–148.
Schuster, G.T., 2010. Basics of Seismic Imaging. KAUST.