Type
ArticleAuthors
Alkhalifah, Tariq Ali
KAUST Department
Earth Science and Engineering ProgramEnvironmental Science and Engineering Program
Physical Science and Engineering (PSE) Division
Seismic Wave Analysis Group
Date
2012-05Permanent link to this record
http://hdl.handle.net/10754/562172
Metadata
Show full item recordAbstract
Many of the explicit prestack traveltime relations used in practice are based on homogeneous (or semi-homogenous, possibly effective) media approximations. This includes the multifocusing, based on the double square-root (DSR) equation, and the common reflection stack (CRS) approaches. Using the DSR equation, I constructed the associated eikonal form in the general source-receiver domain. Like its wave-equation counterpart, it suffers from a critical singularity for horizontally traveling waves. As a result, I recasted the eikonal in terms of the reflection angle, and thus, derived expansion based solutions of this eikonal in terms of the difference between the source and receiver velocities in a generally inhomogenous background medium. The zero-order term solution, corresponding to ignoring the lateral velocity variation in estimating the prestack part, is free of singularities and can be used to estimate traveltimes for small to moderate offsets (or reflection angles) in a generally inhomogeneous medium. The higher-order terms include limitations for horizontally traveling waves, however, we can readily enforce stability constraints to avoid such singularities. In fact, another expansion over reflection angle can help us avoid these singularities by requiring the source and receiver velocities to be different. On the other hand, expansions in terms of reflection angles result in singularity free equations. For a homogenous background medium, as a test, the solutions are reasonably accurate to large reflection and dip angles. A Marmousi example demonstrated the usefulness and versatility of the formulation. © 2012 Society of Exploration Geophysicists.Citation
Alkhalifah, T. (2012). Prestack traveltime approximations. GEOPHYSICS, 77(3), U31–U37. doi:10.1190/geo2011-0465.1Publisher
Society of Exploration GeophysicistsJournal
Geophysicsae974a485f413a2113503eed53cd6c53
10.1190/geo2011-0465.1