Depth-variant mapping and moveout correction of converted-wave data

Robin Tage Slotboom, Donald C. Lawton

Converted-wave imaging is more complex than compressional-wave imaging because of the nonsymmtery of the raypath geometry of converted-wave (P to Sv) data and the variance of the offset location of the conversion point with depth. P to S raytracing through a southern Alberta model shows that this depth variance is most significant at the shallow depths where the offset-to-depth ratio is greater than one, and that the conversion point trajectory tends to an asymptote value with depth. The nonsymmetry of the raypath geometry implies that midpoint gathering cannot be used, and the depth variance of the offset location of the conversion point implies that for correct imaging, gathering must be done on a depth-variant basis. The traveltime curves of converted-wave data are different than those of compressional-wave data and therefore the compressional-wave hyperbolic approximation cannot be used. A review of literature revealed that most converted-wave images to date have been constructed by gathering and stacking in a manner analogous to conventional compressional-wave gathering and stacking, except some value other than the midpoint value is used. This value is usually the asymptote value. Work done shows that depth variance is important. Depth-variant mapping is proposed to properly reconstruct converted-wave images. Application of various methods to synthetic data show that depth-variant mapping gives superior results to other methods which tend to smear the image. An improved expression for removing the moveout of converted wave data in a single isotropic layer is given, and it is shown to be accurate and stable for large offset-to-depth ratios.