Seismic refraction profiles between Cyprus and Israel and their interpretation J, M a k r i s r n s t i t u t e
TESSMER, G. and BEHLE, A. 1988. Common reflection point data-stacking for converted waves. Geophysical Prospecting 36,671-688.For converted waves stacking requires a true common reflection point gather which, in this case, is also a common conversion point (CCP) gather. We consider converted waves of the PSand SP-type in a stack of horizontal layers.The coordinates of the conversion points for waves of PS-or SP-type, respectively, in a single homogeneous layer are calculated as a function of the offset, the reflector depth and the velocity ratio U&.Knowledge of the conversion points enables us to gather the seismic traces in a common conversion point (CCP) record. Numerical tests show that the CCP coordinates in a multilayered medium can be approximated by the equations given for a single layer. In practical applications, an a priori estimate of U& is required to obtain the CCP for a given reflector depth.A series expansion for the traveltime of converted waves as a function of the offset is presented. Numerical examples have been calculated for several truncations. For small offsets, a hyperbolic approximation can be used. For this, the rms velocity of converted waves is defined. A Dix-type formula, relating the product of the interval velocities of compressional and shear waves to the rms velocity of the converted waves, is presented.We consider the first steps towards common reflection point stacking and velocity analysis for converted waves. These steps are: (1) common reflection or common conversion point sorting of data, and (2) traveltimes and rms velocities of converted waves. SORTING OF TRACES W I T H A COMMON CONVERSION POINTSeveral authors (e.g. Behle and Dohr 1985) have discussed the problems associated with the gathering of converted wave data of common conversion points. The sorting depends on the depth of the reflector and on the ratio of compressional and shear-wave velocity v&. For complex models the conversion point of the wave can probably be established only by iterative methods, e.g. ray tracing. For a single horizontal homogeneous layer, Fromm, Krey and Wiest (1985) derived the relation
S U M M A R YWe present a 2-D numerical modelling algorithm based on a pseudo-spectral method which accounts for surface topography. The modelling scheme uses Fourier derivative operators for spatial differencing in the horizontal direction, whereas a Chebyshev operator is used for vertical derivatives. The incorporation of surface topography is achieved by mapping a rectangular grid onto a curved grid. Modelling of surface topography is important to study near-surface effects of wave propagation in field seismic situations, since diffraction and scattering at rough surfaces are non-ray effects and can only be understood as wave phenomena. Static corrections cannot always account for these effects and some care has to be taken in their interpretation.The presented modelling algorithm can serve as a powerful tool for the study of wave propagation phenomena in the vicinity of non-planar surfaces or interfaces.
We present a spectral method for solving the two‐dimensional equations of dynamic elasticity, based on a Chebychev expansion in the vertical direction and a Fourier expansion for the horizontal direction. The technique can handle the free‐surface boundary condition more rigorously than the ordinary Fourier method. The algorithm is tested against problems with known analytic solutions, including Lamb’s problem of wave propagation in a uniform elastic half‐space, reflection from a solid‐solid interface, and surface wave propagation in a haft‐space containing a low‐velocity layer. Agreement between the solutions is very good. A fourth example of wave propagation in a laterally heterogeneous structure is also presented. Results indicate that the method is very accurate and only about a factor of two slower than the Fourier method.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
hi@scite.ai
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
Copyright © 2024 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.