Open AccessDetermination of seismic wavefields in arbitrarily continuously layered media using the modified Cagniard method
Author(s) -
Verweij M. D.,
Hoop A. T.
Publication year - 1990
Publication title -
geophysical journal international
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.302
H-Index - 168
eISSN - 1365-246X
pISSN - 0956-540X
DOI - 10.1111/j.1365-246x.1990.tb05684.x
Subject(s) - transformation (genetics) , laplace transform , mathematical analysis , inverse problem , domain (mathematical analysis) , convergence (economics) , point (geometry) , inverse , mathematics , time domain , wave propagation , geometry , computer science , optics , physics , biochemistry , chemistry , economics , computer vision , gene , economic growth
SUMMARY In this paper we investigate a combination of the WKBJ iterative solution and the modified Cagniard method (also called the Cagniard‐De Hoop method) that, in principle, yields a theoretically exact space–time domain solution for the 3‐D seimic wave propagation problem in continuously layered media. Owing to the application of the Laplace transformation with a real and positive transformation parameter with respect to the time coordinate, the convergence of the iterative scheme for an arbitrary configuration, both before and after the transformation back to the space–time domain, is guaranteed. In constrast to the standard frequency‐domain analysis, difficulties due to turning points can be avoided. This is due to the fact that along the original integration paths of the inverse transformations the propagation coefficient never becomes zero, while during deformation of the integration contour a point that yields a zero propagation coefficient can be dealt with by properly going around it. The inverse transformation procedure is demonstrated for the direct wave and the wave due to single partial reflections in a medium. Numerical results for these components are presented.