Volume 34 Number 2
  • E-ISSN: 1365-2478



In one‐way wave field extrapolation downgoing and upgoing waves are treated independently, which is allowed if propagation at small angles against the vertical in (weakly) inhomogeneous media is considered. In practical implementation the slow convergence of the square‐root operator causes numerical deficiencies. On the other hand, in two‐way wave field extrapolation no assumptions need to be made on the separability of downgoing and upgoing waves. Furthermore, in practical implementation the use of the square‐root operator is avoided. To put the two‐way techniques into perspective, it is shown that two‐way wave field extrapolation could be described in terms of one‐way processes, namely: (1) decomposition of the total wave field into downgoing and upgoing waves; (2) one‐way wave field extrapolation; (3) composition of the total wave field from its downgoing and upgoing constituents. This alternative description of two‐way wave field extrapolation is valid for media which are homogeneous along the ‐coordinate as well as for small dip angles in arbitrarily inhomogeneous media. In addition, it is shown that this description is also valid for large dip angles in 1‐D (vertically) inhomogeneous media, including critical‐angle events, when the WKBJ one‐way wave functions discussed in part I of this paper are considered.

For large dip angles in arbitrarily inhomogeneous media the two‐way wave equation is solved by means of Taylor series expansion. For practical implementation a truncated operator is designed, assuming gentle horizontal variations of the medium properties. This operator is stable and converges already in the first order approximation, also for critical‐angle events.


Article metrics loading...

Loading full text...

Full text loading...


  1. Berkhout, A.J.1982. Seismic Migration, Elsevier, Amsterdam .
    [Google Scholar]
  2. Claerbout, J.F.1976. Fundamentals of Geophysical Data Processing, McGraw‐Hill, New York .
    [Google Scholar]
  3. Kennett, B.L.N.1972. Seismic waves in laterally inhomogeneous media, Geophysical Journal of the Royal Astronomical Society27, 301–325.
    [Google Scholar]
  4. Ursin, B.1983. Review of elastic and electromagnetic wave propagation in horizontally layered media, Geophysics48, 1063–1081.
    [Google Scholar]
  5. Wapenaar, C.P.A. and Berkhout, A.J.1985. Wavefield extrapolation techniques for inhomogeneous media which include critical angle events. Part I: methods using the one‐way wave equations, Geophysical Prospecting33, 1138–1159.
    [Google Scholar]
  6. Wapenaar, C.P.A., Kinneging, N.A. and Berkhout, A.J.1985. Principle of pre‐stack migration based on the full elastic two‐way wave equation, submitted for publication in Geophysics.
  • Article Type: Research Article
This is a required field
Please enter a valid email address
Approval was a Success
Invalid data
An Error Occurred
Approval was partially successful, following selected items could not be processed due to error