The principle assumption in this calculation is that the wavelet is restricted to a specific form, namely, f(ν) = ν n exp(-nν/ν0), where n is a non-negative integer and ν0 is the dominant frequency. The wavelet is displayed at the top of the applet, in both time and frequency domains. Also displayed is the Ricker wavelet, to which it forms a close approximation for some values of n.
This applet also carries out a numerical integration, which allows for imperfection in the results. This imperfection will first be seen near 0 and 90 degree angles of incidence, as an erratic deviation of spherical-wave results from plane-wave results. The region of interest is generally at critical points in the 45 to 60 degree region, which will generally be affected negligibly. Potential errors will increase with α1/(2Zν0), which is a measure of sphericity.
Further details regarding the theory behind this applet are found in "An efficient method for AVO modeling of reflected spherical waves " (Ursenbach, C.P., Haase, A.B., & Downton, J.E., 2005, SEG Expanded Abstracts, Vol. 24).
Do you have feedback on 1) problems with using this applet, 2) suggestions for improvement, or 3) examples of geological systems where consideration of spherical effects may be important? Feel free to contact Chuck Ursenbach (ursenbach@crewes.org).