Notes on the CREWES Energy Ratio Explorer
- To use the applet, select whether the incident wave is P or S, and
whether it originates in the upper or lower level. These choices may be
changed at any time.
- Also select which components you wish to have plotted.
These may also be changed at any time. Only those for one type of incident wave
may be displayed simultaneously.
- The plot shows how the energy component ratios change
with angle of incidence. To see how they change with properties of each medium,
use the six scroll bars in the control panel to change the density and velocities
of each layer. These may be fixed to particular values in the text fields, or
interactively scanned over a range of values using the slider bars. Only four
of these six variables are independent, one for the densities and three for the
velocities. Accordingly one can use the drop down menus to select up to four
density and velocity ratios as well. The slider bars generate ratios between 0
and 2, but other values can be accessed through the text fields. Note that you
are not prevented from selecting properties corresponding to a negative
- The location of critical angles is indicated by
vertical lines, which are annotated with the value of the critical angle, and
the relevant velocity conditions.
- The color code for the various components is given on
the control panel. The scales may be adjusted using the control panel. Angles
may only be adjusted to integer numbers of degrees, and the incident angle must
be between 0 and 90.
- The Aki-Richards and Bortfeld approximations can be
accessed using the appropriate checkbox on the panel. These were originally
defined only for sub-critical angles, but are extended beyond the critical
point in this applet.
- A standard reference for energy ratios and for the Aki-Richards
approximation is Aki & Richards (1980) "Quantitative
Seismology", vol. I, sec. 5.2. Information on the Bortfeld approximation is found in “Bortfeld, R.
(1961) Approximations to the reflection and transmission coefficients of
plane longitudinal and transverse waves. Geophys. Prosp., 9,
- The source code for this applet is available to
sponsors of CREWES (Consortium for Research in Elastic Wave Exploration
Seismology, located at the University of Calgary).
- Version history:
- The Energy Ratio Explorer was created at CREWES in
February 2002 by Chuck Ursenbach.
- The Energy Ratio Explorer was updated September 2, 2005 to correct errors in the calculation of Bortfeld
approximations to Rps and Tps. Note that there is an error in equation 22 of Bortfeld (1961) which was incorporated in the earlier version.
- Updates will be recorded at www.crewes.org.
The energy ratios show what fraction of an
incident wave’s energy is carried away from the interface by various types of
waves. Because of energy
conservation, the energy ratios for all waves corresponding to one of the three
possible incident wave types (P, SV, or SH) sum to
unity. The energy ratios do not
describe however the partitioning of energy flux parallel to the
interface. Thus, after a critical
point, the energy ratio of one wave will always drop to zero, even though that
wave will continue to have a non-zero Zoeppritz coefficient. This indicates an evanescent wave that
travels along the interface, but decays exponentially away from it.
Copyright 2002, CREWES, University of Calgary, All