Reflection/transmission of plane waves
Assignment no. 1 in GEO4620, autumn 2007.
For this exercise you will need the Fortran program coeff2.f and the Matlab program
plot_coeff2.m. The programs should be run on a workstation (i.e., with Unix or Linux o.s.).
The program coeff2.f computes displacement reflection and transmission coefficients for
different kinds of waves which encounter a free surface, a fluid-solid interface, or a solidsolid interface. When running the program, you are asked to specify the following:
- Type of interface.
- Model parameters, i.e., velocities and densities. Either use the default model or specify one
yourself. The default model has two solid layers with velocities and densities α1 = 6.8km/s,
β1 = 3.9km/s, ρ1 = 2.9g/cm3, α2 = 8.1km/s, β2 = 4.5km/s, ρ2 = 3.4g/cm3.
- Incoming wave, which can be one of the following: SH down, SH up, SV down, SV up,
P down, P up. NB! Only one blank between the wave type and the propagation direction.
Having specified these parameters, the program tells you, in a given order (on the screen),
which wave types that will be generated at the boundary. Reflection and transmission are then
computed as a function of horizontal slowness. The results are written to an output file.
The first line in the output file contains information about the type of interface and incoming
wave. The second line gives the number of waves generated when the incoming wave hits the
interface, and on the following lines is written which waves. Then there is a line with the
number of horizontal slowness values (i.e. angles of incidence) for which the coefficients
have been computed. The subsequent lines - one for each slowness value - contains the
slowness value and amplitude(s) and phase(s) of the reflection and transmission coefficient(s),
given in the same order as the waves listed above. I.e., amplitude and phase for the first wave,
amplitude and phase for the second wave and so on.
Amplitude and phase of the coefficients can then be plotted, using the Matlab-program
plot_coeff2.m. Input to the program is the output file from coeff2.f.
There are many possibilities when using the program coeff2.f. It is recommended that you first
try out these using the default model before turning to the questions below.
I. Compute the reflection and transmission coefficients in the cases of P, SV and SH waves
incident on the surface from above and below, using the default model or another solid-solid
model. Then answer the following questions:
- Are there any similarities between the reflection coefficients or between the transmission
coefficients?
- Compare the coefficients for waves of the same type incident from above and below,
respectively. Are there any characteristic features? If yes, try to explain these.
- Concerning P to SV conversion and vice versa: is that a dominating feature? For which
propagation direction is there no conversion?
- For each of the incident waves, the coefficients are calculated for a certain range of
horizontal slowness values. What determines this interval and how does the angle of
incidence of the incoming wave vary within it?
- Are there indications that inhomogeneous waves are generated in any of the cases? If yes,
at which slowness values do they occur?
II. Enclosure 1 shows four different models M1 – M4 each consisting of two solid layers.
The seismograms in enclosure 2 show how the reflected P wave, in case of a P wave incident
on the interface from above, varies with offset in each of the models. The offset ranges from
100m to 3km.
Compute the reflection coefficients in the case of a P wave incident from above in each of the
models. Then answer the following questions:
- How do the coefficients fit the seismograms in enclosure 2?
- Explain the results by the model parameters listed in enclosure 1.
Summarize your answers/comments in a report of 2-3 pages.