1. Introduction to Seismology
Geology 5640/6640
Introduction to Seismology
29 Mar 2017
Last time: Finished Up Normal Modes
• Normal modes have potentially infinite numbers of frequencies
for differing harmonics; we observe many of these up to l ~ 30.
These give information about Earth structure and properties;
source size/location.
Refraction Seismic
For a layer-over-halfspace with source/receiver at the surface,
can have three body wave arrivals: a direct wave,
reflected wave and refracted wave
• These are modeled as travel-times (time from source to
initial deflection of the seismogram)
Read for Fri 29 Mar: S&W (§3.1–3.3)
© A.R. Lowry 2017

2. The layer-over-halfspace here has
three different possible raypaths
from source to receiver:
• The direct wave:
t = x/v0
(a line with slope 1/v0)
• The reflected wave:
(a hyperbolic; asymptotic to the
direct wave)
• The head wave:
(a line with slope 1/v1 and intercept
depends on h0, v1, v0)

3. Given a known source and observations of travel-times at
several different distances, we can get velocities from the
slopes of the direct and head-wave arrivals on a
time-vs-distance plot… And then thickness from the
intercept of the head wave.
Refraction = equation of a line:
with slope m:
and intercept b:

4. Example of crustal-scale seismic refraction: Note that research
seismologists often plot arrivals with “reduced velocity”, so
that some
chosen
velocity would
appear as a
horizontal
line on the
time-distance
plot.
v = 4 km/s
v = 6 km/s
v = 8 km/s

5. Modern research seismic data
tend to be a little more densely
sampled so may look less
linear…
But large-scale (crustal) seismic
reflection/refraction studies
like this one are getting
increasingly rare, as they are
incredibly expensive and we
now find that we can get more
bang for the buck from passive
array studies.

6. A very useful principle to bear in mind as you think about
these approaches is the Principle of Reciprocity: If you
switch positions of a source and receiver, you’ll get the same
ray-paths and travel-times, regardless of the medium.

7. Refraction Examples: two layers over a halfspace
For multiple layers, slope is still 1/v in the medium… Intercept
depends on thickness and
velocity in each of the
overlying layers as:

8. Refraction Examples: A low-velocity zone
A low-velocity layer will not return energy to the surface so is
“invisible” to the refraction method… It’s presence won’t
affect estimates of velocity in the layers below, but it will
affect all estimates of thickness for deeper layers.

9. Refraction Examples: A blind zone
This can be overcome if the arrival is recognized. The problem
is that it will never be a first-arrival, so must be picked later
in the wave train where it gets a bit dodgy…

10. dip, so it’s important to reverse the profile… Then
More generally we
expect that layers may
have some slight
dip, so it’s important to
reverse the profile…
Then a

11. To get structure from more
realistic data sets we usually
use more flexible (& more
complicated) equations…

12. These results
from Meltzer
et al. (BSSA,
1987) were
obtained using
a ray-tracing
approach. Many
studies from the
past two
decades
use Colin
Zelt’s RayInvr
inversion
codes (a
shareware
package)…