1. Introduction to Seismology
13 Mar 2017
Geology 5640/6640
Introduction to Seismology
Last time: Amplitudes: Zoeppritz’ Equations
• A normally-incident (i= 0) P-wave with amplitude Ai yields
reflected (R) and transmitted (T) P-wave amplitudes:
where Z = V is the impedance of the medium.
• More generally, amplitudes of reflected, refracted and
converted waves are described by Zoeppritz’
equations (four equations in four unknown amplitudes).
• Examples of how Zoeppritz’ equations are used in
practical applications (i.e., industry) include amplitude
versus offset (AVO) methods = changes in amplitude
with angle of incidence inform porosity, pore fluid type
Read for Wed 15 Mar: S&W (§2.7–2.8)
© A.R. Lowry 2017

2. Your midterm take-home exam is now posted
on the course website…
Due Monday, March 20 at the beginning of class
Note: Not all of the relationships you’ll need have been
covered in course notes, but if you’ve been reading
the text you’ll know where to look!

3. Post-critical transmitted waves:
Let’s think for a moment about the critically-refracted wave
in a horizontal layer (also called the “head wave”). We
define an apparent velocity for the x-direction, cx, as the
speed of propagation of the
wavefront as it would appear to an
observer on the surface:
cx = v/sin = v/cosi
Note cx is just the inverse of the ray
parameter p, so another statement
of Snell’s Law!
Let’s assume this is an SH-wave.
For a layer at depth,
But if j1 > jc (the critical angle),
sin j1 > sin jc and cx < 2! q

4. So what happens in the transmitted wave? Recall from
last time that
If cx < 2, then
is an imaginary number!
The complex conjugate of r2 is
so the z-dependence of the
wave becomes
This is a wave that decays exponentially with z: I.e., it is
trapped at the surface. We call these evanescent or
inhomogeneous waves!

5. An example of an evanescent wave would be the transmitted
counterpart of a reflection from the Moho at q0 > that of Pn,
the P-wave phase that travels along the Moho (i.e. the
boundary between the crust,
VP ~ 6.5–7 km/s, and mantle,
VP ~ 8 km/s).
If we plug the complex conjugate
into the SH-wave relation for
reflection coefficient R, we get:
This has magnitude 1 but a phase
shift of 2 where

6. Surface Waves Love Waves Rayleigh Waves From our earlier discussion
of types of waves, recall we
had two important types:
Love Waves
Rayleigh Waves

7. Why are surface waves important?
• Their amplitude decreases less (1/√ ) than body waves (1/r),
so they are the largest signal on a typical seismogram. r

8. Consequently, for large earthquakes we observe surface waves
that travel all the way around the world!
Peter Shearer

9. • Surface waves can cause damage to taller buildings at
relatively large distances.