Download presentation
Presentation is loading. Please wait.
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 r2 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.
Similar presentations
© 2025 SlidePlayer.com. Inc.
All rights reserved.