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Introduction to Geophysics
Ali [email protected].
saDepartment of Earth SciencesKFUPM
Seismic Waves (Continue)
Previous Lecture
What is Seismic Wave? Waves in a Pound Sound Wave Analogy What is Wave? Wave Terminology Wavelength and Period Wave Speeds Sources of Seismic Waves Multiple Frequency SignalsWhat is Elastic Behavior? Ductile Deformation
Brittle Deformation Ductile/Brittle Behavior through the
Lithosphere and Asthenosphere
Elastic Constants Bulk Modules Shear Modules Poisson Ratio Typical Values of Elastic Constants
for Selected Materials Body Waves
Surface Waves
Particle Motions of Body Waves
3D Components of Waves
3D Components of P-wave
6.27
3D Components of S-wave
6.35
Types of Surface Waves
Rayleigh Waves
Rayleigh waves are the most complex wave, and theyare also the slowest.
They travel at speeds of 2 to 5 km/sec and vibratethe ground in an elliptical pattern.
= k - =2 E3 ( 1 + ) ( 1 - 2 )
V = = =k + ( ) + 2
p4/3
V = =s
Where are the Lamé coefficients and is
Seismic velocities
P wave velocity α and S wave velocity β depend onphysical properties of medium through which theytravel:
Question: How and depend
on density ?
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B C D E F G H I J K
Rock Type Density Young's Modulus Poisson's Ratio Vp Vs Vp/Vs Vs as %Vp
r E m (m/s) (m/s)Shale (AZ) 2.00 0.120 0.040 2454 1698 1.44 69.22%
Siltstone (CO) 2.00 0.120 0.040 2454 1698 1.44 69.22%Limestone (PA) 2.00 1.100 0.156 7640 4877 1.57 63.84%Limestone (AZ) 2.00 1.100 0.180 7728 4828 1.60 62.47%Quartzite (MT) 3.00 0.636 0.115 4675 3083 1.52 65.96%
Sandstone (WY) 3.00 0.140 0.060 2169 1484 1.46 68.42%Slate (MA) 3.00 0.487 0.115 4091 2698 1.52 65.96%Schist (MA) 3.00 0.544 0.181 4440 2771 1.60 62.41%Schist (CO) 2.70 0.680 0.200 5290 3239 1.63 61.24%Gneiss (MA) 2.64 0.255 0.146 3189 2053 1.55 64.38%Marble (MD) 2.87 0.717 0.270 5587 3136 1.78 56.13%Marble (VT) 2.71 0.343 0.141 3643 2355 1.55 64.65%Granite (MA) 2.66 0.416 0.055 3967 2722 1.46 68.62%Granite (MA) 2.65 0.354 0.096 3693 2469 1.50 66.85%Gabbro (PA) 3.05 0.727 0.162 5043 3203 1.57 63.51%Diabase (ME) 2.96 1.020 0.271 6569 3682 1.78 56.05%Basalt (OR) 2.74 0.630 0.220 5124 3070 1.67 59.91%
Andesite (ID) 2.57 0.540 0.180 4776 2984 1.60 62.47%Tuff (OR) 1.45 0.014 0.110 996 659 1.51 66.20%
Elastic Coefficients and Seismic Velocities
A linear relationship between density and seismic velocity
where a and b are constants V = a ρ + b.
Velocity and Density “Birch’s law”Crust and mantle rock observations
6km 18km 30km
Nafe-Drake Curve
An important empirical relation exists between Pwave velocity and density.
Cross-plotting velocity and density values of crustalrocks gives the Nafe-Drake curve after itsdiscoverers.
Only a few rocks such as salt (unusually low density)and sulphide ores (unusually high densities) lie offthe curve.
Nafe-Drake Curve
Figure 3.10 of Lillie, 1999, modified from Birch, 1960
L=limestone; Q=quartz; Sh=shale; Ss=sandstone.
Sediments and sedimentary rock
Igneous and metamorphic rock
Factors affecting P-wave velocity
Increases with
mafic mineral content (Nafe-Drake curve) pressure (modulus change > density change)
Decreases with
temperature (modulus change > density change)
Factors affecting S-wave velocity
Increases with mafic mineral content (Nafe-Drake curve) with pressure (modulus change > density change)
Decreases due to presence of fluid, e.g. porous sand or partial melt
No S waves in fluids, e.g. water of molten rock. Velocity zero
Grifts and King, 1981
Velocity-Geology
Maximum amplitude of particle motion occurs along
the 90 degree phase wave front. Other wave
fronts correspond to positions where the wave goes
from positive to negative amplitude (180 degree)
and at the minimum amplitude (270).
Amplitude Changes of Particle Motion
Raypaths thus bend (refract) as velocity changes. Seismic energy travels along trajectories perpendicular to wave fronts.
Initial wavefronts for compressional
(P),shear (S), and Rayleigh ( R )waves.Changes in velocity cause segments of wave fronts to
speed up or slow down, distorting the wave fronts from perfect spheres.
Wave Fronts and Raypaths
Seismic waves radiating from a source to one receiver.
Seismic trace recording ground motion by the receiver, as a function of the travel time from the source to the receiver. For controlled source
studies (seismic refraction and reflection), the travel time
is commonly plotted positive downward.
Seismic Trace
V = k + ( )
p4/3
1. Nafe-Drake Curves suggesting that compressional wave velocity and density are directly proportional . The below equation:
Implies that P-wave velocity is inversely proportional
to density, Explain the paradox.
Homework