seismic waves-2

Introduction to Geophysics

Ali Onceloncel@kfupm.edu.

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