basics seismology
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Whats seismology about?
Seismology is the study of the
generation, propagation andrecording of elastic waves in the
Earth (and other celestial bodies)
and of the sources that produce
them.
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Elastic Moduli
Youngs Modulus
Poisson Ratio
Bulk Modulus Shear Modulus
Lambs constants
Vp, Vs.
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s= tensile stress = (F /A)
e= tensional strain = (DL/L) for uniaxial tension or compression
E =s
e
Youngs modulus
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s= tensile stress = (F /A)
e= tensional strain = (DL/L) for uniaxial tension or compression
E =s
e
Youngs modulus
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Poissons ratio = - (eyy/ exx)
Under a stress (sxx) along the x-axis,
longitudinal strain = exx=
and transverse strain = eyy=
DL
L
Then,
DWW
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Bulk Modulus = (DP/Q)
where Q= dilatation = DV/V
and P = pressure
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shear stress = (DF /A)
shear strain = (Dl/L)
L
m=shear stress
shear strain
shear modulus
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From Lay & Wallace (1995)
Elastic Moduli and Densities of Some Common Materials
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From Lay & Wallace (1995)
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l = k - =2m n E3 ( 1 + n) ( 1 - 2n)
V = a = =
K + ( )m l+ 2m
r rp
4/3
V = b =
m
rs
Where m,lare the Lam coefficients andlis
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S-wave
P-wave
dilatations
compressions
wavelength
Body Waves
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Body wave
Surface wave
Amp ~ 1/x
Amp ~ x-1/2
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Late homework policy
Late homework will not be accepted one
week after the deadline.
Late homework will be penalized: 90% (1
day late), 80% (2 day late), 60% (3 day
late), 40 % (4 day late) and 20% (5-7 day
late).
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S-wave
P-wave
dilatations
compressions
wavelength
Body Waves
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Seismic Rays &
Geometric Ray Theory Raysare defined as the normal to the wave
fronts and thus point in the direction ofpropagation. Connecting the thesesuccessive directions forms a ray paths. Inthe case of plane wave, rays are a family ofstraight lines; in the case of spherical wave,rays are spokes radiating out from the
seismic source. They provide a convenientmeans of tracking an expanding wave front.
The seismic rays corresponding to P and Swaves behave very much as light does intraveling through materials of varying indicesof refraction. This leads to many parallels withoptics: rays bend, focus, and defocus
depending on the velocity distribution.Although geometric ray theory is anapproximation, it, however, simplifies theanalysis and yet gives the correct answer or agood approximation.
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Fermats Principle
Ray paths between two points are thosefor which travel time is an extremum,either a minimum or maximum, withrespect to the nearby possible paths.
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Snells Law and Fermat Principle
Fermat Principle: T(x) is either minimum or maximum
2
2
1
1 sinsin
v
i
v
i
Snells Law
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Reynolds (1997)
S h i l R P t
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Rsini
V= constant = p
Spherical Ray Parameter
Wh t t l fl ti d
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What control reflection and
transmission? Continuity of stress
Continuity of displacement
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I =
I =2
1
Reynolds (1997)
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