Basics Seismology

8/11/2019 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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Basics Seismology

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