Geology 5660/6660Applied Geophysics

Last time: Seismic Thought Exercise• Seismic Concepts: Velocity is distance traveled per unit time, V = x/t Different materials have different seismic velocities! Introduced Wavefronts & Rays Huygen’s Principle: Every point on a wavefront can be treated as a point source for the next generation of wavelets. The wavefront at time t = x/V later is a surface tangent to the furthest point on each of these.• Thought exercise: What do wavefronts look like for a slow layer over a fast layer? For fast over slow?

13 Jan 2014

© A.R. Lowry 2014Read for Wed 13 Jan: Burger 1-21 (Ch 1–2.1)

Animation 0S3 from Lucien Saviothttp://www.u-bourgogne.fr/REACTIVITE/manapi/saviot/deform/ 0S3: (25.7 minutes)

Seismology (A Brief Introduction) Four Important Types of Seismic Waves:

(1) P (primary) wave (Velocity VP = 4 to 14 km/s)

(2) S (secondary) wave (VS = 2/5 to 3/5 VP, or 0)

(3) Surface Waves (Love, Rayleigh) V slightly < VS

(4) Normal Modes (Resonant “Tones”, like a bell…) continue for months after largest earthquakes periods of minutes to a few hours “standing waves”

Body Waves}

P

S

Surface (Love)

Surface (Rayleigh)

Seismic waves are strain wavesthat propagate in a medium…

The text begins with an analogy to ripples in a pond. There issimilarity in that both are described by the wave equation;both involve stress & displacements that propagate as individual particles in the medium oscillate between potentialand kinetic energy states… But,

A major difference is rheology. Stress, displacement &strain in a solid continuum are governed by Hooke’s Law.

Elastic Rheology (Hooke’s Law):

Stress (= force per unit area) and Strain (= change in shape) are linearly related via

= c

where c is an elastic coefficient (a material property).

Strain is a spatial derivative of displacement u

described by (in 1-D),

€

=∂u

∂x

A quick “review” of various strains and their elastic constants:

Uniaxial compression:

xx

yy

Elongation(change in

length l)

€

=l

l0

Young’s modulus E: = E

Poisson’s ratio :

€

=−yy

εxx(0 < < 0.5)

For dilatation (change in volume V/V0):Bulk modulus K = P/ (where P is pressure)

Rigidity modulus = s/ = tan

applied s

applied

(strain)

(strain)

(elasticconstant)

(elasticconstant)

(elasticconstant)

(elasticconstant)

(strain)