Seismic Wave Propagation

L

F

L

F = k * L/L (Hooke’s Law) k = Young’s modulus

Rand quartzite

strain

stra

inElastic Materials

Acoustic Waves

F = Mass*Acceleration (Newton rules!)

u u+ dux

x + dx

AF(x) F (x+dx)

Net force = F(x+dx) – F(x) = F = [*A*dx] *acc

F/x = * acc * A]

but F = k *u/x (Hookes law) and S = F/A, so

K * u/xx = * u2/t2 i.e. wave equation where V= (k)1/2

Seismic Wave Equation

k * u/xx = * u2/t2

or

d2u/dx2 = (/k) du2/dt2

which has solutions of the form

u = A e+ikt + Be-ikt

Seismic WavesBody waves

Surface Waves

“Ground Roll” Rayleigh

Love

P

S

Rayleigh Waves

Seismic Wave Speeds

Material P wave Velocity (m/s) S wave Velocity (m/s)

Air 332

Water 1400-1500

Petroleum 1300-1400

Steel 6100 3500

Concrete 3600 2000

Granite 5500-5900 2800-3000

Basalt 6400 3200

Sandstone 1400-4300 700-2800

Limestone 5900-6100 2800-3000

Sand (Unsaturated) 200-1000 80-400

Sand (Saturated) 800-2200 320-880

Clay 1000-2500 400-1000

Glacial Till (Saturated) 1500-2500 600-1000

Seismic Velocities

Wave SimulationsColorado School of Mines Tutorial

Body waves in half space

Huygen’s Principle

Snell’s Law*(acoustic)

*Fermat’s Least Time Principle

Snell’s Law(elastic)

sin 1 = sin 2 = sin 3

Vp1 Vp2 Vs3

Critical Refraction

sin ic = sin (90º) V1 V2

sin ic = V1

V2

Seismic Refraction

Waves passing from slow to fast medium

Snell’s Law

Snell’s Law

Reflection & Refraction

0

200

400T

, mse

c

Direct

Reflected Refracted

Distance, km

Refraction: Two Layers

Engineering Quad 1/27/00 12 gauge source

1m geophone spacing, 1 m minimum offset

Travel Time Curve(Shotpoint Gather

Refraction: 3 layer case

Refraction: Dipping Layer

Refraction:Hidden Layers

Refraction: Lateral Offset

Refraction: Lateral Offset

Refraction: Many Layers

Refraction: Multiple Layers

Refraction: Linear V(z)

Refraction: + Gradients

V

z z

x

x

t

Refraction: - Gradients

V

z z

t

x

x

LVZ

Low velocityzone

Diffraction

Reflection: Basic Geometry

T2 = X2 + (2Z/V)2

V2

T2 = X2 + T0

2

V2

Reflection Hyperbola

Reflection from Dipping Layer

SHOT*

Reflection display convention

Sample shot gathers

offend split spread

Seismic WavesBody waves

Surface Waves

“Ground Roll” Rayleigh

Love

P

S

Rayleigh Waves

Ground Roll(Rayleigh Waves)

x

t

Dispersion

Ewing, Jardetzky and Press (1957)