Snell’s Law

Northern Sh Shot-gather

Seismic Data

Seismic Data

Southern P- Shot-gather

critical

angleV1,rho1

V2,rho2

P`

P`P’

At critical angle of incidence,

angle of refraction = 90 degrees=angle of reflection

Pre- and Post-critical Rays

x

z V1

V2V2> V1

Pre-critical reflections Head wavePost-critical reflections

Direct wave

11

tanV

21

tanV

Critical distance

One-layer Refracted Head Wave

x

z V1

V2

V2> V1

c

Critical distance=Xc

cr1

r1 r3

r2

1x 2

x3x

Xc =? Tc=?

One-layer Refracted Head Wave

x

z V1

V2

V2> V1

c

Critical distance=Xc

cr1

r1 r3

r2

1x 2

x3x

Xc =? Tc=?

1 2 12

cX x x x

02 tan

c cX z

z0

1 1 1

1 1 1

2c

r r rT

V V V

0

1

2cosc

c

zT

V

(9)

One-layer Refracted Head Wave

x

z V1

V2

V2> V1

c

Critical distance=Xc

cr1

r1 r3

r2

1x 2

x3x

Xc =? Tc=?

z0

Xc +

2 0

2

2 1

( ) 2cosc

c

x zT x x

V V

2x

(10)

For an incident S waveS\

S\S\

i

t \ \S P

\ /S Pr

t

S\S/

Example: Three Possible Critical Angles

1

2

1sin 90S oticS

S

VV

1

2

1sin 90S oticP

P

VV

1

1

1sin 90S ori

P

VV