angle of incidence

1
Snell's Law and Refraction
i
v1
air water
angle of incidence
v2
r
angle of refraction
sin(i) / v1 sin(r) / v2

2
where v2 gt v1
i
v1
v2
3
where v2 gt v1
i
4
where v2 gt v1
i
5
where v2 gt v1
critical angle
c
wave travels along interface at velocity v2
6
where v2 gt v1
critical angle
reflected wave
c
interface wave
wave travels along interface at velocity v2
7
where v2 gt v1
headwaves
critical angle
reflected wave
c
interface wave
wave travels along interface at velocity v2
8
where v2 gt v1
critical angle
reflected wave
headwaves
c
interface wave
wave travels along interface at velocity v2
9
Refraction seismology
A
B
C
refracted arrival at velocity v1
v1
interface wave at velocity v2
Path A Path C
10
Refraction seismology
x
v1
A
z
C
v1
ø
ø
B
velocity v2
time z/v1cosø (x-2ztanø)/v2
z/v1cosø
11
Refraction seismology
b
a
a
v1
A
d
C
v1
B
v2
since sinø v1/v2
cosøv (1-(v1/v2)2) t (xsinø)/v1 2zcos
ø /v2 t x/v2 2z (v22 -v12)0.5/v1v2 t
x/v2 tintercept
12
crossover distance (when direct wave and
refracted wave arrive simultaneously)
time
measure
1/v2 (refracted wave obeys t x/v2
tintercept)
extrapolate
t1
1/v1 (direct wave obeys t-x/v2)
distance x
1. calculate the velocities from the slopes 2.
read the time of the intercept ti 3. calculate
the layer thickness z from ti2z (v22
-v12)0.5/v1v2