VẬT lý địa CHẤN 03 geometry

Reflected, Refracted and Diffracted
waves
• Reflected wave from a horizontal layer
• Reflected wave from a dipping layer
• Refracted wave from a horizontal layer
• Refracted wave from a dipping layer
• Diffracted waves


Applications for shallow high
resolution Reflection seismic
•
•
•
•
•

Hydrogeological studies of acquifers
Engineering geology
Shallow faults
Mapping Quaternary deposits
Ground investigation for pipe and sewerage
tunnel detection


Applications for Refraction
seismic
•
•
•
•

•

Depth of groundwater level
Depth and location of hardrock
Elastic medium parameters
Permafrost
Glaciology


Refraction seismic
• Refracted Waves
• Mainly horizontal Wave propagation
• Only refracted waves are used. (Lower layer must
have higher velocity than upper layer)
• Distribution of velocity as well as the depth and
orientation of interfaces between layers

Reflection seismic
•
•
•
•

Reflected Waves (“Echo lot principal”)
Mainly vertical wave propagation
Complete seismic recording is used
Distribution of the velocity variation


Geometrical situation

Direct wave

Reflected wave

Refracted wave


Traveltime curve


Receivers

Source

Receivers


Direct wave
t

1
t= x
v
x
o

x

x

x

x

v

x
v=
t

Velocity of direct wave is derived from the distance and
travel time


Reflection: Horizontal reflector
x
A

B
x

o

4 S 2 = 4h 2 + x 2 = t 2 v 2

s

h
α

v

h
s

4h + x
t =
v2
2
x
2
2
t = t0 + 2 ,
v
2h
t0 =
v
2

2

2


Reflection: horizontal reflector
2
2
4
h
+

x
2
t =
v2
x
t = , for x >> h.
v

h

t2v2 = 4h2+x2
t2v2 - x2 = 4h2
t2v2 - x2 =1
4h2
4h2
Hyperbola


Moveout

1
Difference in travel time t(x1 ) und t(x2 ):

2

x22- x12
t2- t1 ≈
2v2t0

Normal Moveout

1

0

0

Difference in traveltime t

0

und t(x):

1

x12
∆T=t1- t0 ≈
2v2t0


t2v2=4h2+x2- 4hxcos(90+Θ)
X=-2hsinΘ

t2v2=4h2+x2+4hxsin(Θ)
Hyperbola:

∆Tdip

[x+2hsin(Θ)] 2

t2v2
=1
[2hcos(Θ)]2 - [2hcos(Θ)]2
-x

x
h

Θ
h

x

90+Θ
∆Tdip= tx-t-x = 2xsinΘ
v


Refraction seismic

sin ic
v1
v1
=
⇔ sin ic =
sin 90 v 2
v2


Propagation of seismic waves

Headwave

(Roth et al., 1998)


Direct wave

Reflected wave

Refracted wave


Traveltime curve


h

TSG = TSA + TAB + TBG = 2TSA + TAB

(
x − 2h tan ic )
h
=2
+
v1 cos ic
v2

x 2h cos ic
= +

v2
v1


Refraction: horizontal reflector
t

1
----v1

1
----v2
2

2

v2 – v 1
2h
x + -------------------t = --v2
v1 v 2

ti
x

xcross

x
t = ----- + t i
v2

x
h
v1
v2

v2 + v1
xcross = 2h -----------v 2 – v1



x sin(θ c + α ) 2 z a cosθ c
+
td =
v1
v1

For small slopes (α < 100):

x sin(θ c − α ) 2 zb cosθ c
+
v1
v1

vd + vu
v2 ≈
2

tu =

x sin(θ c + α ) 2 z a cosθ c
+
td =
v1
v1

For small slopes (α < 100):

x sin(θ c − α ) 2 zb cosθ c
+
v1
v1

vd + vu
v2 ≈
2

tu =


Huygens’ Principle:

Every point on a wavefront can be considered as a secondary
source of spherical waves


Surface
V=1.6 km/s

800 m

Reflection/Diffraction
Reflection:
tr≈ t0+δt

h

t0=2h/v
δt =x2/(4vh)
Reflection /Diffraction
Diffraction:
td≈ t0+2δt