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

• 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

Direct wave

Reflected wave Refracted wave

Geometrical situation

Traveltime curve

Source ReceiversReceivers

t

x

v

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

o x x x x

t 1v---x=

v xt---=

Direct wave

v

xA

C

B

h s

o x

s

h

Reflection: Horizontal reflector

4S2=4h2+x2=t2v2

t2=(4h2+x2)/v2

Reflection: Horizontal reflector

t0

for x=0:

t(x=0)=t0=2h/v

t2v2=4h2

or

h=t0v/2

t2v2=4h2+x2

t2= x2/v2+t02

h

Reflection: horizontal reflector

t2v2 - x2 = 4h2

t2v2 = 4h2+x2

Hyperbola

t2v2

4h2 4h2x2

- =1

x>>h vxt =

h

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

Moveout

1 2

t2- t1 2v2t0

x22- x1

2

Normal Moveout

Difference in traveltime t 0 und t(x): T=t1- t0 2v2t0

x12

0 1

1

0

90+

h

h

x

t2v2=4h2+x2- 4hxcos(90+)

t2v2=4h2+x2+4hxsin()

Hyperbola:

t2v2

[2hcos()]2 [2hcos()]2

[x+2hsin()] 2

- =1

-x x

X=-2hsin

Tdip

Tdip= tx-t-x =v

2xsin

2

1

2

1 sin90sin

sin

v

vi

v

vic

c

Refraction seismic

(Roth et al., 1998)

Headwave

Propagation of seismic waves

Direct wave

Reflected wave Refracted wave

Traveltime curve

12

21

cos2

tan2

cos2

2

v

ih

v

x

v

ihx

iv

h

TTTTTT

c

c

c

ABSABGABSASG

h

v1

x

v2

ti

t xv2-----

2h 22

v12

–

v1v2--------------------+=

h

txv2-----t i+=

xcros 2hv2 v1+

v2 v1–------------=

xcrossx

t1v2-----

Refraction: horizontal reflector

v

1v1

-----

11

11

cos2)sin(

cos2)sin(

v

z

v

xt

v

z

v

xt

cbcu

cacd

22ud vv

v

For small slopes ( < 100):

11

11

cos2)sin(

cos2)sin(

v

z

v

xt

v

z

v

xt

cbcu

cacd

22ud vv

v

For small slopes ( < 100):

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

t0=2h/v

tr t0+t

t =x2/(4vh)

td t0+2t

/Diffraction

Reflection:

Diffraction:

h

ReceiversSourceReceivers

Direct wave

Reflected wave layer 1/2

Reflected wave layer 2/3

Refracted wave layer 2/3

Refracted wave layer 1/2

x

t