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

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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

t x v Velocity of direct wave is derived from the distance and travel time o x xxx t 1 v --- x = v x t = Direct wave

s o x s h Reflection: Horizontal reflector 4S 2 =4h 2 +x 2 =t 2 v 2 t 2 =(4h 2 +x 2 )/v 2

Reflection: Horizontal reflector t 0 for x=0: t (x=0) =t 0 =2h/v t 2 v 2 =4h 2 or h=t 0 v/2 t 2 v 2 =4h 2 +x 2 t 2 = x 2 /v 2 +t 0 2 h

Reflection: horizontal reflector t 2 v 2 - x 2 = 4h 2 t 2 v 2 = 4h 2 +x 2 Hyperbola t2v2t2v2 4h 2 x2x2 - =1 x>>h  v x t = h

Difference in travel time t(x 1 ) und t(x 2 ): Moveout 12 t 2 - t 1  2v 2 t 0 x 2 2 - x 1 2

Normal Moveout Difference in traveltime t 0 und t(x):  T=t 1 - t 0  2v 2 t 0 x12x12 01 1 0

 90+  h h x t 2 v 2 =4h 2 +x 2 - 4hxcos(90+  ) t 2 v 2 =4h 2 +x 2 +4hxsin(  ) Hyperbola: t2v2t2v2 [2hcos(  )] 2 [x+2hsin(  )] 2 - =1 -xx X=-2hsin   T dip  T dip = t x -t -x = v 2xsin 

Refraction seismic

(Roth et al., 1998) Headwave Propagation of seismic waves

Direct wave Reflected wave Refracted wave

Traveltime curve

h

v 1 x v 2 t i t x v 2 ----- 2h 2 2 v 1 2 – v 1 v 2 --------------------+= h t x v 2 -----t i += x cros 2h v 2 v 1 + v 2 v 1 – ------------= x cross x t 1 v 2 ----- Refraction: horizontal reflector v 1 v 1 -----

For small slopes (  < 10 0 ):

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 t 0 =2h/v t r  t 0 +  t  t =x 2 /(4vh) t d  t 0 +2  t /Diffraction Reflection: Diffraction: h

Receivers SourceReceivers Direct wave Reflected wave layer 1/2 Reflected wave layer 2/3 Refracted wave layer 2/3 Refracted wave layer 1/2 x t

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