wave propagation • hooke’s law • newton’s law wave ... · pdf file•...
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• Wave propagation• Hooke’s law• Newton’s law• � wave equation
• Wavefronts and Rays• Interfaces • Reflection and Transmission coefficients
body wavesP-waves (longitudinal, compressional)
S-waves (shear, transverse)SV-waveSH-wave
Body waves:
Different kind of waves
• Transversal waves(S-waves)
• Longitudinal waves (P-waves)
1 3 542 2 41 3 5
Examples of different waves
Elektromagnetic spectrum
Frequency
AM, FM, Georadar, Visible, X-ray
Acoustic spectrumEarthquake, audible + seismic106100 1019 Hz
Surface waves
Rayleigh-waves
Love-waves
�z
z
�
�
z
2
2 z� �
�
�z
� z�2
� 2�
�
� �z � z
z z �
�
z z �
z ��
�
� z�2
� 2�
�
z ��
�
� z�2
� 2�
�
z � ��
�
�(z) is the Dirac function
�2
� 2�2
� 22 �
� �2
� 2
�� -1/2
Propagation of seismic waves
(Roth et al., 1998)
Object detection using WAVES:
Object detection using WAVES
BSource
OReceiver
• Wavefronts indicate the boundary of the material which already moves and the material which is still undisturbed.
• Rays are plotted perpendicular with respect to the wavefronts and describe the dominant propagation of the seismic energy between two locations
Geometrical Wave propagation
Source ReceiverSource
Rays are perpendicular to the wavefronts,
�1 �2v1
v2
Angle of incidence = angle of reflection
�1 = �2
�1
v1
v2
�1sin�2sin------- -----
v1v2-----=
Interface: Refraction
v1v2 >
�2 v1v2 <
2�
�1
v1
v2�1sin90�sin---------- �1sin
v1v2-----=
�2 90�=
Special case: critical angle
=
�2
�1
vp1,vs1
�1sin�1sin
-------- ---vp1
vs1
--------=
�1
�2�1sin�2sin
------- ---vp1
vs2
--------=
vp2,vs2
Interface: Conversion from P wave to S wave
�1sinvp1
------ = --�1sin
vs1
------ = --�2sin
vp2
-------- = -�2sin
vs2
-------------- = �nsin
vsn
--------- = p = constant
p = Slowness
�1
�2 �2
�3�3
�1
vp1vs1
vp2vs2
vp3vs3
Refraction caused by place dependent propagation velocity
Propagation of seismic waves
(Roth et al., 1998)
E ER
ET
v1���1
v2���2
E = ER + ET
R + T = 1
R = Reflection coefficientT = Transmission coefficient
E = Energy
Transmission- and Reflection coefficients
R
T
v1���1
v2���2
Reflection coefficient
Transmission coefficient
Rv2�2 v1�1–v2�2 v1�1+--------------- = ------------
Z2 Z1–Z2 Z1+--------------------=
T2v1�1
v2�2 v1�1+---------------- = -----------2Z 1
Z2 Z1+--------------------=
with Z = v� = acoustic Impedance
Zoeppritz’s equations at normal incidence
(Sheriff and Geldart, 1995)
Angle-dependent reflection- and transmission-coefficients