Wave propagation • Hooke’s law • Newton’s law wave ... · PDF file•...
-
Upload
truongngoc -
Category
Documents
-
view
218 -
download
1
Transcript of Wave propagation • Hooke’s law • Newton’s law wave ... · PDF file•...
![Page 1: Wave propagation • Hooke’s law • Newton’s law wave ... · PDF file• Interfaces • Reflection and Transmission coefficients. body waves P-waves (longitudinal, ... Microsoft](https://reader034.fdocuments.us/reader034/viewer/2022051523/5a78fbe17f8b9a5a148eacae/html5/thumbnails/1.jpg)
• Wave propagation• Hooke’s law• Newton’s law• � wave equation
• Wavefronts and Rays• Interfaces • Reflection and Transmission coefficients
![Page 2: Wave propagation • Hooke’s law • Newton’s law wave ... · PDF file• Interfaces • Reflection and Transmission coefficients. body waves P-waves (longitudinal, ... Microsoft](https://reader034.fdocuments.us/reader034/viewer/2022051523/5a78fbe17f8b9a5a148eacae/html5/thumbnails/2.jpg)
body wavesP-waves (longitudinal, compressional)
S-waves (shear, transverse)SV-waveSH-wave
![Page 3: Wave propagation • Hooke’s law • Newton’s law wave ... · PDF file• Interfaces • Reflection and Transmission coefficients. body waves P-waves (longitudinal, ... Microsoft](https://reader034.fdocuments.us/reader034/viewer/2022051523/5a78fbe17f8b9a5a148eacae/html5/thumbnails/3.jpg)
Body waves:
![Page 4: Wave propagation • Hooke’s law • Newton’s law wave ... · PDF file• Interfaces • Reflection and Transmission coefficients. body waves P-waves (longitudinal, ... Microsoft](https://reader034.fdocuments.us/reader034/viewer/2022051523/5a78fbe17f8b9a5a148eacae/html5/thumbnails/4.jpg)
Different kind of waves
• Transversal waves(S-waves)
• Longitudinal waves (P-waves)
1 3 542 2 41 3 5
![Page 5: Wave propagation • Hooke’s law • Newton’s law wave ... · PDF file• Interfaces • Reflection and Transmission coefficients. body waves P-waves (longitudinal, ... Microsoft](https://reader034.fdocuments.us/reader034/viewer/2022051523/5a78fbe17f8b9a5a148eacae/html5/thumbnails/5.jpg)
Examples of different waves
Elektromagnetic spectrum
Frequency
AM, FM, Georadar, Visible, X-ray
Acoustic spectrumEarthquake, audible + seismic106100 1019 Hz
![Page 6: Wave propagation • Hooke’s law • Newton’s law wave ... · PDF file• Interfaces • Reflection and Transmission coefficients. body waves P-waves (longitudinal, ... Microsoft](https://reader034.fdocuments.us/reader034/viewer/2022051523/5a78fbe17f8b9a5a148eacae/html5/thumbnails/6.jpg)
Surface waves
Rayleigh-waves
Love-waves
![Page 7: Wave propagation • Hooke’s law • Newton’s law wave ... · PDF file• Interfaces • Reflection and Transmission coefficients. body waves P-waves (longitudinal, ... Microsoft](https://reader034.fdocuments.us/reader034/viewer/2022051523/5a78fbe17f8b9a5a148eacae/html5/thumbnails/7.jpg)
�z
z
![Page 8: Wave propagation • Hooke’s law • Newton’s law wave ... · PDF file• Interfaces • Reflection and Transmission coefficients. body waves P-waves (longitudinal, ... Microsoft](https://reader034.fdocuments.us/reader034/viewer/2022051523/5a78fbe17f8b9a5a148eacae/html5/thumbnails/8.jpg)
�
�
z
2
2 z� �
�
![Page 9: Wave propagation • Hooke’s law • Newton’s law wave ... · PDF file• Interfaces • Reflection and Transmission coefficients. body waves P-waves (longitudinal, ... Microsoft](https://reader034.fdocuments.us/reader034/viewer/2022051523/5a78fbe17f8b9a5a148eacae/html5/thumbnails/9.jpg)
�z
� z�2
� 2�
�
![Page 10: Wave propagation • Hooke’s law • Newton’s law wave ... · PDF file• Interfaces • Reflection and Transmission coefficients. body waves P-waves (longitudinal, ... Microsoft](https://reader034.fdocuments.us/reader034/viewer/2022051523/5a78fbe17f8b9a5a148eacae/html5/thumbnails/10.jpg)
� �z � z
z z �
�
![Page 11: Wave propagation • Hooke’s law • Newton’s law wave ... · PDF file• Interfaces • Reflection and Transmission coefficients. body waves P-waves (longitudinal, ... Microsoft](https://reader034.fdocuments.us/reader034/viewer/2022051523/5a78fbe17f8b9a5a148eacae/html5/thumbnails/11.jpg)
z z �
z ��
�
![Page 12: Wave propagation • Hooke’s law • Newton’s law wave ... · PDF file• Interfaces • Reflection and Transmission coefficients. body waves P-waves (longitudinal, ... Microsoft](https://reader034.fdocuments.us/reader034/viewer/2022051523/5a78fbe17f8b9a5a148eacae/html5/thumbnails/12.jpg)
� z�2
� 2�
�
z ��
�
![Page 13: Wave propagation • Hooke’s law • Newton’s law wave ... · PDF file• Interfaces • Reflection and Transmission coefficients. body waves P-waves (longitudinal, ... Microsoft](https://reader034.fdocuments.us/reader034/viewer/2022051523/5a78fbe17f8b9a5a148eacae/html5/thumbnails/13.jpg)
� z�2
� 2�
�
z � ��
�
�(z) is the Dirac function
![Page 14: Wave propagation • Hooke’s law • Newton’s law wave ... · PDF file• Interfaces • Reflection and Transmission coefficients. body waves P-waves (longitudinal, ... Microsoft](https://reader034.fdocuments.us/reader034/viewer/2022051523/5a78fbe17f8b9a5a148eacae/html5/thumbnails/14.jpg)
�2
� 2�2
� 22 �
� �2
� 2
�� -1/2
![Page 15: Wave propagation • Hooke’s law • Newton’s law wave ... · PDF file• Interfaces • Reflection and Transmission coefficients. body waves P-waves (longitudinal, ... Microsoft](https://reader034.fdocuments.us/reader034/viewer/2022051523/5a78fbe17f8b9a5a148eacae/html5/thumbnails/15.jpg)
Propagation of seismic waves
(Roth et al., 1998)
![Page 16: Wave propagation • Hooke’s law • Newton’s law wave ... · PDF file• Interfaces • Reflection and Transmission coefficients. body waves P-waves (longitudinal, ... Microsoft](https://reader034.fdocuments.us/reader034/viewer/2022051523/5a78fbe17f8b9a5a148eacae/html5/thumbnails/16.jpg)
Object detection using WAVES:
![Page 17: Wave propagation • Hooke’s law • Newton’s law wave ... · PDF file• Interfaces • Reflection and Transmission coefficients. body waves P-waves (longitudinal, ... Microsoft](https://reader034.fdocuments.us/reader034/viewer/2022051523/5a78fbe17f8b9a5a148eacae/html5/thumbnails/17.jpg)
Object detection using WAVES
BSource
OReceiver
![Page 18: Wave propagation • Hooke’s law • Newton’s law wave ... · PDF file• Interfaces • Reflection and Transmission coefficients. body waves P-waves (longitudinal, ... Microsoft](https://reader034.fdocuments.us/reader034/viewer/2022051523/5a78fbe17f8b9a5a148eacae/html5/thumbnails/18.jpg)
• 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
![Page 19: Wave propagation • Hooke’s law • Newton’s law wave ... · PDF file• Interfaces • Reflection and Transmission coefficients. body waves P-waves (longitudinal, ... Microsoft](https://reader034.fdocuments.us/reader034/viewer/2022051523/5a78fbe17f8b9a5a148eacae/html5/thumbnails/19.jpg)
Geometrical Wave propagation
Source ReceiverSource
Rays are perpendicular to the wavefronts,
![Page 20: Wave propagation • Hooke’s law • Newton’s law wave ... · PDF file• Interfaces • Reflection and Transmission coefficients. body waves P-waves (longitudinal, ... Microsoft](https://reader034.fdocuments.us/reader034/viewer/2022051523/5a78fbe17f8b9a5a148eacae/html5/thumbnails/20.jpg)
�1 �2v1
v2
Angle of incidence = angle of reflection
�1 = �2
![Page 21: Wave propagation • Hooke’s law • Newton’s law wave ... · PDF file• Interfaces • Reflection and Transmission coefficients. body waves P-waves (longitudinal, ... Microsoft](https://reader034.fdocuments.us/reader034/viewer/2022051523/5a78fbe17f8b9a5a148eacae/html5/thumbnails/21.jpg)
�1
v1
v2
�1sin�2sin------- -----
v1v2-----=
Interface: Refraction
v1v2 >
�2 v1v2 <
2�
![Page 22: Wave propagation • Hooke’s law • Newton’s law wave ... · PDF file• Interfaces • Reflection and Transmission coefficients. body waves P-waves (longitudinal, ... Microsoft](https://reader034.fdocuments.us/reader034/viewer/2022051523/5a78fbe17f8b9a5a148eacae/html5/thumbnails/22.jpg)
�1
v1
v2�1sin90�sin---------- �1sin
v1v2-----=
�2 90�=
Special case: critical angle
=
�2
![Page 23: Wave propagation • Hooke’s law • Newton’s law wave ... · PDF file• Interfaces • Reflection and Transmission coefficients. body waves P-waves (longitudinal, ... Microsoft](https://reader034.fdocuments.us/reader034/viewer/2022051523/5a78fbe17f8b9a5a148eacae/html5/thumbnails/23.jpg)
�1
vp1,vs1
�1sin�1sin
-------- ---vp1
vs1
--------=
�1
�2�1sin�2sin
------- ---vp1
vs2
--------=
vp2,vs2
Interface: Conversion from P wave to S wave
![Page 24: Wave propagation • Hooke’s law • Newton’s law wave ... · PDF file• Interfaces • Reflection and Transmission coefficients. body waves P-waves (longitudinal, ... Microsoft](https://reader034.fdocuments.us/reader034/viewer/2022051523/5a78fbe17f8b9a5a148eacae/html5/thumbnails/24.jpg)
�1sinvp1
------ = --�1sin
vs1
------ = --�2sin
vp2
-------- = -�2sin
vs2
-------------- = �nsin
vsn
--------- = p = constant
p = Slowness
�1
�2 �2
�3�3
�1
vp1vs1
vp2vs2
vp3vs3
![Page 25: Wave propagation • Hooke’s law • Newton’s law wave ... · PDF file• Interfaces • Reflection and Transmission coefficients. body waves P-waves (longitudinal, ... Microsoft](https://reader034.fdocuments.us/reader034/viewer/2022051523/5a78fbe17f8b9a5a148eacae/html5/thumbnails/25.jpg)
Refraction caused by place dependent propagation velocity
![Page 26: Wave propagation • Hooke’s law • Newton’s law wave ... · PDF file• Interfaces • Reflection and Transmission coefficients. body waves P-waves (longitudinal, ... Microsoft](https://reader034.fdocuments.us/reader034/viewer/2022051523/5a78fbe17f8b9a5a148eacae/html5/thumbnails/26.jpg)
Propagation of seismic waves
(Roth et al., 1998)
![Page 27: Wave propagation • Hooke’s law • Newton’s law wave ... · PDF file• Interfaces • Reflection and Transmission coefficients. body waves P-waves (longitudinal, ... Microsoft](https://reader034.fdocuments.us/reader034/viewer/2022051523/5a78fbe17f8b9a5a148eacae/html5/thumbnails/27.jpg)
E ER
ET
v1���1
v2���2
E = ER + ET
R + T = 1
R = Reflection coefficientT = Transmission coefficient
E = Energy
Transmission- and Reflection coefficients
![Page 28: Wave propagation • Hooke’s law • Newton’s law wave ... · PDF file• Interfaces • Reflection and Transmission coefficients. body waves P-waves (longitudinal, ... Microsoft](https://reader034.fdocuments.us/reader034/viewer/2022051523/5a78fbe17f8b9a5a148eacae/html5/thumbnails/28.jpg)
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
![Page 29: Wave propagation • Hooke’s law • Newton’s law wave ... · PDF file• Interfaces • Reflection and Transmission coefficients. body waves P-waves (longitudinal, ... Microsoft](https://reader034.fdocuments.us/reader034/viewer/2022051523/5a78fbe17f8b9a5a148eacae/html5/thumbnails/29.jpg)
(Sheriff and Geldart, 1995)
Angle-dependent reflection- and transmission-coefficients