1. Seismic waves Wave propagation Hooke’s law Newton’s law  wave equation Wavefronts and Rays Interfaces Reflection and Transmission coefficients

2. Seismic Waves body waves P-waves (longitudinal, compressional) S-waves (shear, transverse) S V -wave S H

3. Body waves:

4. Different kind of waves Transversal waves (S-waves) Longitudinal waves (P-waves) 1 3 5 4 2 2 4 1 3 5

5. Examples of different waves Elektromagnetic spectrum Frequency AM, FM, Georadar, Visible, X-ray Acoustic spectrum Earthquake, audible + seismic 10 6 10 0 10 19 Hz

6. Surface waves Rayleigh-waves Love-waves

7. Newton’s law P(z) P(z+  z) UzUz P is the acoustic pressure U z is the displacement

8. Newton’s law P(z) P(z+  z) P(z+  z) - P(z) = UzUz d2d2 dt 2 UzUz - z- z  is the massdensity

9. Newton’s law P(z) P(z+  z) UzUz -- UzUz 22 t2t2 P =  zz

10. Hooke’s law P -   z P U z (z+  z) - U z (z) = U z (z) U z (z+  z)  is the compressibility

11. Hooke’s law P U z (z) U z (z+  z) U z = -  P  zz

12. Acoustic Wave equation 22 z2z2 P 22 t2t2 P 1 c2c2 = -w(t)  (z)w(t) =  q(t) (sourcesignal) 22 t2t2 c = (  ) -1/2 (wavespeed)

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

14. Object detection using WAVES:

15. Object detection using WAVES B Source O Receiver

16. Wavefronts versus Rays 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

17. Geometrical Wave propagation SourceReceiverSource Rays are perpendicular to the wavefronts,

18.  1  2 v 1 v 2 Angle of incidence = angle of reflection  1 =  2 Interface: reflection

19.  1 v 1 v 2  1 sin  2 ------- ----- v 1 v 2 -----= Interface: Refraction v 1 v 2 >  2 v 1 v 2 < 2 

20.  1 v 1 v 2  1 sin 90  sin ----------  1 sin v 1 v 2 -----=  2 90  = Special case: critical angle =  2

21.  1 v p1, v s1  1 sin  1 -------- --- v p 1 v s 1 --------=  1  2  1 sin  2 ------- --- v p 1 v s 2 --------= v p2, v s2 Interface: Conversion from P wave to S wave

22.  1 sin v p 1 ------ = --  1 sin v s 1 ------ = --  2 sin v p 2 -------- = -  2 sin v s 2 -------------- =  n sin v s n --------- = p = constant p = Slowness  1  2  2  3  3  1 Snell’s law v p 1 v s 1 v p 2 v s 2 v p 3 v s 3

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

24. EE R E T v 1  1 v 2 2 E = E R + E T R + T = 1 R = Reflection coefficient T = Transmission coefficient E = Energy Transmission- and Reflection coefficients

25. R T v 1  1 v 2 2 Reflection coefficient Transmission coefficient R v 2  2 v 1  1 – v 2  2 v 1  1 + --------------- = ------------ Z 2 Z 1 – Z 2 Z 1 + --------------------= T 2v 1  1 v 2  2 v 1  1 + ---------------- = ----------- 2Z 1 Z 2 Z 1 + --------------------= with Z = v  = acoustic Impedance Zoeppritz’s equations at normal incidence