1. Lithospheric Layering

2. Outline Receiver Function Method Mapping time to depth (Basic)
Advanced applications a. Determining Vp/Vs and Moho depth b. Velocity modeling c. Determining layers of anisotropy and dip

3. Receiver functions
Receiver functions are used to isolate the response function that describes P-wave to S-wave conversions at horizontal velocity interfaces (layers) in the earth below the receiver (hence the name receiver function)

4. P-wave to S-wave conversions
Frequency Domain
h - horizontal
v - vertical
w - whitening

5. source * response = signal
Forward Model (Convolution) Generation of recorded signal from Source and Earth Response
source * response = signal = *

6. Inverse Model (Deconvolution ) Using the signal and source to get the Earth Response function
signal / source = response = /
CASE OF NO NOISE! EVEN SMALL % OF NOISE CAN CREATE
UNSTABLE SOLUTION – INVERSE THEORY and REGULARIZATION TO SATBALIZE THE SOLUTION

7. Real Receiver function
3C Seismic Record: P-wave is the source (vertical) P-wave + converted S-wave are signal (isotropic-flat layer -> radial)

8. Outline Receiver Function Method Mapping time to depth (Basic)
Advanced applications a. Determining Vp/Vs and Moho depth b. Velocity modeling c. Determining layers of anisotropy and dip

9. Move-out correction and Mapping time to depth
P-wave
Want to know the timing difference
between the direct P arrival (ts) and the converted S arrival (ts) as a function of depth.
This can be done if we know the velocity of the wave-front in the vertical and horizontal directions x
S-wave z tp ts

10. Move-out correction and Mapping time to depth
Just a geometry problem!
Tpds = ts – tp
1/Vpx
P-wave
S-wave
1/Vpz tp ts

11. Move-out correction and Mapping time to depth
Just a geometry problem!
The horizontal velocity is known, the rayparmeter - ‘p’
We need to know the P-velocity as a function of depth: Vp(z)
And the ratio between Vp and Vs (Poisson’s ratio).

12. Move-out correction and Mapping time to depth
How much do errors in assumptions affect the time to depth mapping?
Vp(z) – An avg velocity difference of 6.2 and 6.5 translates to ~ 3 km at 70 km depth
ie if the Moho is at 70 km and the crust has an avg velocity of 6.5 km/s, we use 6.2 km/s and compute a depth of ~ 67 km
The horizontal velocity is known, the rayparmeter - ‘p’
We need to know the P-velocity as a function of depth: Vp(z)
And the ratio between Vp and Vs (Poisson’s ratio).

13. Move-out correction and Mapping time to depth
How much do errors in assumptions affect the time to depth mapping?
Vp/Vs ratio – An avg difference of 1.72 to 1.79 translates to ~ 7 km at 70 km depth
ie if the Moho is at 70 km and the crust has an avg Vp/Vs of 1.79, we use 1.72 to compute a depth of ~ 63 km
The horizontal velocity is known, the rayparmeter - ‘p’
We need to know the P-velocity as a function of depth: Vp(z)
And the ratio between Vp and Vs (Poisson’s ratio).

14. Data Coverage 8/03 – 10/04 Teleseismic (blue) Distance 30-95 Deg
Magnitude >=5.5 mb
N - 179
Teleseismic
Regional (Green)
Distance <30 Deg
Magnitude >=4.5 mb
N - 571
Regional

15. 70 km piercing pts across the array

16. Cross sections of stacked RF’s

17. Cross sections of stacked RF’s

18. Cross sections of stacked RF’s

19. Cross sections of stacked RF’s

20. Cross sections of stacked RF’s

22. Measurement of depth to Moho assuming Vp of 6.4 and Vp/Vs of 1.75

23. Outline Receiver Function Method Mapping time to depth (Basic)
Advanced applications a. Determining Vp/Vs and Moho depth b. Velocity modeling c. Determining layers of anisotropy and dip

24. Moho depth and Vp/Vs ratio
If we assume Vp(z), we can write a function:
H(Vp/Vs, D) =
Tpms +Tppms + Tpsms
which we can use to
solve
Vp/Vs and D
Figures: Kennett, B

25. Example from station ES02
Moho depth 71 km
Vp/Vs 1.77
Poisson’s 0.27
Pms + Ppms + Psms
Pms + Ppms
Depth below receiver (km)
Vp/Vs ratio

26. Non-linear inversion for velocity and Vp/Vs

27. Identifying layers of Anisotropy and Dip

28. Identifying layers of Anisotropy and Dip

29. Identifying layers of Anisotropy and Dip

30. Thank You! The End…

31. Move-out correction and Mapping time to depth
Just a geometry problem!
Tppds = (ts – tp) + tp + tp = ts + tp
1/Vpx
P-wave
S-wave
1/Vpz tp ts

32. Move-out correction and Mapping time to depth
Just a geometry problem!
Tpsds = (ts – tp) + ts + tp = 2*ts
1/Vpx
P-wave
S-wave
1/Vpz

33. Examples from station ES34
Pms + Ppms + Psms
Pms + Ppms
Moho depth 65 km
Vp/Vs 1.76
Poisson’s 0.26
Depth below receiver (km)
Vp/Vs ratio