1. IRIS Summer Intern Training Course Wednesday, May 31, 2006 Anne Sheehan Lecture 3: Teleseismic Receiver functions Teleseisms Earth response, convolution Receiver functions - basics, deconvolution Stacking receiver functions receiver function ‘imaging’ Complicated Earth Dipping layers Anisotropic receiver functions Applications & Examples - Himalaya, Western US

2. Teleseisms used in Himalayan Receiver Function Study

3. Want to deconvolve source and instrument response so we are just left with the signal from structure

5. layer 2 v p, v s, density layer 1 v p, v s, density dt amplitude converted pulse: delay time dt depends on depth of interface and v p, v s of top layer amplitude depends on velocity contrast (mostly) and density contrast (weakly) at the interface converted arrival: "+" bump = bottom slow, top fast "-" bump = bottom fast, top slow

6. unfortunately, incident P is not a nice simple bump: need to remove these bits...... to isolate phases converted near station source station

7. Receiver Function Construction Convert seismogram from vertical, NS, EW components to vertical, radial, transverse components Source Receiver Wave propagation direction SH: Transverse SV: Radial P wave compression Surface z y X

8. The magic step to isolate near-receiver converted phases via receiver function analysis: incident P appears mostly on the vertical component, converted S appears mostly on horizontal components. -> call the vertical component the "source" (it's as close as we're going to get to the true source function) and remove it from the horizontal components; what remains is close enough to the converted phases. how this works:

9. Linear Systems and Fourier Analysis Recall that for a linear system:

10. Linear Systems and Fourier Analysis Deconvolution is the inverse of CONVOLUTION CONVOLUTION

11. Linear Systems and Fourier Analysis

12. Teton Gravity Research & Warren Miller present: Craig Jones' new radical receiver function movie

13. A single receiver function - hard to interpret time amplitude one receiver function per earthquake -function of slowness (incidence angle) -function of backazimuth (unless flat layered isotropic case)

14. receiver functions are sensitive to discontinuity structure

15. midcrustal conversion "moveout plot": sort receiver functions by incidence angle (slowness) station ILAM (Nepal) radial receiver functions binned by slowness direct P Moho conversion Schulte-Pelkum et al., 2005

16. Moho ~70km Tibet station

17. arrival time/polarity variation with backazimuth (corrections for slowness + elevation applied) azimuthal variation

18. highly coherent transverse component receiver functions transverse components

19. attempt at a standard moveout plot for narrow azimuthal range depth of modelled discontinuity (km) multiples

20. common conversion point (CCP) stacking scale time to depth along incoming ray paths with an assumed velocity model stack all receiver functions within common conversion point bin

21. stack along profile (red):

22. Schulte-Pelkum et al., 2005

23. but where is the decollement?

24. Linear Systems and Fourier Analysis Using Fourier analysis, deconvolution of linear system responses becomes a very simple problem of division in the frequency domain Solution in the frequency domain is converted to a solution in the time domain using the Fourier transform f(t) = 1 F(  )e iwt d  2   --  F(  ) = f(t)e -iwt dt  --  Fourier transform inverse Fourier transform

25. Receiver Function Construction after Langston, 1979 and Ammon, 1991 source signal earth’s responseIn the earth, the source signal is convolved with the earth’s response We want to extract the information pertaining to the earth’s response, because it can tell us about the earth’s structure We also have to worry about the instrument responses from our seismometers

26. Receiver Function Construction This is analogous to the form d = Gm Theoretical Displacement Response for a P plane wave D v (t) = I(t)*S(t)*E v (t) (vertical) D r (t) = I(t)*S(t)*E r (t) (radial) D t (t) = I(t)*S(t)*E t (t) (transverse) Displacement Response Instrument Impulse Response Source Time Function Structure Impulse Response (Receiver Function)

27. Receiver Function Construction Assumption: using nearly vertically incident events, the vertical component approximates the source function convolved with the instrument response D v (t) = I(t)*S(t)

28. Receiver Function Construction In the frequency domain, E r and E t can be simply calculated this implies that D v (t)*E r (t) = D r (t) E r (  ) = D r (  ) = D r (  ) I(  )S(  ) D v (  ) E t (  ) = D t (  ) = D t (  ) I(  )S(  ) D v (  )

29. Receiver Function Construction P SV incident: steep P mostly on vertical component converted phase: SV (in plane) mostly on radial component with dipping interfacewith anisotropic layer Out of plane S conversions (on radial and transverse components)

30. synthetic data Schulte-Pelkum et al., 2005

31. Azimuthal difference stacking flip polarity of all receiver functions incident from northerly backazimuths before stacking

32. -> new interface shows up in stack Schulte-Pelkum et al., 2005

33. interface found with azimuthal difference stack has good match with INDEPTH decollement found anisotropy suggests ductile shear deformation at depth Schulte-Pelkum et al., 2005

35. incident: steep P mostly on vertical component converted phase: SV (in plane) mostly on radial component out-of-plane S conversions (on radial and transverse components): with dipping interface with anisotropic layer P SV

36. Receiver function profiles across the Western United States Gilbert & Sheehan, 2004

37. Western United States crustal thicknesses from receiver functions Gilbert & Sheehan, 2004

38. On-line resources: convolution animation: http://www-es.fernuni- hagen.de/JAVA/DisFaltung/convol.html Chuck Ammon's online receiver function tutorial: http://eqseis.geosc.psu.edu/~cammon/HTML/RftnD ocs/rftn01.html