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Understanding the Earth by Stacking Receiver Functions: The H-K Method

Understanding the Earth by Stacking Receiver Functions: The H-K Method. Andy Frassetto, IRIS Headquarters Office ASI Kuwait, January 20, 2013. Who Am I ?. Halfway along a 20 mile walk, Fimmvörðuháls vent, Iceland, April 2010. hiker, gardener, cook, softball outfielder, traveler.

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Understanding the Earth by Stacking Receiver Functions: The H-K Method

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  1. Understanding the Earth by Stacking Receiver Functions: The H-K Method Andy Frassetto, IRIS Headquarters Office ASI Kuwait, January 20, 2013

  2. Who Am I? Halfway along a 20 mile walk, Fimmvörðuháls vent, Iceland, April 2010 hiker, gardener, cook, softball outfielder, traveler

  3. From: Florida, USA Schools: U. South Carolina (B.S.) U. Arizona (Ph.D.) Currently (near) here:

  4. Mt. Whitney, California, USA ~3 km ? ? ? ? ?

  5. The tip of the iceberg…

  6. Receiver Functions

  7. Importance of Stacking -Suppresses noise -Emphasizes coherent signals -S/N ratio grows by √# of RFs Svenningsen et al., 2007

  8. Abt et al., 2009

  9. Arrivals vs. Ray Parameter

  10. Arrivals vs. Ray Parameter

  11. Arrivals vs. Ray Parameter Vp, Vs A B A B angle of incidence

  12. arrival time of vertically incident S-wave after P-wave Vp, Vs, K H D Easy! Take the integral of the S-wave slowness minus P-wave slowness

  13. Within a layer of constant velocities Vp, Vs H D Find the expected arrival time for vertically traveling P and S waves in layer with Vs=3.5 km/s, Vp=6.4 km/s, H=40 km.

  14. Within a layer of constant velocities Vp, Vs H USUALLY NOT THE CASE! D Find the expected arrival time for vertically traveling P and S waves in layer with Vs=3.5 km/s, Vp=6.4 km/s, H=40 km.

  15. Arrival time of a non-vertically incident Pds wave H Vp, Vs D Need to know Vp, Vs, and p (slowness) of the incident P-wave

  16. vertical component of S slowness Vp, Vs, K vertical component of P slowness p p vertical component of P slowness p is constant vertical component of S slowness

  17. we have done examples solving the forward problem of calculating what TIME a phase from a given depth would arrive Given depth, Vp, Vs, and p, we found t.

  18. now we want to solve for what depth a phase was produced depending on its arrival time with constant Vs and Vp that do not depend on depth arrival time equation becomes: solving then for depth z

  19. we pick the arrival time of the Ps phase, calculate p, and assume Vp, and Vs Pds arrival time = 5 s, p = 0.06 s/km and Vp=6.4 km/s and Vs =3.5 km/s

  20. z = 37 km how sensitive is this value of z to our assumptions?

  21. Vary Vp to observe the SMALL effect on crustal thickness estimates

  22. Vary Vp/Vs to observe the LARGE effect on crustal thickness estimates

  23. arrival time of vertically incident PpPs-wave after P-wave Vp, Vs, K D

  24. as we saw for the direct Ps wave the arrival time is: following the progression explained for the PpPs reverberation phase, its arrival time is: similarly the PsPs + PpSs arrival time is:

  25. we pick the arrival times of the Pds, PpPs, and PsPs+PpSs phases, calculate p, and assume Vp, and Vs 5 16 21 Pds time = 5 s, PpPs = 16 s, PsPs+PpSs time = 21 s, p= 0.06 s/km and Vp=6.4 km/s and Vs =3.5 km/s

  26. How do we account for these differences? Are they all resulting from an interface at the same depth? Were the phases all picked correctly? Could we have made an incorrect assumption?

  27. keep Vp constant and vary Vp/Vs, each system has a different behavior

  28. Only 1 Vp/Vs value leads the travel-times to a unique convergence on a certain thickness.

  29. 6-12 months of events needed for good solution Zhu and Kanamori, 2000

  30. W1 = 0.7 W2 = 0.2 W3 = 0.1 or W1 = 0.34 W2 = 0.33 W3 = 0.33 Zhu and Kanamori, 2000

  31. GOOD BAD

  32. A Review: 3 Equations We Know: t and p We Assume: Vp We Calculate: z and Vs (giving us Vp/Vs)

  33. Example: Arizona Temporary Station LEMN GSN Station TUC Me

  34. Example: Arizona

  35. Example: Arizona

  36. Example: California Frassetto et al., 2011

  37. Example: California

  38. Example: California

  39. Example: Norway Frassetto et al., Submitted

  40. Example: Norway

  41. Example: Norway

  42. Example: USArray

  43. http://www.iris.edu/dms/products/ears/

  44. Phase Weighting Schimmel and Paulssen, 1997

  45. Crotwell and Owens, 2005

  46. Interface Resolution

  47. CCP Stacking

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