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S eismic T omography and Double- D ifference S eismic T omography

Haijiang Zhang University of Science and Technology of China. S eismic T omography and Double- D ifference S eismic T omography. Clifford Thurber University of Wisconsin-Madison. Acknowledgements. Felix Waldhauser , for hypoDD , sharing data, and providing many constructive comments

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S eismic T omography and Double- D ifference S eismic T omography

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  1. Haijiang Zhang University of Science and Technology of China Seismic Tomography and Double-Difference Seismic Tomography Clifford Thurber University of Wisconsin-Madison

  2. Acknowledgements • Felix Waldhauser, for hypoDD, sharing data, and providing many constructive comments • Bill Ellsworth, for suggesting the name "tomoDD" • Charlotte Rowe for assistance • Defense Threat Reduction Agency,NSF, and USGS for financial support

  3. Outline • Seismic tomography basics – conventional and double-difference • Synthetic tests and example applications • Usage of tomoDD

  4. Consider residuals from one earthquake Arrival Time Misfit * LATE * * * Trial Location EARLY * Map View 0 90 180 270 STATION AZIMUTH

  5. Interpretation #1 - earthquake is farther north Arrival Time Misfit True Location * * LATE * * * * * * * EARLY * Map View 0 90 180 270 STATION AZIMUTH

  6. Is mislocation the only explanation? Arrival Time Misfit * LATE * * * Trial Location EARLY * Map View 0 90 180 270 STATION AZIMUTH

  7. Alternative interpretation - velocity structure is slower near event and to the south and faster near the northern station! FASTER * LATE * * * True Location SLOWER EARLY * Map View 0 90 180 270 STATION AZIMUTH

  8. Alternative interpretation - velocity structure is slower near event and to the south and faster near the northern station! Compensate for Structure FASTER * LATE * * * True Location * * * * SLOWER EARLY * Map View 0 90 180 270 STATION AZIMUTH

  9. Alternative interpretation - velocity structure is slower near event and to the south and faster near the northern station! Compensate for Structure FASTER * LATE * * * True Location * * * * SLOWER EARLY * Map View 0 90 180 270 STATION AZIMUTH How can we determine the heterogeneity?

  10. How does seismic tomography work? "Illuminate" fast velocity anomalywith waves from earthquake to array Localizes anomaly to a "cone"

  11. How does seismic tomography work? "Illuminate" fast velocity anomalywith waves from earthquake to array "Illuminate" fast anomaly with waves from another earthquake Localizes anomaly to a "cone" Localizes anomaly to another "cone"

  12. Combine observations from multiple earthquakes to image anomaly

  13. Simple Seismic Tomography Problem h s2 s1 slowness si = 1/velocity h s3 s4

  14. Simple Seismic Tomography Problem h s2 s1 slowness si = 1/velocity h s3 s4

  15. Simple Seismic Tomography Problem h s2 s1 slowness si = 1/velocity h s3 s4 d = G m data model

  16. Simple Seismic Tomography Problem h s2 s1 slowness si = 1/velocity h s3 s4 d = G m QUESTIONS SO FAR? data model

  17. Consider pairs of closely-spaced earthquakes Relative Arrival Time 1 1 LATE 0 1 1 EARLY 1 0 90 180 270 AZIMUTH

  18. Relative Arrival Time 2 LATE 0 2 2 2 EARLY 2 0 90 180 270 AZIMUTH

  19. Relative Arrival Time 3 LATE 0 3 3 3 EARLY 3 0 90 180 270 AZIMUTH

  20. Relative Arrival Time 4 LATE 4 0 4 4 EARLY 4 0 90 180 270 AZIMUTH

  21. Relative Arrival Time 4 LATE 4 0 4 4 EARLY 4 0 90 180 270 AZIMUTH So relative arrival times tell you relative locations

  22. Consider effect of heterogeneity - linear horizontal velocity gradient Relative Arrival Time 1 1 LATE 0 1 1 EARLY 1 0 90 180 270 AZIMUTH SLOWER ====> FASTER gray = homogeneous case

  23. Consider effect of heterogeneity – linear horizontal velocity gradient Relative Arrival Time 1 1 1 LATE 0 1 1 1 1 EARLY 1 1 0 90 180 270 AZIMUTH SLOWER ====> FASTER gray = homogeneous case

  24. Relative Arrival Time 2 LATE 0 2 2 2 EARLY 2 0 90 180 270 AZIMUTH SLOWER ====> FASTER gray = homogeneous case

  25. Relative Arrival Time 2 2 LATE 0 2 2 2 2 2 EARLY 2 2 0 90 180 270 AZIMUTH SLOWER ====> FASTER gray = homogeneous case

  26. Relative Arrival Time 3 LATE 3 0 3 3 3 3 3 EARLY 3 3 0 90 180 270 AZIMUTH SLOWER ====> FASTER gray = homogeneous case

  27. Relative Arrival Time 4 4 LATE 4 0 4 4 4 4 EARLY 4 4 0 90 180 270 AZIMUTH SLOWER ====> FASTER gray = homogeneous case

  28. Ignore heterogeneity – some locations will be distorted, some residuals will be larger! 1 1 4 2 2 4 0 3 3 gray = true white = relocated

  29. Consider effect of different heterogeneity - low velocity fault zone Relative Arrival Time 1 1 1 LATE 0 1 1 1 1 EARLY 1 1 FAST SLOW FAST 0 90 180 270 AZIMUTH gray = homogeneous case

  30. Relative Arrival Time 2 2 LATE 0 2 2 2 2 2 EARLY 2 2 FAST SLOW FAST 0 90 180 270 AZIMUTH gray = homogeneous case

  31. Relative Arrival Time 3 3 LATE 0 3 3 3 3 3 EARLY 3 3 FAST SLOW FAST 0 90 180 270 AZIMUTH gray = homogeneous case

  32. Relative Arrival Time 4 4 LATE 4 0 4 4 4 4 EARLY 4 4 FAST SLOW FAST 0 90 180 270 AZIMUTH gray = homogeneous case

  33. Result - locations are very distorted! 1 1 4 2 2 4 0 3 3 gray = true white = relocated

  34. Implications • Ignoring heterogeneous earth structure will bias estimated locations from true locations • Different heterogeneities have different "signatures" in arrival time difference patterns - so there should be a "signal" in the data that can be modeled

  35. Implications • Ignoring heterogeneous earth structure will bias estimated locations from true locations • Different heterogeneities have different "signatures" in arrival time difference patterns - so there should be a "signal" in the data that can be modeled QUESTIONS?

  36. Our DD tomography approach • Determine event locations and the velocity structure simultaneously to account for the coupling effect between them. • Use absolute and high-precision relative arrival times to determine both velocity structure and event locations. • Goal: determine both relative and absolute locations accurately, and characterize the velocity structure "sharply."

  37. Seismic tomography Arrival-time residuals can be linearly related to perturbations to the hypocenter and the velocity structure: Nonlinear problem, so solve with iterative algorithm.

  38. Double-difference seismic tomography For two events i and j observed at the same station k Subtract one from the other Note:

  39. Combine conventional and double-difference tomography into one system of equationsinvolving both absolute and double-difference residuals doubledifference absolute

  40. Test on "vertical sandwich" model • Constant velocity (6 km/s) west of "fault" • Sharp lateral gradient to 4 km/s • Few km wide low-velocity "fault zone" • Sharp lateral gradient up to 5 km/s • Gentle lateral gradient up to 6 km/s • Random error added to arrival times but not differential times (so latter more accurate) • Start inversions with 1D model

  41. Conventional tomography solution True model, all depths

  42. Double-difference tomography solution True model, all depths

  43. Difference between solutions and true model Double difference Conventional Marginal results near surface DD results superiorthroughoutwell resolvedareas Poor results at model base

  44. Application to northern Honshu, Japan Peacock, 2001

  45. Examples of previous results for N. Honshu Nakajima et al., 2001 Zhao et al., 1992 Note relative absence of structural variations within the slab

  46. Events, stations, and inversion grid Y=40 km Y=-10 km Y=-60 km Zhang et al., 2004

  47. Cross section at Y=-60 km Vp Vs Vp/Vs

  48. Test 1: with mid-slab anomaly Inputmodel Vp Vs Recoveredmodel

  49. Test 2: without mid-slab anomaly Inputmodel Vp Vs Recoveredmodel

  50. Preliminary study of the southern part of New Zealand subduction zone

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