1. Seismic Tomography and Double-Difference Seismic Tomography
Haijiang Zhang
University of Science and Technology of China
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
STATION AZIMUTH

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

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

9. How can we determine the heterogeneity?
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 *
STATION AZIMUTH
How can we determine the heterogeneity?

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

11. How does seismic tomography work?
"Illuminate" fast velocity anomaly with 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
slowness si = 1/velocity h s3 s4

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

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

16. Simple Seismic Tomography Problem
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 1 1
EARLY 1
AZIMUTH

18. Relative Arrival Time 2
LATE 2 2 2
EARLY 2
AZIMUTH

19. Relative Arrival Time 3
LATE 3 3 3
EARLY 3
AZIMUTH

20. Relative Arrival Time 4
LATE 4 4 4
EARLY 4
AZIMUTH

21. So relative arrival times tell you relative locations4
LATE 4 4 4
EARLY 4
AZIMUTH
So relative arrival times tell you relative locations

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

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

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

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

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

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

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

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

30. gray = homogeneous case
Relative Arrival Time 2 2
LATE 2 2 2 2 2
EARLY 2 2
FAST SLOW FAST
AZIMUTH
gray = homogeneous case

31. gray = homogeneous case
Relative Arrival Time 3 3
LATE 3 3 3 3 3
EARLY 3 3
FAST SLOW FAST
AZIMUTH
gray = homogeneous case

32. gray = homogeneous case
Relative Arrival Time 4 4
LATE 4 4 4 4 4
EARLY 4 4
FAST SLOW FAST
AZIMUTH
gray = homogeneous case

33. Result - locations are very distorted!1 1 4 4 2 2 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 QUESTIONS?
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 equations involving both absolute and double-difference residuals
double difference
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. superior throughout well resolved areas
Difference between solutions and true model
Double difference Conventional
Marginal results
near surface
DD results
superior throughout well resolved areas
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
Input model Vp Vs
Recovered model

49. Test 2: without mid-slab anomaly
Input model Vp Vs
Recovered model

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

51. Preliminary study of the New Zealand subduction zone - Vp

52. Preliminary study of the New Zealand subduction zone - Vs

53. Preliminary study of the New Zealand subduction zone - Vp/Vs

54. Comparing Northern Honshu (top) to New Zealand (bottom)

55. Application to Parkfield
Following 4 workshops in , a site just north of the rupture zone for the M6 Parkfield earthquake was chosen for SAFOD because:
Surface creep and abundant shallow seismicity allow us to accurately target the subsurface position of the fault.
Clear geologic contrast across the fault - granites on SW side and Franciscan melange on NE - should facilitate fault's identification (or so we thought!).
Good drilling conditions on SW side of fault (granites).
Fault segment has been the subject of extensive geological and geophysical studies and is within the most intensively instrumented part of a major plate- bounding fault anywhere in the world (USGS Parkfield Earthquake Experiment).

56. SAFOD Drilling Phases 1 2 3 Pilot Hole (summer 2002)
Phase 1: Rotary Drilling to 2.5 km (summer 2004)
Phase 2: Drilling Through the Fault Zone (summer 2005)
Phase 3: Coring the Multi-Laterals (summer 2007)
San Andreas Fault Zone 1 2 3
Target Earthquake
Resistivities: Unsworth & Bedrosian, 2004
Earthquake locations: Steve Roecker, Cliff Thurber, and Haijiang Zhang, 2004

57. PASO-DOS, SUMMER 2001 – FALL 2002

59. Relationship of Seismicity to 3D Structure – Fault-Normal View
Z=-0.5 km NE SW
Z=7.0 km
Viewed from the northwest

60. Relationship of Seismicity to 3D Structure – Fault-Parallel ViewNW
Z=-0.5 km
Z=7.0 km
Viewed from the northeast

61. Revised Locations of Target Events and Borehole Features
Zoback et al. (2011)

62. SUMMARY
DD tomography provides improved relative event locations and a sharper image of the velocity structure compared to conventional tomography.
In both Japan and New Zealand, we find evidence for substantial velocity variations within the down-going slab, especially low Vp/Vs zones around the lower plane of seismicity.
In Parkfield, earthquakes "hug" the edge of the high-velocity zone and repeating earthquakes correlate with structures seen in borehole.

63. Extensions of tomoDD Regional scale tomoDD Adaptive tomoDD
Global scale tomoDD

64. Regional scale version tomoFDD
Considers sphericity of the earth.
Finite-difference ray tracing method [Podvin and Lecomte, 1991; Hole and Zelt, 1995] is used to deal with major velocity discontinuities such as Moho and subducting slab boundary.
Discontinuities are not explicitly specified.

65. Treating sphericity of the Earth
Insert the Earth into a cubic box.
2D slice
Use the rectangular box to cover the region of interest
Flanagan et al., 2000

66. Adaptive-mesh version tomoADD
Uneven ray distribution requires irregular inversion mesh.
Linear and natural-neighbor interpolation based on tetrahedral and Voronoi diagrams.
Zhang and Thurber, 2005, JGR

67. Uneven ray distribution
Nonuniform station geometry
Noneven distribution of sources
Ray bending
Missing data
Mismatch between ray distribution and cells/or grids causes instability of seismic tomography
Using damping and smoothing → possible artifacts

68. The advantage of adaptive grid/cells (or why do we bother to use?)
The distribution of the inversion grid/cells should match with the resolving power of the data.
The inverse problem is better conditioned.
Weaker or no smoothing constraints can be applied.
Less memory space (less computation time?)

69. Construct tetrahedral and Voronoi diagrams around irregular mesh
Represent the model with different scales
Represent interfaces
Place nodes flexibly

70. Linear interpolation
Based on tetrahedra in 3D

71. Natural neighbor (NN) interpolation
where is the natural-neighbor “coordinate”

72. linear interpolation vs. natural neighbor interpolation
Using 4 nodes
Continuity in first derivatives
Easier to calculate
Natural neighbor interpolation
Using n nodes
Continuity in both first and 2nd derivatives
More difficult to calculate

73. Automatic construction of the irregular mesh

74. Application to SAFOD project
~800 earthquakes, ~100 shots, subset of high-resolution refraction data (Catchings et al., 2002); 32 "virtual earthquakes" (receiver gathers from Pilot Hole)

75. The inversion grids for (a) P and (b) S waves at the final iteration using only the absolute data.

76. The DWS value distribution (ray sampling density) for P waves
Regular grid
Irregular grid

77. Natural neighbor interpolation
The across-strike cross-section of P-wave velocity structure through Pilot Hole (absolute and differential data)
Linear interpolation
Natural neighbor interpolation

78. Global scale DD tomography