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Advances in Earthquake Location and Tomography

Advances in Earthquake Location and Tomography. William Menke Lamont-Doherty Earth Observatory Columbia University. Outline. Part 1: Advantage of using differential arrival times to locate earthquakes Part 2: Simultaneous earthquake location and tomography

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Advances in Earthquake Location and Tomography

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  1. Advances in Earthquake LocationandTomography William Menke Lamont-Doherty Earth Observatory Columbia University

  2. Outline Part 1: Advantage of using differential arrival times to locate earthquakes Part 2: Simultaneous earthquake location and tomography Part 3: In depth analysis of the special case of unknown origin time

  3. Part 1 Advantage of using differential arrival times to locate earthquakes

  4. that was the recent Gulf of Mexico earthquake,by the way …

  5. Locating an earthquakerequires knowing theseismic velocity structureaccurately

  6. What’s the best way to represent 3 dimensional structure Best for what? compatibility with data sources ease of visualization and editing facilitating calculation

  7. Overall organization into interfaces Small-scale organization into tetrahedra Linear interpolation within tetrahedra implying rays that are circular arcs

  8. seismometer earthquake

  9. Location Errors: = 0.5 degree = 55 km = 30 miles Note: this preliminary calculation used data from a limited number of stations

  10. Two parallel approaches work to improve earth model design earthquake location techniques that are as insensitive to model as possible

  11. Waves from earthquake first arrived in Palisades NY at 15:00:32 on Sept 10, 2006

  12. Arrival Time ≠Travel TimeQ: a car arrived in town after traveling for an half an hour at sixty miles an hour. Where did it start?A. Thirty miles awayQ: a car arrived in town at half past one, traveling at sixty miles an hour. Where did it start?A. Are you crazy?

  13. Suppose you contour arrival timeon surface of earth Earthquake’s (x,y) is center of bullseye but what about its depth?

  14. Earthquake’s depth related to curvature of arrival time at origin Deep Shallow

  15. Earthquakes in Long Valley Caldera, California located with absolute traveltimes Courtesty of Felix Walhhauser, LDEO

  16. Earthquakes in Long Valley Caldera, California located with differential traveltimes Courtesty of Felix Walhhauser, LDEO

  17. differential arrival time = difference in arrival times

  18. mean origin time cancels out T = arrival time TT = travel time To = Origin Time (start time of earthquake)

  19. Station i

  20. Very accurate DT’s !

  21. A technical question for Applied Math types … Are differential arrival times as calculated by cross-correlation less correlated than implied by the formula They seem to be. If so, the this is another advantage of using the method

  22. How does differential arrival time vary spatially? Depends strongly on this angle

  23. In a 3 dimensional homogeneous box … maximum minimum mean If you can identify the line AB, then you can locate earthquakes

  24. as long as you have more than two earthquakes

  25. In a vertically-stratified earth, rays are bent back up to the surface, so both Points A and B are on the surface. ray wavefront The pattern of differnetial traveltime is more complicated …

  26. The same idea works … p q

  27. B B A B C C C A A A B C C C Patterns of differential arrival time Can you guess the orientation of the two sources in these six cases?

  28. This pattern an be seen in actual data, in this case from a pair of earthquakes on the San Andreas Fault Boxes: differential arrival times observed at particular stations Shading: theoretical calculation for best-fitting locations of the earthquake pair A B C

  29. Another example …

  30. What is the practical advantageof using differential arrival timesto locate earthquakes My approach is to examine the statistics of location errors using numerical simulations Compare the result of using absolute arrival time data And differential arrival time data When the data are noise Or the earth structure is poorly known

  31. Geometry of the numerical experiment …

  32. Effect of noisy data (10 milliseconds of measurement error) differential data differential data absolute data absolute data

  33. Effect of near surface heterogeneities (1 km/s of velocity variation with a scale length of 5 km) differential data absolute data differential data absolute data

  34. Both absolute locations and relative locations of earthquakes are improved by using differential arrival time data when arrival times are nosily measured and when near-surface earth structure is poorly modeled Relative location errors can be just a few meters even when errors are “realistically large”

  35. Part 2 Simultaneous earthquake location and tomography

  36. simultaneous earthquake location and tomography? Many earthquakes with unknown X, Y, Z, To Unknown velocity structure Solve for everything Using either absolute arrival times or differential arrival times

  37. A numerical test 11 stations 50 earthquakes on fault zone Heterogeneity near fault zone only

  38. True earthquake locations And fault zone heterogenity ( 1 km/s) Reconstructed earthquake locations And fault zone heterogenity, using noise free differential data Note the amplitude of the “signal” is only 1 ms, so noise might be a problem.

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