1. Advances in Earthquake Location and Tomography William Menke Lamont-Doherty Earth Observatory Columbia University

2. 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 Outline

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

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

5. that was a Gulf of Mexico earthquake, by the way …

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

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

11. differential arrival time = difference in arrival times

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

13. Station i

16. 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

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

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

20. as long as you have more than two earthquakes

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

22. The same idea works …

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

24. 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 C A B

25. Another example …

26. What is the practical advantage of using differential arrival times to 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

27. Geometry of the numerical experiment …

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

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

30. 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”

32. Part 2 Simultaneous earthquake location and tomography

39. L1L2 Source

41. Line 3 Line 2 Line 1 Distance along receiver array traveltime Very late secondary arrivals Slightly late first arrivals

42. note In a typical tomography experiment, there are lots of secondary arrivals. But nobody really has a good way of analyzing them and extracting useful information from them. Its an area that needs work …

43. What about 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

44. A numerical test 11 stations 50 earthquakes on fault zone Heterogenity near fault zone only

45. 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.

46. Part 3 Is Joint Tomography/Earthquake Location Really Possible ? In depth analysis of the special case of unknown origin time but known location A simplified version of the problem

62. If you can … Then that structure is indistinguishable from a perturbation in origin time!

63. Case of sources near bottom of the model For an event at This velocity perturbation causes constant travel time perturbation for a station on the surface anywhere in the grey box!

64. Case of sources near top of model For an event at This velocity perturbation causes constant travel time perturbation for a station on the surface anywhere in the grey bodx!

65. But you can always find such structures! And they often look ‘geologically interesting’ Yet their presence of absence in an area cannot be proved or disproved by the tomography.

66. Summary Part 1: Earthquake location with differential data is the way to go! Part 2: The “secondary arrival” problem is out there waiting for a clever mind. Part 3: Coupled Tomography/Location is extremely nonunique and extremely likely to fool you.