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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 LocationandTomography 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 Part 3: In depth analysis of the special case of unknown origin time
Part 1 Advantage of using differential arrival times to locate earthquakes
Waves from earthquake first arrived in Palisades NY at 15:00:32 on Sept 10, 2006
Suppose you contour arrival timeon surface of earth Earthquake’s (x,y) is center of bullseye but what about its depth?
Earthquake’s depth related to curvature of arrival time at origin Deep Shallow
mean origin time cancels out T = arrival time TT = travel time To = Origin Time (start time of earthquake)
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
How does differential arrival time vary spatially? Depends strongly on this angle
In a 3 dimensional homogeneous box … maximum minimum mean If you can identify the line AB, then you can locate earthquakes
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 …
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?
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
Another example …
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
Effect of noisy data (10 milliseconds of measurement error) differential data differential data absolute data absolute data
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
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”
Part 2 Simultaneous earthquake location and tomography
Source L1 L2 L2
Line 3 traveltime Line 2 traveltime Very late secondary arrivals Slightly late first arrivals Line 1 traveltime Distance along receiver array
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 …
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
A numerical test 11 stations 50 earthquakes on fault zone Heterogenity near fault zone only
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.
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