Advances in Earthquake Location and Tomography
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Transcript of Advances in Earthquake Location and Tomography
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Advances in Earthquake Locationand
Tomography
William Menke
Lamont-Doherty Earth Observatory
Columbia University
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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
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Part 1
Advantage of using differential arrival times to locate earthquakes
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that was the recent Gulf of Mexico earthquake,
by the way …
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Locating an earthquakerequires knowing the
seismic velocity structure
accurately
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What’s the best way to represent 3 dimensional structure
Best for what?
compatibility with data sources
ease of visualization and editing
facilitating calculation
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Overall organization into interfaces
Small-scale organization into tetrahedra
Linear interpolation within tetrahedra implying rays that are circular arcs
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seismometer earthquake
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Location Errors: = 0.5 degree = 55 km = 30 miles
Note: this preliminary calculation used data from a limited number of stations
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Two parallel approaches
work to improve earth model
design earthquake location techniques that are as insensitive to model as possible
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Waves from earthquake first arrived in Palisades NY at 15:00:32 on Sept
10, 2006
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Arrival Time ≠Travel Time
Q: a car arrived in town after traveling for an half an hour at sixty miles an hour. Where did it start?
A. Thirty miles away
Q: a car arrived in town at half past one, traveling at sixty miles an hour. Where did it start?
A. Are you crazy?
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Suppose you contour arrival timeon surface of earth
Earthquake’s (x,y) is center
of bullseye
but what about its depth?
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Earthquake’s depth related to
curvature of arrival time at
origin
Deep
Shallow
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Courtesty of Felix Walhhauser, LDEO
Earthquakes in Long Valley Caldera, California located with absolute traveltimes
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Courtesty of Felix Walhhauser, LDEO
Earthquakes in Long Valley Caldera, California located with differential traveltimes
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differential arrival time = difference in arrival times
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T = arrival time
TT = travel time
To = Origin Time (start time of earthquake)
mean origin time cancels out
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Station i
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Very accurate DT’s !
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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
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How does differential arrival time vary spatially?
Depends strongly on this angle
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In a 3 dimensional homogeneous box …
maximum
meanminimum
If you can identify the line AB, then you can locate earthquakes
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as long as you have more than two earthquakes
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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
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The same idea works …
p q
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Patterns of differential arrival time
C
CC
C
C
B
C
B BA
A A
B
A
Can you guess the orientation of the two sources in these six cases?
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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
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Anotherexample …
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What is the practical advantageof using differential arrival times
to locate earthquakes
My approach is toexamine the statistics of location errorsusing numerical simulations
Compare the result of usingabsolute arrival time data
Anddifferential arrival time data
Whenthe data are noise
Orthe earth structure is poorly known
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Geometry of the numerical experiment …
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Effect of noisy data(10 milliseconds of measurement error)
absolute data
absolute data
differential data
differential data
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Effect of near surface heterogeneities(1 km/s of velocity variation with a scale length of 5 km)
absolute data
differential data differential
dataabsolute data
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Both absolute locations and relative locations of earthquakes are improved by using differential arrival time data
when arrival times are nosily measured andwhen near-surface earth structure is poorly
modeled
Relative location errors can be just a few meters even when errors are “realistically large”
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Part 2
Simultaneous earthquake location and tomography
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simultaneous earthquake location and tomography?
Many earthquakes with unknown X, Y, Z, To
Unknown velocity structure
Solve for everything
Using either
absolute arrival timesor
differential arrival times
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A numerical test
11 stations
50 earthquakeson fault zone
Heterogeneitynear fault zone only
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True earthquake locationsAnd fault zone heterogenity( 1 km/s)
Reconstructed earthquake locationsAnd 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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Reality Check: How big is the Signal?
How much better are the data fit?
When the earth structure is allowed to vary
compared with holding a simple, layered
earth structure fixed?
Answer: 0.7 milliseconds, for a dataset that has traveltimes of a few seconds
Need very precise measurements!
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Part 3
Is Joint Tomography/Earthquake Location
Really Possible ?
Study a simplified version of the problem
In depth analysis of the special case of unknown origin timebut known location
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Station 1 2 3 4
Event 1
Event 2
Event 3
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If you can …
Then that structure is indistinguishable from a perturbation in origin time!
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Case of sources near bottom of the model
This velocity perturbation causes constant travel time perturbation for a station on the surface anywhere in the grey box for the event at but zero traveltime perturbation for all the sources at !
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Case of sources near top of model
This velocity perturbation causes constant travel time perturbation for a station on the surface anywhere in the grey box for the event at but zero traveltime perturbation for all the sources at !
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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.
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Summary
Part 1: Earthquake location with differential data is the way to go!
Part 2: Simultaneous tomography / earthquake location possible with differential data, but requires high-precision data.
Part 3: Coupled Tomography/Location is extremely nonunique and extremely likely to fool you.
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