Advances%20in%20Earthquake%20Location%20and%20Tomography

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
(No Transcript)
5
that was the recent Gulf of Mexico
earthquake,by the way
6
Locating an earthquakerequires knowing
theseismic velocity structureaccurately
7
(No Transcript)
8
(No Transcript)
9
(No Transcript)
10
Whats the best way to represent 3 dimensional
structure Best for what? compatibility with
data sources ease of visualization and
editing facilitating calculation
11
Overall organization into interfaces
Small-scale organization into tetrahedra
Linear interpolation within tetrahedra implying
rays that are circular arcs
12
seismometer
earthquake
13
Location Errors 0.5 degree 55 km
30 miles
Note this preliminary calculation used data from
a limited number of stations
14
Two parallel approaches work to improve earth
model design earthquake location techniques
that are as insensitive to model as possible
15
Waves from earthquake first arrived in Palisades
NY at 150032 on Sept 10, 2006
16
(No Transcript)
17
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?
18
Suppose you contour arrival timeon surface of
earth
Earthquakes (x,y) is center of bullseye
but what about its depth?
19
Earthquakes depth related to curvature of
arrival time at origin
Deep
Shallow
20
(No Transcript)
21
(No Transcript)
22
Earthquakes in Long Valley Caldera, California
located with absolute traveltimes
Courtesty of Felix Walhhauser, LDEO
23
Earthquakes in Long Valley Caldera, California
located with differential traveltimes
Courtesty of Felix Walhhauser, LDEO
24
differential arrival time difference in arrival
times
25
mean origin time cancels out
T arrival time TT travel time To Origin
Time (start time of earthquake)
26
Station i
27
(No Transcript)
28
Very accurate DTs !
29
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
30
(No Transcript)
31
How does differential arrival time vary
spatially?
Depends strongly on this angle
32
In a 3 dimensional homogeneous box
maximum
minimum
mean
If you can identify the line AB, then you can
locate earthquakes
33
as long as you have more than two earthquakes
34
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
35
The same idea works
p q
36
Patterns of differential arrival time
Can you guess the orientation of the two sources
in these six cases?
37
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
38
Another example
39
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 differentia
l arrival time data When the data are
noise Or the earth structure is poorly known
40
Geometry of the numerical experiment
41
Effect of noisy data (10 milliseconds of
measurement error)
differential data
differential data
absolute data
absolute data
42
Effect of near surface heterogeneities (1 km/s of
velocity variation with a scale length of 5 km)
absolute data
differential data
differential data
absolute data
43

• 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

44

• Part 2
• Simultaneous earthquake location and tomography

45
(No Transcript)
46
(No Transcript)
47
(No Transcript)
48
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
49
A numerical test
11 stations 50 earthquakes on fault
zone Heterogeneity near fault zone only
50
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.
51
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!
52

• 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 time
• but known location

53
(No Transcript)
54
(No Transcript)
55
Station 1 2 3 4
Event 2
Event 3
Event 1
56
If you can
Then that structure is indistinguishable from a
perturbation in origin time!
57
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 !
58
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 !
59
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.
60
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.

61
(No Transcript)