Turning noise into signal: a paradox?

1
Turning noise into signal a paradox? Kees
Wapenaar, Delft University of Technology Roel
Snieder, Colorado School of Mines Presented
at Making Waves about Seismics a Tribute to
Peter Hubrals achievements, not only in
Geophysics Karlsruhe, February 28, 2007
2
(No Transcript)
3
The Greens function emerges from the
cross-correlation of the diffuse wave field at
two points of observation
4
Weaver and Lobkis
5
(No Transcript)
6
Campillo and Paul
7
Campillo and Paul
8
(No Transcript)
9
(No Transcript)
10
(No Transcript)
11
(No Transcript)
12
Seismic interferometry at global scaleUS-Array
13

• Turning noise into signal works in practice and
  we
• have a theory that explains it .
• so what is the paradox?
• Extraction of signal is fairly robust, despite
• Assumptions about source distribution are never
• fulfilled in practical situations.
• Signal extraction relies for a large part on
  multiple
• scattering. Is it stable?

14
Laplace, 1814 The physical world is a
deterministic clockwork
15
(No Transcript)
16
(No Transcript)
17
(No Transcript)
18
Laplace, 1814 The physical world is a
deterministic
clockwork Poincaré, 1903 OK Pierre, but
uncertainties in
initial conditions lead to
chaos at later times
19
(No Transcript)
20
(No Transcript)
21
Laplace, 1814 The physical world is a
deterministic
clockwork Poincaré, 1903 OK Pierre, but
uncertainties in
initial conditions lead to
chaos at later times Heisenberg,
True Henri, but at atomic 1927
scale only probabilities are
determined
22
(No Transcript)
23
Laplace, 1814 The physical world is a
deterministic
clockwork Poincaré, 1903 OK Pierre, but
uncertainties in
initial conditions lead to
chaos at later times Heisenberg,
True Henri, but at atomic 1927
scale only probabilities are
determined Astonishing Werner! But
lets go back to macroscopic physics and now
look at waves
24
(No Transcript)
25
(No Transcript)
26
(No Transcript)
27
(No Transcript)
28
(No Transcript)
29
(No Transcript)
30
(No Transcript)
31
(No Transcript)
32
(No Transcript)
33
(No Transcript)
34
Particle scattering chaotic after 8
scatterers Wave scattering still stable after
30 scatterers
35
Einstein, 1905, Brownian motion Kubo, 1966,
fluctuation-dissipation theorem
36
Conclusion Robustness of turning noise into
signal is explained by stability of wave
propagation Finally, Lets see how this can
be generalized
37
(No Transcript)
38
Dissipating media (no time-reversal
invariance) Applications for EM waves in
conducting media, diffusion, acoustic waves in
viscous media, etc. Systems with higher order
DVs Applications for e.g. bending waves
39
Flowing media (non-reciprocal Greens functions)
40
Flowing media (non-reciprocal Greens functions)
41
Schroedingers equation
Zero offset
42
General vectorial formulation (for example,
electroseismic)