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tion is essential to pushing the limits of local helioseismology, especially
to probe the deepest layers of the convection zone and the high-latitude
meridional
ow. The SDO/HMI instrument\|expected to be launched in60 Gizon, Birch & Spruit
2010\|represents an important technological step towards improved obser-
vations.
3. Helioseismology has beneted from methods developed for the seismology
of the Earth: normal mode theory, travel-time sensitivity kernels, interpre-
tation of the cross-covariance, inverse methods, etc. We expect that local
helioseismology will continue to learn from advances in Earth seismology:
notable progress has been made on numerical simulations of wave propa-
gation, the computation of travel time sensitivity kernels using numerical
methods, and non-linear inversions of travel times (various aspects of mod-
ern seismology are discussed by, e.g., Tape et al. 2009).
ABBREVIATIONS/ACRONYMS
1. GONG: Global Oscillation Network Group
2. SOHO/MDI: Solar and Heliospheric Observatory/Michelson Doppler Im-
ager
3. SDO/HMI: Solar Dynamics Observatory/Helioseismic and Magnetic Im-
ager
4. HELAS: European Helio- and Asteroseismology Network
5. MHD: Magnetohydrodynamics
6. MAG waves: Magneto-Acoustic-Gravity waves
7. OLA: Optimally Localized Averaging (or Averages)
8. RLS: Regularized Least Squares
KEY TERMS/DEFINITIONS
1. Active region: Region of enhanced magnetic activity, including sunspots
and diuse magnetic eld (`plage').
2. Quiet Sun: Regions with low levels of magnetic activity, away from active
regions.
3. Dopplergram: Image of the line-of-sight component of velocity of the solar
surface.
4. The forward problem: The problem of computing the propagation of waves
through a given solar model.
5. The inverse problem: The problem of inferring solar subsurface properties
from helioseismology measurements.
6. Ring-diagram analysis: Analysis of the local frequencies of solar oscillations
over small patches of the solar disk.Local Helioseismology 61
7. Cross-covariance: Measure of similarity of two random signals as a function
of a time-lag applied to one of them.
8. Time-distance diagram: cross-covariance of the helioseismic signal between
two points on the surface, as a function of their separation distance and
time lag.
9. Farside: Side of the Sun that is not visible from the Earth.
ANNOTATED REFERENCES
1. Bogdan (1997): Solar modes, wave packets, and rays.
2. Braun (1995): Mode absorption and mode coupling by sunspots.
3. Cameron, Gizon & Duvall (2008): Observations and modeling of the cross-
covariance around a sunspot.
4. Giles et al. (1997): Inferring meridional circulation with time-distance he-
lioseismology.
5. Gizon & Birch (2002): The forward problem and the rst Born approxima-
tion.
6. Gizon & Birch (2005): Comprehensive open-access review of local helioseis-
mology.
7. Jeeries et al. (2006): Multi-height observations of solar oscillations and
magnetic portals.
8. Komm et al. (2004): Ring-diagram analysis of subsurface
ows.
9. Kosovichev, Duvall & Scherrer (2000): Review of time-distance helioseis-
mology.
10. Lindsey & Braun (2000): Imaging active regions on the farside of the Sun.
RELATED RESOURCES
1. Instrument web sites: GONG web site at http://gong.nso.edu/ and
SOHO/MDI at http://soi.stanford.edu/ .
2. MDI Farside Graphics Viewer at http://soi.stanford.edu/data/full_
farside/farside.html .
3. HELAS local helioseismology web site at http://www.mps.mpg.de/projects/
seismo/NA4/ . Software tools and selected data sets.
4. Solar Physics, Vol. 192, No. 1-2, pp. 1-494 (2000), Topical Issue \Helioseis-
mic Diagnostics of Solar Convection and Activity" edited by T.L. Duvall
Jr., J.W. Harvey, A.G. Kosovichev, and Z. Svestka. Table of contents avail-
able at http://www.springerlink.com/content/h4bhbw3vdj8n/ .62 Gizon, Birch & Spruit
5. Solar Physics, Vol. 251, No. 1-2, pp. 1-666 (2008), Topical Issue \He-
lioseismology, Asteroseismology, and MHD Connections" edited by L. Gi-
zon, P. Cally, and J. Leibacher. Table of contents available at http:
//www.springerlink.com/content/x548678p1725/ .
SIDE BAR: Extracting information from a random wave eld
Duvall et al. (1993) rst used the cross-covariance function to measure the travel
time of wave packets between two locations on the solar surface. The cross-
covariance averages the information over an ensemble of random waves, construc-
tively. The concept of time-distance helioseismology has found many applications
in physics, geophysics, and ocean acoustics (see reviews by Gou edard et al. 2008,
Larose et al. 2006). Various experiments and observations (e.g. Shapiro et al.
2005, Weaver & Lobkis 2001) have shown that the cross-covariance is intimately
connected to the Green's function, G, i.e. the response of the medium to an im-
pulsive source. Recently, Colin de Verdi ere (2006) proved that in an arbitrarily
complex medium containing an homogeneous distribution of white noise sources
(variance2), the cross-covariance is given by
@
@tC(r1;r2;t) =2
4a[G(r1;r2;t) +G(r2;r1;t)]; (14)
when the integration time tends to innity and the coecient of attenuation
(a) tends to zero. In the Fourier domain, this is equivalent to saying that C
is proportional to the imaginary part of the Green's function, Im G(r1;r2;!).
Although the above assumptions are too restrictive to be applied to the solar
case, it is clear that the cross-covariance is a very important diagnostics to probe
media permeated by random elds (wave elds or diuse elds).
DISCLOSURE STATEMENT
The authors are not aware of any biases that might be perceived as aecting the

tion is essential to pushing the limits of local helioseismology, especially

to probe the deepest layers of the convection zone and the high-latitude

meridional

ow. The SDO/HMI instrument|expected to be launched in60 Gizon, Birch & Spruit

2010|represents an important technological step towards improved obser-

vations.

3. Helioseismology has beneted from methods developed for the seismology

of the Earth: normal mode theory, travel-time sensitivity kernels, interpre-

tation of the cross-covariance, inverse methods, etc. We expect that local

helioseismology will continue to learn from advances in Earth seismology:

notable progress has been made on numerical simulations of wave propa-

gation, the computation of travel time sensitivity kernels using numerical

methods, and non-linear inversions of travel times (various aspects of mod-

ern seismology are discussed by, e.g., Tape et al. 2009).

ABBREVIATIONS/ACRONYMS

1. GONG: Global Oscillation Network Group

2. SOHO/MDI: Solar and Heliospheric Observatory/Michelson Doppler Im-

ager

3. SDO/HMI: Solar Dynamics Observatory/Helioseismic and Magnetic Im-

ager

4. HELAS: European Helio- and Asteroseismology Network

5. MHD: Magnetohydrodynamics

6. MAG waves: Magneto-Acoustic-Gravity waves

7. OLA: Optimally Localized Averaging (or Averages)

8. RLS: Regularized Least Squares

KEY TERMS/DEFINITIONS

1. Active region: Region of enhanced magnetic activity, including sunspots

and diuse magnetic eld (`plage').

2. Quiet Sun: Regions with low levels of magnetic activity, away from active

regions.

3. Dopplergram: Image of the line-of-sight component of velocity of the solar

surface.

4. The forward problem: The problem of computing the propagation of waves

through a given solar model.

5. The inverse problem: The problem of inferring solar subsurface properties

from helioseismology measurements.

6. Ring-diagram analysis: Analysis of the local frequencies of solar oscillations

over small patches of the solar disk.Local Helioseismology 61

7. Cross-covariance: Measure of similarity of two random signals as a function

of a time-lag applied to one of them.

8. Time-distance diagram: cross-covariance of the helioseismic signal between

two points on the surface, as a function of their separation distance and

time lag.

9. Farside: Side of the Sun that is not visible from the Earth.

ANNOTATED REFERENCES

1. Bogdan (1997): Solar modes, wave packets, and rays.

2. Braun (1995): Mode absorption and mode coupling by sunspots.

3. Cameron, Gizon & Duvall (2008): Observations and modeling of the cross-

covariance around a sunspot.

4. Giles et al. (1997): Inferring meridional circulation with time-distance he-

lioseismology.

5. Gizon & Birch (2002): The forward problem and the rst Born approxima-

tion.

6. Gizon & Birch (2005): Comprehensive open-access review of local helioseis-

mology.

7. Jeeries et al. (2006): Multi-height observations of solar oscillations and

magnetic portals.

8. Komm et al. (2004): Ring-diagram analysis of subsurface

ows.

9. Kosovichev, Duvall & Scherrer (2000): Review of time-distance helioseis-

mology.

10. Lindsey & Braun (2000): Imaging active regions on the farside of the Sun.

RELATED RESOURCES

1. Instrument web sites: GONG web site at http://gong.nso.edu/ and

SOHO/MDI at http://soi.stanford.edu/ .

2. MDI Farside Graphics Viewer at http://soi.stanford.edu/data/full_

farside/farside.html .

3. HELAS local helioseismology web site at http://www.mps.mpg.de/projects/

seismo/NA4/ . Software tools and selected data sets.

4. Solar Physics, Vol. 192, No. 1-2, pp. 1-494 (2000), Topical Issue \Helioseis-

mic Diagnostics of Solar Convection and Activity" edited by T.L. Duvall

Jr., J.W. Harvey, A.G. Kosovichev, and Z. Svestka. Table of contents avail-

able at http://www.springerlink.com/content/h4bhbw3vdj8n/ .62 Gizon, Birch & Spruit

5. Solar Physics, Vol. 251, No. 1-2, pp. 1-666 (2008), Topical Issue \He-

lioseismology, Asteroseismology, and MHD Connections" edited by L. Gi-

zon, P. Cally, and J. Leibacher. Table of contents available at http:

//www.springerlink.com/content/x548678p1725/ .

SIDE BAR: Extracting information from a random wave eld

Duvall et al. (1993) rst used the cross-covariance function to measure the travel

time of wave packets between two locations on the solar surface. The cross-

covariance averages the information over an ensemble of random waves, construc-

tively. The concept of time-distance helioseismology has found many applications

in physics, geophysics, and ocean acoustics (see reviews by Gou edard et al. 2008,

Larose et al. 2006). Various experiments and observations (e.g. Shapiro et al.

2005, Weaver & Lobkis 2001) have shown that the cross-covariance is intimately

connected to the Green's function, G, i.e. the response of the medium to an im-

pulsive source. Recently, Colin de Verdi ere (2006) proved that in an arbitrarily

complex medium containing an homogeneous distribution of white noise sources

(variance2), the cross-covariance is given by

@

@tC(r1;r2;t) =2

4a[G(r1;r2;t) +G(r2;r1;t)]; (14)

when the integration time tends to innity and the coecient of attenuation

(a) tends to zero. In the Fourier domain, this is equivalent to saying that C

is proportional to the imaginary part of the Green's function, Im G(r1;r2;!).

Although the above assumptions are too restrictive to be applied to the solar

case, it is clear that the cross-covariance is a very important diagnostics to probe

media permeated by random elds (wave elds or diuse elds).

DISCLOSURE STATEMENT

The authors are not aware of any biases that might be perceived as aecting the