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retrieve subsurface solar properties from local helioseismic measurements (Sec-
tion 4). In many cases it is acceptable to assume that the Sun is weakly heteroge-
neous in the horizontal directions: the inverse problem becomes a linear inverse
problem and can be solved with standard techniques. However this is not always
possible, especially in the presence of strong magnetic elds, e.g. in a sunspot.
Time-distance helioseismology aims at inferring subsurface properties at the
best spatial and temporal resolution possible. A spatial resolution as small as a
few Mm can be achieved near the surface. This limit is intimately linked to the
smallest available horizontal wavelength of the solar oscillations (high frequency
surface gravity waves). Detailed 3D maps of vector
ows in the upper convection
zone have provided new insights into the structure, evolution and organization
of magnetic active regions and convective
ows. The most easily detectable
ow
pattern is supergranulation, an intermediate-scale of convection (Section 5).
A particularly challenging aspect of local helioseismology is sunspot helioseis-Local Helioseismology 5
mology (Section 6). Sunspots are regions of intense (kilogauss) magnetic eld
and low gas pressure and density. In spite of an abundance of telling clues from
observations of the solar surface, theories about their formation, subsurface struc-
ture, thermal properties, and deep magnetic eld topology are still controversial.
The nature of solar waves is very signicantly altered as they propagate through
a sunspot and convert into magneto-acoustic-gravity (MAG) waves. Numerical
modeling of wave propagation through model sunspots is currently being devel-
oped by several groups. These simulations will be key to interpret the solar oscil-
lations in the vicinity of sunspots. Realistic numerical simulations also promise to
be an important diagnostic tool for sunspot structure. The main question\|what
keeps a sunspot together as a clearly delineated entity?\|may not ultimately be
answerable by helioseismology, since key elements of the answer may well lie in a
region near the base of the convection zone, where helioseismological tools may
not have enough sensitivity to detect a sunspot-related signal. They may perhaps
be sucient, however, to challenge models that propose the origin of sunspots to
be in the surface layers.
Among the most interesting results of local helioseismology is the detection of
the subsurface meridional
ow (Section 8). The meridional
ow does not aect
global mode frequencies (to rst order) and thus has only been measured in the
solar interior with local helioseismology. The meridional
ow plays an important
role in '
ux transport' theories, according to which the latitudinal transport of
magnetic
ux at the base of the convection zone determines the period of the
solar cycle.
In yet another remarkable application, local helioseismology can be used to
construct maps of active regions on the far side of the Sun (Section 9). In farside
imaging, the Sun as whole is used as an acoustic lens focussing waves at a point on
the invisible hemisphere. Maps of the farside are potentially important to predict
space weather and provide advance warning for coronal mass ejections and solar

ares (violent and sudden release of energy associated with the reconguration of
the magnetic eld in the atmosphere above an active region). Flares can excite
acoustic waves to measurable levels, which can in turn tell us about the physics
of
ares (Section 10).
These examples illustrate the many facets of the science possible with local
helioseismology, as summarized in Figure 1 . In all these cases a taste of the
possibilities has been provided, but improved observations (Section 11) and fur-
ther developments in the techniques of analysis and interpretation are required
to realize the full potential of local helioseismology.6 Gizon, Birch & Spruit
Figure 1: Overview of local helioseismology: Observational data, methods of
analysis, and scientic applications.
2 SOLAR OSCILLATIONS
2.1 Observations
In most cases, local helioseismology uses time-series of Dopplergrams as input
data. A Dopplergram is a digitized image of the line-of-sight velocity of the
solar surface (photosphere or chromosphere) deduced from the Doppler shifts of
a Fraunhofer absorption line (e.g., Scherrer et al. 1995). Solar oscillations have
a higher signal-to-noise ratio in Doppler velocity than in intensity, especially at
low frequencies.
There are two major data sets available for local helioseismology. The rst
one is provided by the Global Oscillation Network Group (GONG, Harvey et al.
1996) headquartered in Tucson, Arizona, which operates a global network of
six stations around the world. The sites are distributed in longitude in order
to observe continuously: Big Bear (California), Mauna Loa (Hawaii), Learmonth
(Australia), Udaipur (India), El Teide (Canary Islands), and Cerro Tololo (Chile).
The cadence of the observations is one minute to avoid temporal aliasing. Each
GONG instrument is a phase-shift interferometer that measures the phase of
the Fourier transform of the solar spectrum around the Ni I absorption line at
6768 A, interpreted as a Doppler shift (Harvey & The GONG Instrument Team
1995). While the original cameras had an image size of 256 256 pixels, full-
disk Dopplergrams have been recorded with 1024 1024 CDD cameras since 2001,Local Helioseismology 7
hence providing a good spatial resolution (5 arcsec) for local helioseismology. The
GONG instruments also acquire intensity images and line-of-sight magnetograms.
The eective duty cycle of the merged observations is over 90%.
The other main data set is provided by the Michelson Doppler Imager (MDI,
Scherrer et al. 1995) on-board the ESA/NASA Solar and Heliospheric Obser-
vatory (SOHO), which was launched in December 1995. SOHO is in a halo
orbit around the Sun-Earth L1 Lagrange point. Observations from SOHO are
not only continuous, but benet from perfect seeing and from a slowly varying
spacecraft-to-Sun velocity. The MDI lter system relies on two tunable Michelson
interferometers in order to measure intensity in ve very narrow lters (94 m A)
in the wings and core of the Ni 6768 line. The Doppler velocity is obtained by
taking the dierence between ltergrams on each side of the absorption line. The
MDI observables are the line depth and continuum, line-of-sight Doppler veloc-
ity, and line-of-sight magnetic eld. The temporal cadence is one minute and
the CCD camera has 1024 1024 pixels. It can operate in two dierent modes:
a full-disk mode (2 arcsec pixel) or a high-resolution mode (0 :6 arcsec pixel).
Figure 2 shows example full-disk SOHO/MDI observables and Supplemental

retrieve subsurface solar properties from local helioseismic measurements (Sec-

tion 4). In many cases it is acceptable to assume that the Sun is weakly heteroge-

neous in the horizontal directions: the inverse problem becomes a linear inverse

problem and can be solved with standard techniques. However this is not always

possible, especially in the presence of strong magnetic elds, e.g. in a sunspot.

Time-distance helioseismology aims at inferring subsurface properties at the

best spatial and temporal resolution possible. A spatial resolution as small as a

few Mm can be achieved near the surface. This limit is intimately linked to the

smallest available horizontal wavelength of the solar oscillations (high frequency

surface gravity waves). Detailed 3D maps of vector

ows in the upper convection

zone have provided new insights into the structure, evolution and organization

of magnetic active regions and convective

ows. The most easily detectable

ow

pattern is supergranulation, an intermediate-scale of convection (Section 5).

A particularly challenging aspect of local helioseismology is sunspot helioseis-Local Helioseismology 5

mology (Section 6). Sunspots are regions of intense (kilogauss) magnetic eld

and low gas pressure and density. In spite of an abundance of telling clues from

observations of the solar surface, theories about their formation, subsurface struc-

ture, thermal properties, and deep magnetic eld topology are still controversial.

The nature of solar waves is very signicantly altered as they propagate through

a sunspot and convert into magneto-acoustic-gravity (MAG) waves. Numerical

modeling of wave propagation through model sunspots is currently being devel-

oped by several groups. These simulations will be key to interpret the solar oscil-

lations in the vicinity of sunspots. Realistic numerical simulations also promise to

be an important diagnostic tool for sunspot structure. The main question|what

keeps a sunspot together as a clearly delineated entity?|may not ultimately be

answerable by helioseismology, since key elements of the answer may well lie in a

region near the base of the convection zone, where helioseismological tools may

not have enough sensitivity to detect a sunspot-related signal. They may perhaps

be sucient, however, to challenge models that propose the origin of sunspots to

be in the surface layers.

Among the most interesting results of local helioseismology is the detection of

the subsurface meridional

ow (Section 8). The meridional

ow does not aect

global mode frequencies (to rst order) and thus has only been measured in the

solar interior with local helioseismology. The meridional

ow plays an important

role in '

ux transport' theories, according to which the latitudinal transport of

magnetic

ux at the base of the convection zone determines the period of the

solar cycle.

In yet another remarkable application, local helioseismology can be used to

construct maps of active regions on the far side of the Sun (Section 9). In farside

imaging, the Sun as whole is used as an acoustic lens focussing waves at a point on

the invisible hemisphere. Maps of the farside are potentially important to predict

space weather and provide advance warning for coronal mass ejections and solar

ares (violent and sudden release of energy associated with the reconguration of

the magnetic eld in the atmosphere above an active region). Flares can excite

acoustic waves to measurable levels, which can in turn tell us about the physics

of

ares (Section 10).

These examples illustrate the many facets of the science possible with local

helioseismology, as summarized in Figure 1 . In all these cases a taste of the

possibilities has been provided, but improved observations (Section 11) and fur-

ther developments in the techniques of analysis and interpretation are required

to realize the full potential of local helioseismology.6 Gizon, Birch & Spruit

Figure 1: Overview of local helioseismology: Observational data, methods of

analysis, and scientic applications.

2 SOLAR OSCILLATIONS

2.1 Observations

In most cases, local helioseismology uses time-series of Dopplergrams as input

data. A Dopplergram is a digitized image of the line-of-sight velocity of the

solar surface (photosphere or chromosphere) deduced from the Doppler shifts of

a Fraunhofer absorption line (e.g., Scherrer et al. 1995). Solar oscillations have

a higher signal-to-noise ratio in Doppler velocity than in intensity, especially at

low frequencies.

There are two major data sets available for local helioseismology. The rst

one is provided by the Global Oscillation Network Group (GONG, Harvey et al.

1996) headquartered in Tucson, Arizona, which operates a global network of

six stations around the world. The sites are distributed in longitude in order

to observe continuously: Big Bear (California), Mauna Loa (Hawaii), Learmonth

(Australia), Udaipur (India), El Teide (Canary Islands), and Cerro Tololo (Chile).

The cadence of the observations is one minute to avoid temporal aliasing. Each

GONG instrument is a phase-shift interferometer that measures the phase of

the Fourier transform of the solar spectrum around the Ni I absorption line at

6768 A, interpreted as a Doppler shift (Harvey & The GONG Instrument Team

1995). While the original cameras had an image size of 256 256 pixels, full-

disk Dopplergrams have been recorded with 1024 1024 CDD cameras since 2001,Local Helioseismology 7

hence providing a good spatial resolution (5 arcsec) for local helioseismology. The

GONG instruments also acquire intensity images and line-of-sight magnetograms.

The eective duty cycle of the merged observations is over 90%.

The other main data set is provided by the Michelson Doppler Imager (MDI,

Scherrer et al. 1995) on-board the ESA/NASA Solar and Heliospheric Obser-

vatory (SOHO), which was launched in December 1995. SOHO is in a halo

orbit around the Sun-Earth L1 Lagrange point. Observations from SOHO are

not only continuous, but benet from perfect seeing and from a slowly varying

spacecraft-to-Sun velocity. The MDI lter system relies on two tunable Michelson

interferometers in order to measure intensity in ve very narrow lters (94 m A)

in the wings and core of the Ni 6768 line. The Doppler velocity is obtained by

taking the dierence between ltergrams on each side of the absorption line. The

MDI observables are the line depth and continuum, line-of-sight Doppler veloc-

ity, and line-of-sight magnetic eld. The temporal cadence is one minute and

the CCD camera has 1024 1024 pixels. It can operate in two dierent modes:

a full-disk mode (2 arcsec pixel) or a high-resolution mode (0 :6 arcsec pixel).

Figure 2 shows example full-disk SOHO/MDI observables and Supplemental