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that are not too far from the antipode of the center of the visible disk. In
order to complete the farside maps, other skip geometries are required (Braun &
Lindsey 2001). The 1+3 skip geometry targets active regions closer to the limb.
In this geometry, the wave packets only skip once before they reach the target
location, and then skip three times before they are observed again. Oslund &
Scherrer (2006, unpublished) combined farside maps from the 2+2 and 1+3 skip
geometries to make maps of the entire farside of the Sun. These farside maps are
produced daily using the MDI/SOHO data and are available online (see Related
Resources ).
Figure 22bandSupplemental Movies 9 and 10 and shows a sequence
of farside maps that show a large active region moving across the farside and
front-side of the Sun. This active region, NOAA 9503, was seen to form on
the farside of the Sun before appearing on the visible disk about 12 days later.
Magnetic maps of the farside provide up to two weeks of advance warning before
large active regions rotate onto the visible disk, and thus are expected to play an
important role in predicting space weather.
In order to interpret the farside maps in terms of physical variables, such as the
total unsigned magnetic
ux, Gonz alez Hern andez, Hill & Lindsey (2007) have
proposed to calibrate the farside images using long lived active regions that are
seen before and after they appear on the farside. Future Sun-orbiting spacecraft
carrying solar and magnetic imagers (e.g., Solar Orbiter) will provide enhanced
opportunities for detailed farside calibration.36 Gizon, Birch & Spruit
Figure 6: ( a) Measured cross-covariance function for MDI medium-degree data
as a function of separation distance and time-lag (Kosovichev, Duvall & Scherrer
2000). Positive values are white, negative values black. The observation duration
isT= 144 days starting in May 1996. ( b) Example ray paths for acoustic wave
packets. In both panels ( a) and ( b) the blue lines correspond to single skip ray
paths, the red lines are for two skip paths, and the green lines are for three-skip
paths.Local Helioseismology 37
Figure 7: Maps of the travel times using the annulus/quadrant geometry and
MDI/SOHO high-resolution data (Duvall et al. 1997). The observation duration
isT= 8:5 hr. Each frame is 370 Mm on a side. Each row corresponds to a dier-
ent annulus radius from 12 Mm to 27 Mm. The columns show the four types of
travel-time measurements. From left to right: (i) travel-time dierence between
the outward-going waves and the inward-going waves, (ii) travel-time dierence
between the westward- and eastward-going waves, (iii) travel-time dierence be-
tween the northward- and southward-going waves, and (iv) mean of the travel
times of the inward- and outward going waves. The average magnetogram and
the average Dopplergram are shown in the right most column. The travel-time
perturbations are mostly due to the supergranular scale horizontal
ows.38 Gizon, Birch & Spruit
Figure 8: Linear sensitivity of a single-skip mean travel-time shift to local changes
in the square of the sound speed. The observation points are located at ( x;y;z ) =
(12:5;0;0:2) Mm. The top panel shows a horizontal slice at a depth of 5 Mm.
The bottom panel shows a vertical slice at y= 0. The heavy black line in the
lower panel shows the single-skip ray path connecting the observation points. The
kernel has been scaled with the background speed to enhance the visibility of the
subsurface structure. The ringing away from the ray path is due to the band-
limited nature of solar oscillations. The linear sensitivity is almost zero along the
ray path, this a generic feature of sound-speed kernels in three dimensions, and
is well known in seismology (Dahlen, Hung & Nolet 2000; Marquering, Dahlen &
Nolet 1999).Local Helioseismology 39
Figure 9: Averaging kernels, K, from 1D RLS inversions for ring-diagram analysis
(depth sensitivity to horizontal
ows). The numbers (in units of Mm) refer to the
average depths of the averaging kernels. Courtesy of Irene Gonz alez-Hern andez.40 Gizon, Birch & Spruit
Figure 10: Ray paths in model surface layers with 2 kG uniform magnetic eld
inclined at30respectively to the vertical, as shown by the background gray
lines. The incoming 5 mHz rays (arrows) have lower turning points at z=5 Mm
and are shown in red. The two frames correspond to two dierent attack angles.
The horizontal gray line indicates where the sound speed and the Alfv en speed
coincide, which is approximately where mode conversion happens. The fractional
energy remaining in each resulting ray is indicated by the color legend. The dots
on the ray paths indicate 1 min group travel time intervals. The thin black curve
represents the acoustic ray that would be there in the absence of magnetic eld.
Note that the fast ray is faster through the surface layers than the non-magnetic
ray. Figure and caption from Cally (2007). Figure copyright Wiley-VCH Verlag
GmbH & Co. KGaA . Reproduced with permission.Local Helioseismology 41
Figure 11: Numerical simulation of the propagation of a p 1plane wave packet
through a model sunspot using the MHD code of Cameron, Gizon & Daiallah
(2007). The sunspot model is similar to the model of Schl uter & Temesv ary
(1958) with a maximum vertical eld Bz= 3 kG at the surface; it is embedded
in a Model S background atmosphere, stabilized with respect to convection. The
wave packet is initially located 40 Mm to the left of the sunspot and propagates to
the right. The x-component of velocity is shown at times t= 0, 80, and 130 min
(positive values in red, negative values in yellow). The a=clevel is represented
by the blue curve. The computational domain is 40 Mm< x < 105 Mm,
36:5 Mm< y < 36:5 Mm and12:5 Mm< z < 1:5 Mm. Only half of the
box (y > 0) is shown. The boundary conditions are periodic in the horizontal
directions and there are two sponge layers (not shown here) at the top and at the
bottom of the box to avoid the re
ection of the waves back into the computational
domain. The t= 80 min snapshot clearly shows the slow magneto-acoustic waves
propagating down the sunspot. Because these slow waves are transverse, they
are easily seen as oscillations in the x-component of velocity. See Supplemental
Movie 8 .42 Gizon, Birch & Spruit
Figure 12: Inversion for vector
ows in the near surface layers. The travel
times were measured for ridges f and p 1through p 4and inverted using an OLA
technique. The observation time is T= 3 days. Top panel : Horizontal slice at
the depth of 1 Mm showing the two horizontal components ( uxanduy, arrows)
and the vertical component ( uz, colors) of the vector
ow eld. The FWHM
of the averaging kernel is 10 Mm (inset in top-left corner). The most visible
features correspond to long-lived supergranules. Bottom panel : Vertical slice at
y=176 Mm (white line in a) showing the horizontal divergence of the
ow eld
as a function of xand depth (colors) from the same 2+1D inversion. The vertical
arrows show the vertical velocity uzfor the three ridges f, p 1, and p 2(from top

that are not too far from the antipode of the center of the visible disk. In

order to complete the farside maps, other skip geometries are required (Braun &

Lindsey 2001). The 1+3 skip geometry targets active regions closer to the limb.

In this geometry, the wave packets only skip once before they reach the target

location, and then skip three times before they are observed again. Oslund &

Scherrer (2006, unpublished) combined farside maps from the 2+2 and 1+3 skip

geometries to make maps of the entire farside of the Sun. These farside maps are

produced daily using the MDI/SOHO data and are available online (see Related

Resources ).

Figure 22bandSupplemental Movies 9 and 10 and shows a sequence

of farside maps that show a large active region moving across the farside and

front-side of the Sun. This active region, NOAA 9503, was seen to form on

the farside of the Sun before appearing on the visible disk about 12 days later.

Magnetic maps of the farside provide up to two weeks of advance warning before

large active regions rotate onto the visible disk, and thus are expected to play an

important role in predicting space weather.

In order to interpret the farside maps in terms of physical variables, such as the

total unsigned magnetic

ux, Gonz alez Hern andez, Hill & Lindsey (2007) have

proposed to calibrate the farside images using long lived active regions that are

seen before and after they appear on the farside. Future Sun-orbiting spacecraft

carrying solar and magnetic imagers (e.g., Solar Orbiter) will provide enhanced

opportunities for detailed farside calibration.36 Gizon, Birch & Spruit

Figure 6: ( a) Measured cross-covariance function for MDI medium-degree data

as a function of separation distance and time-lag (Kosovichev, Duvall & Scherrer

2000). Positive values are white, negative values black. The observation duration

isT= 144 days starting in May 1996. ( b) Example ray paths for acoustic wave

packets. In both panels ( a) and ( b) the blue lines correspond to single skip ray

paths, the red lines are for two skip paths, and the green lines are for three-skip

paths.Local Helioseismology 37

Figure 7: Maps of the travel times using the annulus/quadrant geometry and

MDI/SOHO high-resolution data (Duvall et al. 1997). The observation duration

isT= 8:5 hr. Each frame is 370 Mm on a side. Each row corresponds to a dier-

ent annulus radius from 12 Mm to 27 Mm. The columns show the four types of

travel-time measurements. From left to right: (i) travel-time dierence between

the outward-going waves and the inward-going waves, (ii) travel-time dierence

between the westward- and eastward-going waves, (iii) travel-time dierence be-

tween the northward- and southward-going waves, and (iv) mean of the travel

times of the inward- and outward going waves. The average magnetogram and

the average Dopplergram are shown in the right most column. The travel-time

perturbations are mostly due to the supergranular scale horizontal

ows.38 Gizon, Birch & Spruit

Figure 8: Linear sensitivity of a single-skip mean travel-time shift to local changes

in the square of the sound speed. The observation points are located at ( x;y;z ) =

(12:5;0;0:2) Mm. The top panel shows a horizontal slice at a depth of 5 Mm.

The bottom panel shows a vertical slice at y= 0. The heavy black line in the

lower panel shows the single-skip ray path connecting the observation points. The

kernel has been scaled with the background speed to enhance the visibility of the

subsurface structure. The ringing away from the ray path is due to the band-

limited nature of solar oscillations. The linear sensitivity is almost zero along the

ray path, this a generic feature of sound-speed kernels in three dimensions, and

is well known in seismology (Dahlen, Hung & Nolet 2000; Marquering, Dahlen &

Nolet 1999).Local Helioseismology 39

Figure 9: Averaging kernels, K, from 1D RLS inversions for ring-diagram analysis

(depth sensitivity to horizontal

ows). The numbers (in units of Mm) refer to the

average depths of the averaging kernels. Courtesy of Irene Gonz alez-Hern andez.40 Gizon, Birch & Spruit

Figure 10: Ray paths in model surface layers with 2 kG uniform magnetic eld

inclined at30respectively to the vertical, as shown by the background gray

lines. The incoming 5 mHz rays (arrows) have lower turning points at z=5 Mm

and are shown in red. The two frames correspond to two dierent attack angles.

The horizontal gray line indicates where the sound speed and the Alfv en speed

coincide, which is approximately where mode conversion happens. The fractional

energy remaining in each resulting ray is indicated by the color legend. The dots

on the ray paths indicate 1 min group travel time intervals. The thin black curve

represents the acoustic ray that would be there in the absence of magnetic eld.

Note that the fast ray is faster through the surface layers than the non-magnetic

ray. Figure and caption from Cally (2007). Figure copyright Wiley-VCH Verlag

GmbH & Co. KGaA . Reproduced with permission.Local Helioseismology 41

Figure 11: Numerical simulation of the propagation of a p 1plane wave packet

through a model sunspot using the MHD code of Cameron, Gizon & Daiallah

(2007). The sunspot model is similar to the model of Schl uter & Temesv ary

(1958) with a maximum vertical eld Bz= 3 kG at the surface; it is embedded

in a Model S background atmosphere, stabilized with respect to convection. The

wave packet is initially located 40 Mm to the left of the sunspot and propagates to

the right. The x-component of velocity is shown at times t= 0, 80, and 130 min

(positive values in red, negative values in yellow). The a=clevel is represented

by the blue curve. The computational domain is 40 Mm< x < 105 Mm,

36:5 Mm< y < 36:5 Mm and12:5 Mm< z < 1:5 Mm. Only half of the

box (y > 0) is shown. The boundary conditions are periodic in the horizontal

directions and there are two sponge layers (not shown here) at the top and at the

bottom of the box to avoid the re

ection of the waves back into the computational

domain. The t= 80 min snapshot clearly shows the slow magneto-acoustic waves

propagating down the sunspot. Because these slow waves are transverse, they

are easily seen as oscillations in the x-component of velocity. See Supplemental

Movie 8 .42 Gizon, Birch & Spruit

Figure 12: Inversion for vector

ows in the near surface layers. The travel

times were measured for ridges f and p 1through p 4and inverted using an OLA

technique. The observation time is T= 3 days. Top panel : Horizontal slice at

the depth of 1 Mm showing the two horizontal components ( uxanduy, arrows)

and the vertical component ( uz, colors) of the vector

ow eld. The FWHM

of the averaging kernel is 10 Mm (inset in top-left corner). The most visible

features correspond to long-lived supergranules. Bottom panel : Vertical slice at

y=176 Mm (white line in a) showing the horizontal divergence of the

ow eld

as a function of xand depth (colors) from the same 2+1D inversion. The vertical

arrows show the vertical velocity uzfor the three ridges f, p 1, and p 2(from top