Figure 1:
averaged power spectra of solar oscillations obtained from 512 min series of tracked Doppler images of size 30° × 30° (near disk center) observed by MDI (left) and TON (right), versus spherical harmonic degree and temporal frequency. The ridges are labelled by the value of the radial order . From González Hernández et al. (1998). 

Figure 2:
Power spectrum of solar oscillations observed in brightness from the geographic south pole in 1994 (Ca ii K_{1} line, 6 Å bandpass). Notice that ridges of power can be seen well beyond the acoustic cutoff frequency. Courtesy of T.L. Duvall. 

Figure 3:
Real (red) and imaginary (blue) parts of the horizontal component of normalmode and numerical Green’s functions () for , (just above the resonance), , and a vertical momentum source. The Green’s function has been scaled by the square root of the background density. The horizontal axis is acoustic depth in minutes. The vertical scale is arbitrary. The source depth is shown by the solid blue vertical line. The photosphere is shown by the vertical blue dashed line. The solid curves show the numerical results. The real part of the numerical result has a discontinuity at the source depth while the imaginary part is continuous there. The dashed curves show the normalmode summation approximation. Notice that the normalmode approximation is continuous at the source depth. This is because we have used only a finite number of modes (radial orders not greater than 15). From Birch et al. (2004). 

Figure 4:
Comparison of a model filtered power spectrum with the filtered power spectrum of MDI data. The filter is such that most of the power is in the and ridges. The model power spectrum is computed for a model with spatially uncorrelated quadrupole sources located at 100 km below the photosphere. The model includes the effects of the spatial and temporal window functions and the broadening of the spectrum by the remapping. Without these corrections the model power spectrum would have linewidths much smaller than those of the data. Upper left panel: Observed filtered power spectrum. Upper right panel: Model filtered power spectrum. The solid lines in the upper panels show the location of the fmode ridge, for reference. Lower left panel: Average over wavenumbers of the observed (dashed line) and model (solid line) filtered power spectra. Lower right panel: Average over frequencies of the observed (dashed line) and model (solid line) filtered power spectra. From Birch et al. (2004). 

Figure 5:
A numerical experiment of wave scattering by a spherical region of perturbed sound speed. The left panel shows the geometry and a single frame from a numerical simulation. The circular contours are contours of the soundspeed perturbation, which is a raised cosine with radius and with a maximum fractional sound speed perturbation of . The curved heavy lines show example ray paths leaving the source, at , , and going through the receiver location, at , . The middle and righthand panels show the numerical travel times perturbations (solid lines), the Born approximation travel time perturbations (dashed lines), and the firstorder ray approximation for the perturbed travel times (dotted lines), for positive and negative five percent changes in the sound speed (, middle panel) and positive and negative ten percent changes in the sound speed (, right panel). In both cases, the different travel time perturbations are shown as functions of the sphere radius . Also in both cases, the travel times for negative soundspeed perturbations have and for positive soundspeed perturbations have . From Birch et al. (2001). 

Figure 6:
Geometry for a numerical test of the Born approximation. The wave source is located at the origin of the coordinate system. The open circles show the locations where the wavefield is observed. There is a background flow in the direction confined between the solid horizontal lines. The flow strength varies as a raised cosine, centered between the two horizontal lines, on the coordinate and has a maximum of value of 1/6 of the background sound speed, which is spatially uniform and equal to 10 km s^{–1}. The lines emanating from the source show example ray traces. The flow reflects waves that hit it at . The travel times are shown in Figure 7. From Birch and Felder (2004). 

Figure 7:
Travel times in the Born approximation (heavy line), ray approximation (thin line), and computed numerically (open circles) for the geometry and jetflow configuration described in Figure 6. The top panel is for waves that cross the jetlike flow and the bottom panel is for the waves that do not cross the jet. The horizontal axis is the distance in the upstream or downstream direction traveled by the wave before it is observed, i.e., is for waves traveling perpendicular to the direction of the flow. For the waves that cross almost perpendicularly to the flow direction the Born and ray approximations are good. For waves that hit the jet at a glancing angle, a strong reflected wave is seen and the Born approximation fails. From Birch and Felder (2004). 

Figure 8:
The averaged net power (incoming plus outgoing) as a function of frequency for two representative values of degree . These power spectra were obtained from the analysis of 1988 quietSun south pole data. The pmode ridges are labeled by the value of the radial order . The dashed lines show the background power . From Braun (1995). 

Figure 9:
The total summed power as a function of frequency across the pmode ridge corresponding to and (top panel) and the raw phase measurements across the same range in frequency (bottom panel). The solid lines indicate the predicted value of the spurious phase shifts. 1988 south pole quietSun data. From Braun (1995). 

Figure 10:
Cuts at constant frequency through the threedimensional power spectrum. Panels A, B, and C correspond to cuts at frequencies 2.8, 3.5, and 3.8 mHz, respectively. The outermost ring corresponds to the f mode, and the inner rings to , , , and so forth. Displacements of the rings are caused by horizontal flows, while alterations of ring diameters are produced by sound speed perturbations. The spectrum was computed from an image sequence 1664 minutes long beginning on 1999 May 25 for a region near disk center. From Hindman et al. (2004). 

Figure 11:
Logarithm of the power as a function of and at (left panel) and an unwrapped cylinder at wavenumber corresponding to angular degree as a function of and (; right panel). From Schou and Bogart (1998). 

Figure 12:
Representative resolution kernels for (A) RLS and (B) OLA inversions of ringanalysis frequency splittings, plotted as a function of depth. Numbers indicate target depths. The negative sidelobes near the surface, so prevalent in RLS inversion kernels, are almost absent in the OLA kernels. From Haber et al. (2004). 

Figure 13:
Theoretical crosscovariance function for p modes, , as a function of time lag and arc distance, also called the timedistance diagram. In this calculation the solar model is spherically symmetric. Hence only depends on the distance between and and is symmetric with respect to the time lag . Courtesy of A.G. Kosovichev. 

Figure 14:
Crosscovariance function computed for the Fourier filters given in Table 1. The data are averaged over all pairs of points that correspond to a given distance. Each panel is labelled (on top) by the index of the phasespeed filter listed in the table. The main branch corresponds to the first bounce of pmode wavepackets. The correlation at shorter times is an artifact, while the correlation at later times corresponds to the secondbounce branch. Courtesy of S. Couvidat. 

Figure 15:
Surface gravity wave crosscovariances. Left panel: Observed crosscovariance averaged over all possible pairs of points (, ), as a function of distance and time lag . Red refers to positive values and blue to negative values. The observations are 8hr time series from the MDI highresolution field of view. The Fourier filter is chosen to isolate surface gravity waves. Right panel: Theoretical crosscovariance from a solar model. From Gizon and Birch (2002). 

Figure 16:
Quadrant geometry used in the timedistance averaging procedure to measure flows in the eastwest direction. Here the spatial sampling is 1.46 Mm (MDI fulldisk data). The black regions show the pixels that belong to the east and west quadrants at distance from a central location , denoted by and in the text. The average crosscovariance is computed according to Equation (57). The gray regions include the pixels used for three separate distances. Combined, these four distances are those displayed in Figure 17. From Hindman et al. (2004). 

Figure 17:
Left panel: Measured fmode crosscovariance functions at a particular pixel position and for distances in the range (fulldisk MDI data, ). Middle panel: Crosscovariance functions are shifted along a line of constant phase, such that the reference shift is the same for all . Right panel: Average of the (shifted) crosscovariances over . This type of averaging is also done for pmode data. From Hindman et al. (2004). 

Figure 18:
Maps of measured travel times (quadrant/annulus geometry). The eight pictures vertically are for eight different annulus sizes. The sizes of the annuli are shown, smallest at the top and largest at the bottom. The horizontal size of each image is 370 Mm. Left column: Travel times for outwardgoing waves minus inwardgoing waves with the white displayed as a negative signal. The rms signal in the top image is 0.2 min. Secondtoleft column: Westward travel times minus eastward travel times. Thirdtoleft column: Northward travel times minus southward travel times. Fourthtoleft column: Average of inward and outward travel times with a negative signal displayed as white. The rms signal in the top image is 0.05 min. A correlation with the location of the magnetic features can be seen. Top figure in right column: Magnetic field as seen by MDI. Bottom figure in right column: Average MDI Dopplergram observed for the 8.5 hr interval. From Duvall Jr et al. (1997). 

Figure 19:
Singlesource Born approximation travel time kernel. The left panel is a cut in the plane of the ray path; the right panel is a cut in the plane that is perpendicular to the ray path at the lower turning point. The color scale shows the sensitivity of the travel time to a local change in the sound speed. The solid black line, left panel, shows the ray path. From Birch and Kosovichev (2000). 

Figure 20:
Comparison of the distributed stochastic source model (left panel) and the singlesource model (right panel) for fmode travel time kernels for wave damping perturbations. The observation locations are shown as black plus signs. The kernels are for the oneway travel times (from left to right). From Gizon and Birch (2002). 

Figure 21:
Slices through travel time kernels for the effect of soundspeed perturbations on mean travel times. Top panel: no filters other a filter to remove the f mode; middle panel: also includes an approximate model of the MDI fulldisk MTF; bottom panel: also includes a narrow phase speed filter in addition to the MTF. In all of the panels the kernels are shown in the plane of the ray path, which is shown by the black line. From Birch et al. (2004). 

Figure 22:
Results of fmode timedistance analysis and comparison with the direct Doppler measurements. (a) Direct Doppler measurements averaged over the observation duration (8 hr). (b) Lineofsight projection of the horizontal vector flow field, inferred using fmode timedistance. (c) Horizontal divergence of horizontal flows measured by fmode timedistance analysis 1 Mm beneath the photosphere. (d) Scatter plot of the lineofsight velocity from timedistance analysis against the observed Doppler velocity. The correlation coefficient is 0.7. From Gizon et al. (2000). 

Figure 23:
Tests of an RLS inversion for supergranulationlike flows. Top panel: flow field in the model; middle panel: the inversion result after five iterations of LSQR; bottom panel: inversion result after one hundred inversions of LSQR. In practice one hundred iterations would greatly magnify any noise in the data. From Zhao and Kosovichev (2003a). 

Figure 24:
The sound speed in the model (top panel) and the result of the inversion of the artificial data (lower panel). The gray scale is such that light colors are reduced soundspeed and dark colors are increased sound speed, in both cases relative to the stratified background. From Jensen et al. (2003b). 

Figure 25:
Comparison of the amplitudes (left panel) and phases (right panel) of ingressionegression correlations (Section 4.4.5) at a focus depth of 4.2 Mm computed with ray theory (“eikonal”, Equation (71)) and with the wave theory (“hydromechanical”, Equations (72, 73)). In both cases, an empirical dispersion correction has been applied (see Section 4.4.3). The black points correspond to focus points where the photospheric magnetic field is weaker than 10 G and the red points correspond to focus points where the surface magnetic field is larger than 100 G. There is, in general, good correspondence between the results of the two methods, though the scatter in the phases appears to increase with increasing phase shifts. From Lindsey and Braun (2004). 

Figure 26:
Spatial averages of quiet Sun local control correlations. (a) Results obtained using the wave theory Green’s functions. (b) Results of using ray theory. The numbers along each curve denote the cyclic frequency in units of mHz. In both cases, notice that the phase is not zero. From Lindsey and Braun (2004). 

Figure 27:
Geometry for farside imaging. (a) Twoskip correlation scheme. (b) Oneskip/threeskip correlation. In farside imaging the data on the visible disk are used to estimate the wavefield at focal points on the farside of the Sun. From Braun and Lindsey (2001). 

Figure 28:
Timedistance relations at various focal depths, computed from a standard solar model, based on ray theory, at 3 mHz. Each curve corresponds to different target depths, as indicated. For each curve, the dots correspond to modes whose values are multiples of 10, starting with at the right end of each curve. The highest mode which can reach the target depth is marked by an open circle on each curve. The value decreases in either direction away from the open circle along the curve. From Chou et al. (1999). 

Figure 29:
Lineofsight velocity maps showing supergranularscale flow, based on SOHO/MDI high spatial resolution Dopplergrams. Left panel: Lineofsight projection of nearsurface flows inferred from direct modeling of seismic data. Right panel: Velocity map obtained by averaging the 16 hr sequence of Dopplergrams used in the seismic analysis. From Woodard (2002). 

Figure 30:
Comparison of the timedistance and normal mode methods for determining the solar rotation. The angular velocity is plotted versus latitude for six different depths. The solid curve is the symmetric component of the timedistance results, and the dashed lines are formal errors from the inversion. The dotted curve is the result of an OLA inversion of MDI frequency splittings. From Giles (1999). 

Figure 31:
Northsouth average of rotational velocity at different latitude from ringdiagram analysis. The results obtained using RLS inversions are shown by dashed lines (with dotted lines marking the 1 error limits) and the results obtained by using OLA inversions by crosses with error bars. For comparison, the solid line shows the rotational velocity obtained from inversion of globalmode frequency splittings (after subtracting out the surface rotation velocity used in tracking each region). From Basu et al. (1999). 

Figure 32:
Zonal flows from ringdiagram analysis at depths of 0.9 Mm (dashed curve) and 7.1 Mm (solid curve). Each panel corresponds to the average over yearly MDI Dynamics Program intervals as indicated. The zonal velocity plots for each year have been offset by subtracting a depthdependent constant. The error bars shown are 10 times larger than the estimated formal errors in order to be visible. From Haber et al. (2002). 

Figure 33:
Meridional circulation in 1996 – 98 inferred from pmode travel times at various latitudes as a function of scaled radius . The blue (red) curves are for the northern (southern) latitudes. The turnover point is roughly at . The assymetry between the two hemispheres is probably caused by an error in the orientation of the MDI camera. From Giles (1999). 

Figure 34:
(a) Meridional flow measured by timedistance helioseismology at depths of 4 Mm (solid lines) and 7 Mm (dashdotted lines) as a function of latitude for different Carrington rotations. (b) Northward residual flows, computed by removing the CR1911 flow at each Carrington rotation. The grey regions show the latitudes of activity. The residuals are consistent with a converging flow toward the mean latitude of activity. From Zhao and Kosovichev (2004). 

Figure 35:
(a) Meridional circulation residuals as a function of time and latitude, measured by timedistance helioseismology at a depth of about 50 Mm. The residuals are obtained by removing a time average. The green (red) shades correspond to excess poleward (equatorward) velocities, with values in the range 10 m s^{–1}. The thick black line is the mean latitude of activity. The residuals are consistent with a flow diverging from the mean latitude of activity. (b) Zonal flow residuals (torsional oscillations) as a function of time and latitude. The red (blue) shades correspond to flows that are faster (slower) than average. From (Beck et al., 2002). 

Figure 36:
Sketch of the timevarying components of the largescale flows, averaged in longitude over several rotation periods. Shown is a meridional plane in the northern hemisphere; the prograde direction is coming out of the page. Zonal flows (a) introduce a 10 m s^{–1} shear around the mean latitude of activity (AR). Residual meridional flows ( 10 m s^{–1}) converge toward active latitudes near the surface (e) and diverge deeper inside the Sun (d). The whole pattern of flows drifts equatorward through the solar cycle. The dashed streamlines that connect the horizontal flows are a suggestion by Zhao and Kosovichev (2004). From Gizon (2003). 

Figure 37:
Vertical velocity from ringdiagram inversions constrained by mass conservation, averaged over Carrington rotation CR 1988 (2002 March 30 – April 25), as a function of latitude and depth. Top panel: Surface magnetic flux as a function of latitude (solid line) and averaged over 15° (dotted curve). Bottom panel: Vertical velocity derived from GONG data after removing the largescale flow components. The dashed line indicates the zero contour; the dotted lines indicate 20%, 40%, 60%, and 80% of the minimum and the maximum of the color scale. The dots indicate the depthlatitude grid. From Komm et al. (2004). 

Figure 38:
Decrease in the onebounce travel time at relative to the other s as a function of time. The filled circles denote the MDI results, and the open circles the GONG results. The horizontal bar associated with each point indicates the duration of each observation (the sequence of observing runs is labelled by a series of increasing numbers). The thick horizontal line indicates the range of solar minimum period used for MDI, and the dashed line for GONG. The solid line is the sunspot number from the Greenwich sunspot data. From Chou and Serebryanskiy (2002). 

Figure 39:
Map of nearsurface horizontal flows obtained for Carrington rotation 1949 using fmode timedistance helioseismology. A smooth rotation profile has been subtracted. The dark shades are shorter travel time anomalies that correspond to regions of enhanced magnetic activity. Local flows converge toward complexes of activity with an amplitude of 50 m s^{–1}. Notice also the poleward meridional flow. From Gizon et al. (2001). 

Figure 40:
Left column: OLA inversion of horizontal flows around active region NOAA 9433 on 23 April 2001 obtained using ringdiagram analysis. The depths shown are 7 Mm (upper panel) and 14 Mm (lower panel). The green and red shades are for the two polarities of the magnetic field. The horizontal and vertical axes give the longitude and the latitude in heliospheric degrees. Right panel: Horizontal flows around NOAA 9433 as a function of depth and latitude, averaged over the longitude range (142.5°, 157.5°) and the time period 23 – 27 April 2001. The transition between inflow and outflow occurs near 10 Mm depth. From Haber et al. (2004). 

Figure 41:
Left column: Longitudinal averages of surface horizontal flows obtained with fmode timedistance helioseismology (Carrington rotations 1948 and 1949 in 1999). The vertical lines show the mean latitude of activity. The solid curves show zonal flows and meridional circulation averaged over all longitudes and both hemispheres. The zonal flows are obtained after subtraction of a smooth threeterm fit to the rotation profile. The dashed curves are averages that exclude local areas in and around active regions (all points within 5° of strongly magnetized regions). Right panel: Sketch of surface flows around active regions: (a) 10 m s^{–1} zonal shear flow, (b) 50 m s^{–1} inflow, (c) active region superrotation, and (m) 20 m s^{–1} background meridional circulation. From Gizon (2003). 

Figure 42:
Horizontal flows around a sunspot on 1998 December 6, obtained with fmode timedistance helioseismology. Overplotted is the lineofsight magnetic field (MDI high resolution) truncated at 0.5 kG. The moat flow beyond the penumbra (red) is clearly visible. Adapted from Gizon et al. (2000). 

Figure 43:
Flow maps around a sunspot at depths of (a) 0 – 3 Mm, (b) 6 – 9 Mm, and (c) 9 – 12 Mm, infered using pmode timedistance helioseismology. Arrows show the magnitude and direction of horizontal flows. The color background shows vertical flows (positive values for downward). The contours at the center correspond to the umbral and penumbral boundaries. The longest arrow represents 1 km s^{–1} for (a) and 1.6 km s^{–1} for (b) and (c). From Zhao et al. (2001). 

Figure 44:
Vertical cuts through the sunspot shown in Figure 43. Upper panel: Cut in the eastwest direction. Lower panel: Cut in the northsouth direction. The location of the umbra and the penumbra is indicated at the top of each frame. The longest arrow corresponds to a velocity of 1.4 km s^{–1}. From Zhao et al. (2001). 

Figure 45:
Horizontal Doppler diagnostics applied to 24 hr data from MDI, which includes sunspot group AR 9363. Left: Observed velocity field, shown as vectors, for a focal depth of 3 Mm and superimposed a magnetogram. Middle: Same vector field as shown in the left panel, but superimposed over an image of the horizontal divergence of the velocity. Right: Velocity field and its divergence with the focal plane placed 14 Mm below the surface. The companion Movie 46 shows the flow field as a function of focus depth. From Braun and Lindsey (2003). 

Figure 46:
Movie Companion movie to Figure 45, showing the flow field as a function of focus depth. From Braun and Lindsey (2003). 

Figure 47:
Absorption coefficients plotted as a function of frequency. The left panels show results for sunspot NOAA 5254 and the right panels are for sunspot NOAA 5229. The vertical panels represent different bins of harmonic degree. From Braun (1995). 

Figure 48:
Egression power maps of active region complex NOAA 8179 obtained for the 24 yr period 1998 March 16. (a) MDI magnetogram. Panels (b), (c), and (d) show 5 mHz helioseismic images of the regions with depths at 0, 11.2 and 19.5 Mm below the solar surface, respectively. The dark shades correspond to acoustic absorption. The acoustic glory is seen in panel (b) as a bright halo of excess 5 mHz emission. The linear gray scale at the bottom applies to all of the helioseismic images that are normalized to unity for the mean quiet Sun. From Braun and Lindsey (1999). 

Figure 49:
Phase shifts between outgoing and outgoing waves from Hankel analysis, as a function of frequency for several different radial orders . The data points with error bars are averaged values for NOAA 5254 (Braun, 1995). The solid lines are from a model by Cally et al. (2003). From Cally et al. (2003). 

Figure 50:
Observed acoustic power maps, outgoing intensity maps, phaseshift maps, and envelopeshift maps focusing at the solar surface at 3 mHz (first row), 3.5 mHz (second row), 4 mHz (third row), 4.5 mHz (fourth row), and 5 mHz (fifth row). Gray scales at different frequencies are the same except in the envelopeshift map at 5 mHz, where the gray scale is 1.5 times larger. The envelope peak of the crosscorrelation function provides information about wave travel time, associated with the group velocity along the wave path. The phase time of the crosscorrelation function between ingoing and outgoing waves provides information about phase changes along the wave path, including the phase change at the boundaries of the mode cavity and flux tubes. From Chou et al. (1999). 

Figure 51:
Movie Wave speed perturbation associated with the active region AR 9393. The positive values are shown in red and the negative ones in blue. The movie shows the evolution of the wave speed perturbation from March 25 until April 1, 2001. Courtesy of A.G. Kosovichev. 

Figure 52:
Horizontal slices through the inferred soundspeed perturbations under a sunspot using GONG data. From top to bottom the rows correspond to the depth ranges 1.7 – 2.3 Mm, 3.6 – 4.4 Mm, 6.2 – 7.3 Mm, and 8.5 – 9.8 Mm. The inversion results for uncropped (left column) and cropped data (right column) are qualitatively similar. From Hughes et al. (2005). 

Figure 53:
Relative differences of the squared sound speed between active and quiet regions obtained by inverting the frequency differences measured using ringdiagram analysis. The blue solid line shows the RLS inversion results, with the blue dotted lines showing the 1 error limit. The red points are the SOLA (Subtractive OLA) inversion results. The vertical error bars are the 1 error, and the horizontal error bars mark the distance between the quartile points of the averaging kernels and are a measure of the resolution of the inversions. The magnetic field strengh in each panel is a local magnetic activity index. From Basu et al. (2004). 

Figure 54:
Movie Movie showing farside and frontside images of the Sun from March to June 2001. The large activity complex AR 9393 is seen for several rotation periods. The horizontal axis spans all longitudes measured in the Carrington frame of reference. The fuzzy image shows shorter wave travel times (in red) caused by active regions located on the farside of the Sun. The Earthside image of the Sun shows continuum intensity (active regions appear as red/dark shades). 

Figure 55:
Composite images of SOHO/MDI magnetograms and farside images made using SOHO/MDI Doppler data. The magnetograms have a higher spatial resolution. The boundary in the farside images is where the algorithm is switched from twoskip/twoskip imaging, used to image in center of the farside, to threeskip/oneskip imaging used further from the antipode of the visible disk. See Figure 27 for a diagram of the geometry. The color scale for the farside images shows the time delay between the egression and the ingression. The sign of the signal in active regions is of the sense of faster propagation time underneath active regions. The top four panels show the farside images for 1999 April 22 – 25. The bottom panels shows the magnetogram for Carrington rotation 1999 May 1 – 28. From Braun and Lindsey (2001). 

Figure 56:
Movie Remapped and filtered MDI Dopplergram 25 min after the Bastille Day flare. The flare signal was extracted, enhanced by a factor of 4, and then superimposed on the Dopplergrams. The movie shows the temporal evolution of the signal. From Kosovichev and Zharkova (1998). 

Figure 57:
Movie Movie of the divergence signal (inward travel times minus outward times) with magnetic field signal overlaid. The magnetic field is displayed as green and red (blue and green in the flash movie) for the two polarities when the magnitude of the field is larger than 15 G. The gray scale is for the divergence signal with white shades for outflow and dark shades for inflow. The colorbar indicates the travel time difference in seconds. The line corresponds to the equator and corresponds to Carrington longitude 180°. The timedistance data is averaged over 8.5 hr starting at the time shown on top. The movie shows the time evolution of the supergranulation pattern over 6 days. From Duvall Jr and Gizon (2000). 

Figure 58:
Flow field (arrows) and wavespeed perturbations (greyscale background) inferred by Kosovichev and Duvall Jr (1997) with timedistance helioseismology. Typically there are upflows in the hotter areas where the sound speed is higher, and downflows in the cooler areas. From Kosovichev and Duvall Jr (1997). 

Figure 59:
Correlation coefficient between the horizontal divergence at each depth, derived from pmode time distance helioseismology, and the divergence image of the uppermost layer. The dashed line is from Duvall Jr (1998) and the solid line is from Zhao and Kosovichev (2003a). 

Figure 60:
Comparison of the observed horizontal divergence, derived from seismic holography (leftmost panels), with those from a control computation which assumes that the Doppler signatures are concentrated at the solar surface (rightmost panels). The middle panels show the weighted pupils used in the analysis. The companion Movie 61 shows the observed and control data as a function of focus depth. From Braun and Lindsey (2003). 

Figure 61:
Movie Companion movie to Figure 60, showing the observed and control data as a function of focus depth. From Braun and Lindsey (2003). 

Figure 62:
Effect of the Coriolis force on supergranular flows. (a) Plot of the correlation coefficient, , between the vertical vorticity (curl) and the horizontal divergence (div). (b) Horizontal averages of the vorticity, (solid) and (dashed), over regions with and , respectively. A vorticity of 1 Ms^{–1} corresponds to an angular velocity of 2.5° day^{–1} or a typical circular velocity of 10 m s^{–1}. From Gizon and Duvall Jr (2003). 

Figure 63:
Anomalous pattern motion of supergranulation measured by tracking the horizontal divergence of the flow field observed with timedistance helioseismology. (a) Pattern rotation for timelags = 6, 8, 16, and 22 hr. The cross shows the equatorial pattern rotation measured by Snodgrass and Ulrich (1990) for = 24 hr from Mount Wilson Dopplergrams. (b) Meridional motion of the pattern as a function of timelag . Notice that the meridional motion appears to be equatorward for . A Pangle correction was applied to the data. From Gizon and Duvall Jr (2003). 

Figure 64:
Movie Movie showing the evolution of the spatial crosscorrelation of the divergence signal at the equator as a function of from 0 to 5.5 d. (Movie still for time lag = 24 hr.) The original MDI Doppler velocity images were tracked at the Carrington rate. 

Figure 65:
Movie Movie showing the evolution of the average map of the divergence signal in a 15° × 15° equatorial region as a function of tracking velocity in the range from –200 m s^{–1} to 200 m s^{–1} with respect to the Carrington velocity. The movie still displays the temporal average (5 d) tracked at a velocity 125 m s^{–1} above the Carrington velocity. This average is constructed from maps derived from timedistance helioseismology every 8 hr. Courtesy of J. Zhao. 

Figure 66:
Ratio , as defined by Lisle et al. (2004), at the equator as a function of tracking velocity (offset with respect to Carrington velocity). This curve is an average over one month of data. The vertical dashed lines correspond to tracking offsets –8 m s^{–1} and 123 m s^{–1}. Courtesy of J. Zhao. 

Figure 67:
Power spectrum of the horizontal divergence signal for (equator) in 1997. Divergence maps were tracked in a frame of reference with angular velocity (small magnetic features). Left panel: Cylindrical section at constant wavenumber , as a function of azimuth and frequency . Middle panel: Fit to the data according to the model described in the text. The values of the parameters are measured at fixed by a twodimensional fit to the power spectrum in (, )space. For this particular example, and (excess power in the prograde direction). Right panel: Ratio of the data to the fit; no bias is observed. From Gizon and Duvall Jr (2004). 

Figure 68:
(a) Advective flow versus at . Each curve corresponds to a different year (from blue in 1996 to red in 2002). is measured with respect to the reference (small magnetic features). Only the northsouth symmetric component is shown. (b) Residuals of after subtraction of a smooth fit (dashed line in panel a). The scale bar has units of m s^{–1}. The black curve is an estimate of the mean latitude of activity. (c) Advective flow versus at . Only the northsouth antisymmetric component is shown. (d) Residual meridional circulation with respect to the dashed line in panel (c). The scale bar has units of m s^{–1}. 

Figure 69:
(a) Oscillation frequency versus at latitudes (solid), (dotted), and (dashed). For reference, the orange curve is . Also shown is the half width at half maximum (HWHM, ) of the Lorentzian profiles for the same latitudes. The quality factor is at . (b) Power spectrum corrected for rotation and meridional circulation and averaged over azimuth and latitude. The distribution of power as a function of frequency is affected only by the known temporal window function. From Gizon et al. (2003). 
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