**Time-Distance Helioseismology**

## Time-Distance Helioseismology

The goal of time-distance helioseismology
is to perform a time-distance analysis, where solar oscillations are
characterized. The time-distance analysis measures directly the times
taken by acoustic waves to travel from the solar surface to the bottom
of the cavity and back. We refer to this type of travel as a
raypath. This analysis also measures the distances as an angle at the
surface between the surface reflections. In this analysis, time
series at two separate points are crosscorrelated with all possible
annuli as a function of travel time. From the crosscorrelations, time
delays are measured. Later analysis takes the maps of time delays,
*inverts* the data, and maps of solar interior properties are calculated
-- in particular of the magnetic field, sound speed, flow speed and
direction.

In the figure below, we show some raypaths below the Sun's surface.
The rays go from the center of an annulus to annuli with different
radii. The ray paths are curved because of the increasing sound speed
with depth. The sound speed increases from 7 km/sec near the surface
to 35 km/sec at 10 Mmeters depth. The measured travel times are
sensitive to the component of velocity along the particular path.

You can also download a postscript
version of the above figure.

A rule of thumb that we have found useful is that the horizontal
distance between surface reflections is given approximately by pi
multiplied by the depth of the turning point of the ray. This relation
is exactly true for a polytrope and approximately true for a real
solar model. Another useful rule of thumb is that the length of the
ray is four times the depth.

For a fixed angular distance (in degrees), different waves travel to
different depths in the Sun's convection zone. The shallower waves
"bounce" more, while the deeper waves bounce less (and travel
deeper).

The following diagram is representative of the output from Duvall's
time-distance analysis.

You can also download a postscript
version of the above figure.

You can find more about the initial Time-Distance measurements from
the MDI from the
preprint, (5.4Mb,postscript) titled:
**Time-Distance Helioseismology with the MDI
Instrument: Initial Results**, by
T.L. Duvall, Jr.,
A.G. Kosovichev, P.H. Scherrer, R.S. Bogart, R.I. Bush, C. DeForest,
J.T. Hoeksema, J. Schou, J.L.R. Saba, T.D. Tarbell, A.M. Title,
C.J. Wolfson, and P.N. Milford.

**SOHO SOI/MDI Results.**

**The SOI Main Page.**

Last Modified by Amara Graps,
SOI, on 07 January 1997.