MappingLocal helioseismology tends to be worked on in cartesian corrdinates and so some form of mapping onto a plane is required, usually Postel's projection.
All mappings introduce distortions, and maps are either conformal or equal area. The raw observations are azimuthal projections with the plane (almost) tangent to the surface. The two common projections are transverse cylindrical (all horizontal lines are great circles and the distance along x is preserved) and Postels' projection (all the great circles intersect one another at the centre, and distance is preserved along all directions through the centre).
A useful overview of the currently used helioseismic mappings (F. Hill).There is a wealth of information about map projections on the internet, here is a quick look, Interactive Map Projections, and more detail is provided in the links below.
Some short descriptions of popular mappings used in helioseismology and links to Wolfram descriptions.
Postel: Projected onto a plane. Distances and directions true from the centre of the map. All great circles pass through the centre. Distortion increases away from disk centre.
Gnomonic: Projected onto a plane. The focal point is at the centre of the sphere. Any straight line on the plane is a great circle, but distance is only true from centre of projection.
Stereographic: Projected onto a plane. The focal point is on the opposite surface of the sphere. Directions are only true form centre of projection. Any stright line through the projection is a great circle.
Azimuthal Equal Area: Projected onto a plane. Distortion increases and scale decreases away from centre. Area's are true projections.
Cylindrical Equal Area: Projected onto a cylinder. Distances and directions true only along the equator, areas all distorted.
Sinusoidal equal area: Equal area projection, with one or many central meridians from which distortions increase with distance.
Mercator: Projected onto a cylinder. Distortion increases with distance from the Equator.Useful information regarding HMI coordinate definitions and projections.