How were Mars' zero elevation datum defined? What are their shapes?

Question

Discussions on Boiling ponds and pools on Mars? led me to Wikipedia's Mars; Geography and naming of surface features which says:

Because Mars has no oceans and hence no "sea level", a zero-elevation surface had to be selected as a reference level; this is called the areoid¹²⁴ of Mars, analogous to the terrestrial geoid. Zero altitude was defined by the height at which there is 610.5 Pa (6.105 mbar) of atmospheric pressure.¹²⁵ This pressure corresponds to the triple point of water, and it is about 0.6% of the sea level surface pressure on Earth (0.006 atm).¹²⁶ In practice, today this surface is defined directly from satellite gravity measurements.

¹²⁴NASA (April 19, 2007). "Mars Global Surveyor: MOLA MEGDRs". geo.pds.nasa.gov. Archived from the original on November 13, 2011. Retrieved June 24, 2011.

¹²⁵Zeitler, W.; Ohlhof, T.; Ebner, H. (2000). "Recomputation of the global Mars control-point network" (PDF). Photogrammetric Engineering & Remote Sensing. 66 (2): 155–161. Archived from the original (PDF) on November 13, 2011. Retrieved December 26, 2009.

¹²⁶Lunine, Cynthia J. (1999). Earth: evolution of a habitable world. Cambridge University Press. p. 183. ISBN 978-0-521-64423-5.

Question: For Mars' areoid and geoid (if there is one) or gravitational zero elevation datum:

• How were they defined? For the areoid, how were atmospheric models near the equator and pole measured and averaged (over a day and and over a year) to establish the 610.5 Pa surface. For the gravitational zero elevation datum, how was gravity data process to choose or decide a zero altitude surface?
• What are their shapes? Is either one spherical, or are they prolate spheroids. If so, did they have the same eccentricity or oblateness factor?

Answer 1

The areoid is simply the Mars analogue of the geoid. It's not clear whether the zero elevation level discussed by Zeitler et al. (referenced in the question) is actually a geoid. A more recent paper by Ardalan et al. (2010) defines the geoid using geodetic and gravitational measurements. It is the gravitational equipotential that best fits the shape of Mars in a least squares sense.

The Mars geoid is remarkably similar to Earth's. Both are close to the ellipsoidal shape expected of a rotating fluid (in the case of Mars, this accounts for 95% of the deviation from a sphere). The image below, from Smith et al. (1999), shows what is left after this part is subtracted. There are a couple of highs over dense masses located deep under the surface, at the boundary between the iron core and the silicate mantle. On Mars, one of these masses is under the Tharsis topographic bulge. Major volcanic features such as Olympus Mons, Alba Mons and the Elysium volcanic province are also located above these features. Earth also has a couple of large dense masses near the core-mantle boundary. See Why are the Geoid and the Areoid so Similar?