This is a PDS interim release of Occultation and gravity data
from the Viking Orbiter / Mariner 9 missions to Mars.

An informal validation process has been performed on these data.
It is not a PDS peer-reviewed archive and it is not a fully archived
product.

A complete description of the data can be found in:
Smith and Zuber, 'The shape of Mars and the topographic signature
of the hemispheric dichotomy', Science, v. 271, p. 184-188, 1996.

For more information, contact:
   Jim Alexopoulos
   314-935-8152
   jim@wuzzy.wustl.edu

Below is a list and description of the files available:


JPL50C-final

    This file contains a 50x50 normalized spherical harmonic
    solution for the gravity field of Mars. The planetary gravitational
    constant, or GM for this solution is 42828.37 +/- 0.0 km^3/sec^2, and
    the reference equatorial radius is 3394.2 km.  The 6 columns
    correspond to the degree index m, the order index n, the
    coefficients Cmn and Smn, and the uncertainties in Cmn and Smn.
    
GMM-1-final

    This file contains the GMM-1 50x50 normalized spherical harmonic
    solution for the gravity field of Mars.  The planetary gravitational
    constant, or GM for this solution is 42828.36 +/- 0.0512 km^3/sec^2,
    and the reference equatorial radius is 3394.2 km.  The 6 columns
    correspond to the degree index m, the order index n, the
    coefficients Cmn and Smn, and the uncertainties in Cmn and Smn.
        
M.DATA.OCCs_GEOID_TOPOGRAPHY.txt.done
    
    This file contains occultation data. The 5 columns correspond
    to the latitude and longitude of occultation point, radius of
    occultation point (in meters), radius of GMM-1 geoid at
    occultation point (in meters), and topography (radius-geoid) at
    occultation point (in meters).

M.OCCULTATION.ERRORS.txt.done

    This file contains the errors for the occultation data.  The 8
    columns correspond to the latitude and longitude of occultation
    point, E OCC.RADIUS, Rad.orbit error, Atm.error.(10%),
    occ.time.error.(o.1s)(3km/s)(m), Planet.Eph.error.(GUESS) (m),
    TOTAL Radius Error (rss) (m).

M.GMM-1.50x50.gravity.model.txt.done

    This file contains the GMM-1 50x50 normalized spherical harmonic
    solution for the gravity field of Mars.  It was the gravity field
    used to re-analyze the occultation data and for the geoid calculation
    in the occultation file M.DATA.OCCs_GEOID_TOPOGRAPHY.txt.done.
    The planetary gravitational constant, or GM for this solution is
    42828.36 +/- 0.05 km^3/sec^2, and the reference equatorial radius
    is 3397.0 km.  The 4 columns correspond to the degree index m, the
    order index n, and  the coefficients Cmn and Smn.

GMM-1.ascii.covariance.Z

    This compressed file is the gravity field covariance matrix for
    the GMM-1 gravity model. It is in upper triangular format, row 
    by row.  This is a useful product for understanding the errors
    in the gravity solution.  The gravity field covariance represents
    the complete error description for the GMM-1 gravity field solution,
    including the coefficient variances (sigmas^2), and the correlations
    between all the coefficients.  It is a product of the least squares
    solution that derived GMM-1.  The covariance provides a more complete
    description of the error associated with the GMM-1 gravity field
    solution, than would be available from the sigmas alone.

M.SHAPE.8X8.SPH.HARM.txt.done
  
    This file contains the 8x8 normalized spherical harmonic solution
    for the shape of Mars.   Input data for this calculation was the
    occultation latitude, longitude and radius given in the file
    M.DATA.OCCs_GEOID_TOPOGRAPHY.txt.done.

M.SHAPE.COVARIANCE.txt

    This file is the shape covariance matrix for the spherical harmonic
    model of the shape of Mars (M.SHAPE.8X8.SPH.HARM.txt.done).

M.TOPOGRAPHY.8X8.SPH.HARM.txt.done

    This file contains the 8x8 normalized spherical harmonic solution
    for the topography of Mars.  Input data for this calculation was the 
    occultation latitude, longitude and topography given in the file
    M.DATA.OCCs_GEOID_TOPOGRAPHY.txt.done.

ellheight.out

     This file contains a digital, 1 X 1 degree resolution grid of the
     ellipsoidal heights of Mars relative to a best-fitting triaxial
     ellipsoid. It is a 360 x 180 grid from 89.5 to -89.5 degrees
     latitude, and 0.5 to 359.5 degrees longitude. The observation is
     height in meters. The ellipsoid axes are A=3399.472 km, B=3394.472 km,
     and C=3376.502 km. The center of the ellipsoid is offset from the
     center of mass by x=-130 m, y=-1780 m, and z=-3081 m. The
     ellipsoidal shape is subtracted from the shape calculated from
     the 8x8 spherical harmonic model. 

marsboug.out

     This file contains a digital, 1 X 1 degree resolution grid of
     Bouguer gravity anomalies of Mars.  It is a 360 x 180 grid from
     89.5 to -89.5 degrees latitude, and 0.5 to 359.5 degrees longitude.
     The observation is Bouguer gravity in milligals.
     The Bouguer anomalies are derived from the 50th-degree and -order
     spherical harmonic gravity model, GMM-1, and the 8th-degree
     and -order topography model, M.TOPOGRAPHY.8X8.SPH.HARM.txt.done,
     referred to a geopotential surface, as described in Smith
     and Zuber, 'The shape of Mars and the topographic signature of the
     hemispheric dichotomy', Science, v. 271, p. 184-188, 1996. The Bouguer
     correction to the gravitational potential is calculated, for spherical
     harmonic degree l=1,2,...,8 as:

                CB = 3*(rho/rhobar) / (2*l + 1)

     The topographic reduction density rho was 2900 kg/m3, and mean
     planetary density rhobar was 3340 kg/m3.

marsgeoid.out

     This file contains a digital, 1 X 1 degree resolution grid of
     the Geoid of Mars.  It is a 360 x 180 grid from 89.5 to -89.5
     degrees latitude, and 0.5 to 359.5 degrees longitude. The
     observation is the Geoid in meters. The geoid anomalies were
     calculated from the 50th-degree and -order spherical harmonic gravity
     model, GMM-1, relative to a reference ellipsoid with an inverse
     flattening of 191.1372. 

marsgrav.out

     This file contains a digital, 1 X 1 degree resolution grid of
     free-air gravity accelerations of Mars.  It is a 360 x 180 grid
     from 89.5 to -89.5 degrees latitude, and 0.5 to 359.5 degrees
     longitude.  The observation is free-air gravity in milligals.
     The gravity anomalies are derived from the 50th-degree and -order
     spherical harmonic gravity model, GMM-1.

marsthick.out

     This file contains a digital, 1 X 1 degree resolution grid of
     the crustal thickness of Mars.  It is a 360 X 180 grid from
     89.5 to -89.5 degrees latitude, and 0.5 to 359.5 degrees longitude.
     The array values are crustal thickness in kilometers.  A Bouguer
     correction was applied to the martian gravity field, to degree and
     order 8. The resulting anomalies were then inverted for the 
     topography of a moho (Mohorovicic Discontinuity) at a depth of
     50 km, assuming a laterally constant density structure for the 
     crust and mantle, and a density contrast between crust and mantle 
     of 600 kg/m3.  The difference between the inferred moho topography
     and the surface topography is referred to as the crustal thickness.
     A model satisfying the observed topographic and geopotential
     constraints, such as this one, is not in isostatic equilibrium and
     requires static or dynamic support.

thkerr.out
  
     This file contains a digital, 1 X 1 degree resolution grid of
     the formal error in the crustal thickness of Mars, to degree and
     order 8. It is a 360 X 180 grid from 89.5 to -89.5 degrees latitude,
     and 0.5 to 359.5 degrees longitude. The array values are one-sigma
     errors in kilometers. These errors arise due to uncertainties in
     the gravity and topography used to calculate the Bouguer gravity
     anomaly.  The downward continuation of the Bouguer gravity field
     to a density interface 50 km below the martian surface amplifies
     these errors by as much as 30%.
     Since the topographic model used is complete only
     to degree and order 8, these errors represent errors of a spatially
     averaged model. Thus the error at a particular location is likely to
     be greater than given by this file.

marstopo.out

     This file contains a digital, 1 X 1 degree resolution grid of the
     topography of Mars relative to a geopotential surface. It is a
     360 x 180 grid from 89.5 to -89.5 degrees latitude, and 0.5 to 359.5
     degrees longitude. The observation is topography in meters. The data
     are derived from the 8x8 spherical harmonic topography solution,
     M.TOPOGRAPHY.8X8.SPH.HARM.txt.done. The geoid was subtracted from
     the Mars radii from occultations prior to obtaining the spherical
     harmonic coefficients. 

shapemars.out

    This file contains a digital, 1 X 1 degree resolution grid of the
    shape of Mars relative to a sphere of radius 3394.2 km. It is a
    360 x 180 grid from 89.5 to -89.5 degrees latitude, and 0.5 to 359.5
    degrees longitude. The observation is relative radius in meters. The
    data are derived from the 8x8 spherical harmonic shape solution,
    M.SHAPE.8X8.SPH.HARM.txt.done.