A Matlab Toolbox for Computation of Complete Bouguer Anomalies from Free Air Anomalies

Introduction. We present a toolbox expressly written for MATLAB environment to provide terrain corrections of gravity data. The program performs the complete Bouguer computations, including the Bullard A, Bullard B and Bullard C corrections, from any kind of free air datasets (offshore or on land stations). The gravity contribution due to the relief is computed starting from a gridded topography in which each grid point corresponds to the thickness of a right rectangular prism having its base at the sea level. The computation is carried out on a circular region, whose centre corresponds to the point station, and divided in three different concentric sectors. The contribution due to the relief delimited in the external sector is calculated by means of the harmonic spherical expansion of the potential of each prism. The gravity effect due to the relief enclosed within the intermediate sector is computed by summation of the contributions of any single prism located in this area by means of an analytical formula. In a third phase, the gravity effect due to the inner zone is calculated. It is bounded by the eight nearest grid points and is formed by four squares located around the point station. This effect is computed following two steps: Firstly, the contribution of a flat prism having its top at the elevation of the point station is estimated. Finally, the result is added to the effect due to a conic prism divided in four different quadrants. Each of them slopes continuously from each square of the inner zone toward the point station. The complete terrain correction is obtained by adding the values resulting from eachy step. The program is suitable because it allows to modify all the parameters playing a role in the calculation (i.e., radius of the circular search area, extent of the external and intermediate sectors, reference density, etc.). It is really easy-to-use because all input data are enclosed in a single command line that can be fastly modified. Methodology. It is largely known that gravity measurements at the earth surface must be corrected in order to provide anomalies that are comparable over large geographic districts. These corrections deal with several effects (latitude, tides, instrumental drift, elevation) and, usually, are not difficult. The final result is represented by the free-air anomaly field, that is useful to investigate the isostatic adjustments at a regional scale. However the free air anomalies correlate with topography at long wavelengths and do not take into account the effect of masses located between the topographic surface and the reference ellipsoid. To this purpose, a further correction (Bouguer correction) has to be made to remove the components of the gravity anomalies due to the earth surface