3 Theory

3.1 Bouger gravity anomaly

    Bouger gravity anomaly is a discrepancy between the corrected, measured gravity, and the theoretical gravity. It arises as the density of the Earth’s interior is not homogeneous as assumed. Bouguer gravity anomaly is one of the most common types of gravity anomalies. It (DgB) is defined by Equation (01) where gm and gn are the measured and theoretical gravity respectively, and DgF, DgBP, Dgt, and Dgtide are the free-air, Bouguer plate, terrain, and tide corrections respectively \cite{Nozaki_2006}.
Equation 01:

\(Δg_B=g_m+(Δg_F-Δg_{BP}+Δg_J+Δg_{tide})-g_n\)      

    Due to the simplicity, we assume that there is an amount of excess mass with a spherical shape, the effect of a roughly equidimensional ore body is quite similar to that of a sphere, so our model is not entirely inappropriate. Because we calculate Bouguer anomalies in terms of density variations, we speak in terms of the density contrast when considering the gravity effects of models. The density contrast is the density of the model minus the density of the remaining material. Which we assume to be homogeneous. Derivation of an equation for the gravity effect of a sphere is relatively straight forward because the effect is the same as if all the mass is concentrated at the sphere’s center. Because we deal with the vertical component of gravimeters we need to consider only the vertical component. The gravity anomaly data (fig. 3), g, can be generated by using the Equation (02), where a is the radius of the buried sphere, Dr is the density contrast, G is Newton's universal gravity constant, ZS is the depth of the sphere center, and r is the distance of the sphere center from the reference point. ‘r’ can be expressed by Equation (03), where, xy, and z are the longitudes latitudes and depth of the observed locations respectively.
Equation 02: