The nonlinear modelling of gravity data using estimated depths from all s-values for each shape factor

An inversion algorithm was developed to estimate the depth and the associated model parameters of the anomalous bodies from the gravity measured data (Essa، 2011). These parameters including geometrical and physical ones are defind as the amplitude coefficient and will be estimated through the method which is defined in this paper. One of the most important parameters is the depth of the causative bodies. The problem of depth (z) estimation from the observed data was transformed into a nonlinear equation of the form F (z) = 0. This equation was then solved for z by minimizing an objective functional in the least-squares sense through standard iterative methods. These standard iterative methods can solve the problem very readily and in the shortest time. However other numerical methods can also be used for solving the equation and the more accurate metod gives more precise results. Therefore solving the nonlinear equation is a vital step in obtaining the more precise results. Using the estimated depth، the amplitude coefficient was computed from the measured gravity data. The method was based on determining the root mean square (RMS) of the depths estimated by using all s-values for each shape factor. The primary shape factors for these simple geometrical shapes are defines as the a priori information and are assumed known before the process. The minimum RMS was used as a criterion for estimating the correct shape and depth of the buried structure. When the correct shape factor was used، the RMS of the depths is less than the RMS computed using wrong shape factors. These correct shape factors are actually estimated through the method and are different from the prior ones and reflect the closest shape to the real shape of the subsurface anomaly. In other words، the RMS of the correct shape factor is the least one. The proposed approach was applicable to a class of geometrically simple anomalous bodies، such as the semi-infinite vertical cylinder، the horizontal cylinder and the sphere which can simulate the shape of the most causative bodies. The method is tested for synthetic models with and without random noise. The method gives precise results for synthetic models contaminated by 5 to 10 per cent random noise which is quite acceptable and promising. This technique was also successfully applied to real data for mineral exploration. The applied real data belongs to an area with hilly topography located in the Fars Province close to the Abadeh city where the barite deposite is under exploration. The method is used for a profile of real data that is provided from the residual anomalies and passed from the main detected positive anomaly in the area. It was found that the estimated depths and the associated model parametrers were in good agreement with the results obtained through Euler method and drilling. The simple equations of the method and the precise results show its usefulness for obtaining the unknown parameters of causative bodies in gravity data interpretation. Therefore، the method is quite promising in obtaining the unknowmn parameters for different causative bodies and specially in cases that the shape of the anomaly is close to sphere and cylinder. This is usually the case in ore bodies detection and delineation.