2D modeling of gravity data with the compact inversion method and density variation as a stopping criterion

Potential field data (gravity and magnetic data) are usually analyzed by means of lineartransformations, spectral methods, inversion techniques and analytic signal methods.Nowadays, there are diverse methods of modeling the gravity data, but each has some limitations. One of the limitations of these methods is the assumption of a simple shapefor buried structures, whereas the actual shape could be entirely different. The presentstudy uses two-dimensional 4-sided polygons (prisms) to resolve these limitations,because with these it is possible to make any shape for an unknown underground structure by arranging these prisms.Within the context of this study, the 2D inversion method proposed by Last and Kubik(1983) is reused. For this purpose, a Matlab-based 2D inversion code was developed. Thiscode uses an iterative least squares procedure, which allows the weights to depend on the densities of the previous iteration. Therefore, the solution minimizes both the area of the underground structures or deposits and the weighted sum of squared residuals.According to Last and Kubik, the iterative procedure stops when a minimum area ofthe density distribution is reached. The stopping criteria in inversion algorithms areusually based on the fit between the observed data and theoretical data produced by theproposed model. Typically, a misfit function estimator is used.In the inversion of potential field data, the number of observations is often less thanthe number of unknowns (underdetermined problem). To overcome this problem, thisstudy uses a new method proposed by Ekinci, wherein the density variation is used as anew stopping criterion to find the required number of iterations for convergence themodel. The focusing inversion method proposed by Last and Kubik was modified in orderto produce a compact final model. For this model, the difference between the blockdensities at the last successive iteration is minimal. This method minimizes the volume ofdeposit, which is equivalent to maximizing its compactness. Here, the method for noisefree and noise-corruption synthetic data was used and after obtaining satisfactory results it was applied to real data.The Dehloran Bitumen map in Iran is chosen as a real data application. The area underconsideration is located in the Zagros tectonic zone, in western Iran, where a search forBitumen is under way. Layers of medium bedded limestone with intermediate marllimestoneare the dominant formations in the area, and the hydrocarbon zone is one of themost important characteristics of the area.By using the method for noise-free and noise-corruption synthetic data, the presentstudy produced a program for the Dehloran Bitumen map. Anomaly modeling was usedbecause the anomaly value of the cross section, which is taken from the gravity anomalymap of Dehloran Bitumen, is very close to those obtained from this method.The final result of these methods shows that the deposit starts from the depth of 10meters to about 35 meters. This modeling was a satisfactory representation of the resultsof actual drilling in the region. The results of the drillings show that the lowest depth ofthe deposit varies from 7 to 10 meters. This 2D modeling of gravity data with the compact inversion method and density variation can easily be applied for gravity, microgravity and magnetic data.