Abstarct: The microgravimetry method, which is one of the potential field methods, is used in the exploration of mineral resources and subsurface structures, such as void detection, and has appropriate accuracy and is a non-destructive method. Quantitative interpretation methods are used to obtain the geometry, depth, surface and deep expansion of the mineral resource. Gravity data modeling is one of these methods and is done in two ways: forward and inverse modeling. Modeling of potential field data is usually done on a regular network or mesh, and depending on the type of method and data volume, it is time-consuming in most cases, and increasing the speed of modeling is one of the concerns of researchers in this field. In inverse problems without applying compression constraints; Usually, smooth models are produced and the edges of anomalies are not obvious and are not suitable for revealing many geological features. For this purpose, in this research, in order to better highlight the edges of subsurface structures and mineral resources by the minimum support stabilizer function; The compression constraint was applied in the focusing inversion of the gravity data. One of the methods of solving the focusing inverse problem is the reweighted regularized conjugate gradient method that has iteration steps. One of the main disadvantages of the focusing inverse problems is the time-consuming solution process, one part of which is related to the calculation of the kernel matrix and the other part is related to the inversion process (algorithm). In this thesis, it was proposed to improve the calculation speed of the kernel matrix at the same time with parallel programming and the combination of Plouff's analytical method and point mass numerical method. By implementing this method; The time to solve the kernel matrix in synthetic and real gravity data was improved by about 90%. In the process of solving the inverse problem, using different methods of calculating the conjugate gradient parameter, such as Fletcher, PRP, CD, TAS, HS, NPRP, DPRP, ZA, HSMR, DY, NHMR and the new SM method; The degree of improvement on the reweighted regularized conjugate gradient algorithm and the degree of influence on the speed of solving the inverse problem were investigated. The reweighted regularized conjugate gradient algorithm with different parameters is applied to two synthetic data and two real data sets, i.e. the gravity data of the Ovid nickel, cobalt and copper mine in Canada and the gravity data of a tunnel in the Cloud Chamber area of Yucca Flat, USA. The results show that while having the appropriate accuracy, the speed of solving the inverse problem has increased by more than 30% compared to the basis of Fletcher's method, and convergence has been reached with less iteration. The results of using the improved algorithm for real data modeling show that the PRP, CD, TAS and SM methods achieve the desired solution compared to the conjugate gradient parameter of the Fletcher method, while the results of the focusing inverse modeling were similar, they worked more than 27% faster and converged to the solution with fewer iteration steps. DY and NHMR methods did not reach the misfit value of 0.03 and continued up to the maximum number of iterations, i.e. 1000 times, but did not converge to the solution. The reweighted regularized conjugate gradient algorithm with SM conjugate gradient parameter has the best performance among other parameters, and the convergence of the solution has been done with appropriate accuracy in the lowest iteration stage, and the model result is in complete agreement with the structure of the mineral source and the subsurface obtained from external data such as drilling.