مدل‌سازی سه‌بُعدی داده‌های مغناطیسی معدن مروارید زنجان و اعتبارسنجی آن با داده‌های حفاری اکتشافی

Magnetic survey is one of the most important geophysical methods extensively used in mineral explorations. Therefore, the interpretation and modeling of this data is very important before doing any drilling exploration. Modeling this data makes it possible to choose the best position for drilling. In this study, the magnetic data of Morvarid Zanjan deposit has been modeled and a 3D model of the magnetic susceptibility has been achieved. The results were compared with the real model created with drilling exploration data.
    There are many inversion algorithms for modeling the magnetic data. However, a principal difficulty with the inversion of the potential data is the inherent nonuniqueness. By Gauss’ theorem, if the field distribution is known only on a bounding surface, there are infinitely many equivalent source distributions inside the boundary that can produce the known field. A second source for nonuniqueness is the fact that the magnetic observations are finite in number and are inaccurate. If there exists one model that reproduces the data, there will be other models that will reproduce the data to the same degree of accuracy.
    Faced with this extreme nonuniqueness, authors have mainly taken two approaches in the inversion of magnetic data. The first one is the parametric inversion in which the parameters of a few geometrically simple bodies are sought in a nonlinear inversion and the values are found by solving an overdetermined problem. This methodology is suited for anomalies known to be generated by simple causative bodies, but it requires a great deal of a priori knowledge about the source expressed in the form of an initial parameterization, an initial guess for the parameter values, and limits on the susceptibility allowed.
    In the second approach to inverting magnetic data, the earth is divided into a large number of cells of fixed size but of unknown susceptibility. Nonuniqueness of the solution is recognized and the algorithm produces a single model by minimizing an objective function of the model subject to fitting the data. Based on the second approach, Li and Oldenburg (1996) formed a multicomponent objective function that had the flexibility to generate different types of models. The objective function incorporates an optional reference model so that the constructed model is close to that. It penalizes roughness in three spatial directions, and it has a depth weighting designed to distribute the susceptibility with depth. Because there is no depth resolution inherent in the magnetic field data, the recovered model is occurred  near the surface and takes away from its original position. The depth weighting function helps to locate the recovered model in its real position. Li and Oldenburg (1996, 2000) proposed relations for the depth weighting function. Additional 3-D weighting functions in the objective function can be used to incorporate further information about the model. The user can incorporate other information about the inversion model. The information might be available from other geophysical surveys, geological data, or the interpreter’s qualitative or quantitative understanding of the geologic structure and its relation to the magnetic susceptibility.
    In principle, this algorithm can be applied to large-scale data. Numerically, however, the computational complexity increases rapidly with the increasing size of the problem and the solution of a large-scale inversion of magnetic data is faced with two major obstacles. The first one is the large amount of computer memory required for storing the sensitivity matrix. And the second obstacle is the large amount of CPU time required for the application of the dense sensitivity matrix to vectors. These two factors directly limit the size of practically solvable problems.  To encounter these obstacles, Li and Oldenburg (2003) used the fast wavelet transform along with thresholding the small wavelet coefficients to form a sparse representation of the sensitivity matrix. The reduced size of the resultant matrix allows the solution of large problems that are otherwise intractable. The compressed matrix is used to carry out fast forward modeling by performing matrix vector multiplications in the wavelet domain.
    The algorithm used in this study is based on the mentioned multicomponent objective function and the fast wavelet transform is used to make a sparse representation of the sensitivity matrix to reduce the time and computer memory required for inversion.