Magnetic data inversion has a prominent role in geo-structural investigations. As lots of geological structures, such as faults, dykes, contacts etc are elongated in a specific direction, 2D algorithms became widespread during the previous years. Modifying the existing algorithms on 3D data inversion, a method has been proposed for 2D inversion of profile magnetic data, based on the physical parameter distribution method. The subsurface is divided into a large number of infinitely long horizontal prisms, with square cross section and unknown susceptibilities.
A multi-term objective function is defined and an under-determined system of equation is solved to minimize it. The solution is the magnetic susceptibility of the prisms inside the earth. The regularization parameter makes a trade-off between the data error term and regularization term. The regularization term contains a model length term which defines the total model area in 2D problems and a first order difference model which make sure that the reconstructed model is smooth. Weighting coefficients have been considered for both of these terms to apply smallness as well as smoothness for the recovered model in different directions.
To use the extra information that may be available in the area such as drilling works, other geophysical studies and also the interpreter's imagination of the geological structures, weighting matrices have been inserted in the objective function. As there is no physical and geological meaning to the negative susceptibility, we used a positivity constraint inside the inversion equations to prevent negative values for susceptibility. Having all of these in hand, we expect the final model have a reasonable shape and more satisfy the true earth. In the absence of any extra information about the geological structure of the studied area, acceptable solutions are also obtained and this is the main feature of the physical distribution method. The algorithm uses a Newton step to solve the objective function minimization.
A MATLAB code was prepared to implement the algorithm. As the forward mapping matrix is sometimes very large, a pre-conditioned conjugate gradient routine was used as the main solver for the linear equation that appeared in the Newton minimization. It apparently speeds up the algorithm. The algorithm was tested on two synthetic examples, a dipped dyke and a faulted dyke model. The results show that the method is capable of generating smooth presentation of geological structures. To apply the algorithm on real data, a long aeromagnetic flight line data located at Makran was inverted to model geological structures in the area. Makran has been detected to be an active subduction zone in SE Iran. Subducting the Oman oceanic crust beneath the Lut continental lithosphere has made a typical Trench-Arc complex in the area. The main target along this profile was the Jamurian Depression basin which has been proved to be a fore-arc basin and its magnetic basement has been covered by thick sedimentary rocks.
Ophiolite and ultramafic rock outcrops at the Makran ranges which have made high frequency anomalies, showed that the basement might have the same composition. The results prove that there is a trapped oceanic crust remnant at the basement of the Jazmurian Depression. Geological hypothesis suggest that this basement was made under an extensional regime before or at the time of the subduction.