Linear And Non-linear Inversion Methods Research On Direct Current IP Measurements

Theory and methods of geophysical inversion developed up to now, agglomerating the intelligence of many scientists and practicers, and it had became a valid tool that people revealed the profound mystery of the Earth. Geophysical inversion was an important section of geophysical branch of knowledge, and it had become a core technique of the geophysical data processing, the inverted result provided a beneficial basis for the geological interpretation. Direct current induced polarization method was an important branch of geophysical exploration methods, which played an important part in the energy, mineral resources and engineering exploration. In recent years, with the development of the high density and high precision instrument of electrical method, the applied field of electrical surveying is in continuous evolution, the survey space is gradually expanding from ground to some complex quomodo of underwater, sap and borehole etc. At the same time, people's request for the exploration and interpretation precision is also raising continuously, so, the inversion acting as a core technique of data processing of direct current induced polarization, which will be also facing with new challenge. In this dissertation, we will carry on an investigation in the linear and nonlinear inversion methods of direct current induced polarization measurements, emphasizing to study how to improve the resolution and reduce the multisolution of inverted result, and how to enhance the stabilization and robustness etc.In the chapter 2, firstly, the concept of regularization and idea of regulation technique were introduced beginning with the generalized linear inversion equation of least squares method. Then, we studied the regularization techniques of generalized linear inversion from several aspects, for instance, the choice of regularization parameter, the design of stabilizing functionals, the introduce of some prior restriction and the modification of iteration step etc, whicd can improve the ill-posedness of inversion equation and restrain the non-stability of inversion process and heighten the resolution of inversion result finally.In the chapter 3, we considered that geophysical exploration work was often influenced by the non-Gaussian noise and made the data set of acquisition contain some false data, it could lead to the artifact of inversion and the mistake of interpretation if the data set containing non-Gaussian noise was inverted using generalized linear inversion method based on the least squares principle. Thereby we put forward the optimized inversion method using mixed norm, that is to say, according to the good or poor quality of observed data, the data and model space is measured by different norm, which can gain the ends of inhibiting the disturbance and giving prominence to the useful abnormity. Because of the introduction of mixed norm, which increases the complexity of linear inversion equation, it is more difficult to solve the linear equation than ever. Therefore the problem was settled by normalizing the weighted matrix and solving the linear inversion equation of mixed norm using the iteratively reweighted damping conjugate gradient algorithm. At last, we verified that the optimized inversion method based on mixed norm is workable and effective through inverting the simulated resistivity data containing and not containing abrupt noise.In the chapter 4, we discussed the generalized linear inversion method of direct current IP data from the angle of the least squares method. The computed speed of inversion can be greatly raised by calculating the partial derivatives matrix combining the reciprocity principle with Broyden's quasi-Newton method. Then we solved and improved some technique problems concerning dicrect current IP data inversion for three observed methods. For the 2D inversion of vertical IP sounding data, we studied how to raise the precision of forward and resolution of inversion from three aspects of using dual-grid system, modifing the forward error and giving the initial inversion model. For the least squares time-lapse inversion of resistivity data, we put forward a new method to invert all data sets collected at different time simultaneously, namely get all earth models of different time through only one inversion process. In the inversion, we combined all data sets acquired at different time by introducing the stability functional in time and space to objective function, which could greatly improve the stability and reduced the multi-solution. For the 3D inversion of direct current IP data in complex earth condition, we can say that it is a complex systemic engeering being involved to many important taches, for example, the elevation interpolation of large numbers of gridding nodes on the rolling ground, gridding divition of underground, the storage of rigid matrix elements and the solution of its equation in the forward and the precision and efficiency of forward simulation etc.We studied these problems one by one, which made some problems concerning 3D inversion of direct current IP data be improved further. At last, we verified the effectiveness of method by means of inverting the dicrect current IP data of 3D rolling terrain.In the chapter 5, linear and quasi-linear inversion method can only get the local optimum solution because the geophysical inverse problems are of the characters of multi-parameters, multi-extrema and non-linearity, and the inversion result is related to the initial modeling, we can get good solution if the initial model choose is suitable, otherwise can lead to the artifact of inversion. Whereas the global optimum inversion method based on random process is not limited by the fixed rule, it can freely search the optimized solution in the model space, this powerfully searching ability ensures that the inversion solution basically is the global optimum or hypo-optimum solution. This chapter mainly studied the simulated annealing algorithm and genetic algorithm belonging to non-linear global optimum method. We deeply studied the mixed methods of combining the global with the global and the global with the global optimum method on the foundation of simply introducing the methods amd principles, the mixed method can raise the global searching ability of algorithm. At last, we verified the effectiveness of mixed inversion method by inverting the dicrect current IP sounding data.