Forward And Inversion Method Of Large-scale Gravity Data Based On Fast Multipole Algorithm

Forward and inversion are the core parts in the processing and interpretation of gravity data. With the improvement of the degree of prospecting, its difficulty has increased gradually as well. In order to improve the prospecting precision, more datasets and more sophisticated processing and inversion methods have become the research trend in the area of exploration geophysics. Detailed inversion of large-scale gravity data consumes large computer memory and a great deal of time. Moreover,various constraints, which are incorporated to overcome the inherent multi-solutions mathematically, lead to the increasement of calculation. The work discussed in this dissertation focuses on the detailed inversion of large-scale gravity data, aims to form an integrated and effective inversion framework. We hope to promote further practicality of physical inversion of gravity data. The main contents of this thesis are as follows:1. Gravity forward of density model based on the fast multipole method was proposed. The mathematical foundation of the fast multipole method was introduced firstly. The core theorems and derivation process were described in the appendix part.Then,we analyzed the problem exists in the application of the fast multipole method for gravity forward modelling. Based on the analysis, the black-box fast multipole method was introduced which is not dependent on the mathematical expansion of the integral equation. The black-box fast multipole method was then utilized for the gravity forward problem. Synthetical model test was established to verify effectiveness of the forward method.2. Basic method of the constrained physical inversion of gravity data was studied.The objective function was first defined by data misfit function. The model constraint items were incorporated by regularization items. These constraints stabilized the inversion process and improved the inversion result including depth-weighting,physical boundary and focus function. Several 2D and 3D synthetical density models were established to test the constrained physical inversion algorithm. These theories and programs lay the foundation for the detailed inversion of large-scale gravity data.3.An integrated algorithm for the detailed inversion of large-scale gravity data based on fast multipole method was proposed. The integrated framework consists of three parts: the fast multipole method, data adaptive sampling and data space inversion algorithm. Incorporation of the fast multipole method accelerates the calculation of forward kernel matrix which accelerates the inversion computation. The data adaptive sampling technique can reduce the amount of data pointsgreatly. Here, a new criterion for the determination of sampling parameters was proposed. The dataspace inversion algorithm was utilized and the preconditioned conjugate gradient method was utilized to solve nonlinear inversion equations. During this process,damping factor was suggested to incorporated to stable the iterate process. In addition,certain guidelines are used for selection of the iteration step length and avoid the iteration divergence. In the inversion algorithm, depth weighing factor is used to improve depth resolution of potential field inversion. The sparseness constraint is incorporated by the Cauchy norm. The bound constraint is incorporated by the transfer function to limit the inverted model parameters in a reliable range. A combined density model was established to test the integrated inversion algorithm.Model test denoted that the integrated inversion algorithm can improve the inversion efficiency greatly.