Magnetic, Density Interface And The Polygon Model The Joint Inversion Of Gravity And Magnetic

Inversion problem is the core of geophysics. As we know, the inversion of geophysics is ill-posed, and it usually has the following three problems: First, the solution does't exist; Second, the solution is not unique; Third ,the solution is unstable. In order to solve them, most geophysicists tried their best and did lots of theoretical research and model tests. For the first and the last one, people give a solution which is different from the classical meaning to the inversion results to get the conditionally well posed solutions and so the problems are preliminarily solved. But for the non-uniqueness of solutions, geophysicists recognize that:"non-uniqueness is inherent in geophysical inversion problem."It would be practically impossible to completely eliminate the effects of the non-uniqueness problem in inversion, and we could only reduce the non uniqueness of solutions to some degree through some specific methods, thus improve the reliability. From the current theory support and technical methods, there are two ways to reduce the non uniqueness of solutions: one is to use the known geological and geophysical data to constraint the parameters, and rule out the solutions that not meet with the constraint conditions. The other is to use comprehensive interpretation, make full use of various kinds of geological and geophysical data, constraint each other, complement each other, inverse jointly, so as to achieve the purpose of reduction of the non uniqueness of solutions and improving the reliability.Joint inversion, is to put two or more geophysical data sets into the same one to inverse at the same time. Generally, different data sets are inverted respectively, and then make the further study of interpretation. However, in this article, we normalize the various data sets using the normalized root mean square method, put them together into one set, and then use single inversion method to inverse. Geology model which is compatible with both of the data sets is obtained, thus the non uniqueness of solutions is reducted and the reliability is improved. For example, two kinds of data sets respectively meet the first kind of operator equations: A1 X = b1; A2 X = b2, where X is the unknown set of feature elements of filed sources and X∈H, and bi is the known observation of potential fields and bi∈H 2(i = 1,2). The inversion results should be the intersection of the two solutions which are respectively obtained from inversion of each kind of geological data. This is one reason why joint inversion can reduct the non uniqueness of solutions and improve the reliability. Besides, we know that the sensitivities of different geological data sets to the parameters are different. For example, the changes with depth of the magnitude data are larger than that of the gravity data, which demonstrates the reason why data sets can complement each other, and the results are much better, and have high resolution.Based on the importance of interface inversion in the study of regional geology, the author researches a way to inverse the single two-dimensional gravity and magnetic interface, which is called joint generalized linear inversion of gravity and magnetic. The result shows that joint inversion has some advantages in reducing the non uniqueness and obtaining solution which meet both kinds of data. It's an efficient way to the reduction of the non uniqueness. In view of the current situation that most interface inversion methods are limited by the known average depth Z 0, the author proposes a way to implement iterative inversion of Z 0 by using the known depth to constraint, uses the plate equation to carry out iterative inversion of Z 0 without any prior knowledge, and finally the solutions are improved. For the generalized linear inversion, the author proposes using the values which are multiples of minimum singular value as the regularized parameter, so as to avoid arbitrarily giving the parameters and finally improve the stability of solutions. In order to overcome the ill-conditioned equations resulted from disequilibrium of partitioned matrix in joint inversion, the author uses the root-mean-square defined by the following equation to segmentation normalization. This article will do some analysis and discussions relating to the above problems and linear inverse problem.