Study On The 3D Gravity Inversion Of Density Interface Relief In Spatial Domain

Gravity exploration method is one of the earliest used geophysical prospecting methods and it has the advantages of comparatively economical efficiency, high lateral resolution, great exploration depth and quickly getting information in one region. Therefore, as an important way to understand the structure of interior layers of the earth, the density interface inversion has long been the main content of the gravity research. Study on density interface inversion method not only can solve the problem of geological interface relief, playing an important role in the regional geological survey, minerals and energy exploration, but also can promote the progress of gravity inversion theory research. Consequently, researching of density interface inversion method has important practical value and theoretical significance.Density interface inversion method can be divided into two categories: frequency domain method and spatial domain method. Most of the existed density interface inversion methods can only be used to obtain down-warped interface. Nonlinear inversion method, which is developed later, can be used to inverse rifted interface under some special functions. However, there are just a few 2D methods to be used to get a complex shape interface that consist of down-warped interface and rifted interface simultaneously, for instance, the basement of a sedimentary basin controlled by faults. There is no 3D inversion method for these complex shape interfaces. This paper has studied on the three dimension gravity forward and inversion method of complex shape density interface in spatial domain and researched the related technical measures. Tests conducted with synthetic data and field data confirm the correctness and validity of the method. The main research results and conclusions are as follows:(1) This paper has used the finite element method to calculate the gravity of a density interface in spatial domain and studied the measures of reduce calculation in the case of guaranteeing a certain precision. Model testing results show that these measures are aorrect and effective. The ideal of the finite element method is dividing the density body into many small units(finite element), such as line element and point element(vertical prism), and forward calculating the gravity of each unit respectively, then getting the total response of gravity. Its advantage is easier variable density forward. The line element method has the advantages of small amount of calculation, but it has relatively low calculation accuracy. In contrast, the point element method has higher calculation accuracy but a large calculating quantity. This paper has developed a measure that calculating the gravity using point element method near the calculating point and using line element method in other region, which not only guarantees the calculation precision but also reduces computation cost.(2) The nonlinear inversion method is adopted for 3D inversion of complex shape density interface in spatial domain. The result of inversion is determined by the model constraint function in the objective function of nonlinear inversion method. Model constraint functions are often in the form of norm and can be built using any kind of norms. This paper studies how to choose the objective function for down-warped(continuous) interface or rifted(discontinuous) interface and has formed three main points through model tests of different objective functions under different constraint conditions. Firstly, model constraint functions based on the gradient of model vector ?m are more general than those based on the model vector m and have higher stability. Secondly, Using L1-norm and L0-norm could obtain rifted density interface when reasonably choosing parameter. The L1-norm has higher stability, which can better be used to inverse most faulted density interfaces. The L0-norm has a poor stability and the inversion result is a “completely” nonsmooth shape rifted interface in 2D situation, which also can be used to obtain a narrow rifted interface like oceanic trench, trough, etc. in 3D inversion. The L2-norm only can be used to get a smooth density interface, but its outstanding advantage is more stable. L2-norm can make the inversion converge rapidly whether the constraint function is about m or ?m. The biggest advantage of Ekblom norm is its convenience of selecting the form of norm for calculation. Ekblom norm is similar to infinite norm when the p value is bigger. The inversion result manifests a sawtooth shaped nonsmooth form under this restriction. It can be applied successfully in inversing narrow rifted interface as well as the L0-norm. But the result may be a down-warped form in some deeper region. Thirdly, most of the constraint functions or most of the inversion methods can be used to get the whole relief form of density interface. For more sophisticated density interface, we can only obtain an approximate fuzzy shape. The difficulty of density interface inversion is getting the local shape of interface successfully.(3) This paper has researched the establishing of objective function for complex shape density interface(down-warped interface and rifted interface coexist simutaneously) inversion and has solved the problem of three-dimensional inversion of complex shape density interface by using L1-norm and L2-norm as constraint and using NVDR_THDR(the normalized vertical derivative of the total horizontal derivative) potential field edge recognition method of gravity as weight of these two norm constraint functions. Furthermore, using the inversion result of direct iteration method as the initial value can improve the complex shape density interface inversion efficiency. At the beginning of inversion, the regularization parameter is proposed to set to one in order to ensure good effect and stability of inversion. This measure solves the problem of choosing the value of regularization parameter. For those lateral complex density interface, we can improve the transverse resolution of inversion results by using the NVDR_THDR of the inversion result using direct inversion method instead of NVDR_THDR of gravity anomaly as constraint. In addition, the best strategy to invert those complex density interfaces that lateral composed by completely nonsmooth rifted interfaces and down-warped interfaces is partitioned inversion. If there has no other information as basis of judging the types of interface, we can use the difference between the inversion results using L1-norm as constraint and the results of L2-norm to get the locations of different interface.(4) This paper has obtained gravity anomalies caused by basement relief of Wan’an basin by processing the free air gravity data in the area. Using the gravity for inversion, we get the basement relief of Wan’an basin and confirm its correctness by using seismic data. We redivide the tectonic units of the Wan’an Basin based on the inversion result and the existing tectonic division of the basin. The research results can provide basic data for researching about basin tectonic division, oil and gas exploration and so on.