A Study On Integrated Gravity And Gravity Gradient Data In Inversion

The processing and interpretation of gravity data plays an important role in geophysics. In recent years, with the development of high-performance moving-platform full tensor gradiometry(FTG) systems, gravity gradient data also becomes more and more important in geophysical prospecting. In theory,gravity data are computed by taking the z-derivative of potential field, gravity gradient data are computed by taking the second order derivative of the potential field in three directions. During this process, the part of low frequency information are lost, the high frequency ingromation are enhanced. We made a comparison between gravity data and gravity gradient data. The results showed that gravity data contains more low frequency information, and gravity gradient data contains more high frequency information. So, gravity and gravity gradient data can complement each other. Integrated gravity and gravity gradient data in inversion, the recovered model was more reasonable. The non-uniqueness of the inverse problem can also be reduced. Based on this, we made a study on integrated gravity and gravity gradient data in inversion.We first made an analysis on gravity and gravity gradient data in frequency domain. We deduced the expressions of gravity and gravity gradient data in frequency domain. The relationships between different gravity gradient components have been displayed. We concluded that zzg component contains more information than other components. We displayed the amplitude spectrum of zg and zzg to explore the changes of these two components with depth increasing. The zg and zzg data were applied in inversion methods, the results showed that the resolution of zg inversion was higher than zzg inversion in deep part, while zzg data was more sensitivity to shallow anomalous. Besides, we proposed reweighted inversion methods. With this, we combined the depth weighting functional in the misfit functional. Without other constraints, we applied the method to gravity and gravity gradient components separately. The results showed the influence of different components in inversion results.Then, we made a discussion on integrated gravity and gravity gradient inversion. Compared with single component inversion, multiple components inversion requires more computing time and storages. First, before we applied the inversion method to data, we needed to calculate the sensitivity matrixs of different components. Since the number of components was increased, the computing time and storage to get the sensitivity matrixs were also increased. To solve this problem, we proposed a method, based on forward formulas of gravity and gravity gradient components, to get the sensitivity matrix, the computing time was reduced. We also showed a strategy to store sensitivity matrixs. It saves a lot of storages.Then, we made a discussion on the depth weighting functional. We gave a list of several depth weighting functional, and the functional based on the depth of the anomalous bodies was chosen. Because this functional was the same for different data, so it was suitable for integrated gravity and gravity gradient inversion. We displayed the formulas of reweighted inversion with smoothness operator. Based on this, we explored the relationship of the depth weighting functional with the depth of anomalous body. We found that, even though the estimate depth was not in accordance with the true depth, the inversion result was reasonable. The depth weighting functional was applied in inversion methods. We made a comparison between this weighting functional and the depth weighting functional based on sensitivity matrix, the results showed that this weighting functional can combine depth information in inversion, the resolution of the inversion results was improved.Next, we discussed the stabilizer functional and the optimization algorithm we adopted here. For different types of geologic bodies, different stabilizer functional should be chosen. Here, we choosed the minimum gradient support functional. This functional was suitable for anomalous bodies with sharp boundaries. We adopted non-linear conjugate gradient algorithm to solve the inverse problems. It was suitable to solve large scale inverse problems. It has been widely used in electromagnetic inversion, but seldom been used in gravity and gravity gradient inversion. We made a comparison between non-linear conjugate gradient algorithm and BFGS quasi-newton algorithm. The results showed that the BFGS quasi-newton algorithm converges faster than the non-linear conjugate gradient algorithm. However, the computing time and the requirement for storages of non-linear conjugate gradient algorithm are far less than the BFGS quasi-newton algorithm. Also, to combine density constraints in inversion, we choose inequality constraints during the inversion procedure. In this way, the stability of the inversion procedure would not be influenced.We built a model with multiple anomalous bodies. Made a comparison between different gravity gradient components inversion, the results showed that, combine more components in inversion, the resolution of the inversion results were improved. If there are too many components, the data was better fitted, the inversion result was more focused, while the consistency of the recovered model with the true model was decreased. This requires additional information to constraint the inversion procedure. We also gave the best component combinations based on the inversion results and the most efficient component combinations.Then, we made a comparison between the gravity gradient inversion and integrated gravity and gravity gradient inversion. The result showed that the recovered model was consistent with each other. For some anomalous bodies, the resolution was improved in integrated gravity and gravity gradient inversion.For anomalous bodies at different depths, we introduced the spatial gradient weighting functional. We combined more information in inversion with this functional. The resolution of the recovered model was improved.At last, the method was applied to real data from Vinton salt dome, Louisiana, USA. Through 3-D inversion results, we could deduce the distribution of the salt dome. We found that zg |xyg |xzg |yyg |yzg |zzg inversion result was the best. We displayed the 3-D map of the inversion result. It was accordance to the prior works. The inversion result is reasonable.