| The earth’s gravity is the resultant force of the earth’s gravity and the inertial centrifugal force caused by the earth’s rotation,which all objects on the earth’s surface are affected by.Uneven material density in the underground can cause gravity changes on the earth’s surface(ie,gravity anomaly).Study the law of gravity changes with time and space,which can be used to analyze the change characteristics of material density in the underground to understand and infer the internal structure of the earth,geodynamic characteristics,etc.This has important scientific significance for researching earth tectonics,resource exploration,engineering construction,and disaster prevention.Gravity forward modeling is the basis of gravity research,and the forward modeling in the space domain is to derive the formula for calculating various types of gravity anomalies(and their derivatives)based on the Cartesian coordinate system.The forward modeling in the wavenumber domain is to convert the calculation to the wavenumber domain through Fourier transform to achieve the purpose of calculating the gravity anomaly(and its derivatives)of the underground geological body.Compared with gravity forward modeling in the space domain,gravity forward modeling in the wavenumber domain converts complex convolution integrals into simple product calculations,which greatly simplifies the calculation process,improves calculation efficiency,and solves some complexities that are extremely difficult to calculate in the space domain problem.In this paper,based on the characteristics of fast calculation in the wavenumber domain,the gravity forward and inversion of the regular model(2D&3D),interface model,and potential field imaging are systematically studied.The wavenumber domain spectral characteristics of different types of anomalies in the regular model are analyzed.A joint spectrum inversion method is proposed.The calculation of gravity forward and inversion with different density distributions in the interface model is improved.The iterative calculation of 3D density imaging in potential field imaging is derived.A preliminary system for gravity forward and inversion in the wavenumber domain was built.This lays the foundation for the systematic and comprehensive study of the forward and inverse method of gravity in the wavenumber domain.Different methods in the wavenumber domain gravity forward and inversion system are applied to actual data,including determining the location of the target layer in the Wuqing Sag,inverting the undulations of the Moho on the Qinghai-Tibet Plateau,calculating the 3D density structure of the Decorah area,and inverting the three-dimensional crust of the QinghaiTibet Plateau density structure,etc.The specific content of this paper mainly includes the following aspects:(1)The wavenumber domain gravity anomaly/gravity gradient forward calculation formula of the 2D body and 3D body model is derived.The characteristics of the spectrum curve of the gravity anomaly obtained by the gravity forward modeling of the regular model in the wavenumber domain,and the relationship with the model parameters are systematically analyzed.According to the relationship between the gravity anomaly spectrum and model parameters,a variety of gravity anomaly spectrum inversion methods have been derived,including amplitude spectrum inversion,phase spectrum inversion,power spectrum inversion,moment spectrum inversion,etc.A joint inversion method in the wavenumber domain is proposed,which can be used to accurately invert the parameters of underground geological body.The wavenumber domain regular model gravity anomaly forward and inversion method is used to study the target formation in Wuqing Depression.The corresponding relationship between gravity/gravity gradient anomaly and the model and the characteristics of the gravity/gravity gradient anomaly spectrum are analyzed.The conversion relationship and superposition relationship of the gravity/gravity gradient anomaly in the space domain and the wavenumber domain have been verified,which provides basic theoretical support for the study of gravity/gravity gradient inversion methods in the wavenumber domain.(2)Combined with the Bott iterative method,a hybrid iterative method of space-wavenumber domain interface inversion is proposed.The forward equation of the interface model,which is stable in iteration and quickly calculated,is derived.The wavenumber domain gravity forward modeling and Bott iterative inversion formulas of the interface model with different density distribution characteristics are summarized and analyzed.The gravity anomaly inversion method of the interface model in the wavenumber domain is applied to the depth inversion of the Moho on the Qinghai-Tibet Plateau,which provides support for understanding the deep structure of the QinghaiTibet Plateau and conducting geodynamic analysis.(3)The calculation formula for 3D density imaging of gravity/gravity gradient in the wavenumber domain is derived.This method takes full advantage of the fast calculation speed in the wavenumber domain,improves the calculation efficiency,and is used for accurate three-dimensional underground density distribution structures.The noise immunity of the wavenumber domain gravity/gravity gradient 3D density imaging method is analyzed.This method is used for the inversion of the theoretical model to obtain density imaging results consistent with the initial model.This method was applied in the Decorah area and the Qinghai-Tibet Plateau.Using the gravity/gravity gradient anomaly of the crust after field separation,3D density imaging is performed to obtain the 3D density distribution structure of the Qinghai-Tibet Plateau within the range of 0-80km.Combined with the results of the Moho surface inversion,the subterranean structure and the geodynamic processes of the Qinghai-Tibet Plateau have been more deeply understood. |
