Research On Transformations Of Potential Field Data For Aeromagnetic And Airborne Gravity Survey

Aeromagnetic and airborne gravity survey may be the most effective method to obtain high accuracy information of gravity and magnetic field.Aeromagnetic and airborne gravity technology is one of the key technologies of breakthrough and predominance in the high-tech deployment of deep-sea and deep-ground strategy.However aeromagnetic and airborne gravity measuring can only provide part of characterization information of gravity field and magnetic field,transformations of potential field for aeromagnetic and airborne gravity survey are required by researchers for converting the observation to other parameters of potential field or the field observed under the other measuring condition,which is the key to data processing for aeromagnetic and airborne gravity survey.The purpose of this research project was to research the methods of high-precision potential field transformations according to the practical considerations of aerogeophysical measurements.In the thesis,the author carried out research on expression of potential field transformations in matrices scheme,the regularization method of potential field transformations,multiparameter joint transformation problem of potential field data,and the processing for filling grid dummies and data expanding.The main results from this thesis are summarized as follows.1.Based on the analysed of the history development of the potential field transformations,the author firmly believes that the key to resolving large-scale potential field transformations of aeromagnetic and airborne gravity data must employ fast Fourier transform method.To solve the problems of unstable potential fields transformations and multiparameter joint transformation is the main limit for the further application of aeromagnetic and airborne gravity data.In addition,processing of filling grid dummies and data expanding will significantly affect the accuracy and effect of potential field data transformations.Based on the above considerations,the author puts the technical route for the research of transformations of potential field data for aeromagnetic and airborne gravity survey.2.Based on the potential theory,the author studied the transformations in the Fourier domain.By using the integral solution of upward continuation of potential field and the Poisson's relation between gravitational attraction and magnetic scalar potential,the author derived the expressions performed by multiplying with appropriate factors of linear transformations of gravity and magnetic fields in the frequency domain.A matrix multiplication system for potential field data transformations is proposed by combining the field transformation method with the two dimensional discrete Fourier transform(DFT)matrices expressed as the Kronecker product of DFT matrices of smaller dimension.The novel scheme presented in the spatial domain can also describe the corresponding algorithm in the frequency domain,which is uniform system for potential field data transformations both in the spatial domain and in the Fourier domain.Based on the system,the author discussed the relation between the spatial domain algorithm and the frequency domain algorithm for potential field data transformations.It should be noted that the field used in the potential field data transformations algorithm dicussed above is regarded as a periodic function,and the transformations in the Fourier domain is not exactly equivalent to the algorithm in the spatial domain.In order to realize the algorithms for potential field transformations,the author also discussed the details of of calculating the wave number or discrete frequency.3.Based on the analysis of three types of typical unstable transformations of potential field data including downward continuation,calculation of partial derivative and reduction to the pole at low latitude,the author discussed physical meaning of the instability in transformations,especially for the pole reduction operation at low latitude.In order to solve the problem of unstable transformation,the author formulated the unstable transformation as an inversion problem of corresponding inverse operating,and the regularization approach was introduced to solving it.For example,it is easy to formulate the downward continuation as an inverse problem of upward continuation and solve it with inversion approach.The research shows that the solution obtained by minimizing the data misfit will be equivalent to the results direct applying corresponding unstable transformation,thus the regularization term of the objective function is significant for stabilizing the solution.By applying the regularization method,an acceccpetable result is obtained for unstable potential field transformations.The author derived the regularization solution for potential field transformations with smallest model term,and also introduced a discretized smoothing continuous curvature spline regularization term to solving the problemes,which is approach to obtain the minimum curvature solution of transformed filed both in the spatial domain and in the Fourier domain.The author also studied the method of determing regularization parameter based on generalized cross validation(GCV)and proposed the algorithm for automatic choice of the amount of regularization parameter.4.According to the rapid development of multiparameter measuring for aerogeophysical survey,the author established a procedure framework for multiparameter joint transformations for potential field data.The framework is obtained by constructing the transformation relations between the multiparameter observations and the gravitational attraction or magnetic scalar potential,and minimizes the sum of the data misfit.By using the framework,the author regarded the two orthogonal horizontal compenets or gradients as the observations,and discussed the transformations for vertical compenet or gradient of potential field form the observations.By considering the weights of the two compenets or gradients,a generalized two dimensional Hilbert transform is proposed.When the weights are the same,the generalized Hilbert transform will degrade to the usual two dimensional Hilbert transform.5.The author also discussed the potential field transformations for triaxial aeromagnetic gradient measurements and airborne gravity gradient measurements using the framework of multiparameter joint transformations.A novel method that uses horizontal and vertical total-field gradient data to calculate the full magnetic gradient tensor was proposed.Compared with Nelson's transformations method,the proposed algorithm combined with triaxial aeromagnetic gradient data will effectively employ the spatial rate of change of the total field in three-dimensional space,which will be a better solution for calculating of the magnetic gradient tensor.Aiming at the rapid development of airborne gravity gradient,the author discussed the gravity potential calculated from the raw tensor components,and proposed a generalized transformation,which contains the different weighting factor for raw tensor components.The authors also considered data processing for partial tensor system acquires two curvature components of the gravity gradient tensor,and proposed a generalized transformation for determining the potential from curvature components,which is different from the existing techniques and also contains the different weighting factor of GNE and GNU components.6.Considering the existence of gap area in the measurement and field data expansion,an calculating the equivalent field solution was proposed.The upward continuation of the the equivalent field will fit the observations best.Under this equivalent condition,a smooth continuous field i.e.downward continuation filed will be constructed by fitting the observation field in the the spatial domain.In order to overcome the difficulty of inversion,an approximate frequency domain inversion method was proposed,which will be better to solve the problem of filling grid dummies and expanding data.The technique can improve the accuracy potential field transformations indirectly.Combining with other transformations,the proposed method will realize a robust transformation without dealing with data expansion or replacing dummy values with interpolated values.All the methods proposed were tested by the using corresponding theoretical model or real data,which verifies that the research methods and theoretical analysis in this thesis is correct.