| With the improvement of the accuracy and the increasing of the volume of the gravity and magnetic field exploration data,the space reconstruction of the gravity and magnetic field data,can fully exploit the geological-geophysical information which is contained in the data,and can provide the important basis of interpretation for the geophysical exploration and the construction of the national defense.In addition,as the observation range is broaden and the interpretation depth is deepen,the gravity and magnetic field data inversion of layered medium,is the key guidance for the basic theory research of the geological deep structure and the specific practical use of the industrial deep mineral and oil detecting.Therefore,the spatial reconstruction methods of the gravity and magnetic field data and the interpretation technique of the layered medium inversion have been paid attention to by the professionals for a long time,and are always the classical applying aspect and the leading edge research problem.However,as the critical path of data space reconstruction and the main method of the layered medium inversion,downward continuation and the interface inversion have a lot of problems that need to be solved.According to the problems of the shallow depth of downward,the unstable downward continuation and the inaccurate results,to obtain a more satisfactory potential field downward continuation,the Milne downward continuation and the Adams-Bashforth downward continuation based on the numerical solution of differential equation are proposed.Due to the high frequency amplification factor of the classical Oldenburg interface inversion,new iteration method is introduced to improve the convergence of the Oldenburg inversion,which provides a new way to optimize the density interface inversion.Due to the inaccurate problem of numerical results of the classical Oldenburg inversion method,we use Pade rational expansion to replace Taylor series expasion,which puts forward the new method to solve the magnetic interface inversion.Therefore,based on the above methods and technique,the following research are carried on in this paper:Firstly,the continuation can be used to construct the database of gravity and magnetic potential field for aided-navigation,in which the upward continuation can highlight the deep anomalies,and the downward continuation can highlight the shallow anomalies.The upward continuation of gravity field is stable and convergent,but the downward continuation is unstable and divergent.For this reason,this paper presents a new downward continuation method of gravity field,Milne downward continuation method.Firstly,the gravity field downward continuation of the Milne formula is derivated based on the Milne format of numerical solution of differential equation by the use of gravity field and vertical derivative.The new Milne downward continuation method is applied to the model data,the results of theoretical model test and error curve show that compared with the fast Fourier transform downward continuation method(FFT downward continuation method)and integral iteration downward continuation method,Milne downwared continuation method solves the shallow downward depth,the unstable and inaccurate downward etc.The Milne downward continuation method is accurate,and has large downward depth of 5-10 intervals,and is very stable no matter with noises or not,and the error between the result and the real value is small.In order to verify the effectiveness,this paper apply the Milne downward continuation method to the real measured airborne gravity data in the Nechako basin of Canada,and effective and accurate downward continuation result can be obtained.Some small feature of the anomalies can be distinguished and delineated,which lay the foundation for further application of Milne downward continuation method.Secondly,in this paper,a new method of downward continuation of gravity field is presented for the same problem of downward continuation.First of all,doing upward continuation of gravity field and gravity vertical gradient to obtain the values of different height.Then,the Adams-Bashforth method of downward continuation is presented by differential equation of multi-step linear method.Finally,to test the effect of the derivation of the Adams-Bashforth downward continuation method,the Adams-Bashforth downward continuation method is applied to model data and measured data,respectively.The model test shows that,compared with the FFT downward continuation method and integral iteration downward continuation method,the three order Adams-Bashforth downward continuation method has the stable downward process,the large downward depth,the little boundary effect,the high anti-noise ability,the small relativeness error,and the accurate results.The test of the Canada Nechako basin real data shows,this gravity downward continuation method is stable and accurate,and can effectively identify the small scale anomalies,and recovery the distribution of real anomalies.At the same time,the four order Adams-Bashforth downward continuation method and eight order Adams-Bashforth downward continuation method are compared.The model test and practical examples show that the downward continuation of the higher order Adams-Bashforth method can get better downward continuation results.Furthermore,the Oldenburg inversion can be used to calculate the gravity and magnetic field data quickly,and to determine the distribution of the subsurface interface and the distribution of the sedimentary basin layers.However,for the high precision measurement data,the Oldenburg inversion method,which is used as the classical inversion method of the layered medium,has the problems of divergence.In order to solve the problem of the classical Oldenburg inversion,with integral iterative downward continuation method,the improved Parker-Oldenburg inversion method of density interface is deduced in this paper,to converge the results and to optimize the geometry of the interface.In this paper,the improved iterative Parker-Oldenburg forward and inversion method does not require the low pass filters or other high frequency pressing techniques in the iterative process.In analogy to the divergent downward continuation of rewriting as the convergence upward continuation of the iterative integral downward continuation method,this paper uses the iterative methods of convergent forward,to avoid the exponential amplification factor of the direct inversion.In this paper,we introduce the idea of determining the initial value by using other geophysical information,and do not omit the higher order term in the iterative computation to keep the inversion process convergent and accurate.The superiority of the proposed method is verified by using the gravity data of the model.The improved Parker-Oldenburg inversion method is applied to the Qinghai Tibet Plateau in China,and the Moho depth of the region is inversed.Finally,since the classical magnetic layered medium inversion in wavenumber domain is the use of Taylor series expansion of the exponential function,and is realized by the Fourier transform.So there are the problems of low accuracy,slow calculation rate.Therefore,this paper presents a method of the magnetic interface inversion based on Pade rational expansion instead of Taylor series expansion.According to the mathematical analysis,the Taylor series expansion is not convergent in the case that the extension of the expansion step and the neighborhood of the expansion point are unbounded,but the corresponding Pade rational expansion converges.Compared with Taylor series expansion,the Pade rational expansion is more stable and more accurate.Therefore,this paper derives the expression of the magnetic interface inversion of Pade rational expansion instead of Taylor series expansion.The validity of the Pade rational expansion for magnetic interface inversion is verified by model test.The method is applied to the inversion of the measured data in the Matagami area of Canada,and a stable and reasonable distribution of underground magnetic interface is obtained. |
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