Study On Space Continuation Methods For Geomagnetic Field

As a natural geophysical field,the geomagnetic field contains a lot of useful information.For geophysical prospecting,geomagnetic anomaly data is a sensitive indication signal,therefore,geomagnetic detection has be an oldest geophysical prospecting method because of its low cost,high efficiency,less geographical restrictions and abundant information.For geomagnetic data interpretation and analysis,the geomagnetic field space continuation plays an important role and has be the research hotspot among geophysical workers early.But the requirement of continuation precision in geomagnetic data interpretation and analysis is comparatively low.With the continuous innovation and the development of navigation technique,the geomagnetic field as a natural coordinate system has gradually become a new research target.For geomagnetic matching navigation,spatial geomagnetic database construction must also rely on the continuation technique of geomagnetic field.At the same time,the precision of continuation has be put forward higher requirements.The upward continuation for geomagnetic field is a fixed solution problem,it can be obtained very accurate results by solving the boundary integral equation in mathematics,but the downward continuation is an ill-posed problem,its result cannot be obtained by solving the boundary integral equation like upward continuation.In this paper,it takes the application requirements of geomagnetic navigation as the starting point and the spatial geomagnetic database construction as the target,the geomagnetic field theory is studied.Based on this,the thesis studies the effect of integral radius for geomagnetic field continuation on the continuation results and the downward continuation methods of the geomagnetic field in the frequency domain.The main research contents and contributions include the following aspects:(1)This thesis introduces the seven factors of the geomagnetic field and their interrelation,the composition of geomagnetic field and their characteristics as well as the mathematical principle of geomagnetic continuation briefly,After that,The thesis deduces upward continuation integral formula in spatial domain,and on the basis of this,the thesis deduces upward and downward continuation operator of frequency domain as well as gives the basic process of upward and downward continuation.(2)With the help of the unit impulse function,the thesis studies the effect of integral radius for geomagnetic field continuation,and analyses the contribution of geomagnetic data in different integral radius.The research results provide a reference for determining the integral radius of geomagnetic upward and downward continuation.(3)Based on the summary of the previous research results,Iterative downward continuation method is extended generally in the frequency domain and a general downward continuation iterative formula is given.In addition,The thesis studies and analyzes the convergence condition and the filtering characteristics of the downward continuation operator(,)n x yH k k.The experimental results show that the iteration downward continuation operator in frequency domain essentially belongs to semi-convergence filtering operator.while the number of iteration in a certain range,it can suppress the high frequency effectively,but with the increasing of iteration,it presses on towards the original downward continuation operator so that the continuation result become divergent.Therefore,the appropriate choice of iteration number is very important.(4)The thesis sduties the nature of the ill-posed problem and the principle of regularization method.on the basis of that,the thesis gives a detailed analysis on the Tikhonov regularization method that be widely applied in the field of downward continuation problem;In order to solve the problem that the transition band of Tikhonov regularization operator is too wide,the thesis puts forward an improved regularization method,and constructs the improved regularization operators;Besides We simplify current L-curve method to determine the regularization parameters,and construct the auxiliary function for determining the regularization parameters.These two kinds of regularization method are comparatively analysed by use of marine measured geomagnetic data.The results show that both of these two regularization method have strong anti-interference ability to the geomagnetic data containing noise,and the improved regularization method has higher continuation precision.