Research Of Stable Downward Continuation Method

Downward continuation is widely used in many fields.The downward continuation method that is more stable means the accuracy of the results is better and the depth of the continuation is deeper,but the downward continuation is an inverse problem of mathematical physics and cannot be obtained at present.The methods of previous researchers can often solve the problem of downward continuation within a limited depth.For example,the iterative method of Academician Xu Shizhe,which the depth of downward continuation can reach 10-20 times pitch.Based on previous studies,this paper proposes an iterative-multistep method and continues to explore more stable methods for downward continuation.In order to propose a new method for downward continuation,this paper studies the method for obtaining the vertical first derivative of the field which below the land and the application of the linear multistep method in the downward continuation.Firstly,to obtain the vertical first derivative,the paper proposes derivative iteration method which have good result.Then,this paper applies the linear multi-step method to the downward continuation,and carefully studies and analyzes the error effects and the method characteristics of the linear multi-step method.Finally,by combining the characteristics of the iterative method and the linear multistep method,this paper proposes an iterative-multistep method.This method uses the characteristics of iterative method and linear multistep method,use the good results of iterative method that is obtained at the depth,which is 20 times pith,reduce the step length and initial error of the linear multi-step method,and finally achieved good results in the depth of 40 times pith.This paper analyzes the principle and characteristics of the iterative-multistep method,then explains the advantages of the method,and validates it through model and actual data.The method can reach the depth of 40 times pitch,and can effectively control the influence of noise and suppress the amplification effect of noise.It is a better method of downward continuation.