Study On Method And Technique Of Frequency Domain Forward Modeling Of Gravity And Magnetic Anomaly

The method of frequency-domain forward modeling have characteristics of simple calculation expressions and high speed of calculation,and widely used for interface inversion[1][2]and physical mapping[3].However,It always affected by phenomenon due to the application of traditional standard FFT method.such as 'oscillation of border''significant calculation error' and 'forced periodization',It is considered to be an inaccurate and limited method and has not been widely used especially in the frequency-domain forward of single model.To solve the problems of frequency-domain forward modeling and give full play to the characteristics of its forward speed,Based on frequency-domain forward error sources,this paper analyzes the causes and rule of error.from the perspective of numerical calculation,we prove that the main cause of frequency domain forward error is due to the rectangular integral formula which can not meet the numerical calculation of the oscillating discrete Fourier transform integral.To improve the forward calculation accuracy on frequency-domain,this article adopts the numerical integral method with the highest accuracy at present:Gauss integral method,we deduce the formula of arbitrary order Gauss-Legendre integral method,and promote Gauss-FFT method proposed by Wu Leyuan from even order to arbitrary order.Analogying FFT butterfly calculation method,accelerated arbitrary order Gauss-Legendre integral method is given to calculate the acceleration of algorithms;According to the oscillation of the function,the oscillation part of integral function(1D:ei2?ux,2D:ei2?(ux+vy))is used as the weight function to weaken the oscillation of the integral kernel function,and the two point Gauss integral method formula which the Weight function is oscillating is derived.Through the numerical experiments,it proves that calculation accuracy of arbitrary order Gauss-Legendre integral method is one thousand times higher than the standard FFT method and the calculation speed is slightly higher than the standard FFT method,The calculate time of two point oscillating weight function Gauss integral method is much longer,and its calculation precision is similar to the two point Gauss-Legendre integral method,but it is similar to the four point Legendre-Gauss integral method when the abnormal body is at the edge of the data window,and it takes a long time without the use of FFT butterfly algorithm,the model experiments,it takes about 16.94 sec to complete forward of sphere gravity anomaly with 128 x 128 data window.The unified form of processing and conversion in frequency-domain is given combined with the calculation method of arbitrary order Gauss-Legendre integral method.We have discussed the representative method of continuation of potential field and give the method of Gauss-Legendre upward continuation and tail-weightedly fold Gauss-Legendre downward continuation,It is proved that the method is superiority.