An iterative algorithm in potential-field inversion

1　Principle and MethodAll the problems of potential- field inversioncan be concluded that of solving nonlinear functionas follows:b =f( x) ( 1 )where x =( x1,x2 ,… .xn) T,xj( j =1 ,2 ,… ,n)indicate geometricparameters and physical parame-ters of the object;b=( b1,b2 ,… ,bm) T,bi( i=1 ,2 ,… ,m) indicate potential- field measurements.Main algorithms for expression( 1 ) are leastsquare method ( include damping least squaremethod ) ,gradient method ( conjugate gradientmethod and variable met…

An iterative algorithm in potential-field inversion

The problem of potential field inversion can be become that of solving system of linear equations by using of linear processing. There are a lot of algorithms for solving any system of linear equations, and the regularized method is one of the best algorithms. But there is a shortcoming in application with the regularized method, viz. the optimum regularized parameter must be determined by experience, so it is difficulty to obtain an optimum solution. In this paper, an iterative algorithm for solving any system of linear equations is discussed, and a sufficient and necessary condition of the algorithm convergence is presented and proved. The algorithm is convergent for any starting point, and the optimum solution can be obtained, in particular, there is no need to calculate the inverse matrix in the algorithm. The typical practical example shows the iterative algorithm is simple and practicable, and the inversion effect is better than that of regularized method.