An Iterative Method for the Solution of Linear Inverse Problems in Geophysics

In this work we present a new numerical technique for the solution of geophysical ill-posed inverse problems, in the case of discrete data and discrete model parameters. The Landweber's (1951) algorithm is applied to invert synthetic tomographic data corrupted by noise. The algorithm is given by the simple formula mk+1 = m' - ACT(Gm" - d) , where 0 < A < 2/ a MAX' in order to guarantee the algorithm convergence, and aMAX is the maximum eigenvalue of the matrix C . When using an iterative algorithm one has to investigate: the existence of a solution, the uniqueness of this solution, the speed of convergence, and the properties of the solution. At this stage we are more interested in the speed of convergence. This "new" iterative method is in general faster than the Algebraic Reconstruction Technique (ART), as showed in the numerical simulations.