Recursive estimation in geophysical inverse problems

Abstract EN

Recursive estimation applied to the linear system d = Gm presents a practical alternative to the more direct least-squares solution.

Unlike the conventional stochastic inverse which requires matrix inversion operation, the recursive form avoids that requirement by performing only scalar inversion.

It offers some other useful and interesting features which we investigate in this paper using some examples.

The first example is a simple one illustrating how the method works and the remaining ones are applications of an inverse scattering problem in which the data set is collected in stages.

We find the result obtained by the recursive scheme of inverting one data set at a time is equivalent to that obtained by simultaneous inversion of the whole data vector.

The entire G-matrix is not held in memory at once but instead, each row is used per recursion.

It also offers an opportunity to study how the solution improves as more data are inverted.