Biased estimation: a simple framework for inversion and uncertainty analysis with prior information

Abstract

The use of a priori information to resolve non-uniqueness in geophysical inversion is well known, but the kinds of constraining conditions required for the solution to an inverse problelm to be uniquely assured as well as the problem of extremal inversion with a priori information may still be explored further. An attempt has been made to address some aspects of these problems in inversion and uncertainty analysis within a unifying framework of biased estimation using a simple matrix algebra and taking advantage of the explicit distinction between the a priori information and the starting model in non-linear estimation. The adopted approach is flexible and allows the use of either reliable or diffuse a priori information making it a useful procedure for exploiting the peculiarities of different geophysical situations. It is shown that the more rigorous inversion algorithms can be derived easily from this framework as special cases and a digestible analysis is provided to increase our understanding of the undergirding principles of these classical algorithms.