A unified transformation function for lower and upper bounding constraints on model parameters in electrical and electromagnetic inversion

Abstract

Since many geophysical inverse problems are ill-posed, implementation of model parameter constraints is important in reducing solution ambiguity. This paper presents a unified transformation function for enforcing lower and upper bounds on model parameters to restrict model updates during the inversion process such that unrealistic results are suppressed. The transformation is realized using a logarithmic or inverse hyperbolic tangent function on model parameters, and contains the conventional transformations as special cases. It is straightforward to recast the cost functional gradient in terms of the transformed variable. The interval between lower and upper bounds reflects the reliability of a priori information, which may be obtained from well logging and surface geological surveys. Tests on a synthetic crosswell electromagnetic example reveal that the use of bound constraints is effective in deriving valid physical results from inversion.