Resolution attributes for geophysical inversion models: Depth of investigation and novel measures

Assessing the reliability of inversion models derived from geophysical measurements is crucial for a reliable interpretation. An interpretation depends critically on the interpreter being able to discern between the characteristics of the inversion model that can be trusted as more or less well resolved and the ones that are more dubious. This paper analyses the resolution measure 'depth of investigation' from a conceptual and a computational viewpoint and proposes two definitions that incorporate all aspects of the inversion and that are free of a user-defined ad hoc parameter. Two more resolution attributes are introduced: a qualified depth of investigation and the depth of required structure . The first one answers the question: What is the minimum depth to a homogeneous halfspace with an interpreter-defined conductivity that will not increase the data residual more than a certain amount? The second one is an 'unqualified' depth of investigation that addresses the question: What is the minimum depth to a homogeneous halfspace with any conductivity that will not increase the data residual more than a certain amount? This latter measure indicates the depth below which no structure is needed to fit the data. Finally, measures are defined that will provide estimates of the vertical resolution width as a function of depth. All of the resolution measures presented in this paper are based on the posterior model resolution matrix.