Uniqueness, Stability And Factual Geological Information: The Ingredients Of A Meaningful Geophysical Interpretation

To produce a unique and stable solution in geophysical<br>interpretation, an inversion method must introduce<br>particular constraints. These constraints will, inevitably,<br>restrict the type of geological setting where the method may<br>be applied. However, the constraints, used or invoked to<br>guarantee uniqueness and stability, are formulated in terms<br>of abstract mathematical restrictions. I present a geological<br>interpretation of the mathematical constraints used in three<br>gravity uniqueness theorems and in most stabilizing<br>constraints used in inversion methods. The purpose is to<br>help not only researchers to develop sound gravity<br>inversion methods, but also explorationists to select the best<br>interpretation method for a given geological setting. I found<br>that, in the class of homogeneous sources, uniqueness is<br>favored if the inversion method imposes that the solution be<br>a compact body without curled protrusions at their borders.<br>Additionally, stability may be achieved by the<br>incorporation of five basic types of constraints: i) lower and<br>upper bounds of parameter estimates; ii) proximity of a<br>parameter estimate to a measured or inferred value; iii)<br>spatial smoothness of the estimated physical property; iv)<br>concentration of the estimated anomalous source about a<br>geometrical element such as an axis, and v) source<br>compactness.