GNGTS 2023 - Atti del 41° Convegno Nazionale

Session 3.3 ______ ___ GNGTS 2023 The role of different constraints in the inversion of potential field data L. Bianco, M. Fedi 1 Department of Earth, Environment and Resources Sciences, University of Naples “Federico II”, Naples, Italy We discuss how the simultaneous combination of different types of constraints work in the inversion of potential fields data. Constraints are necessary in order to reduce the non-uniqueness of the solution. The first type of constraint comes immediately from the objective function formulation. For example the minimum-length solution is the simplest kind of solution for undetermined problems. It requires the shortest-possible solution and will produce a physical parameter distribution that cannot be deep due to the inherent minimum length request. The discretization of the source volume has further effect on the solution regularization, acting as a constraint of the infinite-dimensional problem (Engl et al., 1996). Some scenarios could require a compact solution to be found via the introduction of compactness (Last and Lubik, 1983; Portniaguine and Zhdanov, 1999). Other approach to constrain the solution is to limit the range of variation of the physical parameter or to force the matching of the model with some information such as well-logs, surface geology and other geophysical interpretation. These information could be arranged as a upper and lower boundaries of the physical parameter or as a reference model. The constraint mentioned so-far are referred to as hard constraints. Soft constraint is instead the model-weighting function. Many authors have proposed different approaches to this problem. Li and Oldenburg (1996) introduced a depth-weighting function related to the rate decay of the considered field. In the same framework, Portniaguine and Zhdanov (2002) proposed to adopt the sensitivity matrix. Cella and Fedi (2012) were the first to interpret the model-weighting function in a physical sense, as they suggest using the structural index of the source as the exponent of the model-weighting function. Recently, Vitale and Fedi (2020) generalized the approach for complex source-distributions introducing the inhomogeneous model-weighting function. We will show the role, the relative importance, and the coexistence of different constraints in the solution of problems in various scenarios, of separate and joint inversion. References Cella, F., and M. Fedi, 2012, Inversion of potential field data using the structural index as weighting function rate decay: Geophysical Prospecting, 60, no. 2, 313-336. http://dx.doi.org/https: / /doi.org/10.1111/j.1365-2478.2011.00974.x.