Analytical and numerical optimization of gravimetric networks: a case study from Mount Etna, Italy

The transport of magma and magmatic fluids is a key process behind the occurrence, duration and intensity of volcanic crises. Volcano gravimetry allows for unequivocal inference of the location and mass of accumulated or removed magmatic fluids at volcanoes. This task is best accomplished through collecting gravity time series at multiple stations simultaneously. The performance of individual gravimeters and the configuration of the gravimetric array, however, determine the threshold of detectable mass change and the ability of the array to minimize the uncertainty on the inferred quantities.We utilize numerical optimization techniques to design a network including one absolute quantum gravimeter (AQG), two superconducting relative gravimeters (iGRAVs) and several microelectromechanical system (MEMS) relative gravimeters at Mount Etna. We also develop analytical solutions for simple design problems. We show that the analytical solutions are essential for validating the numerical optimization procedure. We provide practical details and caveats that should be considered in similar gravimetric network optimizations. These include 1) specifying the target zone of the network by using the history of mass transport, 2) accounting for the relative importance of different parts of the target zone, 3) accounting for logistic and instrumental constraints in the optimizations 4) calibrating the objective functions associated with various optimizations, 5) analyzing the network sensitivities to different parts of the target zone and identifying blind zones and 6) calculating the optimal number of gravimeters as a function of the sensor sensitivity and accuracies. We show that our optimal solution for Mount Etna provides an improved detection power across the target zone as compared to an equally spaced network of gravimeters with the same existing constraints, surface topography and sensor sensitivities. Furthermore, this optimal solution ensures that a certain range of mass change anywhere in the target zone can be sensed by a given minimum number of gravimeters and at the same time minimizes the impact of random observation errors on the inferred quantities.