We spatially map b-values in the Southern Tyrrhenian Subduction Zone (Italy). A high b-value anomaly 90--200 km beneath the Aeolian Island volcanoes is interpreted as being related to the origin of magma for the Aeolian volcanic district. This result is independent of the sample size, width of the cross-section or its orientation. To assess the stability of these findings, we develop a new, more realistic, uncertainty assessment based on a bootstrap method. Our approach explicitly takes into account the uncertainty in the assessment of the completeness in magnitude reporting. To quantify the significance of the results when compared to a chance occurrence, we compute Monte Carlo style simulations based on catalogs with permuted magnitudes. Our entire tests show that the high b-value anomaly is stable and highly significant.