## 1 Introduction
Actually, a phase of unrest is ongoing, characterized by an uplift of 139 cm from November 2005 to June 2024 at the RITE GNSS station located at the Pozzuoli historical center, with average velocity rates of 20 +/\(-\) 3 mm/month since April 2024 [18]. Seismic activity increased progressively during the unrest, both in frequency and in maximum magnitude [7], to reach a maximum magnitude of Md = 4.4, for a seismic event that occurred on 20 May 2024 [18]. The Campi Flegrei caldera had already experienced significant uplift and seismicity in the periods 1970-1972 and 1982-1984 [7; 13], but hazard assessments in this region have been rather concentrated solely on the eruption hazard rather than on all the possible phenomena linked to unrest [12]. The ongoing unrest has been explained by several volcanological models, which can be classified in two main categories: magma rising at shallow depths, in the form of pressurized sills (e.g., [19; 20; 21; 22]),and an increase in pressure in shallow aquifers due to heating by gases rising from the main magma chamber (e.g., [7; 23]) located at 7-8 km in depth [24]. All of these papers try to explain the main, mostly symmetrical, ground deformation field. Only recently, a few scientific articles have begun to use different approaches to analyzing spatial and temporal second-order anomalies in the ground deformation field at Campi Flegrei caldera. [PERSON] et al. [25] analyzed Sentinel-1 and COSMO-SkyMed Multi-Temporal DInSAR measurements and GNSS (Global Navigation Satellite System) data to reveal and investigate a geodetic anomaly that has been observed since 2021 in the Mt. Olibano-Accademia area, locally deviating from the typical bell-shaped deformation pattern recognized at Campi Flegrei. [PERSON] et al. [26] mapped the last decade of seismicity, providing high-precision location of earthquakes and revealing the presently activated fault zones of the inner caldera; they showed an overall quasi-elliptical distribution of seismicity in the caldera and outlined complex seismogenic structures at a smaller scale, one of which is located at the edge of the Solfatara crater. [PERSON] et al. [27] evaluated the 3D distribution of the b value, which represents the scaling parameter of the Gutenberg-Richter relation, revealing a correlation with the structure and the porosity of the hydrothermal system involved in the unrest phenomena in the Campi Flegrei volcanic area. Finally, [PERSON] and [PERSON] [20] analyzed ground displacements from ERS-ENVISAT and Sentinel-1A SAR images to investigate the 1993-2000 subsidence and 2015-202 uplift by applying an empirical orthogonal function analysis to the displacement time series for detailing deformation linked to local fluid migration in the Solfatara area. All of these papers aimed to find detailed information on secondary volcano-tectonic sources and structures at early stages of development, which are useful in better forecasting eruptive and/or seismic hazards. Our paper presents a simple but robust procedure, developed using Campi Flegrei ground uplift data, to recover such critical information by subtracting the main deformation pattern, which is likely due to the main volcanic source, and considering the second-order anomalies of the ground deformation field.