## 1 Introduction  
Calderas are sub-circular depressions that form during the partial emptying of magma reservoirs associated with large eruptions [1]. A number of calderas are marked by the uplift (resurgence) of their sunken floor, resulting from magma accumulation at depth and accompanied by minor eruptions. Caldera resurgence, with radial or elliptical shape, represents the largest and most peculiar type of volcanic ground deformation, with amounts ranging from centimeters to a thousand meters and a duration of up to several thousand years [1]. The processes driving caldera uplift generally relate resurgence to the input of new magma, which is often stimulated by the pressure drop that follows a caldera-forming eruption [2, 3, 4]. However, part of the caldera resurgence can be related to the increase in the pressure of the geothermal system, as a consequence of the heating due to magmatic gas inflow [5; 6; 7]. Unrest episodes may be indicative of short-term inflation events that give rise to caldera resurgence [8]. Most volcanic eruptions are preceded and accompanied by a period of unrest. This is defined as a change from the normal state or usual behavior of a volcano. Large calderas may show episodes of unrest that commonly occur for years, decades or centuries, with or without a following eruption [9; 10; 11]. The potential hazards associated with unrest also include volcano-tectonic seismicity, ground uplift and horizontal deformation, hydrothermal explosions or gas emissions, fault and fracture opening, increased degassing, and landslides [9; 12]. Such events may result in significant physical damage to buildings, critical infrastructure (i.e., electricity, telecommunications, and water and sewerage networks), roads and railways, and harbor functionality [13; 14]. These damages may also result in significant economic loss through business interruption, tourism income drop, decreases in property values, and increases in insurance premiums [12; 14; 15; 16]. Ground deformation during unrest phases is characterized by high uplift and/or subsidence rates, related to inflation and deflation of the caldera floor due to magmatic and/or hydrothermal processes. It is usually characterized by marked radial or elliptical symmetry (first-order ground deformation), which rapidly decreases with distance from the caldera center. The general, symmetrical pattern of ground deformation is indicative of the main source activated, which can be magmatic or hydrothermal [7]. However, mostly hidden by the main field, ground deformations are also affected by structural discontinuities or secondary inflation sources, i.e., faults and/or smaller pressure sources including rising magma dykes, etc. Investigation of the smaller, second-order anomalies of unrest-related ground deformation is generally neglected, possibly leading to deficiencies in hazard analysis of the unrest phenomena and hiding the identification of possible pathways for magma rising, eventually leading to an eruption. In this paper, we propose a simple procedure for filtering the first-order ground deformation radial signal, i.e., the one produced by the main volcanic source, in an active volcanic caldera during unrest phases by using Sentinel-1 Synthetic Aperture Radar Multi-Temporal Interferometry (MT-InSAR) data. Such filtering, almost eliminating the effect of the main volcanic source, allows us to highlight second-order ground deformations or local anomalies that characterize the complex volcano-tectonic evolution of a caldera during unrest. The early detection of local trends in ground deformation within or around the caldera can provide useful elements for monitoring main fault and fracture openings, the main volcano-tectonic structural features, and the most likely areas of possible vent opening. The proposed procedure was developed during the study of the unrest phase affecting the Campi Flegrei caldera, Italy, as this caldera is considered one of the highest volcanic risk areas in the world [17].