Fig. 4: Regimes of crustal deformation.
From: Potential for rupture before eruption at Campi Flegrei caldera, Southern Italy
a Ideal evolution from elastic (white), through quasi-elastic (yellow, A-B) to inelastic (magenta, B-C) deformation before rupture at C. The stress drops after rupture (see Fig. 5b). b The corresponding seismicity-deformation trend follows the difference between actual (solid curve) and linear elastic (dashed line) stress-deformation trends in (a). It increases exponentially (quasi-elastic regime) and then linearly (inelastic regime) with strain36. Since strain is proportional to deformation, similar shapes of trend appear on stress-strain diagrams. Notice that the trend A-B resembles non-linear elastic behaviour; such a description gives a misleading impression that only elastic deformation is taking place, instead of elastic deformation in unbroken rock combined with subordinate rock fracture and slip, which we describe as quasi-elastic36. c Changes in the number of VT events with corrected uplift during Aug 2010–Jan 2015 (squares), Jan 2015–Jan 2020 (triangles), and May 2020–June 2021 (diamonds). The exponential increase began in 2015–2016 (Fig. 2) and became linear in 2020. Best fit trends yield ΣN ∝ exp (hcor/49) and dN/dhcor = 120 events per cm (both with r2 = 0.99). d Similar transitions are seen for completeness magnitudes of 0.2 and 0.5; the corresponding pairs of best-fit trends give ΣN ∝ exp (hcor/36), dN/dhcor = 29 events per cm and ΣN ∝ exp (hcor/37), dN/dhcor = 14 events per cm (all with r2 > 0.98). ΣN denotes the total number of events and hcor is in cm. Supplementary Figs. 1 and 2 analyse the variances of the exponential and linear trends (Supplementary Information). Data from INGV-Sezione di Napoli (Osservatorio Vesuviano)71,72.
