Longer aftershocks duration in extensional tectonic settings

Aftershocks number decay through time, depending on several parameters peculiar to each seismogenic regions, including mainshock magnitude, crustal rheology, and stress changes along the fault. However, the exact role of these parameters in controlling the duration of the aftershock sequence is still unknown. Here, using two methodologies, we show that the tectonic setting primarily controls the duration of aftershocks. On average and for a given mainshock magnitude (1) aftershock sequences are longer and (2) the number of earthquakes is greater in extensional tectonic settings than in contractional ones. We interpret this difference as related to the different type of energy dissipated during earthquakes. In detail, (1) a joint effect of gravitational forces and pure elastic stress release governs extensional earthquakes, whereas (2) pure elastic stress release controls contractional earthquakes. Accordingly, normal faults operate in favour of gravity, preserving inertia for a longer period and seismicity lasts until gravitational equilibrium is reached. Vice versa, thrusts act against gravity, exhaust their inertia faster and the elastic energy dissipation is buffered by the gravitational force. Hence, for seismic sequences of comparable magnitude and rheological parameters, aftershocks last longer in extensional settings because gravity favours the collapse of the hangingwall volumes.

Every day, moderate-to-large magnitude earthquakes release seismic energy stored within the Earth's crust. This energy is accumulated for tens or thousands of years during the inter-seismic phase and released instantaneously (i.e., within seconds) through an earthquake (i.e., the mainshock) during the co-seismic phase [1][2][3][4] . After the mainshock, the energy release continues (for months to years) during the post-seismic phase in the form of aftershocks, generally characterized by magnitudes smaller than the mainshock 5 . A worldwide earthquake analysis using as data the Global Harvard Centroid-Moment-Tensor (CMT) Catalog 6,7 shows that earthquakes within contractional tectonic settings are characterized by higher magnitude values (up to 9.5) than those within extensional tectonic settings (generally up to 7 with few exceptions; Fig. 1b). Schorlemmer et al. 8  where N is the number of events within a certain range of magnitude, a and b are two costants and M is the minimum magnitude. Their estimated b-value is equal to 1.1 for extensional and to 0.9 for contractional tectonic settings. Large earthquakes affect smaller crustal volumes in extensional tectonic settings than in contractional settings; this was proposed as the main reason for the occurrence of smaller magnitude earthquakes in rift zones 9 . On the contrary, few studies have focused on the control of the tectonic setting on the duration of aftershock sequences. A better understanding of the processes ruling the decay of aftershock with time (aftershocks decay) is fundamental to better constrain seismic hazard during ongoing seismic sequences.
Within a seismic sequence, seismological observations indicate that the aftershocks decay follows the Omori-Utsu law 10,11 : where k and c are constants, t is the time and p indicates the decay rate. The aftershocks decay also depends on several parameters peculiar to each seismogenic region, such as the tectonic setting (i.e., extensional, strike-slip, contractional regimes), the stress changes along fault, the structural heterogeneities, and the crustal rheology [12][13][14] .
However, the geological and seismotectonic parameters that control the aftershocks decay during seismic sequences are still unclear 13 .
In this work, we focus on how the tectonic setting controls the aftershocks decay within seismic sequences. In particular, we analyse data from international catalogues with two different methods, comparing the aftershock sequences following five extensional settings mainshocks ( Fig. 1a; Table 1) and five contractional settings mainshocks ( Fig. 1a; Table 1). The average duration of aftershock sequences is longer, and the number of events is larger within extensional tectonic settings with respect to contractional tectonic settings. We propose an interpretation of these different behaviours in terms of differences in the orientation of forces acting during earthquake nucleation processes in the two settings.

Materials and Methods
Collected data. In order to achieve comparable and homogeneous seismic sequences, we adopted the following criteria during the selection of earthquake sequences: (1) presence of local and well-distributed seismometric stations to avoid the occurrence of spatial gaps within the seismic sequence; (2) existence of complete seismological catalogues to avoid the occurrence of temporal lacks within the seismic sequence; (3) maximum hypocentral depth of 40 km (i.e., crustal earthquakes), thus excluding deeper subduction-related earthquakes; (4) mainshocks of M > 5.5 to obtain representative aftershock sequences; We selected the following seismic sequences within extensional tectonic settings: Italian Central Apennines We used seismic data presented in following catalogues: the INGV Earthquake Centre (National Institute of Geophysics and Volcanology, Italy, http://iside.rm.ingv.it, to analyse the 1997 Colfiorito, 2009 L' Aquila and 2012 Emilia sequences); the CENC (China Earthquake Network Center, China, http://www.csi.ac.cn/sichuan/ index080512001.htm, to analyse the 2008 Wenchuan sequence, 2013 Lushan sequence and 2015 Gorkha sequences); the KOERI (Kandilli Observatory and Earthquake Research Institute, Turkey, http://www.koeri. boun.edu.tr, to analyse the 2002 Sultandagi sequence) and the NOA (National Observatory of Athens, Greece, http://www.gein.noa.gr, to analyse the 1995 Kozani-Grevena and the 1999 Athens sequences). We compared these data with those from the ISC 25 (International Seismological Centre) catalogue. Specifically, in case of the 2003 Zemmouri sequence (Algeria), we only used seismological data included in the ISC catalogue because, at the moment, a local Algerian seismological catalogue is unavailable.
Methods to determine the duration of aftershocks. In addition to the classical Omori law analysis performed to verify the completeness of the used seismic catalogues (results are reported in Figs S1 and S2 and Table S1 of the Supplementary Material), we employed two novel approaches to determine the duration and the number of events of the selected aftershock sequences: 1) Tangents method. We used the QtiPlot software to elaborate a statistical-descriptive analysis of seismic sequences. We adopted a completeness (threshold) magnitude (M c ) of 2.5 as, below this threshold, the number of recorded seismic events strongly depends on the sensitivity of the seismic network, which varies from place to place. The adoption of a completeness magnitude, chosen on the basis of the minimum magnitude reported in each catalogue, allowed us to remove the seismic noise. The methodology is based on the comparison of the curves representing the cumulative number of earthquakes for each seismic sequence versus the days elapsed from the mainshock (Fig. 2). In principle, the lower the completeness magnitude, the greater the completeness of the curve. The corresponding curves present an initial non-linear increase followed by a linear one (Figs 2 and 3). T he initial non-linear trend suggests that the seismic sequence related to the mainshock is still active, whereas the linear increment represents the characteristic background seismicity of the region. We consider the day when the tangent to the linear increment starts from the cumulative curve as indicative of the end of the aftershock sequence.
We  characterized by similar magnitudes and recorded by the same seismometric network (Fig. 4). In this case, we adopted a completeness magnitude (M c ) of 1.6.
To understand the physical reason of the change of slope in the cumulative curves, we calculated the strain energy release E s generated by the earthquakes nucleation, which is related to the magnitude values M by the following empirical relation 26,27 (Figs S3 and S4): where E s is in Joule. In particular, we want to investigate the relationship between the energy released during the seismic sequence and the number of seismic events, represented by the cumulative curves.
2) Mandelbrot method. We used a numerical computing software to examine faulting and fragmentation processes using the fractals theory 28,29 . In this context, the fractal geometries are strictly related to the fragmentation processes caused by earthquake nucleation. The variation of fractal parameters can thus be indicative of the temporal and spatial evolution of the fragmentation processes along a fault system in time and space. We analysed the seismological data with the software, fitting the same data with a linear regression, and obtained the fractal dimension and the related coefficient of determination (i.e., R-squared).
This method allows the representation of the magnitude-frequency distribution of earthquakes. We realized semi-logarithmic graphs for each seismic sequence, in which we compared the number of earthquakes occurred in certain magnitude ranges. The fitting straight line represents a simple linear regression according to the following equation, which also defines a fractal set: where N i is the number of objects with a characteristic linear dimension r i , C is a constant of proportionality, and D is the fractal dimension 30 (Figs 5 and 6). All these parameters directly derive from the regression lines automatically calculated by the used software. R-squared can range between 0 and 1. The higher the R-squared values, the higher the model accuracy. The high R-squared values in our studies (R 2 > 0.95 in 90% of the cases and in one case R 2 = 0.91) point to a good fit between the model accuracy and the data instability. According to this topological analysis, the fractal dimension value represents the level of irregularity of the selected fractal set 29 and is indicative of the fragmentation process occurred during the mainshock and the following aftershocks. If D = 0, it represents the classical Euclidean dimension of a point; if D = 1, the dimension of a line segment; if D = 2, the dimension of a surface and, finally, if D = 3, the Euclidean dimension of a volume 29,30 .
To check data accuracy, we calculated the coefficient of determination (R-squared) connected with Equation 4 for each seismic sequence (Figs S5,S6,S7 and S8). R-squared represents the variability between data instability and model accuracy. To establish the durations of aftershock sequences, we applied the Tangents method on the obtained fractal dimension trend.

Discussion
The Tangents and Mandelbrot methods provide comparable durations for each seismic sequence ( Table 1). The analysis of these sequences highlights the relationships between the aftershocks decay and the tectonic settings in which the seismic sequences occurred: 1) According to the Tangents method, the average duration of aftershock sequences within extensional and contractional tectonic settings are about 390 days and 120 days, respectively; extensional sequences are thus 270 days longer than contractional ones (Figs 2-4). Aftershock sequences within extensional tectonic settings comprise more seismic events (1045 aftershocks on average) than sequences within contractional earthquakes (790 aftershocks on average). Surprisingly, a M w 6.0 extensional earthquake (i.e., Colfiorito earthquake, 1997, Italy) is characterized by a longer aftershocks sequence duration than a M s 8.0 contractional earthquake (i.e., Wenchuan earthquake, 2008, China).
2) According to the Mandelbrot method, the average duration of aftershock sequences within extensional tectonic settings is about 430 days, 295 days longer than that of aftershock sequences within contractional tectonic settings (about 135 days; Figs 5 and 6). Furthermore, extensional aftershock sequences comprise more seismic events (1056 aftershocks on average) than those within contractional earthquakes (795 aftershocks on average).
The fractal dimension (D) values calculated for extensional and contractional sequences are also different. D varies between ca. 2-3 and ca. 1-2 for extensional and compressional earthquakes, respectively. As the fractal dimension is indicative of the geometrical fragmentation process, with time extensional seismic sequences are thus spatially distributed within a volume, while contractional seismic sequences closer to a fault along a surface. The average coefficient of determination R-squared (or R 2 ) is, greater than 0.95 for nine seismic sequences (i.e., Our analyses strongly support the conclusion that, irrespective of the magnitude of the mainshocks, extensional seismic sequences are longer than compressional sequences. We propose that the type of energy released during the earthquakes, in turn related to the tectonic setting, controls the different duration of seismic sequences. The observed variability of the duration of aftershock sequences, however, could be conditioned by rock properties and fault characteristics. Doglioni et al. 9 proposed that single extensional seismic sequences dissipate gravitational energy (Fig. 7a) stored during the interseismic phase, within a hangingwall volume confined by the main normal fault and an antithetic fractured dilated zone. When the stresses related to this gravitational energy exceed the strength of the dilated zone and of the main normal fault, the rock volume collapses slipping along the main fault, generating the earthquake 60 (Fig. 7a). The downward hangingwall block movement is favoured by gravity 61 . This induces an increase of potential energy and facilitates fracturing processes both during the pre-seismic period and the coseismic phase. The potential energy is transformed into kinetic energy as indicated by the double-couple mechanism of the earthquakes generated by the shear on the fault planes. In this case, most of the involved forces are distributed within the fault hangingwall volume. After the onset of slip, the hangingwall preserves its inertia for a longer period since in this case external and internal (body) forces sum up downward.
The aftershock sequences can be interpreted as related to the rock wedge settlement due to the closure of fractures and to the complete dissipation of gravitational energy within the dilated antithetic wedge 61,62 .
On the contrary, thrust-related earthquakes are characterized by dissipation of elastic energy 61,62 (Fig. 7b), which is stored both within the rock volume above the thrust fault (i.e., the hangingwall block) and along the thrust fault itself during the pre-seismic period (Fig. 7b). When the elastic energy exceeds the fault resistance, the hangingwall block generates the earthquake by moving upward along the fault 57 . The elastic energy dissipation is buffered by the gravitational force. The downward directed gravitational force is opposite to the upward sense of motion of the fault hangingwall. As a consequence: (1) the work that the tectonic forces have to do on the block is greater and (2) after the onset of slip the hangingwall block preserves its inertia for a shorter period because most of the system energy is spent during rupture and slip along the main fault to overcome the gravitational force. For this reason (i.e., to overcome the inertial system), contractional earthquakes are of higher magnitude. Most of the energy stored during the interseismic phase is used to activate the main fault and stresses are concentrated at the interface between hangingwall and footwall blocks.
Since the amount of elastic energy necessary to move downward (i.e., in favour of the gravity force) the hangingwall block during extensional earthquakes is low, we suggest that aftershocks can be easily generated until gravitational equilibrium is reached again, producing longer extensional aftershock sequences. On the contrary, since the amount of elastic energy necessary to move upward (i.e., against the gravity force) the hangingwall block during compressional earthquakes is necessarily higher, the sequence of aftershocks can be interrupted earlier. Compressional aftershock sequences are thus shorter and comprise less earthquakes than in extensional aftershock sequences (Fig. 7). The physical model is based on both the versus and the different type of energy involved in extensional tectonic settings with respect to the contractional tectonic environments, as proposed in a previous study 61 .

Conclusions
A comparative analysis of ten aftershock sequences occurred in extensional and contractional tectonic settings using two different methods (i.e., the Tangents method and the Mandelbrot method) allowed us to argue that, irrespective of the mainshock magnitude, aftershock sequences in extensional tectonic settings are longer comprised of more seismic events than those in contractional settings (Table 1).
We propose that these differences can be due to the different type of energy stored in extensional and contractional tectonic settings during the interseismic stage and dissipated during the earthquake sequences: (1) gravitational energy with a minor elastic component dominates in extensional sequences whereas (2) pure elastic Figure 7. (a) Geological model of the seismic cycle (i.e., interseismic and coseismic periods) associated with a normal fault. (b) Geological model of the seismic cycle (i.e., interseismic and coseismic periods) associated with a thrust. In both models we assume a steady state strain rate in the ductile lower crust and a stick-slip motion in the brittle upper crust (modified from Doglioni et al. 62 ). Extensional tectonic settings are characterized by longer aftershocks duration because the hangingwall moves in favour of gravity and the volume will collapse until a gravitational equilibrium is reached. energy is dissipated in contractional sequences. Therefore, for mainshocks of comparable magnitudes, extensional aftershock sequences last longer because the downward hangingwall movement is favoured by gravity and will continue until the gravitational equilibrium is reached. During contractional earthquakes, the upward hangingwall motion occurs instead against gravity and thrust-related aftershocks end earlier because the elastic energy dissipation is hindered by the gravitational force.
This comparative analysis of aftershock seismic sequences is useful in understanding the mid-term behaviour of an ongoing seismic sequence within different tectonic settings, providing useful inputs to improve seismic hazard assessment.