T1 (21 m long and 3 m high) is located in the eastern flank of the LAG crater (Figure 2c), and exposes the phreatomagmatic sequence affected by normal faults and conjugated fractures with NNW-SSE, NW-SE and E-W trends (Figure 5). These faults were classified in main faults (first-order structures) and small-scale faults (second-, third- and fourth-order structures) according to their size and the number of stratigraphic units affected (Supplementary Table 2). T1 shows a graben-horst-graben geometry, limited by the first-order structures, identified as F1, F2, F3, F4, F5, and F6 (Figure 5b, 5c). F1 (N67°W-53°SW) is the main fault exposed in the trench; we measured the vertical displacement on its plane. However, the total displacement in the trench could not be calculated because of the lack of correlative beds across the outcrop and the geometry of the wedged strata.

Figure 5 Figure 5 a) Composed photography of the trench T1, an artificial outcrop exposed along the path that connects the crater border with the lake, inside the LAG maar. In the photo, the main faults are delineated. b) Simplified diagram of T1 with the main faults identified (first-, second-, third- and fourth-order). c) Rose diagram of the measured faults indicating a preferential NW-SE strike. d) Sketch map showing the orientation of these outcrop-scale faults with respect to the La Alberca-Teremendo fault and their interpretation as Riedel faults.

Table 2 Table 2 Slip rates (SR) obtained for partial displacements measured for NW-SE faults in trench T1 and for total and partial displacements of LATF measured in trench T2. Recurrence intervals (RI) obtained for the measured displacements. Ev = Displacement event. (*) = age of the LAG maar from Kshirsagar et al., 2015.

The first graben (graben a) is delimited by F1, F2 (N23°W-83°SW), and F3 (N10°W-84°SW). In F1 we measured two displacements: at the top, a 92 cm-displacement of an alternated sequence of coarse ash layers with accretionary lapilli and gravel strata; at the bottom, a 107 cm-displacement of a lithified, fine ash layer (green and yellow layers in Figure 5a, respectively). The differential displacement indicates that, at least, two rupture events occurred on the F1 fault plane. F1 and the space between F2 and F3 are filled with a mix of phreatomagmatic materials, soil, and imbricated rocks with diameters between 10 and 20 cm.

The horst is delimited by F3 and F4 (N83°W-62°SW). The latter is filled with a mix of phreatomagmatic materials and soil; the vertical displacement measured on F4 was 123 cm of a layer of fine ash with accretionary lapilli (brown layer in Figure 5a). Finally, the second graben (graben c) is delimited by F4, F5 (N08°W-75°E), and F6 (N39°W- 61°NE); F5 is filled with phreatomagmatic materials mixed with soil; the displacement measured on F6 was 20 cm of a gravel layer overlaid by lithified ash strata (purple layer in Figure 5a).

The small-scale faults (second-, third-, and fourth-order structures) are more abundant in the horst, followed by graben c, and less abundant in graben a; they create small-scale graben, semi-graben and horst geometries, and also merge forming faults nets. These structures do not show vertical displacement across the grabens, and the third-, and fourth-order structures disappear, both, upwards and downwards in the sequence. These characteristics suggest accommodation of materials due to horizontal extension of non-tectonic nature; accordingly, they cannot be used in the paleoseismic estimations.

T2 trench (10 m long and 4.5 m deep) is located at the western end of the LATF (Figure 2c and Figure 6). The trench exposes the phreatomagmatic sequence of the LAG maar covered by two dark brown, superposed soils with thicknesses between 0.5 and 1.5 m. The soils characteristics are described in detail in the next section.

Figure 6 Figure 6 a) Microtopography of the La Alberca-Teremendo fault scarp at the western flank of the LAG maar crater (Equidistance of contour lines: 1 m), and location of trenches T2 and T3. b) Photography of the scarp at the T2 location. c) Photography of the contact between the phreatomagmatic sequence and the soil along the LATF plane. d) Scheme of the photography c). e) Opening of trench T2 with the fault plane exposed.

T2 shows the LATF trace and three smaller antithetic faults (A1- 2-3, Figure 7), as well as second- and third-order faults and associated fractures, which displace the phreatomagmatic sequence. The LATF is a normal fault trending N260° and 76°NW dip; at the bottom, it changes to vertical, and at the top has an 89° dip, and a 60° rake. It has a total vertical displacement of 335 cm and a net vertical displacement of 262 cm. The antithetic faults that limit the blocks were identified as A1 (N60°E-80°SE), A2 (N80°E-60°SE) and A3 (N85°W-80°SW). These faults accumulate a vertical displacement of 73 cm (10 cm for A1, 57 cm for A2, and 6 cm for A3). The hanging wall shows a domino-style, normal faulting, integrated by three blocks which rotate 8° to 15° away from the foot wall; the spaces between blocks (4 to 61 cm) are filled with a mix of phreatomagmatic materials and soil (Figure 7).

Figure 7 Figure 7 Log of trench T2, rose diagram of the fault planes exposed, directions of the stress field, and pedological analysis and classification of the soil affected by the LATF. Abbreviations: A1-3 = Antithetic faults; s1-5 = second order faults; LATF = La Alberca-Teremendo fault.

The soils analyzed in the study area (hanging wall and footwall) were classified as a Luvisol with well-developed A and B horizons, formed from the phreatomagmatic materials with andesitic composition. The on-fault exposed soil (T2 trench) shows variations in its physicochemical properties: the bottom was classified as Luvisol, but at the top, the vertic properties become important, suggesting an evolution towards a Vertisol (Supplementary Table 3). The main variations in the soil exposed on T2 trench are:

A noticeable textural change caused by the increase in percentage of clay at 100 cm- depth (terminus Abruptic, Jahn et al., 2006).

The previous characteristics are not related to the andic properties of the soil, but rather suggest a disordered soil, with high rates of skeleton and expansive clay.

Table 3 Table 3 Resolved scaling relations for assessment of potential Mw magnitude in the displacement events identified in T1 and T2 trenches. The values obtained for the Mohammadioun and Serva (2001) relation are referred as surface wave magnitude (Ms). VD = Vertical displacement. SRL = Surface rupture length. Data marked with (*) were obtained from Clemente-Chavez et al. (2013) and Singh et al. (2011, 2012).

The soil profile exposed in T2 can be interpreted as two superimposed soils. At the base is an older, primary soil composed by two horizons 2C, characterized by vertic properties, a clayey texture and the presence of slickensides. This soil lacks horizons A and B, possibly due to increased erosion (Figure 7). According to the radiocarbon dates, the lower limit of this soil has an age of 21240–20900 cal yr. BP.

The primary soil is covered by a secondary soil, made of horizons A1-2, B and C. A1-2 have humified organic matter mixed with altered minerals; horizon B is characterized by argillic properties, accumulation of clay, high expansibility, and slickensides; finally, horizon C has vertic properties, slickensides, and a sandy texture (Figure 7). The radiocarbon age at the base of the soil is 12660–12435 cal yr. BP, and continues its development until today.

The differences between the superimposed soils that evolved at different times, suggest a disruption in the pedogenic evolution of the buried soil. This fact may be related to the vertical displacement of the fault and the subsequent formation of a surface soil with unique characteristics derived of the previous soil as parental material. This new soil was displaced again in recent times. The soils analysis suggests that, at least, two ancient earthquakes in the LATF occurred after the emplacement of the LAG maar.

The net vertical displacement measured for the LATF in the fault plane in T2 was of 262 cm (335 cm of total synthetic displacement minus 73 cm of total antithetic displacement). We suggest that the observed displacement could be the result of three events: the first could be a volcano-tectonic event related to the LAG maar emplacement; the second event was identified from a net vertical displacement of 59 cm of the buried soil; finally, the third earthquake was identified from a net vertical displacement of 115 cm of the surface soil that likely occurred at prehistoric times. It is clear that the surface soil is displaced and the scarp shows little erosion, but neither historic nor instrumental record exists about this event; therefore, we assigned a maximum age of 1000 yr. BP for this earthquake.

However, estimations should be carefully considered because of the nature of the LATF, and the coexistence of magmatic and tectonic activity in the area.

According to the scenario previously proposed, we defined a model for the reconstruction of the deformation in trench T2 (Figure 8). The first phase is the deposit of the non-deformed, phreatomagmatic sequence during the formation of the La Alberca de Guadalupe maar around 23434–21000 yr. cal BP. The second phase is the occurrence of a volcano-tectonic earthquake related to the formation of the LAG maar around 23434–21000 years ago, causing an 88-cm vertical displacement of the phreatomagmatic sequence and generating a fracture filling of pyroclastic material that resembles a colluvial wedge. This event is followed by a quiescence period (third phase) characterized by the erosion of the upper layers of the phreatomagmatic sequence in the hanging wall (Units 5a-d), and followed by the development of a primary soil (phases fourth and fifth, Units 4a-b, Figure 8). The sixth phase is the occurrence of a tectonic event 12660–12435 years ago, that caused a vertical displacement of 59 cm of the primary soil and the phreatomagmatic sequence. The seventh phase is a quiescence period characterized by the erosion of unit 4a in the hanging wall, followed by the development of a secondary soil from material of the buried soil (eighth phase). Finally, the ninth phase is a third event occurred in recent times, causing a vertical displacement of 115 cm of the newly formed soil. The scarp is still visible today.

Figure 8 Figure 8 Retrodeformation model for the activity of La Alberca-Teremendo fault (LATF) based on the record from trench T2, indicating the main events (earthquakes) and the current aspect of the trench site. Abbreviations: A1-3 = Antithetic faults; VD = Net vertical displacement; LAG = La Alberca de Guadalupe.

To measure the slip rate (SR) we followed the methodology used by McCalpin (1996) that considers:

(Eq. 1)

The average slip rate was estimated for the net vertical displacement of the LATF (262 cm) measured in T2 and for the displacements of F1 measured in T1 (92 and 107 cm). The slip rates for individual events were estimated but considered with caution because of the lack of datable material in the area (Table 2).

If we assumed a purely tectonic behavior, the average SR obtained for the net vertical displacement of the LATF was 0.114 mm/year, this value represents 23 % of the SR estimated by Suter et al. (2001) using geomorphological indicators (0.5 mm/year). The slip rates of individual events show great variation (from 0.037 to 0.141 mm/year) indicating a high degree of uncertainty, consequently, they cannot be used in the evaluation of seismic cycles. The slip rate obtained for the vertical displacements measured in F1 was 0.046 mm/year, but F1 is a secondary fault that could have moved with the volcano-tectonic events of the LATF.

The slip rate values for the LATF are similar to the SR obtained for other faults in the MAFS, especially in the Morelia-Cuitzeo region (0.05 to 0.18 mm/year) (Suter et al., 2001); whereas in the Acambay graben and the Patzcuaro region, the SR is more variable: 0.03–0.37 mm/year and 0.009–2.78 mm/year, respectively (Suter et al., 1992; Langridge et al., 2000; Garduno-Monroy et al., 2009).

According to McCalpin (1996), the recurrence interval can be assessed with two methods: the direct method and the geological method. The first one produces an average recurrence interval; the second method produces individual recurrence intervals, better reflecting the dynamics of individual faults and their seismic cycles (Scholz, 1990).

For the LATF, we used the direct method to estimate the average recurrence interval for the average vertical displacement considering three displacement events (total = 111.7 and net = 87.3 cm), with the following relation (Eq. 2; McCalpin, 1996):

(Eq. 2)

Where VDaver is the average vertical displacement (mm); SR is coseismic slip rate (mm/yr) and C is slip rate per creep. Recurrence intervals for individual events in T2 trench cannot be calculated because of the uncertainty of the associated slip rates. For all the calculations, we assumed that in the LATF, C = 0.

We obtained average recurrence intervals of 7784 } 81 years for total displacement and 7726 } 68 for net displacement for the LATF in T2; and an average of 11630 years recurrence interval for F1. These values are closer to the recurrence intervals calculated for other segments of the MAFS such as the Pastores fault (10-15 Ka according to Langridge et al., 2013; Ortuno et al., 2015), and the San Mateo fault (11570 } 5320 years according to Sunye-Puchol et al., 2015). In the faults of the Patzcuaro-Morelia region the values are more variable: our RI is similar to the Huiramba fault, the La Paloma fault, the Charo fault and the Querendaro-Indaparapeo fault (4.5 to 20 Ka; Garduno-Monroy et al., 2009). These recurrence intervals are a first approach to evaluate the fault activity and should be taken cautiously, as occurrence of strong earthquakes could be clustered in time, with few years and even days of separation, as has been observed elsewhere in the world (Iezzi et al., 2018). We must also consider the frequency of events in the LATF that is influenced by the magmatic activity in the area, which likely changes the fault stresses.

The probable magnitude for fault ruptures can be assessed using empirical relations that use fault parameters such as: the surface rupture length, vertical displacement per event, slip rate, and recurrence intervals. Published empirical relations were constructed with global data bases and can be used as reference for sites with scarce or null information. The most used empirical relationships apply the surface rupture length (SRL), but its main uncertainty resides in the lack of information about the geometry and prehistoric length of the faults (Lafuente-Tomas, 2011).

The LATF has characteristics that indicate it could move under the influence of both, an extensional volcanic environment and the actual tectonic regime. So, in order to obtain a reliable evaluation of the deformation for this fault, a specific paleoseismic relation should be constructed; however, more information is needed from others structures in this area in order to achieve a reliable relation. We used published relations for the LATF, although we took into consideration that they could produce an overestimation of magnitudes of the paleoseismic events, and magnify the fault seismic potential. We applied relations that include the average vertical displacement (VD) to assess the probable magnitude associated to individual events, and relations that use SRL and SR to estimate the maximum magnitude for an earthquake that displaces the entire fault trace; finally, we made a comparison between relations to establish the best estimation (Supplementary Table 4).

Table 4 Table 4 Summary of parameters for the paleoseismic analysis in trenches T1 (NW-SE faults) and T2 (La Alberca - Teremendo fault).

For the LATF (Table 3), if we assume that all the deformation is of tectonic nature and that the segments are connected in depth, the magnitude M _w values based on the total surface rupture length of 26.1 km, ranges between 6.7 and 7.3, and between 5.9 and 6.7 for superficial magnitude (M _S). These values are slightly higher than those obtained for other segments of the MAFS. For example, for the Pastores, Acambay-Tixmadeje, Maravatio, La Paloma, Venta de Bravo, San Mateo faults, values range between 6.4 and 7.0, and for the Patzcuaro-Morelia faults, the M _w values are 5.8 to 7.1. Meanwhile, for the individual events, the probable magnitude M _w, based on the average slip, ranges between 6.6 and 7.0. Finally, for the slip measured in F1 of T1, the estimated magnitudes range M _w = 6.5–6.6. The similar displacements values of trenches T1 and T2 suggest that the inferred events on the LATF trace influence the fault F1 movement, and the faulting could be simultaneous. The M _w figures obtained using the relations of Anderson et al., (1996) and Stirling et al., (2002) are higher than those obtained using the relations of Wells and Coppersmith (1994) and Wesnousky (2008), but the minimum magnitude remains around 6.7 for a rupture of 26 km of the LATF.

If we assume a purely tectonic activity, the magnitudes predicted for the LATF are greater than expected, suggesting the possibility of multi-fault ruptures (primary and secondary displacements triggered by other fault ruptures in the area), in a similar scenario to that of the Acambay graben during the 1912 earthquake (Arzate, et al., 2018; Ortuno et al., 2019). We must consider that secondary behavior on a fault system can also be triggered by large volcanic eruptions (as mentioned in Ortuno et al., 2019). For the LATF in particular both triggers are equally probable.

In a different scenario, if we assume that the movement of the LATF is the result of volcano-tectonic events produced by dikeinduced structures under an extensional environment, the estimated magnitudes M _w should be in a range of 4.0 to 5.5 (exceptionally up to 6.5, Hackett et al., 1996), as has been observed in others areas of the world (e.g. Africa, Iceland and the USA, Hackett et al., 1996). Moderate magnitude events could be the most probable scenario for a displacement of the LATF or the NW-SE associated faults. However, moderate magnitudes events are not harmless; for example, in the Chapala graben, on October 2, 1847, an earthquake (M _I 5.7) caused several human losses and serious damages to the villages of Poncitlan and Ocotlan (Suter, 2017).