Introduction

Magmatic and hydrothermal fluid flow through the brittle crust is governed by fracture mechanics laws that account for the formation of open-fractures (i.e., extension or hybrid fractures)1,2,3, and which depends on the balance between the state of stress and the total fluid-pressure4. Around volcanoes, it is crucial to understand these variables to address processes that control fluid circulation, and thereby potential volcanic hazards and geothermal resources5,6,7. The state of stress around volcanoes has been studied in different tectonic settings6,8, from which oblique convergence margins represent one of the most recorded tectonic settings worldwide, including long-lived volcanic arcs such as the Sunda Arc (Indonesia), Northeast Honshu (Japan), Central America volcanic arc, Aleutian-Alaska volcanic arc, and the Andes (South America)9,10,11,12,13,14. In this study, we focus on understanding the state of stress and the conditions required to generate extension fractures in the Southern Volcanic Zone of the Andes (SVZ), where oblique convergence between the Nazca and South-American plates generates a volcanic arc that is closely linked to partitioned continental deformation14,15.

Here, we defined the regional and local stress state for sixteen volcanic complexes of the SVZ using seismological (short-term) and structural geology (long-term) data (Fig. 1). Then, we analyzed dilatational tendency and fluid-pressure conditions that can trigger extension fractures using a novel Monte Carlo simulation, to reveal the preferred pathways of magmatic and hydrothermal fluids. We then discuss (i) the reliability of our results, (ii) the similarity between short- and long-term states of stress, (iii) propose a holistic conceptual model for the volcano-tectonic processes occurring in volcanoes within the SVZ, and (iv) discuss how our results can be extended to other volcanic arcs within oblique subduction settings.

Fig. 1: Analyzed volcanoes of the SVZ.
figure 1

a Map of the Andean Southern Volcanic Zone showing the five regions defined in this study and the analyzed volcanoes (red triangles). NP Nazca Plate, AP Antarctic Plate, SAP South American Plate. The background layer is the ERSI Shaded Relief freely available through QuickMapService of QGis software. b Kaverina plot of volcanoes and analyzed regions. c Stress/strain fields as represented in the Kaverina plot.

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Revealing the state of stress, dilatational tendency and fluid-pressure to trigger extension fractures in a regional context and in individual volcanic complexes

Here we present a consolidated compilation and careful selection of published focal mechanisms (short-term “instantaneous” data) and fault slip data (FSD, long-term data) from the SVZ16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36 used to unravel the regional and local state of stress around volcanoes. The double-couple component of focal mechanisms and FSD represent shear fractures6,37,38, and can be used to identify the orientation of the principal stress axes and the stress ratio (ɸ)37,38 by using the same physical and mathematical framework, as the Wallace-Bott hypothesis39,40. In this work, the term “state of stress” or “state stress” is used to refer to the orientation of the principal stress axes and the stress ratio (ɸ).

Present regional stress state was calculated from short-term/instantaneous focal mechanism data18,19,22,23,41,42 for five regions. These were defined by considering the latitudinal volcano-tectonic segmentation of the SVZ14,15: Maipo (33°–34°S), Maule (34°–37°), Araucanía (38°–40°), Chiloé (42°–43°S) and Cisnes (44°–45°S) shown in Fig. 1.

For individual volcanoes, we calculated both the short- and long-term stress state from focal mechanisms and FSD16,17,18,19,20,21,24,25,26,27,28,29,30,31,32,33,34,35,36. The raw seismological and structural database can be found in the Supplementary Note S1, Supplementary Data 1, Supplementary Table 1, and in an online repository declared in Data availability. Earthquake magnitudes range from Mw 1.0 to 4.1, and fault slip data include a wide range of fault sizes, from millimeters to meters. Each component of the database employed here has already been collected, discussed, and published in previous works16,17,18,19,20,21,24,25,26,27,28,29,30,31,32,33,34,35,36, but here they are analyzed holistically to understand the tectono-magmatic processes occurring in the SVZ rather than in individual volcanoes only. To build our database we only considered volcanoes with existing seismic and/or field data within a conservative radius of 2 kilometers from the volcanic edifice or located in major faults spatially associated with volcanoes. The data shortage (due to inaccessibility to some volcanic flanks) and short duration of seismic temporal records generate different spatial and temporal biases, which are detailed individually for each volcanic complex in Supplementary Discussion 1, and later is discussed how these biases affect our results and conclusions.

In total, we conducted seven short-term16,17,18,19,20,21 and thirteen long-term24,25,26,27,28,29,30,31,32,33,34,35,36 analyses, accounting for 23% of the volcanoes within the SVZ, that include 16 different volcanic complexes (i.e., 12 polygenetic volcanoes and 4 monogenetic volcanic fields; Figs. 1, 2). The selected volcanoes are broadly representative of the SVZ tectono-magmatic context since they are distributed along the arc’s length and volcano-tectonic segmentation. They also represent a wide range of lava compositions, edifice volumes, and fault settings including the most relevant fault systems within the intra-arc region, namely the Liquiñe-Ofqui Fault System and Andean Transverse Faults (Fig. 1).

Fig. 2: State of stress of regions and volcanoes of the SVZ.
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The figure shows the density distribution of σ1- and σ3- directions colored in red and blue contours, respectively. We include the median ɸ value, the percentage of data compatible with the most representative stress setting (Methods), and the amount of data “n” (focal mechanisms or FSD). Some volcanoes present two stress states separated in two rows. The specific location of short- and long-term data for each volcano can be found in the folder “raw data” explained in Supplementary Note 1. The time window of short-term data represents the period of recorded seismicity by local seismic networks. The relative age of fault slip data was taken from literature16,17,18,19,20,21,24,25,26,27,28,29,30,31,32,33,34,35,36, and mostly ranges from Miocene to Quaternary. They are considered maximum faulting ages because they are defined from the rock unit(s) they crosscut. However, the internal consistency between the geometry and kinematics of faults cross-cutting Pliocene to Pleistocene rock units with those from older plutonic and volcanic units strongly suggests that the fault populations analyzed represent post-Pliocene deformation. This interpretation is further supported by the stability of the tectonic regime governing the SVZ, as well as the magnitude and direction of the convergence vector, which has remained nearly constant since the mid-Miocene57,81.

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The likely distribution of principal stress axes and stress ratio (ɸ) were calculated using the Multiple Inverse Method (MIM)37,38. We chose this method because it is adapted to analyze focal mechanisms as well as FSD, and allows for the identification of heterogeneous or polyphase stress states, which is crucial when analyzing long-term data24,29,31. From the MIM results, we selected the most representative stress solution for each volcano and evaluated the compatibility of the data with this selected solution (see Methods section). Compatibility was evaluated by quantifying the amount of data with a misfit angle (i.e. angle between the slip-direction of the data and the predicted-slip direction) lower than 30°31,37,43. If less than 70% of the data were compatible with the most representative solution, we calculated a secondary stress solution, excluding the data that were compatible with the primary stress solution. The results of principal stress directions and stress ratio are presented in Fig. 2.

Potential fluid-pathways in volcanoes can be inferred by identifying the planes showing the highest values of dilatation tendency, or the lowest values of total fluid-pressure required to trigger hydrofractures. Both scenarios should promote the generation of extension fractures. To calculate the dilatation tendency and total fluid-pressure, we used the principal stress orientation and stress ratio previously calculated for each volcano, and the non-Andersonian equations (Methods). Unknown variables for these equations are the tensile strength (\(T\)), the magnitude of differential stress (\(\tau ={\sigma }_{1}{-}{\sigma }_{3}\)), and the plunge of the principal stresses (\({\varphi }_{1},{\varphi }_{2},{\varphi }_{3}\)), which makes the calculation of dilatational tendency and total fluid-pressure uncertain. Therefore, we created a Monte Carlo simulation of 1000 cases for each volcano to test the most likely values for dilatation tendency and total fluid-pressure. These parameters depend on six variables (\(z{,\varphi }_{1},{\varphi }_{3},\phi ,\tau ,T\) - depth, plunge of σ1 and σ3, stress ratio, differential stress, and tensile strength, respectively). All six-variables varied randomly within a reasonable range in either linear or probabilistic distributions. As a result, we obtained 1000 simulations that can be re-organized to show statistical parameters as percentiles, median, or standard deviations (see Fig. 3a). This novel Monte-Carlo simulation reveals the likely orientation of extension fractures and thus, of geofluid circulation pathways at individual volcanoes (Figs. 3b, 4). For readers interested in reproducing or expanding upon this analysis in other volcanic arc settings, the codes developed here can be found in Supplementary Note 2, Supplementary Folder “Code”, and the link declared in Code availability statement, where a test case is also provided.

Fig. 3: Results of the Monte Carlo simulation.
figure 3

a Graphical explanation of the Monte Carlo simulation, and the percentile calculations, for the case of Copahue-Caviahue Volcanic Complex. Top left shows an example of one Monte Carlo simulation, randomly chosen. At the middle, 1000 Monte Carlo simulations are organized by the number of the simulation. Top right shows the results of the 1000 simulations reorganized statistically in percentiles. The total fluid-pressure that triggers extension fractures is presented normalized by the lithostatic pressure or the vertical stress. Thus, this variable is the fraction of the lithostatic pressure required for fluid-pressure to trigger extension fractures in a specific plane of strike (x-axis) and dip (y-axis). b Results of Monte Carlo simulation separated by the four types of stress patterns identified in the SVZ. The volume of volcanic edifices, lava composition, and the orientation of σ2 axes also are shown. The total fluid-pressure results are displayed in the space of strike (x-axis) and dip (y-axis), where each coordinate (x,y) represents a specific plane with strike/dip orientation. We show the 10- and 90- percentile results of the Monte Carlo simulation because they allow the observation of a representative range that includes 80% of the results of the Monte Carlo simulation. 5- 25- 75- and 95- percentiles, mean, and standard deviation can be found in Supplementary Note 3, in the “Supplementary Figure” folder. Synthetic fractures are modeled by randomly selecting their orientation (strike/dip) considering the lower total fluid-pressure values. The purpose of showcasing these synthetic fractures is to illustrate the results of the Monte Carlo simulation in terms of how the orientation of extension fractures should be according with the models. Comparison between the models and actual data is shown in Fig. 4 and in the discussion section of the reliability of results.

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Fig. 4: Reliability of Monte Carlo simulation.
figure 4

a Rose diagram of veins and dikes considered in this work to test Monte Carlo simulation in four volcanoes of the SVZ: Puyuhuapi volcanic group; Tolhuaca; San Pedro-Tatara and Puyehue-Cordón Caulle. Note that these data only represent a small proportion of dikes around a volcano, because near 90% of dikes are arrested or deflected at depth, considering the small percentage of feeder dikes observed worldwide7,49. b Dilatational tendency and (c) total fluid pressure required to trigger extension fractures, as revealed by the Monte Carlo approach in the same cases as (a). Black dots represent vein and dike orientation measured in the field. At Puyuhuapi and Tolhuaca volcanoes, the radius of black dots is related to veins width. Vein and dike orientations were obtained from previous works in Tolhuaca32, San Pedro-Tatara28 and Caulle82 volcanoes, and represent Quaternary processes. Data from Puyuhuapi were obtained directly by the authors. All Puyuhuapi veins crosscut the Holocene basaltic rocks of Puyuhuapi volcanic group.

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Results and discussions

Regional and local states of stress in the Southern Volcanic Zone

Our results from the short-term analysis show that the regional stress state in the SVZ is governed by a sub-horizontal σ1 trending between N30°E and N60°E, and a sub-horizontal σ3 trending between N05°E and N40°W (Fig. 2). Apart from the Maipo Region, all regional stress state can be classified as strike-slip normal according to the Kaverina plot44,45 (Fig. 1b). The outlier compressional solution obtained for the Maipo Region (33°–34°S) is, however, in agreement with previous works documenting a compressional regime at these latitudes, linked to the Chile-Argentina flat-slab (28°–33°S)14,22. In turn, the sub-horizontal ~NE-trending σ1 for remaining regions suits an intra-arc strike-slip regime associated with strain/deformation partitioning described by many authors14,23,31,35.

For individual volcanoes, a wide range of stress classifications is evident in the Kaverina plot ranging from normal to strike-slip reverse (Fig. 1b). Overall, we determined four states of stress patterns:

  • Type A: Strike-slip state of stress with a sub-horizontal σ1 and σ3, consistent with the far-field regional tectonic stress imposed by the oblique convergence. This pattern is commonly observed in monogenetic volcanic fields such as Puyuhuapi and Los Pescados (Fig. 2).

  • Type B: Local extensional state of stress defined by a vertical σ1 and a horizontal σ3 that is not necessarily equal to the regional far-field tectonic σ3 trend. This is the case for several polygenetic volcanoes with large composite edifices such as Copahue-Caviahue (long-term), Tolhuaca, and San Pedro-Tatara.

  • Type C: Strike-slip state of stress where σ1 is horizontally rotated between 50–90° from Type-A, indicating a NW-trending σ1. This pattern is observed as the primary stress state solution for the Villarrica volcano, and as secondary stress state solutions for Tolhuaca, Copahue-Caviahue (long-term), Planchón-Peteroa, and Nevados de Chillán volcanic complexes.

  • Hybrid Type (A + B, or B + C): A single state of stress containing two of the aforementioned stress patterns/types, for example, Type A and B, where σ3 is equal to the regional far-field direction, and σ1 varies in a NE-oriented sub-vertical plane; observable, for example, in Copahue-Caviahue or Mentolat (short-term). Another example is the primary stress state of Puyehue-Cordón Caulle, where σ1 varies in a NW-striking sub-vertical plane containing Type B and C.

The outlier solutions with a single case are Carrán Los Venados and Callaqui.

Orientation of dikes and veins as a proxy for magma and hydrothermal fluid migration plumbing system

The results of the total fluid-pressure required to trigger extension fractures are presented in Fig. 3b, where eight volcanoes were selected to show the expected dike and vein orientations for the four, previously described, volcanic stress patterns. We focus on total fluid-pressure conditions to induce extension fractures, rather than dilatational tendency, as the former provides a more accurate prediction of dike and vein orientation (discussed in the next section).

Results of the Monte Carlo simulation of Type A pattern show two main orientations where fluid circulation should be concentrated, as depicted by the blue bands (Type A results in Fig. 3b). Normally, these bands are limited to the range 50–80° in the NE-quadrant, which is consistent with the occurrence of NE-striking dikes and veins with dip angles >40–50°. In contrast, Type B stress pattern promote fluid circulation in dikes and veins with all possible strikes (0° to 360°) and with dips >20–30°. Type C concentrates its most-likely conditions for extension fracture development in NW-striking dikes and veins. Lastly, some examples of Hybrid Type are consistent with Type A, but extension fractures can occur in a wider range of orientations (~100°) falling in the NE-quadrant.

The spatial and temporally biases of database and reliability of results

The reliability of the results presented here may be affected by several biases due to data limitations. Firstly, there is a spatial bias due to inaccessibility and limited outcrops that restricts the structural database. Secondly, there is a temporal bias resulting from the limited temporal seismic networks in the region (see Supplementary Discussion 1, for spatial and temporal bias of each volcano). These biases limit the comprehensive definition of stress states related to volcanoes, which can be mostly resolved when instrumentation records several eruptions cycles. Even then, a new different stress signature could emerge as a result of tectonic variability or a stress disequilibrium. Despite these issues, here we have partially revealed the state of stress of volcanoes in the SVZ, which shows the existence of three end-member stress patterns repeated throughout the region (Type-A, B, and C). We acknowledge that the spatio-temporal biases in our database do not allow us to conclude that these are the only stress patterns in the region, and that patterns not reported here might emerge as more data becomes available.

The reliability of the Monte Carlo simulations is discussed and evaluated by comparing the results with field data (strike/dip) of dikes and hydrothermal veins documented within and around four volcanoes (Fig. 4). We observed that the orientations of dikes and veins (black circles in Fig. 4b, c) coincide with the preferred dilatational planes and the orientations where the total fluid-pressure required to trigger extension fractures is the lowest. Compatibility between the models and field data was evaluated by quantifying the number of dikes and veins that are constrained between a range of one standard deviation from the highest value of dilatational tendency and the lowest total fluid-pressure value. Median models contain 65% and 77% of field data for dilatational tendency and total fluid-pressure models. The 10-percentile models contain 84% and 80% of data from dikes and veins for dilatational tendency and total fluid-pressure respectively, whereas the 90-percentile models contain 38% and 72%, respectively. These percentages suggest that fluid-pressure models are better predictors of dike and vein occurrence than dilatational tendency. Moreover, there are populations of dikes and veins that are not consistent with our modeling (i.e., the remaining percentage of data) which can be explained by other local geologic and tectonic factors not considered in the present work. These may include (1) the local rotation of principal stresses due to dike emplacement46,47,48; (2) local mechanical heterogeneities that can arrest or redirect propagation pathways7,49; (3) spatial and temporal variation in the local stress at the vicinity of a magma chamber, or ahead of the dike tip7,50. However, considering that most of the field data fit with the total fluid-pressure models (previous testing percentage greater than 70%), the state of stress calculated from shear fractures printed in focal mechanisms and fault-slip data coupled with the Monte Carlo method presented here seem to be reliable first-order predictors of fluid pathways within the upper crust in volcanic regions, at least in cases where extension fractures are associated with the documented state of stress.

Whilst some authors have argued that hydrothermal veins are commonly restricted to fault zones51,52, the vein data presented here are recorded within Holocene volcanic edifices and are not restricted to fault zones. Therefore, they are most likely dominated by a volcano-driven stress effect rather than tectonic-driven stress occurring within a fault. As shown in Fig. 4, the presented Monte Carlo simulation can predict vein orientations when they are related to the documented stress state in the volcanoes. In the case that veins are restricted to fault-zones, our method should be tested considering the specific stress state of the fault, which is beyond the scope of this work.

Comparison between long-term and short-term state of stress

In the four cases where evidence of both long- and short-term stress states can be compared, three volcanic displayed striking similarities (Los Pescados, Puyuhuapi, and Laguna del Maule). Although a subtle rotation in the orientation of the principal stress axes and some variability in the ɸ histograms were noticeable in Laguna del Maule, the orientation of the principal stress axes was nearly identical in all three cases (Fig. 2).

The Copahue-Caviahue volcanic complex (Fig. 2) is the only exception where long- and short-term solutions differ. A reasonable explanation of these differences could be the temporal variability of the stress state in the volcanic complex during an eruption46,47,53, or in the subduction cycle29,54,55,56. This implies short-term data with earthquakes Mw<4 reveal only a part of the entire deformation process. During an eruption or a megathrust subduction earthquake, significant changes in the stress state should vary fault-kinematics producing a fingerprint in the long-term that is not necessarily comparable to the short-term seismological observation, that in the Copahue-Caviahue database, is restricted to the subduction interseismic period. An alternative explanation would be local stress rotations47 in the walls of the long-lived fissure volcanism reported for the bulk Callaqui-Copahue-Caviahue-Mandolehue volcanic chain26.

The long-term analysis shows that seven out 13 cases present two stress state solutions, suggesting a complex stress distribution around volcanoes. The most significant solution of long-term cases (i.e, the primary stress solution that represents the most % of the data) is compatible with 41% up to 81% of the FSD, whereas the secondary stress solution is subordinate, and compatible with 23% up to 30% of the FSD. The deformation pattern during and after the 2011 Cordón Caulle eruption confirms the above-mentioned stress distribution complexity, showing that extensional and the opposite compressional state of stress coexist for about 8 months (short-term local variability), that could be attributed to a compressional environment coupled with extensional mechanisms triggered by the evacuation of magma from the chamber during the eruption21. The absence of a secondary stress solution in most of the short-term cases suggests that the datasets used to define the short-term stress state do not reveal the entire deformation process occurring around volcanoes (which can be as long as hundreds or thousands of years). This observation underscores the significance of long-term data as a valuable source of information for comprehending the volcano-tectonic processes that govern volcanic arcs.

The geological significance of the different stress patterns in the SVZ

The geological processes accounting for the previously described stress patterns are discussed below, and summarized in Fig. 5. The main finding is that, unlike Hybrid Types, stress patterns A, B, and C characterize end-member state of stress.

Fig. 5: Summary of the volcano-tectonic process dominating the SVZ, as discussed in the text.
figure 5

Each of the three end-member stress patterns identified (Types A, B, and C) represent different volcano-tectonic processes. Note that Type-C stress can be explained by two volcano-tectonic processes, hypothesis 1 or hypothesis 2.

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The strike-slip Type A stress pattern represents volcanoes that are coupled with the far-field regional tectonic stress setting of the interseismic deformation on the overriding South American plate14,54,57 (Fig. 5). This stress pattern is expected to control volcano-tectonic processes in monogenetic groups, as Puyuhuapi volcanic group; around volcano edifice flanks58, influencing the geometry and location of parasitic cones26; or within kinematically-coupled volcanoes14. In terms of magma chambers, this stress pattern indicates that any hypothetical shallow chamber does not significantly alter the regional tectonic stress, thus, there are at least three possibilities: (i) the absence of a shallow magma chamber located in the brittle crust (where data are located), (ii) the stress effect of a magma chamber is enclosed in another stress state solution (i.e., the primary or the secondary state of stress, in volcanoes that have more than one stress state solution); or (iii) the spatial and/or temporal biases of the data do not capture the potential magma chamber-driven stress state. In the case of the small volcanic groups like Puyuhuapi or Los Pescados, an absence of a shallow magma chamber in the brittle crust is plausible, given their basaltic nature and the fact they have erupted less than 2 km3 of lava. In the case of Laguna del Maule, the primary Type-A pattern should reflect a local stress dominated by the far-field tectonic stress, as shown by the dextral NE-striking Troncoso fault16, whereas the secondary stress state solution in the long-term results (Fig. 2) may reflect the inflation of a sill at ~5 km depth59, fitting with the second possibility. In the case of Planchón-Peteroa, MT surveys reveal the absence of a magma chamber immediately beneath the volcanic edifice60, and NNE to NE-striking normal fault and fractures, suggest the existence of extension fractures aligned with σ1 of a Type-A stress pattern25. Similarly, Nevados de Chillán is spatially associated predominantly with NE-striking dextral faults and dikes aligned with σ1 of a Type-A stress pattern29. Normal faults, fractures and dikes aligned with σ1 of a Type-A stress pattern suggest that fluid circulation in the brittle crust at Nevados de Chillan and Planchón-Peteroa volcanic complexes should be controlled, at least in part, by this stress pattern. Indeed, if fluid circulation only depends on that, it should be restricted to subvertical NE-striking dikes and veins (e.g, Puyuhuapi in Fig. 5). However, we cannot discard that the migration of magmatic and hydrothermal fluids also occurs within preexisting high permeability zones, such as faults, which are not necessarily NE-striking. Overall, the Type-A stress pattern is attributed to the far-field tectonic stress resulting from oblique subduction, should promote the occurrence of NE-striking dikes and veins, and it is associated with scenarios such as the absence of a shallow magma chamber (e.g., Puyuhuapi or Planchón-Peteroa) or the presence of a magma chamber in the brittle crust, as indicated by other state of stress solution (e.g., Laguna del Maule).

The extensional Type-B stress pattern was observed in the largest volcanic edifices, such as San Pedro-Tatara and Puyehue-Cordón Caulle. This stress pattern can be explained by (1) a progressive increase in the magnitude of the vertical stress due to edifice growth during volcano building61, (2) increase in the magnitude of vertical stress above a magma storage zone (sills, laccoliths or chambers7,62), or alternatively (3) local stress rotation in dilatation jogs or horse-tail structures5. These three processes can coexist. The existence of this stress pattern may suggest the presence of a shallow magma chamber in the brittle crust, or a magma reservoir located in the ductile crust, either of which may be capable of modifying and controlling the stress at shallower levels where focal mechanisms and FSD occur. Several magnetotelluric (MT) surveys conducted in the SVZ have documented electrically conductive volumes in the upper crust associated with magma storage regions, including San Pedro-Tatara, Tiguiririca, Copahue-Caviahue and Tolhuaca volcanoes60,63,64,65, all of which display a Type B stress signature. Additionally, from surface deformation modeling using InSAR, an inflating sill at 5 km depth was documented in the Laguna del Maule volcanic complex59 and several pulses of upper crustal magma injection were interpreted for Cordón Caulle66, both presenting Type-B pattern. Lastly, Mentolat volcano has geobarometric evidence indicating a magma storage depth as shallow as 5 km67, which allows us to state that in all seven cases presenting the Type-B stress pattern there is evidence of magma stored in the upper brittle crust. Type-B stress pattern promotes dike and vein formation in radial directions (0 to 360°, see Fig. 5). This is suggested by Monte Carlo models and confirmed with field data from Tolhuaca, as seen in Fig. 4. Notoriously, Type B stress pattern have the lowest total fluid-pressure values compared to the other stress patterns (Fig. 3) suggesting that this stress pattern promotes the formation of extension fractures more easily. Thus, representing a positive feedback process that promotes magma injection. In other words, magma storage should increase the magnitude of vertical stress, which in turn facilitates later magma injection in the form of dikes and inclined sheets and generating more magma storage and eruptions. This incresed rate of magma injection, together with the plausible magma storage zone located in the upper crust, would likely create a heated volume in the crust near Type-B volcanoes, and thus, the vicinity of these volcanoes could represent ideal geothermal targets.

Finally, the strike-slip Type-C pattern is an enigmatic signature present in several volcanoes that have had eruptions within the past 300 years (Fig. 6). In fact, considering the volcanoes analyzed here, six out of nine volcanoes with recorded historical eruptions have a Type C signature, either as a primary or secondary stress solution. The exceptions are Mentolat, Carrán Los Venados and Callaqui. Previous authors have documented a similar Type-C pattern in Nevados de Chillán and Puyehue-Cordón Caulle29,34 and have hypothesized that: (i) it is linked to the co-seismic period of megathrust earthquakes where the elastic rebound generated in the overlying plate allows for extension and/or (ii) the reactivation of NW-striking basement faults. However, the former seems to be small to generate the stress change required to trigger an eruptive cycle by itself55,68. The second hypothesis is also difficult to reconcile in all cases, since NW-striking basement faults have not been identified in many of the volcanoes with Type-C signature. Therefore, there is no unequivocal geological process that can account for this signature.

Fig. 6: Contrasting the stress patterns with historical eruptions.
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Plot showing the last 300 years of documented eruptions and subduction megathrust earthquakes in the SVZ. Volcanoes are organized by latitude (y-axis) and color-coded by the type of stress setting (A, B, and C). The volcanoes are subclassified as A + B; A + C; or B + C, when they have a stress state that included two end-member stress pattern (i.e., hybrid stress type) or when they have two stress fields containing two different end-member types. Further details of the stress state classification are shown in Fig. 7, and Supplementary Table 2. Eruption dates were obtained from the Global Volcanism Program83. The slip segment of each megathrust earthquake was approximated from Watt et al.84. The area affected by elastic and viscoelastic deformation was approximated to be two times longer than the slip segment; the period of elastic effects was set to 3 years70, and viscoelastic effects were constrained to 35 years considering the discussion of Bonali et al.55.

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We hypothesize that at least two main processes can explain this stress pattern: (1) reactivation of preexisting NW-striking faults as parallel-to-the-fault hydrofractures promoted by the ascent of overpressurized deep magmatic or hydrothermal fluids, and (2) local ninety-degree rotation of principal stress axes during intrusion and inflation of a NE-striking dike at its walls47 (Fig. 5). Our first hypothesis is similar to those previously suggested, but here we highlighted the reactivation of the NW-structures as hydrofractures (extension fracture) that require an overpressure fluid. The first hypothesis implies transient perturbations of magmatic or hydrothermal reservoirs creating a large-scale NW-striking channel of fluids capable of modifying the local stress. The second hypothesis suggests that ongoing magmatic injections aligned with the far-field tectonic regional stress axes exert a fluid-driven force against wall rocks. When subduction megathrust events occur, hypothesis (1) is plausible considering the permeability enhancement in inherited faults after dynamic alteration of seismic waves69 and volumetric dilatation of the crust70. Otherwise, we propose that the long-term secondary Type-C stress pattern documented in Planchón-Peteroa, Nevados de Chillán, Copahue-Caviahue, and Tolhuaca volcanoes is coherent with the second hypothesis since, in all these cases, Type-C is rotated 90-degrees from the primary stress state solution (see Fig. 2). On the contrary, at Villarrica and Puyehue-Cordón-Caulle volcanic complexes, the first hypothesis fits better with the geological context, considering previously defined NW-faults associated with both volcanoes14,18,34, and seismicity elongated in a NW-trending direction (see expanded discussion in Supplementary Discussion 2). Interestingly, both hypotheses used to explain the Type-C pattern implies pressure made by fluid circulation through open-fractures (i.e, extension or hybrid fracture), which leads us to consider that Type-C is a potential eruption footprint. Of the total number of eruptions that occurred in the last 300 years, 49% have been recorded in volcanoes with a Type-C signature, and this percentage increases up to 96% if we only consider the volcanoes analyzed in this work (Fig. 6). This demonstrates the importance of the Type-C stress pattern for understanding and assessing volcanic hazards in the SVZ. Although the volcanoes associated with this stress pattern are the most active along the SVZ (Fig. 6) and appear to have a positive correlation with megathrust earthquakes, eruptions from these volcanoes cannot be exclusively explained by megathrust earthquakes, since most of the eruptions occurred within interseismic periods. Therefore, subduction earthquakes, along the megathrust, should be viewed as a disturbance for a system ready to erupt rather than as the trigger for eruptions in Type-C volcanoes.

Summarizing the fundamental findings of this investigation, the three pivotal end-member stress patterns proposed here are: Type-A, the regional far-field tectonic stress; Type-B, the local, volcanic load and magmatic-dominated stress state; and Type-C, the local and probably transient stress driven by fluid passing through open-fractures. We propose a classification of volcanoes based on the stress state constrained in this work, which is presented in Fig. 7. If volcanoes exhibit a Hybrid-type stress state, or have two or more distinguishable stress state solutions (two rows in Fig. 2) representing different stress pattern/types, they are classified as A + B, A + C, B + C or A + B + C (details in Supplementary Table 2). There is no direct correlation between the stress patterns and the geochemical composition of volcanoes, the volume of volcanoes, nor the type of volcanoes (i.e., stratovolcanoes, calderas), as can be observed in Fig. 3 and Supplementary Table 3. However, minor eruptive centers, commonly of basaltic composition, mostly exhibit a Type-A signature. Importantly, the classification presented in Fig. 7 could be improved in the future, as new data emerge, reducing the spatial and temporal biases of our database. For example, petrological data71,72, crustal deformation revealed by InSAR73, long-period seismic signals74, and MT-surveys75 within Villarrica volcano provide evidence of a shallow magma chamber in the upper ~5 km that should imply the Type-B pattern, but the stress inversion conducted here does not reveal this pattern in Villarica (Figs. 2, 7). The limited short-term seismic data restricted to ~one year of measurements, with earthquakes confined to the eastern flank of the volcano within 7 and 9 km depth, does not fully reveal the full complex stress pattern of this stratovolcano. Similarly, other long-lived stratovolcanoes and calderas with variable compositions, eruption styles, and chemical evolution might have a complex stress history that could not be completely represented in our database, or in our classification.

Fig. 7: Volcanoes of the SVZ, as classified in this work onto a triangular plot, which is based on the amount of compatible data with each stress type (Type A, B, C).
figure 7

The volcanoes are subclassified as A + B; A + C; or B + C, when they have a stress state that includes two end-member stress patterns (for example, volcanoes as Mentolat, with hybrid stress type that include Type A and B) or when the volcanoes that record two state of stress containing two different end-member types (for example, Planchón-Peteroa that has a primary stress state classified as Type-A, and its secondary stress state pertaining to Type C, shown in Fig. 2). The relative proportion of each stress pattern for each volcano is explained in Supplementary Table 2.

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The contribution of this work in the context of other volcanic arcs

Our results can be compared with the state of stress documented in other compressional and strike-slip volcanic arcs worldwide, related to oblique subduction (e.g., Aleutians-Alaska, Northeast Honshu, Java arcs). A remarkable similarity with the Aleutian-Alaska arc is that the most common stress state recorded in volcanoes is consistent with the far-field tectonic stress arising from oblique convergence and slip partitioning, named here as Type-A (i.e., 40 out of 49 in Aleutian-Alaska volcanoes12, and 10 out of 16, exposed here). The type-A pattern is also the most recurrent in Quaternary stratovolcanoes and Mio-Pliocene calderas in the Northeast Honshu arc, and in different types of volcanic cones along the Java volcanic arc9,10. This suggests that the far-field tectonic stress exerts a first-order control on the fracturing process occurring in compressional and strike-slip volcanic arcs. Type-B pattern has been suggested in NE Honshu in volcanoes with recurrent sill emplacement6,10, and has been documented as the background state of stress in the Redoubt volcano in the Aleutians53. Additionally, local horizontal rotation of the far-field tectonic stress, similar to Type-C pattern, has been documented in volcanoes in the Aleutians12,46,53, and in Mt. Argopuro within the Java arc9, but not clearly in NE Honshu. Hence, the identified stress patterns likely reflect volcano-tectonic processes occurring in both strike-slip- and compressional-dominated volcanic arcs, extending beyond the SVZ.

Lastly, more than one stress state has been observed in seven out of 49 volcanoes of the Aleutians12, but none out of the 23 in the Java volcanic arc9. In contrast, at least nine of the 16 volcanoes analyzed in the SVZ have been found to exhibit more than one stress state (Figs. 2, 7). This difference can be explained by the stress inversion performed in this study, which has been shown to better describe the complex and variable tectonic setting around volcanoes, compared to traditional morphometric tools. Traditional morphometric analyses rely on surface strain expressions at the volcano-scale, limiting interpretation to horizontal principal stress axes. The high number of volcanoes with more than one stress state (>50% in SVZ) highlight the importance of the formal inversion of the stress around volcanoes, which could include all three stress patterns in the same volcano (e.g., Copahue-Caviahue, Fig. 7).

Furthermore, evidence has shown that the local state of stress can rotate during eruption cycles, as seen along the Aleutian-Alaska, the Japanese arcs and the Andean Northern Volcanic Zone46,47,53. Here we have demonstrated that the local rotation of the stress state around volcanoes is also recorded in long-term structural data, and most importantly, is present in most of the volcanoes with historical eruptions (Fig. 6). Thus, defining the background state of stress for individual volcanoes is crucial to detecting changes in the stress state that can be correlated with coming eruptions.

Conclusions

From our results, we conclude that volcanic stress state can be decoded by combining an analysis of fault slip data and earthquake focal mechanisms. The coupling between long-term and short-term signatures allows to extension of the understanding of the stress state in volcanoes without decades of instrumental seismic data, using field structural geology studies. The long-term approach should be important considering that volcanoes that are likely to yield destructive eruptions during the next decades might lack prior instrumental data76.

Three main volcano-tectonic processes occur in the SVZ, and each one generates an end-member stress pattern. These processes can be summarized in: (i) regional far-field tectonic deformation (Type A); (ii) local state of stress driven by volcanic edifice and magma storage processes (Type B), and (iii) local transient stress driven by fluid circulation through open-fractures (Type-C). These stress patterns have been observed in other volcanic arcs, suggesting that these stress patterns are not restricted to the SVZ. The most recurrent pattern in the SVZ, as well as in Aleutians-Alaska, Northeast Honshu, and Java volcanic arcs, is Type-A.

Stress analysis from earthquake focal mechanisms and fault slip data should be further combined with the Monte Carlo method proposed here to determine likely fluid pathways in individual volcanoes. This analysis could be extended to most, if not all, active volcanoes in the SVZ, to assess potential fluid pathways within the upper crust, and can be applied to other volcanic arcs.

Applying the Monte Carlo simulation to the SVZ, our findings indicate that volcanoes with Type-B stress state have the most favorable conditions for triggering extension fractures, that promote magmatic and hydrothermal fluid circulation. Furthermore, this stress pattern may reflect the presence of a magma storage zone nested in the brittle upper crust, as all seven of the volcanoes with Type-B patterns have shown evidence of this. Therefore, these volcanoes may have a heated crustal volume in their vicinity generated by hot-fluid circulation around magma bodies, making them attractive geothermal targets.

Type-C stress patterns should be carefully examined in the future as an eruption forecast, considering that from the analyzed volcanoes, 96% of eruptions in the last 300 years have occurred in volcanoes with this stress signature, and both reliable hypotheses to explain its occurrence imply fluid migration. Therefore, it is necessary to further evaluate the causality between eruptions and Type-C stress patterns.

Methods section

Principal stress definition

The calculation of the principal stress directions and the stress ratio was done using the Multiple Inverse Method (MIM) software of Yamaji et al.37,38. The MIM reveals the stress state from shear fracture data, by minimizing the misfit angle between the shear fracture data and the shear direction predicted on the fault plane77,78, following the Wallace-Bott hypothesis39,40. However, not all shear fractures of a database obtained in the same outcrop (fault-slip data) or in the same seismic experiment (focal mechanisms) can be explained with a single stress state. For example, when several tectonic phases occur in the same site57, or when the stress state ephemerally changes, due to a volcanic eruption47 or megathrust earthquake54, more than one single stress state is commonly recorded. For this reason, we choose MIM software that calculates the principal stress orientation and the stress ratio of several sub-sets of data, allowing the observation of stress states that are hiding behind one dominating state of stress. As a result, this method shows the distribution of several possible σ1 and σ3 directions and their corresponding stress ratios.

The procedure described next was conducted to define whether the dataset should be represented by one or more stress states and to evaluate how much of the data are compatible with one specific stress state. First, we calculate σ1 and σ3 possibilities using the MIM with all the data. Second, we calculate a density distribution of σ1 and σ3 from the MIM results and we select σ1 and σ3 directions from the highest values of the density distributions. Third, we select all possible σ1 and σ3 closer than 10° from the previously obtained σ1 and σ3 directions and calculate the median value of stress ratio (ɸ). With the selected σ1 and σ3 directions and the median ɸ value, we define the selected stress setting. Fourth, we evaluate the selected stress setting by counting how many fault slip data, or focal mechanisms, are compatible with it. In the case of fault slip data, compatible means a misfit angle lower than 30°; and in the case of focal mechanisms, compatible means that at least one of the possible planes has a misfit angle lower than 30°. We choose 30° considering the threshold widely used in literature31,37,43. If more than 70% of the data are compatible, a single stress state is selected and shown as the result. Otherwise, we repeat all the processes without the fault slip data, or focal mechanisms, that are compatible with the first selected stress setting, and calculate a second stress setting. To follow the calculation of the second stress setting, a minimum of seven data (focal mechanisms or FSD) are required, and the second selected stress should reflect at least 20% of the total data. The stress states that represent less than 20% of the total data are not presented in this work.

Finally, the σ2 direction was calculated from a cross-product between each σ1 and σ3 directions.

Density distribution of principal stress orientations

The selection of a single stress setting is useful to evaluate how much data is compatible with a specific state of stress; however, a probabilistic tool such as a Monte Carlo simulation can evaluate the variability of the state of stress. Therefore, it will be better to define a stress state probabilistic distribution rather than a single representative stress state. In this way, the range of possibilities can be better explored and results can represent confidence intervals.

Here, the probabilistic distribution of a stress state was defined from a density distribution of MIM results. First, we define the most representative stress setting of a stress state (the selected stress setting explained in the previous section) and calculate its angular distance to all possibilities defined by MIM results. The 75% of the closest principal stress direction was subtracted and used to build a density distribution using the Kamb method79. We chose 75% of the results instead of 100% of the results since, in the case of two existing stress settings, the first MIM results might be confused with the second stress state. Selecting 75% of the MIM results, the primary stress state is modeled without noise. The specific number of 75% was chosen by observing the variability of stress distribution of volcanoes and regions; actually, the exact value should vary for each volcano and may be a function of the compatibility percentage of data. However, for the sake of simplicity, we select a single value (75%) that allows an approximation of the density distribution of principal stress orientations. In the case that MIM results represent a single stress state, the density distribution was calculated with 75% of the MIM results to avoid giving weight to outlier solutions. Results for each volcano and region are shown in Supplementary Note 3 which included results of 100% of MIM-results; 75% of the MIM results and the histogram distribution of MIM results in a stereonet plot.

Dilatational tendency and total fluid pressure for triggering extension fractures

The calculation of both variables was done by applying the non-Andersonean equations for the stress distribution in the crust (e.g.52). Two assumptions were made: (1) the stress in the vertical direction is equal to the lithostatic pressure and (2) the shear stress is unknown, but it is a value restricted between 1 to 250 MPa. These assumptions lead to the following equations that apply to each volcano:

$$\rho {gz}=\sin {\varphi }_{1}\,{\sigma }_{1}\left(z\right)+\sin {\varphi }_{2}\,{\sigma }_{2}\left(z\right)+\sin {\varphi }_{3}\,{\sigma }_{3}(z)$$
(1)
$$\phi =\frac{{\sigma }_{2}\left(z\right)-{\sigma }_{3}(z)}{{\sigma }_{1}\left(z\right)-{\sigma }_{3}(z)}$$
(2)
$${\sigma }_{1}\left(z\right)-{\sigma }_{3}\left(z\right)=\tau ,\tau \,\epsilon \,\left[1,250\right]{MPa}$$
(3)

Where \(\rho\) is the crustal density, approximated to 2.700 kg/m3 in this work; “g” is the gravity force approximated to 9.8 m/s; “z” is depth in meters; \({\varphi }_{i}\) is the plunge of the principal stress “i” which is unknown, but varies as the density distribution obtained from MIM results, defined in the previous section; \({\sigma }_{i}(z)\) is the scalar value of the principal stress “i” which depend on depth; ɸ is the stress ratio parameter defined in Eq. (2); and finally, \(\tau\) is an auxiliary unknown variable that helps to develop the calculation. With these three equations, we can resolve the scalar-magnitude of the three principal stresses since there are three incognita \(({\sigma }_{1},{\sigma }_{2},{\sigma }_{3})\) and three Eqs. (1,2,3):

$${\sigma }_{3}\left(z,\tau \right)=\frac{\rho {gz}-\tau * (\sin {\varphi }_{1}+\phi \sin {\varphi }_{2})}{\sin {\varphi }_{1}+\sin {\varphi }_{2}+\sin {\varphi }_{3}}$$
(4)
$${\sigma }_{2}\left(z,\tau \right)=\phi \tau +{\sigma }_{3}\left(z,\tau \right)$$
(5)
$${\sigma }_{1}\left(z,\tau \right)=\tau +{\sigma }_{3}\left(z,\tau \right)$$
(6)

With these Eqs. (4) to (6) we can evaluate how principal stresses vary depending on depth, the stress ratio, and shear stress “τ”, allowing the presentation of a heat map of any variable which depends on the stresses (e.g. see Figs. 3, 4). In this work, we focus on the dilatational tendency and the total fluid pressure required to trigger extension fracture, which can be calculated as follows:

$${Dt}(z,\tau ,{strike},{slip})=\frac{{\sigma }_{n}\left(z,\tau ,{strike},{slip}\right)-{\sigma }_{3}(z,x)}{{\sigma }_{1}\left(z,x\right)-{\sigma }_{3}(z,x)}$$
(7)
$${p}_{t}\left(z,\tau ,{strike},{slip}\right)={\sigma }_{n}\left(z,\tau ,{strike},{slip}\right)+T$$
(8)
$${p}_{t}/{\sigma }_{v}\left(z,\tau ,{strike},{slip}\right)=\frac{{p}_{t}\left(z,\tau ,{strike},{slip}\right)}{\rho {gz}}$$
(9)

Where “Dt” is the dilatational tendency; \({\sigma }_{n}\) is the normal stress to a specific plane of a given strike and dip; “\({p}_{t}\)” is total fluid pressure required to trigger extension fractures; and “T” is the tensile resistance of the rock assumed to vary between 3 and 10 MPa around the entire Southern Volcanic Zone. The last assumption was constrained considering the average tensile strength recorded for lithologies that are observed in the SVZ; which are Basalt, Graniodiorite, Granite, Gneiss, Sandstone, Limestone; and the average values of tensile strength or resistance were compiled by Perras and Diederichs80 from Brazilian and Direct tensile strength tests. “\({\rho }_{t}/{\sigma }_{v}\)” represent an unidimensional parameter to evaluate the total fluid pressure normalized by the lithostatic pressure \({\sigma }_{v}=\rho {gz}\). Therefore, when \({p}_{t}/{\sigma }_{v}\) is 1, to trigger extension fractures a total fluid-pressure equal to the lithostatic one is required, whereas when \(p/{\sigma }_{v}\) is 0.4 extension fractures are triggered with hydrostatic pressure. As Eqs. (7) to (9) show, Dt, \({p}_{t}\) and \({p}_{t}/{\sigma }_{v}\) also depend on the attitude of a specific plane (strike/dip). Therefore, to reveal the most favorable direction for fluid pathways it is necessary to evaluate the entire physical space of planes (i.e., strike between 0 and 360° and dip between 0 and 90°). For this purpose, we develop a Monte Carlo simulation, that randomly select the values of parameters required to resolve Eqs. (7) to (9) (i.e., \(z{,\varphi }_{1},{\varphi }_{3},\phi ,\tau ,{T}\)), and calculate the solution of (7) to (9) for planes striking in the range of 0 to 360°, and dip** ranging between 0 to 90°, with a resolution of 1° in both strike and dip.

Monte Carlo simulation

Applying Eqs. (3) to (9), the conditions required to generate an open fractures in the crust are decoded, allowing the observation of the orientation for fluid migration in the brittle crust. To carry out this calculation, we need a set of six parameters. None of these parameters have a single value, instead, they have a range defined as follows:

$$z\,\epsilon \,\left[1,15\right]{km}$$
(10)
$$\tau \,\epsilon \,\left[1,250\right]{MPa}$$
(11)
$$T\,\epsilon \,\left[3,10\right]{MPa}$$
(12)

\({\varphi }_{1},{\varphi }_{3}\epsilon\) density distribution calculated with the Kamb method and MIM-results, as was explained in Sections 1 and 2 of the methods.

\(\phi \epsilon\) histogram obtained form MIM results.

With this range of parameters, we can develop a Monte Carlo simulation approach to understand the possible realistic values for dilatational tendency and total fluid pressure required to trigger extension fractures, and more importantly, its dependency with the strike/dip orientation of planes. For \(z,\tau\) and \(T\) simulation takes random values from a linear distribution constrained between the ranges defined in (10, 11 and 12); whereas \({\varphi }_{1},{\varphi }_{3}\) and \(\phi\) area randomly selected from the density distributions defined from MIM-results and its histograms assuming that they represent a probabilistic distribution of these parameters.

Results are reorganized and sort by statistical parameters of each stike/dip plane (see Fig. 3a), and are presented as plots of 5-, 10-, 25-, 75-, 90- and 95-percentiles discretized in 1° cells, with maximum and minimum values, mean, median and standard deviation shown in Supplementary Note 3. We computed 1000 cases of the Monte-Carlo simulation to have a better approximation; however, from the 200th case onwards, the results between 10 and 90-percentiles remain unchanged.