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Joint inversion of tectonic stress and magma pressures using dyke trajectories

Published online by Cambridge University Press:  23 August 2022

F. Maerten Open the ORCID record for F. Maerten [Opens in a new window] ,
L. Maerten ,
R. Plateaux  and
P. H. Cornard
F. Maerten*
Affiliation:
YouWol, Le Lancaster, 455 rue Alfred Sauvy, Pérols 34470, France
L. Maerten
Affiliation:
YouWol, Le Lancaster, 455 rue Alfred Sauvy, Pérols 34470, France
R. Plateaux
Affiliation:
Open Plateau Ltd, F14-3, N57, Fuxing North Road, Songshan District Taipei City 105, Taipei, Taiwan
P. H. Cornard
Affiliation:
Department of Geology, University of Innsbruck, Innrain 52, Innsbruck, Austria
*
Author for correspondence: Frantz Maerten, Email: fmaerten@gmail.com
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Abstract

In volcano-tectonic regions, dyke propagation from shallow magmatic chambers is often controlled by the interaction of the local and regional stress fields. The variations of the stress fields result from a combination of factors including the regional tectonic stress, the geometry of pressurized magma chambers, the layering and the pre-existing discontinuities (e.g. fractures). In this contribution, we describe and apply a new multiparametric inversion technique based on geomechanics that can invert for both the far field stress attributes and the internal pressure of magma chambers or stocks, constrained by observed dyke or eruptive fissure orientations. This technique is based on the superposition principle and uses linear elastic models that can be solved using many types of numerical methods. For practical reasons, we chose a 3D boundary element method (BEM) for a heterogeneous elastic half-space, where magma chambers are modelled as pressurized cavities. To verify this approach, the BEM solution has been validated against the known 3D analytical solution of a pressurized cylindrical cavity. Then the effectiveness of this technique and its practical use is demonstrated through application to natural examples of dyke network development around two different volcanic systems, the Spanish Peaks (USA) and the Galapagos Islands (Ecuador). Results demonstrate that regional stress characteristics as well as the internal pressure of magma chambers can be estimated from observed radial and circumferential dyke patterns and some knowledge of magma chamber geometry.

Keywords

volcanoesstress inversionpressure inversiongeomechanicsdykes
Type
FAULTS, FRACTURES AND STRESS
Information
Geological Magazine , Volume 159 , Issue 11-12: THEMATIC ISSUE: Faults and fractures in rocks: mechanics, occurrence, dating, stress history and fluid flow , November 2022 , pp. 2379 - 2394
Copyright
© The Author(s), 2022. Published by Cambridge University Press

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References

Anderson, EM (1905) The dynamics of faulting. Transactions of the Edinburgh Geological Society 8, 387–402.CrossRefGoogle Scholar
Anderson, EM (1951) The Dynamics of Faulting and Dyke Formation with Applications to Britain, 2nd edition. Edinburgh: Oliver and Boyd, 206 pp.Google Scholar
Angelier, J (1979) Néotectonique de l’arc Égéen. PhD thesis, Université Pierre et Marie Curie, Paris. Published thesisGoogle Scholar
Angelier, J (1994) Fault slip analysis and palaeostress reconstruction. In Continental Deformation (eds WM Dunne and PL Hancock), pp. 53–100. Oxford: Pergamon Press.Google Scholar
Angelier, J (2002) Inversion of earthquake focal mechanisms to obtain the seismotectonic stress-IV: a new method free of choice among nodal planes. Geophysical Journal International 150, 588–609.CrossRefGoogle Scholar
Armstrong, RL (1969) K-Ar dating of Laccolithic centers of the Colorado Plateau and vicinity. Geological Society of America Bulletin 80, 2081–6.CrossRefGoogle Scholar
Baer, G and Reches, Z (1991) Mechanics of emplacement and tectonics implications of the Ramon dike system, Israel. Journal of Geophysical Research 96, 11895–910.CrossRefGoogle Scholar
Bauve, V, Plateaux, R, Rolland, Y, Sanchez, G, Bethoux, N, Delouis, B and Darnault, R (2014) Long-lasting transcurrent tectonics in SW Alps evidenced by Neogene to present-day stress fields. Tectonophysics 621, 85–100.CrossRefGoogle Scholar
Bazargan, M and Gudmundsson, A (2019) Dike-induced stresses and displacements in layered volcanic zones. Journal of Volcanology and Geothermal Research 384, 189–205.CrossRefGoogle Scholar
Bazargan, M and Gudmundsson, A (2020) Stresses and displacements in layered rocks induced by inclined (cone) sheets. Journal of Volcanology and Geothermal Research 401, 106965.CrossRefGoogle Scholar
Bergerat, F (1987) Stress fields in the European platform at the time of Africa-Eurasia collision. Tectonics 6, 99–132.CrossRefGoogle Scholar
Bistacchi, A, Tibaldi, A, Pasquar, FA and Rust, D (2012) The association of cone-sheets and radial dykes: data from the Isle of Skye (UK), numerical modelling, and implications for shallow magma chambers. Earth and Planetary Science Letters 339–340, 46–56.CrossRefGoogle Scholar
Bourne, SJ and Willemse, EJM (2001) Elastic stress control on the pattern of tensile fracturing around a small fault network at Nash Point, UK. Journal of Structural Geology 23, 1753–70.CrossRefGoogle Scholar
Brillouin, L (1946) Wave Propagation in Periodic Structures: Electric Filters and Crystal Lattices. New York: McGraw-Hill.Google Scholar
Browning, J and Gudmundsson, A (2015) Caldera faults capture and deflect inclined sheets: an alternative mechanism of ring dyke formation. Bulletin of Volcanology 77, 1–13.CrossRefGoogle Scholar
Célérier, B, Etchecopar, A, Bergerat, F, Vergely, P, Arthaud, F and Laurent, P (2012) Inferring stress from faulting: from early concepts to inverse methods. Tectonophysics 581, 206–19.CrossRefGoogle Scholar
Chadwick, WW and Dieterich, JH (1995) Mechanical modeling of circumferential and radial dyke intrusion on Galapagos volcanoes. Journal of Volcanology and Geothermal Research 66, 37–52.CrossRefGoogle Scholar
Chadwick, WW and Howard, KA (1991) The pattern of circumferential and radial eruptive fissures on the volcanoes of Fernandina and Isabela islands, Galapagos. Bulletin of Volcanology 53, 259–75.CrossRefGoogle Scholar
Chestler, SR and Grosfils, EB (2013) Using numerical modeling to explore the origin of intrusion patterns on Fernandina volcano, Galapagos Islands, Ecuador. Geophysical Research Letters 40, 4565–9.CrossRefGoogle Scholar
Corbi, F, Rivalta, E, Pinel, V, Maccaferri, F, Bagnardi, M and Acocella, V (2015) How caldera collapse shapes the shallow emplacement and transfer of magma in active volcanoes. Earth and Planetary Science Letters 431, 287–93.CrossRefGoogle Scholar
De Joussineau, G, Petit, J-P and Gauthier, BD (2003) Photoelastic and numerical investigation of stress distributions around fault models under biaxial compressive loading conditions. Tectonophysics 363, 19–43.CrossRefGoogle Scholar
Dorigo, M (1992) Optimization, Learning and Natural Algorithms. PhD thesis, Politecnico di Milano, Milan. Published thesis.Google Scholar
Etchecopar, A, Vasseur, G and Daignieres, M (1981) An inverse problem in microtectonics for the determination of stress tensors from fault striation analysis. Journal of Structural Geology 3, 51–65.CrossRefGoogle Scholar
Fjaer, E, Holt, RM, Horsrud, P and Raaen, AM (2008) Petroleum Related Rock Mechanics. Amsterdam: Elsevier.Google Scholar
Geist, DJ, McBirney, AR and Duncan, RA (1986) Geology and petrogenesis of lavas from San Cristobal Island, Galapagos Archipelago. Geological Society of America Bulletin 97, 555–66.2.0.CO;2>CrossRefGoogle Scholar
Griffith, WA, Becker, J, Cione, K, Miller, T and Pan, E (2014) 3D topographic stress perturbations and implications for ground control in underground coal mines. International Journal of Rock Mechanics and Mining Sciences 70, 59–68.CrossRefGoogle Scholar
Gudmundsson, A (2011) Deflection of dykes into sills at discontinuities and magma-chamber formation. Tectonophysics 500, 50–64.CrossRefGoogle Scholar
Gudmundsson, A (2012) Magma chambers: formation, local stresses, excess pressures, and compartments. Journal of Volcanology and Geothermal Research 237–238, 19–41.CrossRefGoogle Scholar
Gudmundsson, A (2020) Volcanotectonics. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
Gudmundsson, A and Andrew, REB (2007) Mechanical interaction between active volcanoes in Iceland. Geophysical Research Letters 34, 1–5.CrossRefGoogle Scholar
Hills, RC (1901) Description of the Spanish Peaks quadrangle, Colorado. US Geological Survey Geologic Atlas of the United States, Folio 71, 7 pp. Denver, CO: US Geological Survey.Google Scholar
Jaeger, JC, Cook, NG and Zimmerman, R (2009) Fundamentals of Rock Mechanics. Chichester: John Wiley & Sons.Google Scholar
Johnson, RB (1961) Patterns and origin of radial dyke swarms associated with West Spanish Peak and Dyke Mountain, south-central Colorado. Geological Society of America Bulletin 72, 579–90.CrossRefGoogle Scholar
Johnson, RB (1968) Geology of the igneous rocks of the Spanish Peaks region, Colorado. US Geological Survey Professional Paper 594-G, 47 pp.Google Scholar
Jolly, RJH and Sanderson, DJ (1995) Variation in the form and distribution of dykes in the Mull swarm, Scotland. Journal of Structural Geology 17, 1543–57.CrossRefGoogle Scholar
Kattenhorn, SA, Aydin, A and Pollard, DD (2000) Joints at high angles to normal fault strike: an explanation using 3D numerical models of perturbed stress fields. Journal of Structural Geology 22, 1–23.CrossRefGoogle Scholar
Kaven, J, Maerten, F and Pollard, DD (2011) Mechanical analysis of fault slip data: implications for paleostress analysis. Journal of Structural Geology 33, 78–91.CrossRefGoogle Scholar
Knopf, A (1936) Igneous geology of the Spanish Peaks region, Colorado. Bulletin of the Geological Society of America 47, 1727–84.CrossRefGoogle Scholar
Lisle, RJ, Orife, TO, Arlegui, L, Liesa, C and Srivastava, DC (2006) Favoured states of paleostress in the earth’s crust: evidence from fault-slip data. Journal of Structural Geology 28, 1051–66.CrossRefGoogle Scholar
Lister, JR (1990) Buoyancy-driven fluid fracture: similarity solutions for the horizontal and vertical propagation of fluid-filled cracks. Journal of Fluid Mechanics 217, 213–39.CrossRefGoogle Scholar
Luo, G, Nikolinakou, MA, Flemings, PB and Hudec, MR (2012) Geomechanical modeling of stresses adjacent to salt bodies. Part 1 – Uncoupled models. AAPG Bulletin 96, 43–64.CrossRefGoogle Scholar
Maccaferri, F, Bonafede, M and Rivalta, E (2011) A quantitative study of the mechanisms governing dyke propagation, dyke arrest and sill formation. Journal of Volcanology and Geothermal Research 208, 39–50.CrossRefGoogle Scholar
Maerten, F (2010a) Geomechanics to solve geological structure issues: forward, inverse and restoration modeling. Université Montpellier II, Sciences et techniques du Languedoc, Montpellier. Published thesis.Google Scholar
Maerten, F (2010b) Adaptive cross-approximation applied to the solution of system of equations and post-processing for 3D elastostatic problems using the boundary element method. Engineering Analysis with Boundary Elements 34, 483–91.CrossRefGoogle Scholar
Maerten, F, Madden, EH, Pollard, DD and Maerten, L (2016) Incorporating fault mechanics into inversions of aftershock data for the regional remote stress, with application to the 1992 Landers, California earthquake. Tectonophysics 674, 52–64.CrossRefGoogle Scholar
Maerten, F and Maerten, L (2008) Iterative 3D BEM solver on complex faults geometry using angular dislocation approach in heterogeneous, isotropic elastic whole or half-space. Skerget and Brebbia Editors, Boundary Elements and other Mesh Reduction Methods 30, 201–208.Google Scholar
Maerten, F, Maerten, L and Pollard, DD (2014) iBem3D, a three-dimensional iterative boundary element method using angular dislocations for modeling geologic structures. Computers & Geosciences 72, 1–17.CrossRefGoogle Scholar
Maerten, F, Resor, P, Pollard, DD and Maerten, L (2005) Inverting for slip on three-dimensional fault surfaces using angular dislocations. Bulletin of the Seismological Society of America 95, 1654–65.CrossRefGoogle Scholar
Maerten, L (2000) Variation in slip on intersecting normal faults: implications for paleostress inversion. Journal of Geophysical Research: Solid Earth 105, 25553–65.CrossRefGoogle Scholar
Maerten, L, Maerten, F and Lejri, M (2018) Along fault friction and fluid pressure effects on the spatial distribution of fault-related fractures. Journal of Structural Geology 108, 198–212.CrossRefGoogle Scholar
Maerten, L, Maerten, F, Lejri, M and Gillespie, P (2016) Geomechanical paleostress inversion using fracture data. Journal of Structural Geology 89, 197–213.CrossRefGoogle Scholar
Maerten, L, Pollard, DD and Karpuz, R (2000) How to constrain 3-D fault continuity and linkage using reflection seismic data: a geomechanical approach. AAPG Bulletin 84, 1311–24.Google Scholar
Martel, SJ (2000) Modeling elastic stresses in long ridges with the displacement discontinuity method. Pure and Applied Geophysics 157, 1039–57.CrossRefGoogle Scholar
McBirney, AR and Williams, H (1969) Geology and petrology of the Galapagos Islands. Geological Society of America, Memoir 118, 197 pp.Google Scholar
Michael, AJY (1984) Determination of stress from slip data: faults and folds. Journal of Geophysical Research 89, 11517–26.CrossRefGoogle Scholar
Michael, JAY (1987) Use of focal mechanisms to determine stress: a control study. Journal of Geophysical Research 92, 357–68.CrossRefGoogle Scholar
Mogi, K (1959) Relations between the eruptions of various volcanoes and the deformations of the ground surfaces around them. Bulletin of Earthquakes Research Institute, University of Tokyo 36, 99–134.Google Scholar
Muller, OH (1986) Changing stresses during emplacement of the radial dyke swarm at Spanish Peaks, Colorado. Geology 14, 157–9.2.0.CO;2>CrossRefGoogle Scholar
Muller, OH and Pollard, DD (1977) The stress state near Spanish Peaks, Colorado, determined from a dyke pattern. Pure and Applied Geophysics 115, 69–86.CrossRefGoogle Scholar
Munro, AC and Rowland, SK (1996) Caldera morphology in the western Galapagos and implications for volcano eruptive behavior and mechanisms of caldera formation. Journal of Volcanology and Geothermal Research 72, 85–100.CrossRefGoogle Scholar
Nakamura, K, Jacob, KH and Davies, JN (1977) Volcanoes as possible indicators of tectonic stress orientation – Aleutians and Alaska. Pure and Applied Geophysics 115, 87–112.CrossRefGoogle Scholar
Nikkhoo, M and Walter, TR (2015) Triangular dislocation: an analytical, artefact-free solution. Geophysical Journal International 201, 1119–41.CrossRefGoogle Scholar
Nordlie, E (1973) Morphology and structure of the Western Galapagos volcanoes and a model for their origin. Geological Society of America Bulletin 84, 2931–56.2.0.CO;2>CrossRefGoogle Scholar
Odé, H (1957) Mechanical analysis of the dyke pattern of the Spanish Peaks area, Colorado. Geological Society of America Bulletin 68, 567–76.CrossRefGoogle Scholar
Okada, Y (1992) Internal deformation due to shear and tensile faults in a half-space. Bulletin of the Seismological Society of America 82, 1018–40.CrossRefGoogle Scholar
Pham, DT, Ghanbarzadeh, A, Koc, E, Otri, S, Rahim, S and Zaidi, M (2005) The Bees Algorithm. Technical Note. Cardiff: Manufacturing Engineering Centre, Cardiff University.Google Scholar
Pinel, V and Jaupart, C (2004) Magma storage and horizontal dyke injection beneath a volcanic edifice. Earth and Planetary Science Letters 221, 245–62.CrossRefGoogle Scholar
Plateaux, R, Béthoux, N, Bergerat, F and de Lépinay, BM (2014) Volcano-tectonic interactions revealed by inversion of focal mechanisms: stress field insight around and beneath the Vatnajökull ice cap in Iceland. Frontiers in Earth Science 2, 9 pp.CrossRefGoogle Scholar
Pollard, DD (1987) Elementary fracture mechanics applied to the structural interpretation of dykes. In Mafic Dyke Swarms (eds Halls, HC and Fahrig, WF), pp. 5–24. Toronto: Geological Association of Canada, Special Paper no. 34.Google Scholar
Pollard, DD and Muller, OH (1976) The effect of gradients in regional stress and magma pressure on the form of sheet intrusions in cross section. Journal of Geophysical Research 81, 975–84.CrossRefGoogle Scholar
Rivalta, E, Taisne, B, Bunger, AP and Katz, RF (2015) A review of mechanical models of dyke propagation: schools of thought, results and future directions. Tectonophysics 638, 1–42.CrossRefGoogle Scholar
Rubin, AM (1995) Propagation of magma-filled cracks. Annual Review of Earth and Planetary Sciences 23, 287–336.CrossRefGoogle Scholar
Rubin, AM and Gillard, D (1998) Dyke-induced earthquakes: theoretical considerations. Journal of Geophysical Research: Solid Earth 103, 10017–30.CrossRefGoogle Scholar
Segall, P (2010) Earthquake and Volcano Deformation. Princeton, New Jersey: Princeton University Press.CrossRefGoogle Scholar
Sigmundsson, F, Hooper, A, Hreinsdóttir, S, Vogfjörd, KS, Ófeigsson, BG, Heimisson, ER, Dumont, S, Parks, M, Spaans, K, Gudmundsson, GB, Drouin, V, Árnadóttir, T, Jónsdóttir, K, Gudmundsson, MT, Högnadóttir, T, Fridriksdóttir, HM, Hensch, M, Einarsson, P, Magnússon, E and Eibl, EPS (2014) Segmented lateral dyke growth in a rifting event at Bárðarbunga volcanic system, Iceland. Nature 517, 191–5.Google Scholar
Smith, RP (1975) Structure and Petrology of Spanish Peaks Dykes, South-Central Colorado. Boulder: University of Colorado, Boulder. Published thesis.Google Scholar
Smith, RP (1978) Geologic maps of part of the Spanish Peaks dyke system, south-central Colorado. Denver, CO: Geological Survey of America Map and Chart Series MC-22, scale 1:36000, 1 sheet, 2 pp. text.Google Scholar
Soliva, R, Maerten, F, Petit, J-P and Auzias, V (2010) Field evidences for the role of static friction on fracture orientation in extensional relays along strike slip faults: comparison with photoelasticity and 3-D numerical modelling. Journal of Structural Geology 32, 1721e1731.CrossRefGoogle Scholar
Stormer, JC (1972) Ages and nature of volcanic activity on the southern high plains, New Mexico and Colorado. Geological Society of America Bulletin 83, 2443–8.CrossRefGoogle Scholar
Thomas, AL (1993) Poly3D, a three-dimensional, polygonal-element, displacement discontinuity boundary element computer program with applications to fractures, faults, and cavities in the earth’s crust . Master Thesis at Stanford University.Google Scholar
Yamakawa, N (1955) On the strain produced in a semi-infinite elastic solid by an interior source of stress. Journal of the Seismological Society Japan 8, 84–98.Google Scholar
Yun, S, Segall, P and Zebker, H (2006) Constraints on magma chamber geometry at Sierra Negra Volcano, Galapagos Islands, based on InSAR observations. Journal of Volcanology and Geothermal Research 150, 232–43.CrossRefGoogle Scholar
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