Abstract
This chapter summarizes the main methods and problems in the modeling of ground deformations in volcanic areas. The basic model is assumed as a strain source embedded within an elastic medium. In particular, the success in explaining ground deformations in several volcanic areas by the simplest model, a nucleus of isotropic strain (generally known as the Mogi’s model) is emphasized, as well as the main limitations of this model, which are often misleading. The effect of varying the shape of the source is reviewed, showing why only the joint use of both vertical and horizontal deformations are effective in constraining source shape and depth. Formulas are also reported for computing ground deformations due to point sources of various shapes in homogenous elastic media. More complex sources, resulting from heterogeneous distributions of source intensity can be built by a superposition of elementary sources. Such complex sources can arise, for instance, from heterogeneous pressure distributions in porous rocks saturated by fluids (magma or water), or from heterogeneous crack opening along volcanic rifts. A general inversion scheme is given in order to allow computation of heterogeneous strain-source distributions from ground deformation data. Furthermore, the effect of the rheology of the medium is examined, considering the main deviations, from the most commonly used homogeneous elastic media, expected in volcanic areas. These include heterogeneities of the elastic parameters and the visco-elastic behavior of rocks. Both of these effects can be thought of, in volcanic areas, as being due to the presence of high temperatures nonuniformly distributed within the medium, and to the presence of different products of the eruptions. Such effects, in principle, can modify the shape of the deformation field for a given source, and/or introduce a complex time dependence of the deformation from the source-time function. Finally, the effect of the presence of stress-strain discontinuities in the elastic medium is thoroughly examined. Such discontinuities are represented, for instance, by faults. In addition, surfaces of contact between different lithologies can be caused, in volcanic areas, by eruptive activity involving different products. In particular, in collapse calderas, where younger and lighter pyroclastic products fill the depressions formed in the more competent rock, the borders of collapsed basins can represent a discontinuity in the medium. In this case, it is shown that the shapes of the ground deformations are strongly affected by the geometry of the caldera structure, and are much less sensitive to the depth of the pressure source. As a consequence, the modeling of ground deformations in calderas should take into account the presence of caldera borders, in order to obtain meaningful results about the shape and depth of the pressure source.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Berrino G, Corrado G, Luongo G, Toro B (1984) Ground deformation and gravity changes accompanying the 1982 Pozzuoli uplift. Bull Volcanol 47,2: 187–200
Bianchi R, Coradini A, Federico C, Giberti G, Sartoris G, Scandone R (1984) Modelling of surface ground deformation in the Phlegraean Fields volcanic area, Italy. Bull Volcanol 47,2: 321–330
Bianchi R, Coradini A, Federico C, Giberti G, Lanciano P, Pozzi JP, Sartoris G, Scandone R (1987) Modelling of surface ground deformation in volcanic areas: the 1970–1972 and 1982–1984 crises of Campi Flegrei, Italy. J Geophys Res 92,B13: 14139–14150
Björnsson A, Saemundsson K, Einatsson P, Tryggvason E, Grönvold K (1977) Current rifting episode in North Iceland. Nature 266: 318–323
Bonaccorso A, Velardita R, Villari L (1994) Ground deformation modelling of geodynamic activity associated with the 1991–1993 Etna eruption. Acta Vulcanol 4: 87–96
Bonafede M, Dragoni M, Quareni F (1986) Displacement and stress fields produced by a centre of dilatation and by a pressure source in a viscoelastic half-space: application to the study of ground deformation and Scismic activity at Campi Flegrei, Italy. Geophys J R Astron Soc 87: 455–485
Corrado G, Guerra I, Lo Bascio A, Luongo G, Rampoldi R (1976–1977) Inflation and micro-earthquake activity of Phlegraean Fields, Italy. Bull Volcanol 40,3: 169–188
Crouch SL (1976) Solution of plane elasticity problems by the displacement discontinuity method. Int J Numeric Math Eng 10: 301–343
Davis PM (1983) Surface deformation associated with a dipping hydrofracture. J Geophys Res 88,B7: 5826–5834
Davis PM (1986) Surface deformation due to inflation of an arbitrarily oriented triaxial ellipsoidal cavity in an elastic half-space, with reference to Kilauea volcano, Hawaii. J Geophys Res 91: 7429–7438
Decker RW, Koyanagi RY, Dvorak JJ, Lockwood JP, Okamura AT, Yamashita KM, Tanigawa WR (1983) Scismicity and surface deformation on Mauna Loa volcano, Hawaii. EOS 64,37: 545–547
De Natale G (1989) Inversion of ground deformation data for variable slip fault models. Software Engin Workstations 5: 140–150
De Natale G, Pingue F (1992) Scismological and geodetic data at Campi Flegrei (Southern Italy): Constraints on volcanological models. In: Gasparini P, Scarpa R, Aki K (eds) Volcanic Scismology. IAVCEI Proc in Volcanology, vol. 3, pp 484–502, Springer-Verlag, Berlin
De Natale G, Pingue F, (1993) Ground deformations in collapsed caldera structures. J Volcanol Geotherm Res 57: 19–38
De Natale G, Pingue F, Allard P, Zollo A (1991) Geophysical and geochemical modelling of the 1982–1984 unrest phenomena at Campi Flegrei caldera (Southern Italy). J Volcanol Geotherm Res 48: 199–222
Denlinger RP, Riley F (1984) Deformation of Long Valley, Mono County, California, from 1975 to 1982. J Geophys Res 89, BIO: 8303–8314
Dieterich JH, Decker RW (1975) Finite element modelling of surface deformation associated with volcanism. J Geophys Res 80,29: 4094–4102
Dvorak JJ, Berrino G (1991) Recent ground movement and Scismic activity in Campi Flegrei, Southern Italy: episodic growth of a resurgent dome. J Geophys Res 96,B2: 2309–2323
Dvorak JJ, Okamura A, Dieterich JH (1983) Analysis of surface deformation data, Kilauea volcano, Hawaii, October 1966 to September 1970. J Geophys Res 88,B11: 9295–9304
Dvorak JJ, Okamura AT, English TT, Koyanagi RY, Nakata JS, Sako MK, Tanigava WT, Yamashita KM (1986) Mechanical response of south flank of Kilauea volcano, Hawaii to intrusive events along the rift systems. Tectonophysics 124: 193–209
Eshelby JA (1957) The determination of the elastic field of an ellipsoidal inclusion and related problems. Proc R Soc Lond Ser A 241: 376–396
Kasahara K (1981) Earthquakes mechanics. Cambridge University Press, Cambridge
Lawson CL, Hanson RJ (1974) Solving least squares problems. Prentice Hall, Englewood Cliffs
Maruyama T (1964) Static elastic dislocations in an infinite and semi-infinite medium. Bull Earthq Res Inst Univ Tokyo 42: 289–364
McKee CO, Lowenstein PL, De Saint Ours P, Talai B, Itikarai I, Mori JJ, (1984) Scismic and ground deformation crises at Rabaul Caldera: Prelude to an eruption? Bull Volcanol 47,2: 397–411
Menke W (1984) Geophysical data analysis: discrete inverse theory. Academic Press, Orlando
Mogi K (1958) Relation between eruptions of various volcanoes and the deformations of the ground surfaces around them. Bull Earthq Res Inst 36: 99–134
Okada Y (1985) Surface deformation due to shear and tensile faults in a half-space. Bull Scismol Soc Am 75,4: 1135–1154
Okada Y (1992) Internal deformation due to shear and tensile faults in a half-space. Bull Scismol Soc Am 82,2: 1018–1040
Pollard DD, Holzhausen G, (1979) On the mechanical interaction between a fluid-filled fracture and the Earth’s surface. Tectonophysics 53: 27–57
Rundle JB (1978) Viscoelastic crustal deformation by finite quasi-static sources. J Geophys Res 83,B12: 5937–5945
Rundle JB, Whitcomb JH (1984) A model for deformation in Long Valley, California, 1980–1983. J Geophys Res 89: 9391–9380
Ryan MP (1988) The mechanics and three dimensional internal structure of active magmatic systems: Kilauea volcano, Hawaii. J Geophys Res 93B5: 4213–4248
Savage JC, Cockerham RS, Estrem JE (1987) Deformation near the Long Valley, Eastern California, 1982–1986. J Geophys Res 92B3: 2721–2746
Soeda K (1944) On the determinations produced in a sem-infinite elastic solid by an interior source of stress. Quart J Scism, 13,263–291 (in Japanese)
Steketee JA (1958a) On Volterra’s dislocations in a semi-infinite elastic medium. Can Journ Phys 36: 192–205
Steketee JA (1958b) Some geophysical application on the elasticity theory of dislocations. Can Journ Phys 36: 1168–1198
Troise C (1993) Deformazioni del suolo e campo di sforzo associati alle eruzioni laterali del vulcano Kilauea (Hawaii). Phys Sci Thesis, University of Naples, Naples (in Italian)
Vasco DW, Johnson LR, Goldstein NE, (1988) Using surface displacement and strain observation to determine deformation at depth, with application to Long Valley Caldera, California. J Geophys Res 93 B4: 3232–3242
Walsh JB (1975) An analysis of local changes in gravity due to deformation. Pageoph 113: 97–106
Walsh JB, Decker RW, (1971) Surface deformation associated with volcanism. J Geophys Res 76,14: 3291–3302
Yamakawa N, (1955) On the strain produced in a semi-infinite elastic solid by an interior source of stress. J. Scismol Soc Jpn, 8: 84–98 (in Japanese)
Yang X, Davis PM, Dieterich JH (1988) Deformation from inflation of a dipping finite prolate spheroid in an elastic half-space as a model for volcanic stressing. J Geophys Res, 93,B5: 4249–4257
Yang X, Davis PM, Delaney PT, Okamura AT (1992) Geodetic analysis of dike intrusion and motion of the magma reservoir beneath the summit of Kilauea volcano, Hawaii: 1970–1985. J Geophys Res 97,B3: 3305–3324
Yokoyama I (1971) A model for the crustal deformations around Volcanoes. J Phys Earth 19,3: 199–207
Yokoyama I (1986) Crustal deformation caused by the 1914 eruption of Sakurajima volcano, Japan and its secular changes. J Volcanol Geotherm Res 30: 283–302
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 1996 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
De Natale, G., Pingue, F. (1996). Ground Deformation Modeling in Volcanic Areas. In: Monitoring and Mitigation of Volcano Hazards. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-80087-0_11
Download citation
DOI: https://doi.org/10.1007/978-3-642-80087-0_11
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-80089-4
Online ISBN: 978-3-642-80087-0
eBook Packages: Springer Book Archive