Stresses and displacements in layered rocks induced by inclined (cone) sheets

• Currently, the sheet-intrusion paths and geometries, including the sheet opening/thickness as well as the depth to sheet tip, are commonly determined from geodetic surface data using elastic dislocation models. These models assume the volcanic zone/central volcano to be an elastic half-space of uniform mechanical properties. Field observations, however, show that volcanic zones/volcanoes are composed of numerous layers whose mechanical properties (primarily Young's modulus) vary widely. Here we provide new numerical models on the effects of a typical variation in Young's modulus in an active volcanic zone/central volcano on the internal and surface stresses and displacements induced by a sheet-intrusion whose tip is arrested at a depth below the surface of 100 m. The sheet has a dip dimension (height) of 2 km. It's opening (thickness) depends on the magmatic overpressure, sheet dimension and host-rock Young's modulus. For the values used here, sheet thickness would be in the range of 0.5–1.4 m, similar to commonly measured sheet thicknesses in the field. The only loading is internal magmatic overpressure in the sheet of 5 MPa. The modelled crustal segment/volcano consists of 5 layers, all with the same Poisson's ratio (0.25). Each of the 4 uppermost layers is 10 m thick. Layer 1 (the top or surface layer) has Young's modulus of 3 GPa, layer 2 a modulus of 20 GPa, layer 3 a modulus of 30 GPa, and layer or unit 5 a modulus of 40 GPa. We vary Young's modulus or stiffness of the fourth layer from 10 GPa to 0.01 GPa, while the dip of the sheet takes the following values: 30°, 45°, 60° (for an inclined sheet) and 90° (for a dike). The resulting displacement and stresses are highly asymmetric across the sheet tip (except for the dike), with the main surface stresses and displacements being above the dipping sheet and highest for the 30°-dipping sheet. For comparison, three elastic half-space models of the same sheet configuration and loading but uniform Young's modulus in each model (40GPa, 20GPa, and 10 GPa) all yield much higher surface stresses and displacements than any of the layered models. As the stiffness of layer 4 decreases the surface stresses gradually decrease while changes in vertical displacements are comparatively small but greater in horizontal displacements. In particular, as the stiffness of layer 4 decreases from 10 GPa to 0.01 GPa, for the 30°-dipping sheet, the maximum surface shear stress decreases from about 6.6 MPa to 2.2 MPa and the maximum tensile stress from about 6.9 MPa to about 2.3 MPa. Thus, even a single comparatively thin (10 m) soft layer close to the surface of a central volcano/volcanic zone (where such layers are almost universal) may cause a great change in the maximum sheet-induced stresses at the surface and, thereby, in any sheet-induced fracture pattern. Furthermore, the stress peaks in the layered models do not coincide with the displacement peaks; fracture formation is most likely at the location of the stress peaks. The results have important implications for the correct interpretation of geodetic data and fracturing during unrest periods with magma-chamber rupture and sheet injection.

Ämnesord

NATURVETENSKAP  -- Geovetenskap och miljövetenskap -- Geologi (hsv//swe)

NATURAL SCIENCES  -- Earth and Related Environmental Sciences -- Geology (hsv//eng)

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