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fractures (dykes) that are opened by magmatic overpressure. While (inferred) dyke injections are frequent during unrest
periods, volcanic eruptions are, in comparison, infrequent, suggesting that most dykes become arrested at certain
depths in the crust, in agreement with field studies. The frequency of dyke arrest can be partly explained by the numerical
models presented here which indicate that volcanic edifices and rift zones consisting of rocks of contrasting mechanical properties, such as soft pyroclastic layers and stiff lava flows, commonly develop local stress fields that encourage dyke arrest. During unrest, surface deformation studies are routinely used to infer the geometries of arrested dykes, and some models (using homogeneous, isotropic half-spaces) infer large grabens to be induced by such dykes. Our results, however, show that the dyke-tip tensile stresses are normally much greater than the induced surface stresses, making it difficult to explain how a dyke can induce surface stresses in excess of the tensile (or shear)
strength while the same strength is not exceeded at the (arrested) dyke tip. Also, arrested dyke tips in eroded or active
rift zones are normally not associated with dyke-induced grabens or normal faults, and some dykes arrested within a few metres of the surface do not generate faults or grabens. The numerical models show that abrupt changes in Young's moduli(stiffnesses), layers with relatively high dyke-normal compressive stresses (stress barriers), and weak horizontal contacts may make the dyke-induced surface tensile stresses too small for significant fault or graben formation to occur in rift zones or volcanic edifices. Also, these small surface stresses may have no simple relation to the dyke geometry or the depth to its tip. Thus, for a layered crust with weak contacts, straightforward inversion of
surface geodetic data may lead to unreliable geometries of arrested dykes in active rift zones and volcanic edifices.
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