Quantitative volcanic susceptibility analysis of Lanzarote and Chinijo Islands based on kernel density estimation via a linear diffusion process
Risk management stakeholders in high-populated volcanic islands should be provided with the latest high-quality volcanic information. We present here the first volcanic susceptibility map of Lanzarote and Chinijo Islands and their submarine flanks based on updated chronostratigraphical and volcano structural data, as well as on the geomorphological analysis of the bathymetric data of the submarine flanks. The role of the structural elements in the volcanic susceptibility analysis has been reviewed: vents have been considered since they indicate where previous eruptions took place; eruptive fissures provide information about the stress field as they are the superficial expression of the dyke conduit; eroded dykes have been discarded since they are single non-feeder dykes intruded in deep parts of Miocene-Pliocene volcanic edifices; main faults have been taken into account only in those cases where they could modified the superficial movement of magma. The application of kernel density estimation via a linear diffusion process for the volcanic susceptibility assessment has been applied successfully to Lanzarote and could be applied to other fissure volcanic fields worldwide since the results provide information about the probable area where an eruption could take place but also about the main direction of the probable volcanic fissures.
Basaltic feeder dykes in rift zones: geometry, emplacement, and effusion rates
Abstract. Most volcanic hazards depend on an injected dyke reaching the surface to form a feeder. Assessing the volcanic hazard in an area is thus related to understanding the condition for the formation of a feeder dyke in that area. For this latter, we need good field data on feeder dykes, their geometries, internal structures, and other characteristics that distinguish them from non-feeders. Unfortunately, feeder dykes are rarely observed, partly because they are commonly covered by their own products. For this reason, outcrops are scarce and usually restricted to cliffs, ravines, and man-made outcrops. Here we report the results of a study of feeder dykes in Tenerife (Canary Islands, Spain) and Iceland, focusing on their field characteristics and how their propagation is affected by existing structures. Although Holocene fissure eruptions have been common in both islands, only eleven basaltic feeder dykes have been identified: eight in Tenerife and three in Iceland. They are all well preserved and the relation with the eruptive fissure and/or the deposits is well exposed. While the eruptive fissures are generally longer in Iceland than in Tenerife, their feeders show many similarities, the main ones being that the feeder dykes (1) are generally sheet-shaped; (2) are segmented (as are the associated volcanic fissures); (3) normally contain elongated (prolate ellipsoidal) cavities in their central, topmost parts, that is, 2–3 m below the surface (with solidified magma drops on the cavity walls); (4) contain vesicles which increase in size and number close to the surface; (5) sometimes inject oblique dyke fingers into the planes of existing faults that cross the dyke paths; and (6) may reactivate, that is, trigger slip on existing faults. We analyse theoretically the feeder dyke of the 1991 Hekla eruption in Iceland. Our results indicate that during the initial peak in the effusion rate the opening (aperture) of the feeder dyke was as wide as 0.77 m, but quickly decreased to about 0.56 m. During the subsequent decline in the effusion rate to a minimum, the aperture decreased to about 0.19 m. At a later abrupt increase in the effusion rate, the feeder-dyke opening may have increased to about 0.34 m, and then decreased again as the effusion rate gradually declined during the end stages of the eruption. These thickness estimates fit well with those of many feeders in Iceland and Tenerife, and with the general dyke thickness within fossil central volcanoes in Iceland.
Inverse modeling for estimating fluid-overpressure distributions and stress intensity factors from an arbitrary open-fracture geometry
Abstract We present a new solution for estimating the fluid overpressure (driving-pressure or net-pressure) acting on the walls of a fracture with an arbitrary opening displacement. In the paper, we first present a forward modeling solution, using Fourier cosine series, for the opening displacement of a fracture subject to an overpressure that varies irregularly along the length of a fracture. By changing the form of the solution, we provide a matrix equation for estimating the Fourier coefficients and thereby obtain the overpressure variation from the fracture geometry. As numerical tests of this inverse analysis, we estimated the overpressure variation from fracture-opening displacements given by well known analytical solutions, and found that this method can be used for overpressure estimates for a variety of fluid-driven fractures. We apply our solutions to a mineral vein hosted by gneiss (West Norway) and conclude from the aperture variation that, at the time of vein formation, the overpressure increased toward the vein tip. We also discuss the physical meaning of the Fourier coefficients by applying our results to man-made hydraulic wing fractures. The results indicate that the coefficients of n  = 0 and n  = 1 relate to the fluid overpressure and the critical stress intensity factor.