Hydraulic fracturing is an important and abundant process in both industrial applications and natural environments. The current work is the first systematic quantitative study of the effect of interaction in and between complex hydraulic fractures at different spatial scales. A mathematical model, based on the boundary collocation method, has been developed. The model has been employed for a typical field case, a highly segmented vein. This vein is well-mapped, and therefore, represents a well constrained example. The computed apertures are compared to the measured apertures. By using the simplest constitutive model, based on an ideal elastic material, and including the effect of interaction between the segments, it was possible to obtain an excellent match at all considered scales. It was also shown that the concept of effective fracture, as currently accepted in the literature, is not always applicable and may lead to unbounded inaccuracy. Unfortunately, in most cases, very little (if any) directly measured data on fracture and material properties is available. An important example of such a weakly constrained case, involving hydraulic fracturing, is diking beneath the seafloor at mid-oceanic ridges. In this study, it is shown that the commonly accepted scenario of a dike propagating from the center of the pressurized magma chamber to the ocean floor is not consistent with conventional fracture mechanics due to the fact that the chamber has the shape of a thin lens. Even at such a large scale (i.e., a kilometer or more), the mechanical principles of elastic interaction appear to be applicable. Since diking is likely to generate a region of high permeability near its margin, in addition to heat, the ongoing hydrothermal activity becomes localized. Our modeling suggests the probable positions of the propagating dikes. Consequently, comparing the observed locations of hydrothermal sites with respect to that of the magma chamber could be useful for constraining the mechanisms of magma lens evolution.

Heard Island is a remote Australian territory which lies in the South-middle sector of the Indian Ocean.The island lies in the central province of the Kerguelen Plateau. On the north-western face of the islandlies the Laurens Peninsula, where modern volcanism has been periodic since approximately 10 ka, butno eruption has been recorded. The main volcanic feature of the peninsula is Mt Dixon of which noactivity has been observed but it is thought to have erupted within the past few hundred years. This thesis applied the crystal size distribution method to three thin sections from the LaurensPeninsula. The samples were collected from a phonolite from Jacka valley, a teprhiphonolite from thebase of the Red Island cone, and a tephrite east of Cape Cartwright. Crystal dimensions were calculatedusing ImageJ Fiji, these dimensions were corrected for 3D dimensions using CSDslice, and the datawas plotted using CSDcorrections. Microcrysts were traced using backscattered electron (BSE) images,and high resolutions scans of the thin section were used to trace phenocrysts. The results of the crystalsize distributions show concave-up shapes in all plots with steep slopes for smaller crystals, followedby shallow slopes for larger crystals. This suggests binary magma mixing by replenishment occurred inthe magmas associated with all three samples. The different slopes suggest two separate crystallisationconditions: Phenocrysts crystalized slowly in the chamber and microcrysts crystallized relativelyquickly during or after eruption. Textural differences in the three samples suggest that the tephrite hadthe longest residence time and underwent the most replenishment events, followed by thetephriphonolite and lastly the phonolite. Finally, since replenishment is the mechanism of mixingbeneath the Laurens Peninsula, then volcanism might still be active, and the chambers could currentlybe replenishing, which could trigger an eruption. / Heard Island är ett avlägset australiensiskt territorium som ligger i den södra delen av den Indiskaoceanen. Ön ligger i den centrala provinsen på Kerguelenplatån. På den nordvästra sidan av ön liggerLaurens-halvön, där modern vulkanism daterar sig till cirka 10 ka. Den främsta vulkaniska strukturenpå halvön är Mt Dixon där ingen aktivitet har registrerats, men som tros ha haft ett utbrott under desenaste hundra åren. Denna avhandling tillämpade metoden för kristallstorleksfördelning på tre tunnslipar frånLaurenshalvön. Proverna samlades in från en fonolit från Jacka valley, en tefrifonolit från basen av RedIsland cone och en tefrit öster om Cape Cartwright. Kristalldimensioner beräknades med ImageJ Fiji,dessa dimensioner korrigerades för 3D-dimensioner med CSDslice, och datat plottades medCSDcorrections. Mikrokristaller spårades med hjälp av backscattered electron images (BSE) ochhögupplösta skanningar av tunnslipen användes för att spåra fenokryster. Resultaten avkristallstorleksfördelningarna föreslog binär magmablandning via påfyllning i alla tre proverna. Dessavisade konkava former i alla plotter med branta sluttningar för mindre kristaller, följt av plattaresluttningar för större kristaller. De olika lutningarna på kurvorna föreslog två separatakristallisationsförhållanden: fenokryster kristalliserade långsamt i kammaren, och mikrokristallerkristalliserade relativt snabbt under eller efter utbrottet. Texturella skillnader i de tre proverna antyddeatt tefriten hade den längsta residenstiden och genomgick flest påfyllningshändelser, följt avtefrifonoliten och slutligen fonoliten. Slutligen, om påfyllning var mekanismen för att blandas underLaurenshalvön, så kan vulkanismen fortfarande vara aktiv, men för närvarande i ettpåfyllningsuppehåll.