10001 manuscripts in practice: Perl, XML, medieval chronicles, and why Unicode rocks‎

I work in the field of Armenian historiography. This means I get to play with medieval manuscripts. The things I'm doing with the manuscripts are theoretically interesting, but pretty boring in practice, so I'm using Perl to program away the most boring bits. I will talk about the problems of text criticism in general, what sorts of things can and can't be done by the computer, my initial aversion to XML, how I was shown (some of) the error of my ways, and how I'm combining a bunch of isolated pieces of technology that were mostly already in use to achieve fame and fortune in the world of Armenian studies.

High-resolution sequence stratigraphic correlation in the Upper Jurassic (Kimmeridgian)–Upper Cretaceous (Cenomanian) peritidal carbonate deposits (Western Taurides, Turkey)

Upper Jurassic (Kimmeridgian)±Upper Cretaceous (Cenomanian) inner platform carbonates in the Western Taurides are composed of metre-scale upward-shallowing cyclic deposits (parasequences) and important karstic surfaces capping some of the cycles. Peritidal cycles (shallow subtidal facies capped by tidal-¯at laminites or fenestrate limestones) are regressive- and transgressive-prone (upward-deepening followed by upward-shallowing facies trends). Subtidal cycles are of two types and indicate incomplete shallowing. Submerged subtidal cycles are composed of deeper subtidal facies overlain by shallow subtidal facies. Exposed subtidal cycles consist of deeper subtidal facies overlain by shallow subtidal facies that are capped by features indicative of prolonged subaerial exposure. Subtidal facies occur characteristically in the Jurassic, while peritidal cycles are typical for the Lower Cretaceous of the region. Within the foraminiferal and dasyclad algal biostratigraphic framework, four karst breccia levels are recognized as the boundaries of major second-order cycles, introduced for the ®rst time in this study. These levels correspond to the Kimmeridgian±Portlandian boundary, mid-Early Valanginian, mid-Early Aptian and mid-Cenomanian and represent important sea level falls which affected the distribution of foraminiferal fauna and dasyclad ¯ora of the Taurus carbonate platform. Within the Kimmeridgian±Cenomanian interval 26 third-order sequences (types 1 and 2) are recognized. These sequences are the records of eustatic sea level ¯uctuations rather than the records of local tectonic events because the boundaries of the sequences representing 1±4 Ma intervals are correlative with global sea level falls. Third-order sequences and metre-scale cyclic deposits are the major units used for long-distance, high-resolution sequence stratigraphic correlation in the Western Taurides. Metre-scale cyclic deposits (parasequences) in the Cretaceous show genetical stacking patterns within third-order sequences and correspond to fourth-order sequences representing 100±200 ka. These cycles are possibly the E2 signal (126 ka) of the orbital eccentricity cycles of the Milankovitch band. The slight deviation of values, calculated for parasequences, from the mean value of eccentricity cycles can be explained by the currently imprecise geochronology established in the Cretaceous and missed sea level oscillations when the platform lay above fluctuating sea level.

River loads and modern denudation of the Alps — A review

This paper presents the first comprehensive analysis of sediment and dissolved load across an entire mountain range. We investigate patterns and rates of modern denudation of the European Alps based on a compilation of data about river loads and reservoir sedimentation from 202 drainage basins that are between ca. 1 to 10,000 km2 large. The study basins cover about 50% of the total area of the Alps. Modern glaciated basins have the highest sediment yields of up to 7000 t km− 2 a− 1, which are on average 5 to 10 times higher than in non-glaciated basins. Likewise sediment yield and glacial cover are positively correlated. Instead, relief is a relatively weak predictor of sediment yield. The strong glacial impact in the correlations is due to glacier recession since the 19th century as well as due to glacial conditioning during repeated Quaternary glaciations which have produced the strong transient state of the Alpine landscape. We suggest that this is the major cause for ca. 3 fold enhanced denudation of the western compared to the eastern Alps. Chemical denudation rates are highest in the external Alps dominated by carbonate sedimentary rocks, where they make up about one third of total denudation. The high rates cannot be explained without anhydrite dissolution. We estimated that only 45% of the sediments mobilized in headwaters are exported out off the Alps, most sediments being trapped in artificial reservoirs. The total amount of sediment annually trapped within the Alps equates to 43 Mt. When corrected for sediment storage, we obtain an area-weighted mean total denudation rate for the Alps of about 0.32 mm a− 1. The pre-dam rate might be as high as 0.42 mm a− 1. In total, ca. 35 plus 23 Mt of mass are exported each year out of the Alps as solids and solutes, respectively. These rates are not enough to out pace modern rock uplift. Nevertheless, pattern of sediment yield across the Alps coincides roughly with the intensity of glacial conditioning and modern rock uplift, supporting the hypothesis of an erosion-driven uplift of the Alps.

Neotethys closure history of Anatolia: insights from 40Ar–39Ar geochronology and P–T estimation in high pressure metasedimentary rocks

The multiple high-pressure (HP), low-temperature (LT) metamorphic units of Western and Central Anatolia offer a great opportunity to investigate the subduction- and continental accretion-related evolution of the eastern limb of the long-lived Aegean subduction system. Recent reports of the HP–LT index mineral Fe-Mg-carpholite in three metasedimentary units of the Gondwana-derived Anatolide–Tauride continental block (namely the Afyon Zone, the Ören Unit and the southern Menderes Massif) suggest a more complicated scenario than the single-continental accretion model generally put forward in previous studies. This study presents the first isotopic dates (white mica 40Ar–39Ar geochronology), and where possible are combined with P–T estimates (chlorite thermometry, phengite barometry, multi-equilibrium thermobarometry), on carpholite-bearing rocks from these three HP–LT metasedimentary units. It is shown that, in the Afyon Zone, carpholite-bearing assemblages were retrogressed through greenschist-facies conditions at c. 67–62 Ma. Early retrograde stages in the Ören Unit are dated to 63–59 Ma. In the Kurudere–Nebiler Unit (HP Mesozoic cover of the southern Menderes Massif), HP retrograde stages are dated to c. 45 Ma, and post-collisional cooling to c. 26 Ma. These new results support that the Ören Unit represents the westernmost continuation of the Afyon Zone, whereas the Kurudere–Nebiler Unit correlates with the Cycladic Blueschist Unit of the Aegean Domain. In Western Anatolia, three successive HP–LT metamorphic belts thus formed: the northernmost Tavşanlı Zone (c. 88–82 Ma), the Ören–Afyon Zone (between 70 and 65 Ma), and the Kurudere–Nebiler Unit (c. 52–45 Ma). The southward younging trend of the HP–LT metamorphism from the upper and internal to the deeper and more external structural units, as in the Aegean Domain, points to the persistence of subduction in Western Anatolia between 93–90 and c. 35 Ma. After the accretion of the Menderes–Tauride terrane, in Eocene times, subduction stopped, leading to continental collision and associated Barrovian-type metamorphism. Because, by contrast, the Aegean subduction did remain active due to slab roll-back and trench migration, the eastern limb (below Southwestern Anatolia) of the Hellenic slab was dramatically curved and consequently teared. It therefore is suggested that the possibility for subduction to continue after the accretion of buoyant (e.g. continental) terranes probably depends much on palaeogeography.

Geochemical synthesis for the Effingen Member in boreholes at Oftringen, Gösgen and Küttigen

The Effingen Member is a low-permeability rock unit of Oxfordian age (ca. 160 Ma) that occurs across northern Switzerland. It comprises sandy calcareous marls and (argillaceous) limestones. This report describes the hydrogeochemistry, mineralogy and supporting physical properties of the Effingen Member in three boreholes in the Jura-Südfuss area: Oftringen, Gösgen and Küttigen, where it is 220–240 m thick. The top of the Effingen Member is at 420, 66 and 32 m depths at the three sites. Core materials are available from Oftringen and Gösgen, whereas information from Küttigen is limited to cuttings, in-situ hydrogeological testing and geophysical logging. Hydrogeological boundaries of the Effingen Member vary between locations. Ground-water flows were identified during drilling at the top (Geissberg Member), but not at the base, of the Effingen Member at Oftringen, at the base (Hauptrogenstein Formation) of the Effingen Member at Gösgen, and in a limestone layer (Gerstenhübel unit) within the Effingen Member at Küttigen. The marls and limestones of the Effingen Member have carbonate contents of 46–91 wt.-% and clay-mineral contents of 5–37 wt.-%. Pyrite contents are up to 1.6 wt.-%, but no sulphate minerals were detected by routine analyses. Clay minerals are predominantly mixed-layer illite-smectite, illite and kaolinite, with sporadic traces of chlorite and smectite. Veins filled with calcite ± celestite occur through the Effingen Member at Oftringen but not at Gösgen or Küttigen. They formed at 50–70 ºC from externally derived fluids, probably of Miocene age. Water contents are 0.7–4.2 wt.-%, corresponding to a water-loss porosity range of 1.9–10.8 vol.-%. Specific surface areas, measured by the BET method, are 2–30 m2/g, correlating with clay-mineral contents. Water activity has been measured and yielded surprisingly low values down to 0.8. These cannot be explained by pore-water salinity alone and include other effects, such as changes in the fabric due to stress release or partial saturation. Observed variations in measurements are not fully understood. Cation exchange capacity (CEC) and exchangeable cation populations have been studied by the Ni-en method. CEC, derived from the consumption of the index cation Ni, is 9–99 meq/kgrock at a solid:liquid ratio of 1, correlating with the clay-mineral content. Cation concentrations in Ni-en extract solutions are in the order Na+≥Ca2+>Mg2+>K+>Sr2+. However, the analytical results from the Ni-en extractions have additional contributions from cations originating from pore water and from mineral dissolution reactions that occurred during extraction, and it was not possible to reliably quantify these contributions. Therefore, in-situ cation populations and selectivity coefficients could not be derived. A suite of methods have been used for characterising the chemical compositions of pore waters in the Effingen Member. Advective displacement was used on one sample from each Oftringen and Gösgen and is the only method that produces results that approach complete hydrochemical compositions. Aqueous extraction was used on core samples from these two boreholes and gives data only for Cl- and, in some cases, Br-. Out-diffusion was used on core samples from Oftringen and similarly gives data for Cl- and Br- only. For both aqueous extraction and out-diffusion, reaction of the experimental water with rock affected concentrations of cations, SO42 and alkalinity in experimental solutions. Another method, centrifugation, failed to extract pore water. Stable isotope ratios (δ18O and δ2H) of pore waters in core samples from Oftringen were analysed by the diffusive exchange method and helium contents of pore water in Oftringen samples were extracted for mass spectrometric analysis by quantitative outgassing of preserved core samples. Several lines of evidence indicate that drillcore samples might not have been fully saturated when opened and subsampled in the laboratory. These include comparisons of water-loss porosities with physical porosities, water-activity measurements, and high contents of dissolved gas as inferred from ground-water samples. There is no clear proof of partial saturation and it is unclear whether this might represent in-situ conditions or is due to exsolution of gas due to the pressure release since drilling. Partial saturation would have no impact on the recalculation of pore-water compositions from aqueous extraction experiments using water-loss porosity data. The largest uncertainty in the pore-water Cl- concentrations recalculated from aqueous extraction and out-diffusion experiments is the magnitude of the anion-accessible fraction of water-loss porosity. General experience of clay-mineral rich formations suggests that the anion-accessible porosity fraction is very often about 0.5 and generally in a range of 0.3 to 0.6 and tends to be inversely correlated with clay-mineral contents. Comparisons of the Cl- concentration in pore water obtained by advective displacement with that recalculated from aqueous extraction of an adjacent core sample suggests a fraction of 0.27 for an Oftringen sample, whereas the same procedure for a Gösgen sample suggests a value of 0.64. The former value for anion-accessible porosity fraction is presumed to be unrepresentative given the local mineralogical heterogeneity at that depth. Through-diffusion experiments with HTO and 36Cl- suggest that the anion-accessible porosity fraction in the Effingen Member at Oftringen and Gösgen is around 0.5. This value is proposed as a typical average for rocks of the Effingen Member, bearing in mind that it varies on a local scale in response to the heterogeneity of lithology and pore-space architecture. The substantial uncertainties associated with the approaches to estimating anion-accessible porosity propagate into the calculated values of in-situ pore-water Cl- concentrations. On the basis of aqueous extraction experiments, and using an anion-accessible porosity fraction of 0.5, Cl- concentrations in the Effingen Member at Oftringen reach a maximum of about 14 g/L in the centre. Cl- decreases upwards and downwards from that, forming a curved depth profile. Cl- contents in the Effingen Member at Gösgen increase with depth from about 3.5 g/L to about 14 g/L at the base of the cored profile (which corresponds to the centre of the formation). Out-diffusion experiments were carried out on four samples from Oftringen, distributed through the Effingen Member. Recalculated Cl- concentrations are similar to those from aqueous extraction for 3 out of the 4 samples, and somewhat lower for one sample. Concentrations of other components, i.e. Na+, K+, Ca2+, Mg2+, Sr2+, SO42- and HCO3- cannot be obtained from the aqueous extraction and out-diffusion experimental data because of mineral dissolution and cation exchange reactions during the experiments. Pore-water pH also is not constrained by those extraction experiments. The only experimental approach to obtain complete pore-water compositions for samples from Oftringen and Gösgen is advective displacement of pore water. The sample from Oftringen used for this experiment is from 445 m depth in the upper part of the Effingen Member and gave eluate with 16.5 g/L Cl- whereas aqueous extraction from a nearby sample indicated about 9 g/L Cl-. The sample from Gösgen used for advective displacement is from 123 m depth in the centre of the Effingen Member sequence and gave eluate with about 9 g/L Cl- whereas aqueous extraction gave 11.5 g/L Cl-. In both cases the pore waters have Na-(Ca)-Cl compositions and SO42- concentrations of about 1.1 g/L. The Gösgen sample has a Br/Cl ratio similar to that of sea water, whereas this ratio is lower for the Oftringen sample. Taking account of uncertainties in the applied experimental approaches, it is reasonable to place an upper limit of ca. 20 g/L on Cl- concentration for pore water in the Effingen Member in this area. There are major discrepancies between pore-water SO42- concentrations inferred from aqueous extraction or out-diffusion experiments and those obtained from advective displacement in both the Oftringen and Gösgen cases. A general conclusion is that all or at least part of the discrepancies are attributable to perturbation of the sulphur system and enhancement of SO42- by sulphate mineral dissolution and possibly minor pyrite oxidation during aqueous extraction and out-diffusion. Therefore, data for SO42- calculated from those pore-water sampling methods are considered not to be representative of in-situ conditions. A reference pore-water composition was defined for the Effingen Member in the Jura Südfuss area. It represents the probable upper limits of Cl- contents and corresponding anion and cation concentrations that are reasonably constrained by experimental data. Except for Cl- and possibly Na+ concentrations, this composition is poorly constrained especially with respect to SO42- and Ca2+ concentrations, and pH and alkalinity. Stable isotope compositions, δ18O and δ2H, of pore waters in the Effingen Member at Oftringen plot to the right of the meteoric water line, suggesting that 18O has been enriched by water-rock exchange, which indicates that the pore waters have a long residence time. A long residence time of pore water is supported by the level of dissolved 4He that has accumulated in pore water of the Effingen Member at Oftringen. This is comparable with, or slightly higher than, the amounts of 4He in the Opalinus Clay at Benken. Ground waters were sampled from flowing zones intersected by boreholes at the three locations. The general interpretation is that pore waters and ground-water solutes may have similar origins in Mesozoic and Cenozoic brackish-marine formations waters, but ground-water solutes have been diluted rather more than pore waters by ingress of Tertiary and Quaternary meteoric waters. The available hydrochemical data for pore waters from the Effingen Member at these three locations in the Jura-Südfuss area suggest that the geochemical system evolved slowly over geological periods of time, in which diffusion was an important mechanism of solute transport. The irregularity of Cl- and δ18O profiles and spatial variability of advective ground-water flows in the Malm-Dogger system suggests that palaeohydrogeological and hydrochemical responses to changing tectonic and surface environmental conditions were complex.

Squeezing of Pore-water from Core Samples of DGR Boreholes: Feasibility Study

Three archived core samples from boreholes DGR-4, DGR-5 and DGR-6 from the Salina F Unit, Queenston Formation and the Georgian Bay Formation were subjected to squeezing tests at pressures of up to 500 MPa. Two samples did not yield any water, while a total of 0.88 g pore water was obtained from a clay-rich sample from the Blue Mountain Formation (water content = 2.8 wt.%, porosity = 8 %). This water mass was sufficient for a full chemical and water-isotope analysis – the first direct determination of pore-water composition in rocks from the DGR boreholes. The results are generally in reasonable agreement with those of independent methods, or the observed differences can be explained. Ancillary investigations included the determination of water content, densities and mineralogy, aqueous extraction of squeezed cores, and SEM investigations to characterise the microtexture of unsqueezed and squeezed rock materials. It is concluded that squeezing is a promising method of pore-water extraction and characterisation and is recommended as an alternative method for future studies. Selection criteria for potentially squeezable samples include high clay-mineral content (correlating in a high water content) and low carbonate content (low stiffness, limited cementation). Potential artefacts of the method, such as ion filtration or pressure solution, should be explored and quantified in future efforts.

Solute transport in crystalline rocks at Äspö — I: Geological basis and model calibration

Water-conducting faults and fractures were studied in the granite-hosted A¨ spo¨ Hard Rock Laboratory (SE Sweden). On a scale of decametres and larger, steeply dipping faults dominate and contain a variety of different fault rocks (mylonites, cataclasites, fault gouges). On a smaller scale, somewhat less regular fracture patterns were found. Conceptual models of the fault and fracture geometries and of the properties of rock types adjacent to fractures were derived and used as input for the modelling of in situ dipole tracer tests that were conducted in the framework of the Tracer Retention Understanding Experiment (TRUE-1) on a scale of metres. After the identification of all relevant transport and retardation processes, blind predictions of the breakthroughs of conservative to moderately sorbing tracers were calculated and then compared with the experimental data. This paper provides the geological basis and model calibration, while the predictive and inverse modelling work is the topic of the companion paper [J. Contam. Hydrol. 61 (2003) 175]. The TRUE-1 experimental volume is highly fractured and contains the same types of fault rocks and alterations as on the decametric scale. The experimental flow field was modelled on the basis of a 2D-streamtube formalism with an underlying homogeneous and isotropic transmissivity field. Tracer transport was modelled using the dual porosity medium approach, which is linked to the flow model by the flow porosity. Given the substantial pumping rates in the extraction borehole, the transport domain has a maximum width of a few centimetres only. It is concluded that both the uncertainty with regard to the length of individual fractures and the detailed geometry of the network along the flowpath between injection and extraction boreholes are not critical because flow is largely one-dimensional, whether through a single fracture or a network. Process identification and model calibration were based on a single uranine breakthrough (test PDT3), which clearly showed that matrix diffusion had to be included in the model even over the short experimental time scales, evidenced by a characteristic shape of the trailing edge of the breakthrough curve. Using the geological information and therefore considering limited matrix diffusion into a thin fault gouge horizon resulted in a good fit to the experiment. On the other hand, fresh granite was found not to interact noticeably with the tracers over the time scales of the experiments. While fracture-filling gouge materials are very efficient in retarding tracers over short periods of time (hours–days), their volume is very small and, with time progressing, retardation will be dominated by altered wall rock and, finally, by fresh granite. In such rocks, both porosity (and therefore the effective diffusion coefficient) and sorption Kds are more than one order of magnitude smaller compared to fault gouge, thus indicating that long-term retardation is expected to occur but to be less pronounced.

Solute transport in crystalline rocks at Äspö — II: Blind predictions, inverse modelling and lessons learnt from test STT1

Based on the results from detailed structural and petrological characterisation and on up-scaled laboratory values for sorption and diffusion, blind predictions were made for the STT1 dipole tracer test performed in the Swedish A¨ spo¨ Hard Rock Laboratory. The tracers used were nonsorbing, such as uranine and tritiated water, weakly sorbing 22Na+, 85Sr2 +, 47Ca2 +and more strongly sorbing 86Rb+, 133Ba2 +, 137Cs+. Our model consists of two parts: (1) a flow part based on a 2D-streamtube formalism accounting for the natural background flow field and with an underlying homogeneous and isotropic transmissivity field and (2) a transport part in terms of the dual porosity medium approach which is linked to the flow part by the flow porosity. The calibration of the model was done using the data from one single uranine breakthrough (PDT3). The study clearly showed that matrix diffusion into a highly porous material, fault gouge, had to be included in our model evidenced by the characteristic shape of the breakthrough curve and in line with geological observations. After the disclosure of the measurements, it turned out that, in spite of the simplicity of our model, the prediction for the nonsorbing and weakly sorbing tracers was fairly good. The blind prediction for the more strongly sorbing tracers was in general less accurate. The reason for the good predictions is deemed to be the result of the choice of a model structure strongly based on geological observation. The breakthrough curves were inversely modelled to determine in situ values for the transport parameters and to draw consequences on the model structure applied. For good fits, only one additional fracture family in contact with cataclasite had to be taken into account, but no new transport mechanisms had to be invoked. The in situ values for the effective diffusion coefficient for fault gouge are a factor of 2–15 larger than the laboratory data. For cataclasite, both data sets have values comparable to laboratory data. The extracted Kd values for the weakly sorbing tracers are larger than Swedish laboratory data by a factor of 25–60, but agree within a factor of 3–5 for the more strongly sorbing nuclides. The reason for the inconsistency concerning Kds is the use of fresh granite in the laboratory studies, whereas tracers in the field experiments interact only with fracture fault gouge and to a lesser extent with cataclasite both being mineralogically very different (e.g. clay-bearing) from the intact wall rock.

Assessing Initial Conditions for Chloride Transport Across Low- permeability Argillaceous Rocks, Wellenberg, Switzerland

Information about fluid evolution and solute transport in a low-permeability metamorphic rock sequence has been obtained by comparing chloride concentrations and chlorine isotope ratios of pore water, groundwater, and fluid inclusions. The similarity of d37Cl values in fluid inclusions and groundwater suggests a closed-system evolution during the metamorphic overprint, and signatures established at this time appear to form the initial conditions for chloride transport after exhumation of the rock sequence.

Subcritical Propagation and Coalescence of Oil-Filled Cracks: Getting the Oil Out of Low-Permeability Source Rocks

We use a fracture mechanics model to study subcritical propagation and coalescence of single and collinear oil-filled cracks during conversion of kerogen to oil. The subcritical propagation distance, propagation duration, crack coalescence and excess oil pressure in the crack are determined using the fracture mechanics model together with the kinetics of kerogen-oil transformation. The propagation duration for the single crack is governed by the transformation kinetics whereas the propagation duration for the multiple collinear cracks may vary by two orders of magnitude depending on initial crack spacing. A large amount of kerogen (>90%) remains unconverted when the collinear cracks coalesce and the new, larger cracks resulting from coalescence will continue to propagate with continued kerogen-oil conversion. The excess oil pressure on the crack surfaces drops precipitously when the collinear cracks are about to coalesce, and crack propagation duration and oil pressure on the crack surfaces are strongly dependent on temperature. Citation: Jin, Z.-H., S. E. Johnson, and Z. Q. Fan (2010), Subcritical propagation and coalescence of oil-filled cracks: Getting the oil out of low-permeability source rocks, Geophys. Res. Lett., 37, L01305, doi:10.1029/2009GL041576.

Metamorphism, Transient Mid-Crustal Rheology, Strain Localization and the Exhumation of High-Grade Metamorphic Rocks

We present a series of three-dimensional numerical models investigating the effects of metamorphic strengthening and weakening on the geodynamic evolution of convergent orogens that are constrained by observations from an exposed mid-crustal section in the New England Appalachians. The natural mid-crustal section records evidence for spatially and temporally variable mid-crustal strength as a function of metamorphic grade during prograde polymetamorphism. Our models address changes in strain rate partitioning and topographic uplift as a function of strengthening/weakening in the middle crust, as well as the resultant changes in deformation kinematics and potential exhumation patterns of high-grade metamorphic rock. Results suggest that strengthening leads to strain rate partitioning around the zone and suppressed topographic uplift rates whereas weakening leads to strain rate partitioning into the zone and enhanced topographic uplift rates. Deformation kinematics recorded in the orogen are also affected by strengthening/weakening, with complete reversals in shear sense occurring as a function of strengthening/weakening without changes in plate boundary kinematics.

Magma-Driven Multiple Dike Propagation and Fracture Toughness of Crustal Rocks

Dike swarms consisting of tens to thousands of subparallel dikes are commonly observed at Earth's surface, raising the possibility of simultaneous propagation of two or more dikes at various stages of a swarm's development. The behavior of multiple propagating dikes differs from that of a single dike owing to the interacting stress fields associated with each dike. We analyze an array of parallel, periodically spaced dikes that grow simultaneously from an overpressured source into a semi-infinite, linear elastic host rock. To simplify the analysis, we assume steady state (constant velocity) magma flow and dike propagation. We use a perturbation method to analyze the coupled, nonlinear problem of multiple dike propagation and magma transport. The stress intensity factor at the dike tips and the opening displacements of the dike surfaces are calculated. The numerical results show that dike spacing has a profound effect on the behavior of dike propagation. The stress intensity factors at the tips of parallel dikes decrease with a decrease in dike spacing and are significantly smaller than that for a single dike with the same length. The reduced stress intensity factor indicates that, compared to a single dike, propagation of parallel dikes is more likely to be arrested under otherwise the same conditions. It also implies that fracture toughness of the host rock in a high confining pressure environment may not be as high as inferred from the propagation of a single dike. Our numerical results suggest fracture toughness values on the order of 100 MPa root m. The opening displacements for parallel dikes are smaller than that for a single dike, which results in higher magma pressure gradients in parallel dikes and lower flux of magma transport.