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We combine a power-law microfracture size distribution function with an expression for fracture propagation rate derived from subcritical fracture propagation theory and linear elastic fracture mechanics, to derive a geomechanically based deterministic model for the growth of a network of layer-bound fractures. This model also simulates fracture termination due to intersection with perpendicular fractures or stress-shadow interaction. We use this model to examine key controls on the emergent geometry of the fracture network. First, we examine the effect of fracture propagation rates. We show that at subcritical fracture propagation rates, the fracture nucleation rate increases with time; this generates a very dense network of very small fractures, similar to the deformation bands generated by compaction in unconsolidated sediments. By contrast, at critical propagation rates, the fracture nucleation rate decreases with time; this generates fewer but much larger fractures, similar to the brittle open fractures generated by tectonic deformation in lithified sediments. We then examine the controls on the rate of growth of the fracture network. A fracture set will start to grow when the stress acting on it reaches a threshold value, and it will continue to grow until all the fractures have stopped propagating and no new fractures can nucleate. The relative timing and rate of growth of the different fracture sets will control the anisotropy of the resulting fracture network: if the sets start to grow at the same time and rate, the result is a fully isotropic fracture network; if the primary fracture set stops growing before the secondary set starts growing, the result is a fully anisotropic fracture network; and if there is some overlap but the secondary set grows more slowly than the primary set, the result is a partially anisotropic fracture network. Although the applied horizontal strain rates are the key control on the relative growth rates of the two fracture sets, we show that the vertical effective stress, the initial horizontal stress, the elastic properties of the rock and the inelastic deformation processes, such as creep, grain sliding and pressure solution, all exert a control on the fracture growth rates, and that more isotropic fracture networks will tend to develop if the vertical effective stress is low or if the fractures are critically stressed prior to the onset of deformation. Thematic collection: This article is part of the Naturally Fractured Reservoirs collection available at: https://www.lyellcollection.org/cc/naturally-fractured-reservoirs

Deep learning has become an area of interest in most scientific areas, including physical sciences. Modern networks apply real-valued transformations on the data. Particularly, convolutions in convolutional neural networks discard phase information entirely. Many deterministic signals, such as seismic data or electrical signals, contain significant information in the phase of the signal. We explore complex-valued deep convolutional networks to leverage non-linear feature maps. Seismic data commonly has a lowcut filter applied, to attenuate noise from ocean waves and similar long wavelength contributions. Discarding the phase information leads to low-frequency aliasing analogous to the Nyquist-Shannon theorem for high frequencies. In non-stationary data, the phase content can stabilize training and improve the generalizability of neural networks. While it has been shown that phase content can be restored in deep neural networks, we show how including phase information in feature maps improves both training and inference from deterministic physical data. Furthermore, we show that the reduction of parameters in a complex network outperforms larger real-valued networks., 17 pages total, 15 pages, 2 pages references, paper, 11 figures, 28 networks

Kilometre-scale geobodies of diagenetic origin have been documented for the first time in a high-resolution 3D seismic survey of the Upper Cretaceous chalks of the Danish Central Graben, North Sea Basin. Based on detailed geochemical, petrographic and petrophysical analyses it is demonstrated that the geobodies are of an open-system diagenetic origin caused by ascending basin fluids guided by faults and stratigraphic heterogeneities. Increased amounts of porosity-occluding cementation, contact cement and/or high-density/-velocity minerals caused an impedance contrast that can be mapped in seismic data, and represent a hitherto unrecognized, third type of heterogeneity in the chalk deposits in addition to the well-known sedimentological and structural features. The distribution of the diagenetic geobodies is controlled by porosity/permeability contrasts of stratigraphic origin, such as hardgrounds associated with formation tops, and the feeder fault systems. One of these, the Top Campanian Unconformity at the top of the Gorm Formation, is particularly effective, and created a basin-wide barrier separating low-porosity chalk below from high-porosity chalk above (a regional porosity marker, RPM). It is in particular in this upper high-porosity unit (Tor and Ekofisk formations) that the diagenetic geobodies occur, delineated by ‘Stratigraphy Cross-cutting Reflectors’ (SCRs) of which 8 different types have been distinguished. The geobodies have been interpreted as the result of: 1) escaping pore-fluids due to top seal failure, followed by local mechanical compaction of high-porous chalks, paired with 2) ascension of basinal diagenetic fluids along fault systems that locally triggered cementation of calcite and dolomite within the chalk, causing increased contact cements and/or reducing porosity. The migration pathway of the fluids is marked by the SCRs, which are the outlines of high-density bodies of chalk nested in highly porous chalks. This study thus provides new insights into the 3D relationship between fault systems, fluid migration and diagenesis in chalks, and has important applications for basin modeling and reservoir characterization.

Ground-penetrating radar (GPR) and satellite ERS-2 synthetic aperture radar (SAR) are used to map the thickness and extent of the superimposed ice (SI) zone on the surge-type glacier Kongsvegen, Svalbard. GPR imagery shows sub-horizontal SI layers lying unconformably above a discrete boundary. Below this boundary, the ice has a GPR signature similar to that of ice further down-glacier in the ablation zone. This boundary is posited to represent the closing of crevasses that were created during the last surge of Kongsvegen in ∼1948. Open crevasses would have interrupted the formation of sheet layers of SI due to efficient vertical drainage of the snowpack. Aerial photographs suggest that the crevasses closed sometime in the period 1956–66. A classified SAR image from 2003 is used to delineate the extent of the SI zone. The SI extent in the SAR image agrees well with the SI zone mapped by GPR. Using the SI spatial depth distribution, we estimate the mean annual accumulation of superimposed ice to be 0.16 ± 0.06 m w.e. a−1 (locally up to 0.43 m a−1 w.e.). This corresponds to ∼15–33% of the local winter balance and ∼5–10% of the total winter balance measured since 1987.

We present a model study investigating the summer evolution of supraglacial lakes on the Greenland ice margin. Using a one-dimensional (1-D) model we calculate the surface ablation for a bare ice surface and beneath supraglacial lakes for 30 days in the summers of 1999 and 2001. The surface ablation beneath the lake was enhanced by 110% in 1999 and 170% in 2001 compared with the ablation for bare ice. We then use the results from the 1-D model to further model the vertical and horizontal evolution of the supraglacial lakes, the results of which are compared with satellite images. Within the region of the ice sheet where supraglacial lakes presently occur, the area covered by supraglacial lakes is found to be more or less independent of the summer melt rate but controlled by topography. We therefore predict that, inside this region, the area covered by supraglacial lakes will remain constant even in a warmer climate. However, in a warmer climate, surface melting will occur higher on the ice sheet where small surface slopes favour formation of large supraglacial lakes. Enhanced surface melting beneath such lakes is a hitherto overlooked feedback mechanism related to climate warming.

[1] We present a mathematical model describing the summer melting of sea ice. We simulate the evolution of melt ponds and determine area coverage and total surface ablation. The model predictions are tested for sensitivity to the melt rate of unponded ice, enhanced melt rate beneath the melt ponds, vertical seepage, and horizontal permeability. The model is initialized with surface topographies derived from laser altimetry corresponding to first-year sea ice and multiyear sea ice. We predict that there are large differences in the depth of melt ponds and the area of coverage between the two types of ice. We also find that the vertical seepage rate and the melt rate of unponded ice are important in determining the total surface ablation and area covered by melt ponds.