Robust system size reduction of discrete fracture networks: a multi-fidelity method that preserves transport characteristics

We propose a multi-fidelity system reduction technique that uses weighted graphs paired with three-dimensional discrete fracture network (DFN) modelling for efficient simulation of subsurface flow and transport in fractured media. DFN models are used to simulate flow and transport in subsurface fractured rock with low-permeability. One method to alleviate the heavy computational overhead associated with these simulations is to reduce the size of the DFN using a graph representation of it to identify the primary flow sub-network and only simulate flow and transport thereon. The first of these methods used unweighted graphs constructed solely on DFN topology and could be used for accurate predictions of first-passage times. However, these techniques perform poorly when predicting later stages of the mass breakthrough. We utilize a weighted-graph representation of the DFN where edge weights are based on hydrological parameters in the DFN that allows us to exploit the kinematic quantities derivable a posteriori from the flow solution obtained on the graph representation of the DFN to perform system reduction and predict the later stages of the breakthrough curve with high fidelity. We also propose and demonstrate the use of an adaptive pruning algorithm with error control that produces a pruned DFN sub-network whose predicted mass breakthrough agrees with the original DFN within a user-specified tolerance. The method allows for the level of accuracy to be a user-controlled parameter.     

A new Jurassic cow shark (Chondrichthyes,Hexanchiformes) with comments on Jurassic hexanchiform systematics

A new taxon, ?Crassodontidanus gen. nov. of Hexanchiformes (cow sharks) from the Jurassic of Germany is described. It is characterized by peculiar teeth combining apomorphic (serrated mesial cutting edge of the main cusp) and plesiomorphic features (deep root with convex mesial and distal margins in labial and lingual views; protruding lingual root bulge). This character combination readily distinguishes members of the new taxon from all other known extant (Heptranchias, Hexanchus, Notorynchus) and extinct (?Gladioserratus, ?Notidanodon, ?Notidanoides, ?Pachyhexanchus, ?Paraheptranchias, ?Weltonia) hexanchiforms. Currently, two species, ?C. serratus (type species; Late Jurassic, Late Kimmeridgian of Nusplingen, South Germany) and ?C. wiedenrothi (Early Jurassic, Early Pliensbachian of Gretenberg (Hanover), North Germany) are assigned to this taxon. ?Crassodontidanus gen. nov. is member of ?Crassonotidae fam. nov. and sister to ?Notidanoides Maisey, 1986 and ?Pachyhexanchus Cappetta, 1990. We consider ?Notidanus amalthei Oppel, 1854 from the Pliensbachian of South Germany, ?Notidanus insignis Seguenza, 1887 from the Oxfordian of Sicily (Italy) and ?Notidanus wagneri Agassiz, 1843 from the Early Tithonian of Solnhofen (South Germany) nomina dubia and nomina nuda, respectively. The family ?Crassonotidae comprises plesiomorphic hexanchiforms ranging from the Sinemurian (Early Jurassic) to the Hauterivian (Early Cretaceous).     

Analysis of the Influence of a Natural Fracture Network on Hydraulic Fracture Propagation in Carbonate Formations

A new experimental model has been designed to simulate the influence of a natural fracture network on the propagation geometry of hydraulic fractures in naturally fractured formations using a tri-axial fracturing system. In this model, a parallel and symmetrical pre-fracture network was created by placing cement plates in a cubic mold and filling the mold with additional cement to create the final testing block. The surface of the plates will thus be weakly cemented and form pre-fractures. The dimension and direction of the pre-fractures can be controlled using the plates. The experiments showed that the horizontal differential stress $\Updelta \sigma$ and the angle $\Updelta \theta$ between the maximum horizontal principal in situ stress and the pre-fracture are the dominating factors for the initiation and propagation of hydraulic fractures. For $\Updelta \theta = 90^\circ$ and $\Updelta \sigma \ge 2{\text{ MPa}}$ or $\Updelta \theta = 60^\circ$ and $\Updelta \sigma \ge 4{\text{ MPa}}$ , the direction of the initiation and propagation of the hydraulic fractures are consistent with or deviate from the normal direction of the pre-fracture. When the hydraulic fractures approach the pre-fractures, the direction of the hydraulic fracture propagation will be consistent with the normal direction of the pre-fracture. Otherwise, the hydraulic fracture will deflect and perpendicularly cross the parallel and symmetric pre-fracture network. For $\Updelta \theta = 90^\circ$ and $\Updelta \sigma < 2{\text{ MPa}},\,\Updelta \theta = 60^\circ$ , and $\Updelta \sigma < 4{\text{ MPa}}$ or $\Updelta \theta = 45^\circ$ and $\Updelta \sigma = 4 - 8{\text{ MPa}}$ , before the hydraulic fracture and the pre-fractures intersect, the direction of the hydraulic fracture propagation remains unchanged, and the pre-fractures open or dilate when the hydraulic fracture propagates to the intersection point, forming a complicated hydraulic fracture network with the propagation region of the overall hydraulic fracture network taking the shape of an ellipse. In this condition, the complexity level of the hydraulic fracture is controlled by the net pressure, the compressive normal stress acting on the pre-fractures, the shearing strength and the cohesion strength of the planes of weakness. The conclusions of this research are inconsistent with the formulation of the approach angle that has been widely accepted by previous studies. The principle of hydraulic fracture propagation is that it follows the least resistance, the most preferential propagation, and the shortest propagation path.     

Correlation factors for impurity diffusion on the sublattice of dodecahedral sites in garnet

The method of Koiwa and Ishioka (Philos Mag A 47:927–938, 1983) is used, with slight modification, to evaluate the correlation factor for vacancy-mediated diffusion of impurity atoms on the sublattice of dodecahedral sites in garnet, as a function of the relevant vacancy-jump frequencies. The required values of the lattice Green’s function were obtained from multiple Monte Carlo simulations in lattices of progressively larger size, extrapolated to an infinite lattice using a model that linearizes the dependence of the functional value on lattice size. As Online Resources, codes are provided that permit evaluation of the correlation factor for any chosen set of vacancy-jump frequencies, for implementation in either Mathematica ^® or Matlab ^®.     

Experimental anatexis and genesis of migmatites: A reply

Recentlyvon Platen applied the results of his laboratory experiments to a migmatite studied byHärme. Some comments are presented upon that re-interpretation.     

Multiscale model reduction for shale gas transport in fractured media

In this paper, we develop a multiscale model reduction technique that describes shale gas transport in fractured media. Due to the pore-scale heterogeneities and processes, we use upscaled models to describe the matrix. We follow our previous work (Akkutlu et al. Transp. Porous Media 107(1), 235–260, 2015), where we derived an upscaled model in the form of generalized nonlinear diffusion model to describe the effects of kerogen. To model the interaction between the matrix and the fractures, we use Generalized Multiscale Finite Element Method (Efendiev et al. J. Comput. Phys. 251, 116–135, 2013, 2015). In this approach, the matrix and the fracture interaction is modeled via local multiscale basis functions. In Efendiev et al. (2015), we developed the GMsFEM and applied for linear flows with horizontal or vertical fracture orientations aligned with a Cartesian fine grid. The approach in Efendiev et al. (2015) does not allow handling arbitrary fracture distributions. In this paper, we (1) consider arbitrary fracture distributions on an unstructured grid; (2) develop GMsFEM for nonlinear flows; and (3) develop online basis function strategies to adaptively improve the convergence. The number of multiscale basis functions in each coarse region represents the degrees of freedom needed to achieve a certain error threshold. Our approach is adaptive in a sense that the multiscale basis functions can be added in the regions of interest. Numerical results for two-dimensional problem are presented to demonstrate the efficiency of proposed approach.     

Modeling competing hydraulic fracture propagation with the extended finite element method

We present an extended finite element framework to numerically study competing hydraulic fracture propagation. The framework is capable of modeling fully coupled hydraulic fracturing processes including fracture propagation, elastoplastic bulk deformation and fluid flow inside both fractures and the wellbore. In particular, the framework incorporates the classical orifice equation to capture fluid pressure loss across perforation clusters linking the wellbore with fractures. Dynamic fluid partitioning among fractures during propagation is solved together with other coupled factors, such as wellbore pressure loss (\(\Delta p_w\)), perforation pressure loss (\(\Delta p\)), interaction stress (\(\sigma _\mathrm{int}\)) and fracture propagation. By numerical examples, we study the effects of perforation pressure loss and wellbore pressure loss on competing fracture propagation under plane-strain conditions. Two dimensionless parameters \(\Gamma = \sigma _\mathrm{int}/\Delta p\) and \(\Lambda = \Delta p_w/\Delta p\) are used to describe the transition from uniform fracture propagation to preferential fracture propagation. The numerical examples demonstrate the dimensionless parameter \(\Gamma \) also works in the elastoplastic media.     

Reappraisal of the metamorphic facies concept

Eskola's concept of metamorphic facies, now 50 years old, is reappraised in the light of current knowledge and usage among petrologists. Facies should be defined solely in terms of observable geologic criteria. LikeEskola, we continue to view each facies as a set of mineral assemblages that approximate equilibrium within a definite range of temperature; but this is inference and must be excluded from the definition of facies. Mutual boundaries between facies are transitional. Division into subfacies has proved unacceptable to many writers, and has led to confusion in the physical interpretation of metamorphic parageneses. We propose henceforth not to recognize subfacies. Eleven facies are recognized in this paper, and their terminology has been adapted as nearly as possible to current general usage:

1. A.
   Low-pressure facies commonly but not exclusively of contact metamorphism. In order of increasing temperature:

   1. (1)
      Albite-epidote-hornfels.     
      
      

Experimental Investigation of Seepage Properties of Fractured Rocks Under Different Confining Pressures

The effectiveness of transmitting underground water in rock fractures is strongly influenced by the widths of the fractures and their interconnections. However, the geometries needed for water flow in fractured rock are also heavily controlled by the confining pressure conditions. This paper is intended to study the seepage properties of fractured rocks under different confining pressures. In order to do this, we designed and manufactured a water flow apparatus that can be connected to the electro-hydraulic servo-controlled test system MTS815.02, which provides loading and exhibits external pressures in the test. Using this apparatus, we tested fractured mudstone, limestone and sandstone specimens and obtained the relationship between seepage properties and variations in confining pressure. The calculation of the seepage properties based on the collection of water flow and confining pressure differences is specifically influenced by non-Darcy flow. The results show that: (1) The seepage properties of fractured rocks are related to confining pressure, i.e. with the increase of confining pressure, the permeability $ k $ decreases and the absolute value of non-Darcy flow coefficient $ \beta $ increases. (2) The sandstone coefficients $ k $ and $ \beta $ range from $ 1.03 \times 10^{ - 18} $ to $ 1.53 \times 10^{ - 17} $  m² and $ - 1.13 \times 10^{17} $ to $ - 2.35 \times 10^{18} $  m^?1, respectively, and exhibit a greater change compared to coefficients of mudstone and limestone. (3) From the regression analysis of experimental data, it is concluded that the polynomial function is a better fit than the power and logarithmic functions. The results obtained can provide an important reference for understanding the stability of rock surrounding roadways toward prevention of underground water gushing-out, and for developing underground resources (e.g. coal).     

Appalachenprofil 1964

Our knowledge of the Appalachians has grown very satisfoctorily during the last ten years. Folding took place at least twice: 1. In the Ordovician the basement including the crystalline axis as far as the Blue Ridge became consolidated. This region became highland and furnished the material for upper Ordovician to Carboniferous sediments. This has been established by three methods: first, facies examinations; second,Pettijohn and his students found that sediments were transported from East to West during the upper Ordovician, Silurian, Devonian, and Carboniferous periods; and finallyHopson has summarized absolute age determinations which show that the basement, (Cambrian, and lower Ordovician rocks included) were consolidated and uplifted about 440 million years ago. Thus, in the first period of folding the Blue Ridge Zone, which is the western margin of the basement complex, was uplifted and crowded westward. Cambrian and Ordovician sediments which cover the basement as a thin layer were folded simultaneously. Folding intensity decreases from East to West and regional cleavage and lineation disappear at the “tectonite Front”. 2. The upper part of the Paleozoic column was folded during Appalachian orogeny presumably near the surface and with little or no influence by the basement. Maybe both the Foreland and the folded Appalachians “crept” over the basement forming sharply marked anticlinal axes and broad synclinal troughs. However,Cooper supposes that the basement took part through vertical movements and in this way was partly responsible for sedimentation and possibly also for structures. In the Maryland profile lateral reduction is less than further south where folds grade into nappe-like overthrusts and the foothill folds disappear below great horizontal thrusts.     

Untersuchungen an Grundwässern der Ost-Sahara

In a joint enterprise, mostly Eastern Sahara artesian waters have been investigated. Age determinations and geochemistry allow geological conclusions. The rains responsible for the waters probably fell in a Pluvial about 25–35000 years ago. Their infiltration took place (simultaneously with or shortly after the lowest Würm-level of the Mediterranean) mainly in Nubian sandstone regions and within Oasis-depressions of Western Egypt. The upper levels of the geological reservoir seem to have been leaked out during the eustatic lowering of the Mediterranean level via an overdeepened Nile-bed. Infiltration trapped air within the pore-space of Nubian sandstone. This air re-appears to-day — after having lost its Oxygene etc.-content — as Nitrogene-gas.Münnich andVogel describe (?Untersuchungen an pluvialen Wässern etc.“) detailed investigations concerning the absolute age of these (and generally such) waters. E. T.Degens, in his part ?Geochemische Untersuchungen etc.“, deals with the geochemistry of the occurrences, mainly with some stable isotopes.     

Ultimate Bearing Capacity Prediction of Eccentrically Inclined Loaded Strip Footings

Extensive laboratory model tests have been carried out on a strip footing resting over dry sand bed subjected to eccentrically inclined load to determine the ultimate bearing capacity (Patra et al. in Int J Geotech Eng 6(3):343–352, 2012a.  https://doi.org/10.3328/IJGE.2012.06.03.343-352, Int J Geotech Eng 6(4):507–514, b.  https://doi.org/10.3328/IJGE.2012.06.04.507-514). Similarly, lower bound calculations based on finite element method were performed to compute the bearing capacity of a strip footing subjected to an eccentric and inclined load lying over a cohesionless soil with varying embedment depth and relative density (Krabbenhoft et al. in Int J Geomech ASCE, 2014.  https://doi.org/10.1061/(ASCE)GM.1943-5622.0000332). The load may be applied in two ways namely, towards the center line and away from the center line of the footing. Based on the results (both experimental and numerical analyses), a neural network model is developed to predict the reduction factor that will be used in computing the ultimate bearing capacity of an eccentrically inclined loaded strip footing. This reduction factor (RF) is the ratio of the ultimate bearing capacity of the footing subjected to an eccentrically inclined load to the ultimate bearing capacity of the footing subjected to a centric vertical load. A thorough sensitivity analysis is carried out to evaluate the parameters affecting the reduction factor. Based on the weights of the developed neural network model, a neural interpretation diagram is developed to find out whether the input parameters have direct or inverse effect on the output. A prediction model equation is framed with the trained weights of the neural network as the model parameters. The predictions from ANN, and those from other approaches, are compared with the results computed from both experimentation and FEM analyses. The ANN model results are found to be more accurate and well matched with other results.     

The dilatant behaviour of sand–pile interface subjected to loading and stress relief

Property and behaviour of sand–pile interface are crucial to shaft resistance of piles. Dilation or contraction of the interface soil induces change in normal stress, which in turn influences the shear stress mobilised at the interface. Although previous studies have demonstrated this mechanism by laboratory tests and numerical simulations, the interface responses are not analysed systematically in terms of soil state (i.e. density and stress level). The objective of this study is to understand and quantify any increase in normal stress of different pile–soil interfaces when they are subjected to loading and stress relief. Distinct element modelling was carried out. Input parameters and modelling procedure were verified by experimental data from laboratory element tests. Parametric simulations of shearbox tests were conducted under the constant normal stiffness, constant normal load and constant volume boundary conditions. Key parameters including initial normal stress ( $ \sigma_{{{\text{n}}0}}^{\prime } $ ), initial void ratio (e ₀), normal stiffness constraining the interface and loading–unloading stress history were investigated. It is shown that mobilised stress ratio ( $ \tau /\sigma_{\text{n}}^{\prime } $ ) and normal stress increment ( $ \Updelta \sigma_{\text{n}}^{\prime } $ ) on a given interface are governed by $ \sigma_{{{\text{n}}0}}^{\prime } $ and e ₀. An increase in $ \sigma_{{{\text{n}}0}}^{\prime } $ from 100 to 400 kPa leads to a 30 % reduction in $ \Updelta \sigma_{\text{n}}^{\prime } $ . An increase in e ₀ from 0.18 to 0.30 reduces $ \Updelta \sigma_{\text{n}}^{\prime } $ by more than 90 %, and therefore, shaft resistance is much lower for piles in loose sands. A unique relationship between $ \Updelta \sigma_{\text{n}}^{\prime } $ and normal stiffness is established for different soil states. It can be applied to assess the shaft resistance of piles in soils with different densities and subjected to loading and stress relief. Fairly good agreement is obtained between the calculated shaft resistance based on the proposed relationship and the measured results in centrifuge model tests.     

Salinization of porewater in a multiple aquitard-aquifer system in Jiangsu coastal plain,China

Chemical and isotopic compositions were analyzed in porewater squeezed from a clayey aquitard in Jiangsu coastal plain, eastern China, to interpret the salinity origin, chemical evolution and water-mass mixing process. A strong geochemical fingerprint was obtained with an aligned Cl/Br ratio of 154 in the salinized aquitard porewater over a wide Cl^? concentration range (396–9,720 mg/L), indicating that porewater salinity is likely derived from a mixing with old brine with a proportion of less than 20%. Very small contributions of brine exerted limited effects on water stable isotopes. The relationships between porewater δ¹⁸O and δD indicate that shallow and intermediate porewaters could be original seawater and were subsequently diluted with modern meteoric water, whereas deep porewaters with depleted stable isotopic values were probably recharged during a cooler period and modified by evaporation and seawater infiltration. The cation–Cl relationship and mineralogy of associated strata indicate that porewater has been chemically modified by silicate weathering and ion-exchange reactions. ⁸⁷Sr/⁸⁶Sr ratios of 0.7094–0.7112 further confirm the input source of silicate minerals. Numerical simulations were used to evaluate the long-term salinity evolution of the deep porewater. The alternations of boundary conditions (i.e., the third aquifer mixed with brine at approximately 70 ka BP, followed by recharge of glacial meltwater at 20–25 ka BP, and then mixing with Holocene seawater at 7–10 ka BP) are responsible for the shift in porewater salinity. These timeframes correspond with the results of previous studies on ancient marine transgression-regression in Jiangsu coastal plain.     

Indirect economic losses of drought under future projections of climate change: a case study for Spain

This study presents the results of numerical simulations of the 2004 Indian Ocean earthquake and tsunami in the Bay of Lhok Nga (northwestern coast of Sumatra, Indonesia) integrating sediment erosion and deposition. We investigate the transport of sediment both by suspension and by bedload under different scenarii of long breaking dispersive waves through a series of numerical experiments. The earthquake source model used by Koshimura et al. (Coast Eng J 51:243–273, 2008) with a 25-m dislocation better reproduces the wave travel time, flow depth and inundation area than the other models tested. The model reproduces realistically the pronounced coastal retreat in the northern part of Lhok Nga Bay (retreat ranging between 50 and 150 m), where Paris et al. (Geomorphology 104:59–72, 2009) estimated a mean retreat of 80 m. There is also a good agreement between the simulated area of coastal retreat (195,400 m²) and the field observations (203,200 m²). The simulation may underestimate the volume of tsunami deposits (611,700 m³ vs. 500,000–1,000,000 m³ estimated by Paris et al. (2009). The model fully reproduces the observed thickness of tsunami deposits when considering both bedload and suspension, even if bedload transport dominates. Limitations are due to micro-scale topographic, anthropic features (which are not always represented by the DEM) and the amount of debris which may influence flow dynamics and sediment transport.     

Flow rule in a high-cycle accumulation model backed by cyclic test data of 22 sands

The flow rule used in the high-cycle accumulation (HCA) model proposed by Niemunis et al. (Comput Geotech 32: 245, 2005) is examined on the basis of the data from approximately 350 drained long-term cyclic triaxial tests (N = 10⁵ cycles) performed on 22 different grain-size distribution curves of a clean quartz sand. In accordance with (Wichtmann et al. in Acta Geotechnica 1: 59, 2006), for all tested materials, the “high-cyclic flow rule (HCFR)”, i.e., the ratio of the volumetric and deviatoric strain accumulation rates \(\dot{\varepsilon}_{\rm{v}}^{{\rm acc}}/\dot{\varepsilon}_{\rm{q}}^{{\rm acc}}\) , was found dependent primarily on the average stress ratio η ^av = q ^av/p ^av and independent of amplitude, soil density and average mean pressure. The experimental HCFR can be fairly well approximated by the flow rule of the modified Cam-clay (MCC) model. Instead of the critical friction angle \(\varphi_{\rm{c}}\) which enters the flow rule for monotonic loading, the HCA model uses the MCC flow rule expression with a slightly different parameter \(\varphi_{\rm{cc}}\) . It should be determined from cyclic tests. \(\varphi_{\rm{cc}}\) and \(\varphi_{\rm{c}}\) are of similar magnitude but not always identical, because they are calibrated from different types of tests. For a simplified calibration in the absence of cyclic test data, \(\varphi_{\rm{cc}}\) may be estimated from the angle of repose \(\varphi_{\rm{r}}\) determined from a pluviated cone of sand (Wichtmann et al. in Acta Geotechnica 1: 59, 2006). However, the paper demonstrates that the MCC flow rule with \(\varphi_{\rm{r}}\) does not fit well the experimentally observed HCFR in the case of coarse or well-graded sands. For an improved simplified calibration procedure, correlations between \(\varphi_{\rm{cc}}\) and parameters of the grain-size distribution curve (d ₅₀,   C _u) have been developed on the basis of the present data set. The approximation of the experimental HCFR by the generalized flow rule equations proposed in (Wichtmann et al. in J Geotech Geoenviron Eng ASCE 136: 728, 2010), considering anisotropy, is also discussed in the paper.     

A new model for flow in shale-gas reservoirs including natural and hydraulic fractures

In this work, we construct a new coupled Multiscale/Discrete Fracture Model for compressible flow in a multiporosity shale gas reservoir containing networks of natural and hydraulic fractures. The geological formation is characterized by four distinct length scales and levels of porosity. The window of observation of the finest (nanoscale) portraits the nanopores within organic matter containing adsorbed gas. At the microscale, the medium is formed by two solid phases: organic, composed by kerogen aggregates, and inorganic (clay, quartz, calcite). Such phases are separated by the network of partially-saturated interparticle pores where microscopic free gas flow influenced by Knudsen effects along with gas diffusion in the immobile water phase occur simultaneously. The upscaling of the local flow to the mesoscale gives rise to a nonlinear homogenized pressure equation in the shale matrix which lies adjacent to the system of natural fractures. Homogenization of the coupled matrix/preexisting fractures to the macroscale leads to a microstructural model of dual porosity type. Such homogenized model is subsequently coupled with the hydrodynamics in the network of induced fractures which, in the context of the discrete fracture modeling, are treated as (n ? 1), (n = 2, 3) lower dimensional objects. In order to handle numerically the nonlinear interaction between the different flow equations, we adopt a superposition argument, firstly proposed by Arbogast (1996), in each iteration of a fixed-point algorithm. The resultant governing equations are discretized by the finite element method and numerical simulations of gas production in stratified arrangements of the fracture networks are presented to illustrate the potential of the multiscale approach.     

Fracture-Induced Anisotropic Attenuation

The triaxial nature of the tectonic stress in the earth’s crust favors the appearance of vertical fractures. The resulting rheology is usually effective anisotropy with orthorhombic and monoclinic symmetries. In addition, the presence of fluids leads to azimuthally varying attenuation of seismic waves. A dense set of fractures embedded in a background medium enhances anisotropy and rock compliance. Fractures are modeled as boundary discontinuities in the displacement u and particle velocity v as $[{\varvec{ \kappa}}\cdot {\bf u} + {\varvec{\eta}} \cdot {\bf v} ],$ where the brackets denote discontinuities across the fracture surface, ${\varvec{\kappa}}$ is a fracture stiffness, and ${\varvec{\eta}}$ is a viscosity related to the energy loss. We consider a transversely isotropic background medium (e.g., thin horizontal plane layers), with sets of long vertical fractures. Schoenberg and Muir’s theory combines the background medium and sets of vertical fractures to provide the 13 complex stiffnesses of the long-wavelength equivalent monoclinic and viscoelastic medium. Long-wavelength equivalent means that the dominant wavelength of the signal is much longer than the fracture spacing. The symmetry plane is the horizontal plane. The equations for orthorhombic and transversely isotropic media follow as particular cases. We compute the complex velocities of the medium as a function of frequency and propagation direction, which provide the phase velocities, energy velocities (wavefronts), and quality factors. The effective medium ranges from monoclinic symmetry to hexagonal (transversely isotropic) symmetry from the low- to the high-frequency limits in the case of a particle–velocity discontinuity (lossy case) and the attenuation shows typical Zener relaxation peaks as a function of frequency. The attenuation of the coupled waves may show important differences when computed versus the ray or phase angles, with triplication appearing in the Q factor of the qS wave. We have performed a full-wave simulation to compute the field corresponding to the coupled qP–qS waves in the symmetry plane of an effective monoclinic medium. The simulations agree with the predictions of the plane-wave analysis.     

Indirect unstructured hex-dominant mesh generation using tetrahedra recombination

Corner-point gridding is widely used in reservoir and basin modeling but generally yields approximations in the representation of geological interfaces. This paper introduces an indirect method to generate a hex-dominant mesh conformal to 3D geological surfaces and well paths suitable for finite-element and control-volume finite-element simulations. By indirect, we mean that the method first generates an unstructured tetrahedral mesh whose tetrahedra are then merged into primitives (hexahedra, prisms, and pyramids). More specifically, we focus on determining the optimal set of primitives that can be recombined from a given tetrahedral mesh. First, we detect in the tetrahedral mesh all the feasible volumetric primitives using a pattern-matching algorithm (Meshkat and Talmor Int. J. Numer. Meth. Eng. 49(1-2), 17–30 2000) that we re-visit and extend with configurations that account for degenerated tetrahedra (slivers). Then, we observe that selecting the optimal set of primitives among the feasible ones can be formalized as a maximum weighted independent set problem (Bomze et al. 1999), known to be \(\mathcal {N}\mathcal {P}\)-Complete. We propose several heuristic optimizations to find a reasonable set of primitives in a practical time. All the tetrahedra of each selected primitive are then merged to build the final unstructured hex-dominant mesh. This method is demonstrated on 3D geological models including a faulted and folded model and a discrete fracture network.     

Variations of trace gases over the Bay of Bengal during the summer monsoon

In situ measurements of near-surface ozone (\(\hbox {O}_{3})\), carbon monoxide (CO), and methane (\(\hbox {CH}_{4})\) were carried out over the Bay of Bengal (BoB) as a part of the Continental Tropical Convergence Zone (CTCZ) campaign during the summer monsoon season of 2009. \(\hbox {O}_{3}\), CO and \(\hbox {CH}_{4}\) mixing ratios varied in the ranges of 8–54 ppbv, 50–200 ppbv and 1.57–2.15 ppmv, respectively during 16 July–17 August 2009. The spatial distribution of mean tropospheric \(\hbox {O}_{3}\) from satellite retrievals is found to be similar to that in surface \(\hbox {O}_{3}\) observations, with higher levels over coastal and northern BoB as compared to central BoB. The comparison of in situ measurements with the Monitoring Atmospheric Composition & Climate (MACC) global reanalysis shows that MACC simulations reproduce the observations with small mean biases of 1.6 ppbv, –2.6 ppbv and 0.07 ppmv for \(\hbox {O}_{3}\), CO and \(\hbox {CH}_{4}\), respectively. The analysis of diurnal variation of \(\hbox {O}_{3}\) based on observations and the simulations from Weather Research and Forecasting coupled with Chemistry (WRF-Chem) at a stationary point over the BoB did not show a net photochemical build up during daytime. Satellite retrievals show limitations in capturing \(\hbox {CH}_{4}\) variations as measured by in situ sample analysis highlighting the need of more shipborne in situ measurements of trace gases over this region during monsoon.