Facies Field Research Articles

Improved groundwater modeling by incorporating geological information from hydrogeological sections

Geological cross-sections are usually employed in the hydrogeological model conceptualization, but their usage may not be easily exploited in subsequent modeling phases. The spatial distribution of geological facies along a geological section’s track may significantly vary when using random facies fields, and these may not be faithful to the original conceptualization described by the geological section. The present work offers a novel framework for improving available hydrogeological models using geological sections as a more quantitative source of information, hence by taking into account of information coming from a geological section. Then, this information given by the change in the distribution of porosities is transferred from the section’s track to surrounding locations through a proper kriging procedure upon a chosen Correlation Scale (R), which is exponentially correlated in space. This procedure is tested by using porosity distributions upon several R, associating a conductivity value with each porosity one through empirical formulations, and informing several numerical models related to a real case study (an aquifer in the province of Lecco, Northern Italy). The proposed procedure enables to significantly outperform the former calibrated numerical model. Best-calibrated models show that the convenient R could be from 2 to 5 kilometers long, consistent with the width of the alluvial and fluvioglacial floodplain that characterizes the aquifer under examination.

Tectonic slices of greenschist – epidote blueschist – epidote amphibole schist – garnet epidote amphibole schist from the Nagaland ophiolite complex, NE India: a look into their metamorphic and tectonic evolution

ABSTRACT Tectonic slices of greenschist – epidote blueschist – epidote amphibole schist – garnet epidote amphibole schist are exposed in the northern part of the NOC. Metamorphic P-T conditions and P-T paths of the garnet epidote amphibole schist and epidote blueschist were determined with the help of pseudosection calculations in the MnNCKFMASHTO system using the software Perple_X. The garnet epidote amphibole schist records a pre-peak metamorphic stage at ~12 kbar and ~360°C in the lawsonite blueschist facies field. Lawsonite and glaucophane are not preserved in the rock and are attributed to progressive metamorphic reactions during prograde metamorphism. The peak metamorphic stage is constrained at ~14 kbar and ~570°C in the hornblende eclogite facies field. Post-peak metamorphism shows slight cooling and decompression from ~550°C and ~13 kbar, possibly down to ~350°C and ~7 kbar in the greenschist facies field. These three metamorphic stages reveal a clockwise metamorphic P-T path of evolution for the garnet epidote amphibole schist. The geotherm at metamorphic peak P-T condition is ~12.5°C/km, which is hotter by ~350°C compared to thermal models of mature subduction zones but shows good agreement with models of warm subduction zones. Therefore, the low geothermal gradient of ~8°C/km during the prograde metamorphism possibly reflects the subduction of cold Neo-Tethyan ocean crust when the temperature conditions of the subduction zone were still warm. The epidote blueschist shows peak metamorphism at ~10 kbar and 380°C with a clockwise P-T path. It indicates metamorphism at a more mature stage of subduction. Buoyancy-driven exhumation along the subduction channel due to the serpentinization of the upper mantle wedge played a vital role in the detachment and exhumation of the tectonic slivers of metamorphic rocks from different depth sections in the northern margin of the NOC.

A new methodology based on finite element method (FEM) for generation of the probability field of rock types from subsurface

In this paper, we present a novel methodology by employing the finite element method (FEM) for creating probability fields of rock types (facies) present in a reservoir. The method is developed for a hydrocarbon reservoir, which, situated thousands of meters underground, has a high uncertainty regarding its geology. However, from the exploration phase, are collected facies observations (hard data) about the rock types present at some sparse locations of the reservoir domain. These observations are projected into a continuous probabilistic space, which is the environment of the FEM. The novelty consists of the fact that the probability field of a facies type is viewed as a deformation field of a plate. For each facies type, the FEM constructs a deformation profile which will be a probability field. The fields generated with the FEM verify the conditions of the probability theory without post-regularization techniques. We test the methodology for a two-dimensional reservoir model with three facies types. We also show the applicability of the new method by introducing the probability fields in the truncated pluri-Gaussian simulation method for simulating facies fields which are the inputs in the assisted history matching of the reservoir.

Warrumbungle Volcano: facies architecture and evolution of a complex shield volcano

We present a new geological map of Warrumbungle Volcano created from volcanic facies field mapping, new geophysical, geochemical and geochronological data as well as data from previous studies. Field mapping and petrography defined 19 volcanic and two mixed volcanic--sedimentary facies. Facies identification and distribution in conjunction with geochemical analyses indicate an early shield-forming phase of predominantly mafic and intermediate lavas and pyroclastic deposits, and minor felsic lavas deposited on an irregularly eroded basement of Surat and Gunnedah basin rocks. The shield was subsequently intruded by felsic intermediate to felsic magmas that formed dykes and other intrusions, including possible cryptodomes, and also erupted as lava domes and block-and-ash-flow deposits. A radial dyke swarm cross-cuts most units, although it is concentrated within basement sandstone surrounding the central area of the volcano, suggesting late inflation accompanied by dyke emplacement. Geochemistry indicates differentiation of a single although repeatedly recharged alkaline magmatic suite. Fractionation of olivine, Ti-magnetite and clinopyroxene occurred in mafic magmas, and after reaching 62 wt% SiO2, crystallisation of apatite and alkali feldspar took place. A new U–Pb zircon SHRIMP magmatic crystallisation age of 16.25 ± 0.12 Ma on a felsic block-and-ash flow deposit is in agreement with the recalculated 40Ar/39Ar isochron dates of previous workers. Based on our mapping and the use of volcanic facies to define mappable units, we recommend that the previous Warrumbungle Volcanics be elevated from formation to group status and renamed the Warrumbungle Volcanic Complex. KEY POINTS New geological map of Warrumbungle Volcano based on volcanic facies mapping. The volcanic facies and their distribution suggest a complex alkaline shield volcano erupted along regional-scale basement lineaments over an intracontinental ‘hot-spot’ or heat plume, and intruded by lava domes, cryptodomes, dykes and a radial dyke swarm. New and previous geochemical data suggest differentiation of a single, although repeatedly recharged, alkaline magmatic suite. A new U–Pb zircon SHRIMP date of 16.25 ± 0.12 Ma is in agreement with the recalculated 40Ar/39Ar isochron dates of previous workers.

Two-stage garnet growth in coesite eclogite from the southeastern Papua New Guinea (U)HP terrane and its geodynamic significance

Mineral compositions and textures of Late Miocene coesite eclogite from Tomagabuna Island were investigated to constrain P–T conditions during UHP metamorphism and subsequent exhumation. Two stages of garnet growth (core and rim), at eclogite-facies conditions, were documented. In addition to core garnet (I), peak assemblages include omphacite, coesite, phengite, and rutile. Rim garnet (II), amphibole, paragonite, plagioclase, quartz, and accessory biotite and spinel were formed after peak pressure conditions. Although a compositional gradient is present at the core–rim garnet interface, the garnet core has a relatively flat compositional profile, suggesting its crystallization in the coesite stability field. Together with minerals formed subsequent to peak pressure (UHP) conditions, the composition of the garnet rim indicates heating of the eclogite during its decompression into the amphibolite facies mineral stability field. Based on compositional zoning in garnet and application of diffusion modelling, we propose that eclogite-facies metamorphism of the mafic protolith and its host lithologies occurred at, or near, UHP conditions. The core garnet (I) formed at 650 °C at 8 Myr in the coesite stability field and was partially resorbed during the onset of exhumation. We infer that garnet rim growth at < 7.1 Ma occurred at P–T conditions corresponding to the boundary between the eclogite and amphibolite facies fields. Diffusion modelling for the garnet core–rim boundary compositions suggests a transient heating event (0.3 Myr) occurred at 1.5 GPa that we infer resulted from heat transport within the Australian—Woodlark plate boundary zone as the coesite eclogite was exhumed. Results caution that apparent P–T paths documented for many UHP terranes may not result from isothermal decompression corresponding to peak temperatures. Instead, paths may link P–T points’ set during transient mineral growth events when the UHP rocks form within the subduction channel, and during subsequent heating events, when UHP rocks are exhumed from mantle depths.

Channelized reservoir estimation using a low-dimensional parameterization based on high-order singular value decomposition

Prior to the estimation process of channelized reservoirs, in the context of any Assisted History Matching method, the parameterization of facies field is a necessary task. The parameterization of the facies field consists of defining a numerical field (parameter field) on the reservoir domain so that, using a projection function, we are able to recover the facies field from the values of parameter field. One of the most important issues encountered is the loss of the multipoint geostatistical properties in the updates (channel continuity). In this study, we start from an initial (global) parameterization of the channelized field and infer from it a low-dimensional parameterization obtained after a high-order singular value decomposition of a tensor built with the parameter fields. We decompose the parameter field as a linear combination of some basis functions with coefficients. The decomposition is followed by a truncation so that we keep the relevant information from the channel continuity perspective, but with a small number of coefficients. The coefficients will represent the low-dimensional parameterization and are further introduced in the estimation process of facies field, using the Ensemble Smoother with Multiple Data Assimilations (ES-MDA). For a fair assessment of the parameterization, we perform a comparison of the results with those obtained by applying the traditional truncated singular value decomposition and the global parameterization. In addition, we compare the parameterization with a low-dimensional parameterization defined with the PCA decomposition. The comparison is done from the perspective of multipoint geostatistical characteristics of the updates and predictions. We show that the new parameterization is able to better keep the multipoint geostatistical structure in the updates than the other parameterizations, while the prediction capabilities are the same.

Delineating Facies Spatial Distribution by Integrating Ensemble Data Assimilationand Indicator Geostatistics With Level‐Set Transformation

AbstractThe facies‐based approach has been widely adopted to delineate an aquifer into distinct geological units with unique distributions of hydraulic, physical, and/or chemical properties. The recent development in ensemble‐based data assimilation methods allows both the direct and indirect data to be used to improve facies delineation. A major difficulty in those applications is to honor the spatial continuity and avoid overfitting after data assimilation. We introduce a new facies delineation framework to integrate ensemble data assimilation with traditional transition probability‐based geostatistics. A level‐set concept is used to parametrize discrete facies indicators and for updating facies shape. During the iterative data assimilation process, we impose spatial continuity by conditioning facies field generation on points selected adaptively based on their sensitivity to observation data. This reconditioning step is a key step to maintain spatial continuity and overcome overfitting problems in inversion. We selected two examples to evaluate the performance of the new framework in estimating facies‐based permeability field. The first example is a two‐dimensional synthetic system with transient head data induced by pumping tests used for delineating two facies. The second example is a three‐dimensional case with three facies, conceptualized from a field tracer experiment within the Columbia River corridor in Washington State, USA. Both examples demonstrate that the new method can adequately capture the spatial pattern of hydrofacies with reconditioning, which leads to the improved prediction of system behaviors.

Sampling Strategies for Uncertainty Reduction in Categorical Random Fields: Formulation, Mathematical Analysis and Application to Multiple-Point Simulations

The task of optimal sampling for the statistical simulation of a discrete random field is addressed from the perspective of minimizing the posterior uncertainty of non-sensed positions given the information of the sensed positions. In particular, information theoretic measures are adopted to formalize the problem of optimal sampling design for field characterization, where concepts such as information of the measurements, average posterior uncertainty, and the resolvability of the field are introduced. The use of the entropy and related information measures are justified by connecting the task of simulation with a source coding problem, where it is well known that entropy offers a fundamental performance limit. On the application, a one-dimensional Markov chain model is explored where the statistics of the random object are known, and then the more relevant case of multiple-point simulations of channelized facies fields is studied, adopting in this case a training image to infer the statistics of a non-parametric model. In both contexts, the superiority of information-driven sampling strategies is proved in different settings and conditions, with respect to random or regular sampling.

Joint estimation of facies boundaries and petrophysical properties in multi-facies channelized reservoirs through ensemble-based Kalman filter and level set parametrization

Ensemble-based assimilation methods are the most promising tools for dynamic characterization of reservoir models. However, because of inherent assumption of Gaussianity, these methods are not directly applicable to channelized reservoirs wherein the distribution of petrophysical properties is multimodal. Transformation of facies field to level set functions have been proposed to alleviate the problem of multimodality. Level set representation ensures that the estimated fields are facies realizations as well as no modification of the assimilation method is required. Moreover, due to the complexity of the history matching problem in the channelized reservoirs, most researchers conventionally assume that the petrophysical properties within each facies are constant and spatially uniform. In this study, an ensemble-based assimilation technique along with the level set parameterization are applied to estimate absolute and relative permeabilities jointly in the channelized reservoirs. That is, categorical facies variables together with petrophysical properties of the facies are simultaneously updated within the assimilation framework. To the best of our knowledge, the current study is the first one that investigates the simultaneous estimation of absolute permeability fields and relative permeability curves in the channelized reservoirs. The proposed method is justified by two different cases in a synthetic channelized reservoir. The first case is a two-facies reservoir, whereas the second case is more complex and contains four facies. Observation data include production rates of the producers, bottomhole pressure of the injectors, and facies types at the well locations. History matching process results in an accurate estimation of the channel structure together with monotonic reduction of the root-mean-squared error between the estimated and the true permeability field. Furthermore, relative permeability parameters are correctly estimated, history match is improved, and uncertainty of the model parameters is reduced.

Calibration of categorical simulations by evolutionary gradual deformation method

Methods to simulate facies (or categorical) fields are numerous. However, calibration of simulated facies fields to large-scale or dynamic data still remains an important challenge due to the discrete nature of the fields, the non-linearity of the response with respect to the facies fields, and the non-derivability of the objective function used in calibration. A new gradual deformation method (GDM) is presented and tested for the calibration of facies realizations obtained by patch-multipoint simulation (MPS). The proposed method borrows ideas from pluriGaussian simulation, evolutionary algorithms, and GDM. Various test cases are considered: proportion maps, section of seismic amplitudes, inlet to outlet travel time along the shortest path, and water-cut curves obtained with a flow simulator. Both conditional/unconditional MPS simulations and 2D/3D problems are considered. In all studied test cases, the new GDM approach has provided excellent calibration to the target variables. The method is general as it can be used in conjunction with any facies simulator.

P-T conditions of earliest Late Cretaceous metamorphism in the Western Sonobari Complex, northwestern Mexico: tectonic implications

ABSTRACTThe Western Sonobari Complex in northwestern Mexico consists of metamorphosed rocks mostly derived from Palaeozoic (?) sedimentary and Mesozoic igneous protoliths. Rocks of this complex display amphibolite facies orogenic metamorphism, pervasive foliation, migmatization, and four folding phases. These features are ascribed to a contractional tectonic event with NNW–SSE shortening direction, which caused thrusting, thickening of the crust, and sinking of the lithological units. U–Pb geochronology of migmatitic leucosome bands indicates that peak metamorphic conditions were reached between ~93 and 89 Ma. Post-tectonic Late Cretaceous peraluminous aplite-pegmatite dikes transect the metamorphic foliation. Traditional thermobarometry in the metamorphic rocks yields average pressures and temperatures of 9.0–7.1 kbar and 745–663°C, typical of intermediate P/T Barrovian metamorphism. On the basis of its age and contractional character, the thickening event originating the metamorphism may be related to collision of the Alisitos island arc against crustal blocks of Mexico. Thermobarometric data of post-tectonic intrusives including Late Cretaceous granodiorite and Eocene gabbro indicate emplacement within an overthickened crust, while P-T conditions of post-tectonic dikes point towards an almost isothermal decompression path along the amphibolite facies field. Rock units of similar age and metamorphic character are discontinuously exposed from the Islas Marias offshore the Nayarit coast to the Peninsular Ranges batholith of Baja California, and even extend north into the Sierra Nevada batholith and the Sevier hinterland. This extensive belt of Barrovian metamorphic rocks thus provides a record of middle Cretaceous shortening and crustal thickening related to arc-continent collision followed by subduction resuming.

Integrated Work Flow of Preserving Facies Realism in History Matching: Application to the Brugge Field

Summary Data assimilation with ensemble-based inversion methods was successfully applied for parameter estimation in reservoir models. However, in certain complex-reservoir models, it remains challenging to estimate the model parameters and to preserve the geological realism simultaneously. In particular, when handling special-reservoir model parameters such as facies types concerning fluvial channels, one must realize that geological realism becomes one of the key concerns. The main objective of this work is to address these issues for a complex field with a newly extended version of a recently proposed facies-parameterization approach coupled with an ensemble-based data assimilation method. The proposed workflow combines the new facies parameterization and the adaptive gaussian mixture (AGM) filter into the data assimilation framework for channelized reservoirs. To handle discrete-facies parameters, we combine probability maps and truncated Gaussian fields to obtain a continuous parameterization of the facies fields. For the data assimilation, we use the AGM filter, which is an efficient history matching approach that incorporates a resampling routine that allows us to regenerate facies fields with information from the updated probability maps. This work flow is evaluated, for the first time, on a complex field case—the Brugge field. This reservoir model consists of layers with complex channelized structures and layers characterized by reservoir properties generated with variograms. With limited prior knowledge on the facies model, this work flow is shown to be able to preserve the channel continuity while reducing the reservoir model uncertainty with AGM. When applied to a complex reservoir, the proposed work flow provides a geologically consistent and realistic reservoir model that leads to improved capability of predicting subsurface flow behaviors.

Complex geology estimation using the iterative adaptive Gaussian mixture filter

In the past years, multi-point geostatistical simulation (MPS) geo-models have been used successfully to create realistic geological instances (facies fields). However, the conditioning of such geological deposits to production data is still a challenge, especially when an assisted history matching (AHM) model based on Bayesian inversion is used. This is hampered when we deal with complex geometry and topology and when the number of the facies types is greater than two. The estimation of the facies field is carried out combining two components: a parameterization of the facies field and a AHM method. In this study, we extend a parameterization of the facies fields, defined in a multidimensional normalized space by drawing from a marginal conditional Gaussian distribution. This is a generalization of a parameterization used in a previous study for channelized reservoirs and can be used for any type of geological layouts of the prior (in the MPS case, the training image). The parameterization ensures that the updates are always facies realization. However, traditional history matching methods tend to either destroy this topological structure or collapse into a single realization giving an unrealistic description of the uncertainty. To improve this issue, the iterative adaptive Gaussian mixture (IAGM) has been used as AHM method with a maximum of three iterations for the case studies. The method is tested for a 2D reservoir model, where four facies types are present, of which one exhibits channelized geometry. The topology is complex because two of the facies types cannot be in contact with each other. After assimilation of the production data, the IAGM was able to reduce the prior uncertainty toward an ensemble with realistic geological structure, with a good data match and predictive capacity.

Facies Analysis, Sedimentary Environment and Sequence Stratigraphy of the Lower Cretaceous Deposits in the Kalahroud Area, at North of Esfahan, Iran

Background/Objectives: Rocks of the Mesozoic era in Iran, especially Cretaceous period, have been studied frequently from stratigraphic point of view, but little research has been done from sedimentology viewpoint. This study aims to restore the sedimentation condition and the conditions governing the sedimentary basins during that period (lower Cretaceous). Methods: One stratigraphic section was measured along the outcrop in Kalahroud Area, at North of Esfahan. 52 thin sections samples were studied to determine the facies and a polarizan microscope was used for the procedure. Findings: Based on lithological properties, 3 lithostratigraphic units have identified in the area. Facies analysis and field observations led to identification of 6 carbonate facies, 4 terrigenous facies and also 3 mixed (terrigenous and carbonate). Kalahroud area was deposited on a homoclinal ramp setting within four zones including Continental, tidal flat, lagoon and bar environments. Sequence stratigraphic analysis identified one third-order depositional sequences in the studied area. Lower boundary in this sequence is unconformity first-type boundary (SB1) (with Jurassic deposits) and consists of Lowstand Systems Tract (LST), Transgressive Systems Tract (TST) and Highstand Systems Tract (HST). Application: These results could be used for comparison with other worldwide localities and provide additional data for lower Cretaceous paleogeographic reconstructions.

Benchmark problems for subsurface flow uncertainty quantification

Summary In this work, we design a series of benchmark problems for subsurface flow uncertainty quantification. Three basic subsurface flow problems with increasing complexity are selected, which are steady state groundwater flow, groundwater contamination, and multi-phase flow. For the steady state groundwater flow, hydraulic conductivity is assumed to be uncertain, and the uncertain model parameter is assumed to be Gaussian random constant, Gaussian random field, and facies field, respectively. For the other two flow problems, the uncertain model parameter is assumed to be Gaussian random field and facies field, respectively. The statistical property of the uncertain model parameter is specified for each problem. The Monte Carlo (MC) method is used to obtain the benchmark results. The results include the first two statistical moments and the probability density function of the quantities of interest. To verify the MC results, we test the convergence of the results and the reliability of the sampling algorithm. For any existing and newly developed uncertainty quantification methods, which are not (fully) verified, the designed benchmark problems in this work can facilitate the verification process of those methods. For illustration, in this work, we provide a verification of the probabilistic collocation method using the benchmark results.

Sedimentary Environment and Sequence Stratigraphy of the Lower Cretaceous Deposits in the Bideshk Area, at North of Esfahan, Iran

Background/Objectives: Rocks of the Mesozoic era in Iran, especially Cretaceous period, have been studied frequently from stratigraphic point of view, but little research has been done from sedimentology viewpoint. This study aims to restore the sedimentation condition and the conditions governing the sedimentary basins during that period (lower Cretaceous). Methods: One stratigraphic section was measured along the outcrop in Bideshk Area, at North of Esfahan. 63 thin sections samples were studied to determine the facies and a polarized microscope was used for the procedure. Findings: Based on lithological properties, 3 lithostratigraphic units have identified in the area. Facies analysis and field observations led to identification of 10 carbonate facies, 4 terrigenous facies and also 4 mixed (terrigenous and carbonate). Bideshk area was deposited on a homoclinal ramp setting within four zones including Continental, tidal flat, lagoon and bar environments. Sequence stratigraphic analysis identified three third-order depositional sequences in the studied area. Lower boundary in the first sequence is unconformity first-type boundary (SB1) (with Jurassic deposits) and consists of Transgressive Systems Tract (TST). Sequence number 2 consists of Low stand Systems Tract (LST), Transgressive Systems Tract (TST) and High stand Systems Tract (HST). Sequence 3 also consists of LST, TST and HST. Application: These results could be used for comparison with other worldwide localities and provide additional data for lower Cretaceous paleogeographic reconstructions.

Jointly updating the mean size and spatial distribution of facies in reservoir history matching

There exist several methods for history matching of reservoir facies distribution. When using these methods, the facies mean size is usually supposed to be prior information known without uncertainty. However, in reality, it is often difficult to acquire an accurate estimation of the facies mean size due to limited measurement data. Thus, it is more reasonable to treat the facies mean size as an uncertain model parameter for updating. In this work, we propose a methodology to jointly update the mean size and spatial distribution of facies in reservoir history matching. In the parameterization step, we utilize a Gaussian random field and a level set algorithm to parameterize each facies. The range of the Gaussian field controls the facies mean size of the generated facies distribution realizations. To accomplish jointly updating the mean size and spatial distribution of facies, the Gaussian random field is further parameterized by the Karhunen–Loeve (KL) expansion. We choose the range of the Gaussian field and the independent Gaussian random variables in the KL expansion as model parameters. After model parameterization, we use the Levenberg–Marquardt ensemble randomized maximum likelihood filter (LM_EnRML) to perform history matching. Three synthetic cases are set up to test the performance of the proposed method. Numerical results show that for estimating the facies field, the mean size and spatial distribution of facies can be jointly updated to match the reference distribution using the proposed method.

The contribution of amphibole from deep arc crust to the silicate Earth's Nb budget

Abstract The continental crust (CC) and the depleted mantle (DM) are generally assumed to be complementary reservoirs within the Earth. However, the mixture between CC and upper mantle does not generate the Nb/Ta and Nb/La ratios of chondrites. A reservoir with superchondritic ratios for Nb/Ta and Nb/La is thus required in the Earth's system. The occurrence of a hidden amphibole reservoir in the lower arc crust has been recently proposed. This, coupled with the capability of calcic amphibole to give rise to a superchondritic Nb/Ta and Nb/La reservoir, led us to determine to what extent amphibole-rich ultramafic rocks can account for the Nb (and Nb/Ta, Nb/La as well) imbalance on Earth. We have considered lower crust mafic and ultramafic amphibole-rich intrusive rocks from collisional settings worldwide. Because CC is considered to have primarily formed in collisional setting these rocks are important for its genetic model. We modeled Nb, Ta and La contents of the hidden Nb reservoir by mass balance calculations between continental crust, depleted mantle and primitive mantle. Modeling shows that amphibole-rich mafic lower crust can solve the so-called Nb paradox if large volumes of materials are supposed to be returned into the mantle during the Earth's history. A possible mechanism is recycling, particularly in Precambrian times, of eclogites that underwent pre-eclogitic melting in the amphibolite facies field and then recrystallized under eclogite-facies conditions.

Facies estimation through data assimilation and structure parameterization

Data assimilation in a reservoir with facies description using the ensemble Kalman filter (EnKF) is challenging. An important reason is that probability density functions for pixel-based representations of facies fields seldom follow the unimodal Gaussian assumption underlying traditional EnKF implementations. Different approaches for identification of facies fields, aiming to overcome this challenge, have been proposed within the EnKF framework. Level set (LS) representations of the facies field have been reported to alleviate the problems of multimodality. Several authors have, however, pointed out that the most commonly applied LS representation suffers from topological constraints that can create difficulties in an estimation setting. An alternative LS representation, that overcomes these topological constraints, leads to instabilities in the assimilated ensemble members. To overcome topological constraints, the recently proposed hierarchical LS representation is applied in an estimation setting for the first time in this paper. To improve stability and to alleviate challenges associated with model nonlinearities, we apply regularization by reduced representation of the LS functions and adjustable smoothing of the LS representation. The resolution of the reduced LS representation is selected based on the variability of the initial ensemble, aiming at preserving enough flexibility to disclose unexpected features. 2D and 3D estimation results demonstrate that the hierarchical LS representation does avoid topological constraints and that instabilities are avoided. The results suggest that the method is capable of handling estimation of facies fields while preserving geological plausibility.

Kinematics and dynamics of tectonic nappes: 2-D numerical modelling and implications for high and ultra-high pressure tectonism in the Western Alps

We present two-dimensional numerical simulations of lithospheric shortening with a crust containing weak and strong inclusions. Thermo-mechanical coupling is included, and a crustal-scale shear zone develops self-consistently due to viscous heating and thermal softening of temperature dependent viscosities. Several tests for crustal conditions are performed showing that 1) the thickness of and strain rates within the shear zone are independent on the numerical resolution and applied numerical method (finite element and finite difference method), 2) the shear zone is stable and rotates during large strain deformation, 3) the numerical algorithm conserves total thermal and mechanical energies, and 4) the bulk horizontal force balance is fulfilled during large strain deformation. A fold nappe develops around the shear zone in the lithospheric shortening simulation. In this simulation the stresses in the crust are limited by a friction angle of 30°. Significant tectonic overpressure (PO) occurs in strong lower crustal rocks and in strong inclusions. Significant PO also occurs in a weak inclusion that is only partly surrounded by strong crustal rock suggesting that a continuous strong “vessel” is not required to generate significant PO in weak rocks. Maximal values of PO are ~2.2GPa with corresponding deviatoric stresses ~1.5GPa and occur in a depth of ~42km. Maximal pressure of~3.4GPa and maximal temperatures>700°C occur during the formation of the fold nappe in crustal depth. Synthetic pressure–temperature paths exhibit entire cycles of pressure and temperature increase and decrease, and suggest that crustal rocks in depths<50km can reach the ultrahigh pressure metamorphic facies fields. Applications to tectonic nappes with high and ultra-high pressure rocks in the Western Alps are discussed, and a dynamic model for the evolution of fold nappes in the Western Alps is proposed.