An analytical solution for the exhumation of an orogenic wedge and a comparison with thermochronology data

Abstract. Thermochronology data is key for quantifying the exhumation history and dynamics of mountain belts. Here we present a new analytical solution for the steady-state exhumation of an orogenic wedge that undergoes transport along a basal detachment, uniform internal deformation, basal and frontal accretion. The solution predicts an increase in exhumation towards the interior of the wedge, with the rate of increase dependent on the degree of internal deformation. Application of the solution to a cross section in the Himalayas shows that in spite of its simplicity the solution provides a good fit to thermochronology data, with a coefficient of determination (R2) of 0.75. This implies that, although the solution does not capture the effects of individual faults and folds, at a large scale deformation can be described by uniform compression and transport. The results also imply that this part of the Himalayas may be in steady-state. The equations presented here can be used to quantify exhumation, deformation and shortening rates in mature orogens that are in steady-state.

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Role of rift-inheritance and segmentation for orogenic evolution: example from the Pyrenean-Cantabrian system

BSGF - Earth Sciences Bulletin ◽

10.1051/bsgf/2020021 ◽

2020 ◽

Vol 191 ◽

pp. 18 ◽

Cited By ~ 1

Author(s):

Rodolphe Lescoutre ◽

Gianreto Manatschal

Keyword(s):

Cross Sections ◽

Seismic Data ◽

Large Scale ◽

Sedimentary Cover ◽

First Order ◽

Segment Boundary ◽

Orogenic Wedge ◽

Mountain Belts ◽

Two Phases

The Basque-Cantabrian junction corresponds to an inverted rift accommodation zone at the limit between the former hyperextended Pyrenean and Cantabrian rift segments. The recognition of an inherited rift segment boundary allows to investigate the reactivation associated with large-scale rift segmentation in an orogenic system. We use criteria from published field observations and seismic data to propose a new map of rift domains for the Basque-Cantabrian junction. We also provide balanced cross-sections that allow to define the along-strike architecture associated with segmentation during rifting and subsequent Alpine reactivation. Based on these results, this study aims to characterize and identify reactivated and newly formed structures during inversion of two rift segments and its intermitted segment boundary. It also aims to describe the timing of thin-skinned and thick-skinned deformation associated with the inversion of segmented rift systems. During convergence, two phases have been recognized within the rift segment (eastern Mauléon basin). The Late Cretaceous to Paleocene underthrusting/subduction phase was mostly governed by thin-skinned deformation that reactivated the former hyperextended domains and the supra-salt sedimentary cover. The Eocene to Miocene collisional phase, controlled by thick-skinned deformation that took place once necking domains collided and formed an orogenic wedge. At the rift segment boundary, the underthrusting/subduction phase was already controlled by thick-skinned deformation due to the formation of shortcutting thrust faults at the termination of overlapping V-shaped rift segments. This led to the formation of a proto-wedge composed of the Basque massifs. We suggest that this proto-wedge is responsible for the preservation of pre-Alpine structures in the Basque massifs and for the emplacement of subcontinental mantle rocks at a crustal level beneath the western Mauléon basin. These results argue for a first order cylindrical orogenic architecture from the Central Pyrenean segment to the Cantabrian segment (up to the Santander transfer zone) despite rift segmentation. They also highlight the control of 3D rift-inheritance for the initial phase of orogenic evolution and for the local architecture of mountain belts.

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Identification of Efficient Sampling Techniques for Probabilistic Voltage Stability Analysis of Renewable-Rich Power Systems

Energies ◽

10.3390/en14082328 ◽

2021 ◽

Vol 14 (8) ◽

pp. 2328

Author(s):

Mohammed Alzubaidi ◽

Kazi N. Hasan ◽

Lasantha Meegahapola ◽

Mir Toufikur Rahman

Keyword(s):

Monte Carlo ◽

Stability Analysis ◽

Power Systems ◽

Large Scale ◽

Voltage Stability ◽

Sampling Technique ◽

Coefficient Of Determination ◽

Sampling Techniques ◽

Quasi Monte Carlo ◽

Efficient Sampling

This paper presents a comparative analysis of six sampling techniques to identify an efficient and accurate sampling technique to be applied to probabilistic voltage stability assessment in large-scale power systems. In this study, six different sampling techniques are investigated and compared to each other in terms of their accuracy and efficiency, including Monte Carlo (MC), three versions of Quasi-Monte Carlo (QMC), i.e., Sobol, Halton, and Latin Hypercube, Markov Chain MC (MCMC), and importance sampling (IS) technique, to evaluate their suitability for application with probabilistic voltage stability analysis in large-scale uncertain power systems. The coefficient of determination (R2) and root mean square error (RMSE) are calculated to measure the accuracy and the efficiency of the sampling techniques compared to each other. All the six sampling techniques provide more than 99% accuracy by producing a large number of wind speed random samples (8760 samples). In terms of efficiency, on the other hand, the three versions of QMC are the most efficient sampling techniques, providing more than 96% accuracy with only a small number of generated samples (150 samples) compared to other techniques.

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Cyclic Breathing Simulations in Large Scale Models of the Lung Airway From the Oronasal Opening to the Terminal Bronchioles

Volume 2: Biomedical and Biotechnology ◽

10.1115/imece2012-88901 ◽

2012 ◽

Author(s):

D. Keith Walters ◽

Greg W. Burgreen ◽

Robert L. Hester ◽

David S. Thompson ◽

David M. Lavallee ◽

...

Keyword(s):

Steady State ◽

Boundary Conditions ◽

Large Scale ◽

Whole Body ◽

Patient Specific ◽

Cfd Simulations ◽

Reduced Order ◽

Scale Models ◽

Steady State Simulation ◽

Conducting Zone

Computational fluid dynamics (CFD) simulations were performed for unsteady periodic breathing conditions, using large-scale models of the human lung airway. The computational domain included fully coupled representations of the orotracheal region and large conducting zone up to generation four (G4) obtained from patient-specific CT data, and the small conducting zone (to G16) obtained from a stochastically generated airway tree with statistically realistic geometrical characteristics. A reduced-order geometry was used, in which several airway branches in each generation were truncated, and only select flow paths were retained to G16. The inlet and outlet flow boundaries corresponded to the oronasal opening (superior), the inlet/outlet planes in terminal bronchioles (distal), and the unresolved airway boundaries arising from the truncation procedure (intermediate). The cyclic flow was specified according to the predicted ventilation patterns for a healthy adult male at three different activity levels, supplied by the whole-body modeling software HumMod. The CFD simulations were performed using Ansys FLUENT. The mass flow distribution at the distal boundaries was prescribed using a previously documented methodology, in which the percentage of the total flow for each boundary was first determined from a steady-state simulation with an applied flow rate equal to the average during the inhalation phase of the breathing cycle. The distal pressure boundary conditions for the steady-state simulation were set using a stochastic coupling procedure to ensure physiologically realistic flow conditions. The results show that: 1) physiologically realistic flow is obtained in the model, in terms of cyclic mass conservation and approximately uniform pressure distribution in the distal airways; 2) the predicted alveolar pressure is in good agreement with previously documented values; and 3) the use of reduced-order geometry modeling allows accurate and efficient simulation of large-scale breathing lung flow, provided care is taken to use a physiologically realistic geometry and to properly address the unsteady boundary conditions.

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The Research of Production Process Statistical Steady-State Based on the Hypothesis Test

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.314-316.2433 ◽

2011 ◽

Vol 314-316 ◽

pp. 2433-2438

Author(s):

Wei Zhi Wang

Keyword(s):

Quality Control ◽

Steady State ◽

Production Process ◽

Quantitative Method ◽

Large Scale ◽

Hypothesis Test ◽

Influence Factors ◽

Normal Operation ◽

Scale Production ◽

Large Scale Production

By only applying a after the event exam in the quality control of the batch production is not enough to meet the needs of modern large-scale production. To a certain extent, modern quality control is a dynamic process of the steady-state judge and adjustment. A simple and reliable steady-state judge rule and method is the premise to guarantee the normal operation. This paper provides a quantitative method to evaluate production process steady-state by analyzing influence factors based on mathematical statistics. The method is both suitable for simple production process and complex production process with sub-processes.

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Nonlinear Steady-State Optimization of Large-Scale Gas Transmission Networks

Energies ◽

10.3390/en14102832 ◽

2021 ◽

Vol 14 (10) ◽

pp. 2832

Author(s):

Andrzej J. Osiadacz ◽

Małgorzata Kwestarz

Keyword(s):

Steady State ◽

Large Scale ◽

Optimization Problem ◽

Operating Cost ◽

Network Efficiency ◽

Major Objective ◽

Transmission Networks ◽

Sqp Method ◽

Gas Network ◽

Compressor Power

The major optimization problem of the gas transmission system is to determine how to operate the compressors in a network to deliver a given flow within the pressure bounds while using minimum compressor power (minimum fuel consumption or maximum network efficiency). Minimization of fuel usage is a major objective to control gas transmission costs. This is one of the problems that has received most of the attention from both practitioners and researchers because of its economic impact. The article describes the algorithm of steady-state optimization of a high-pressure gas network of any structure that minimizes the operating cost of compressors. The developed algorithm uses the “sequential quadratic programming (SQP)” method. The tests carried out on the real network segment confirmed the correctness of the developed algorithm and, at the same time, proved its computational efficiency. Computational results obtained with the SQP method demonstrate the viability of this approach.

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INFLUENCE OF LARGE-SCALE ATMOSPHERIC PROCESSES ON SEASONAL RUNOFF OF LARGE SIBERIAN RIVERS

Meteorologiya i Gidrologiya ◽

10.52002/0130-2906-2021-10-36-47 ◽

2021 ◽

pp. 36-47

Author(s):

L. N. VASILEVSKAYA ◽

◽

I. A. LISINA ◽

D. N. VASILEVSKII ◽

◽

...

Keyword(s):

Atmospheric Circulation ◽

River Runoff ◽

Large Scale ◽

Annual Runoff ◽

Spring Flood ◽

Atmospheric Circulation Indices ◽

Rate Of Increase ◽

Circulation Indices ◽

Seasonal Runoff ◽

Kolyma River

Based on daily runoff volumes of four large Siberian rivers (the Ob, Yenisei, Lena, and Kolyma) for 1936-2018, the regime and changes in the total annual and seasonal runoff are analyzed. High synchronous and asynchronous correlations between monthly river runoff and atmospheric circulation indices of hemispheric and regional scales are revealed. In recent decades, the total annual runoff and its variations have increased (the rate of increase is most pronounced for the Kolyma River). A change in water content within a year is heterogeneous: weak positive trends are characteristic of the spring flood runoff and the summer-autumn period, and a significant increase occurred in the winter months. High correlations with a 1-8-month shift made it possible to identify the most informative regions, the atmospheric circulation over which makes a certain contribution to the variance of river runoff.

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Coriolis force influence on the AKA effect

10.5194/egusphere-egu21-13421 ◽

2021 ◽

Author(s):

Peter Rutkevich ◽

Georgy Golitsyn ◽

Anatoly Tur

Keyword(s):

Steady State ◽

Stokes Equation ◽

Nonlinear Equations ◽

Coriolis Force ◽

Large Scale ◽

Fluid Velocity ◽

Navier Stokes ◽

Basic Solution ◽

Navier Stokes Equation ◽

Alpha Effect

Large-scale instability in incompressible fluid driven by the so called Anisotropic Kinetic Alpha (AKA) effect satisfying the incompressible Navier-Stokes equation with Coriolis force is considered. The external force is periodic; this allows applying an unusual for turbulence calculations mathematical method developed by Frisch et al [1]. The method provides the orders for nonlinear equations and obtaining large scale equations from the corresponding secular relations that appear at different orders of expansions. This method allows obtaining not only corrections to the basic solutions of the linear problem but also provides the large-scale solution of the nonlinear equations with the amplitude exceeding that of the basic solution. The fluid velocity is obtained by numerical integration of the large-scale equations. The solution without the Coriolis force leads to constant velocities at the steady-state, which agrees with the full solution of the Navier-Stokes equation reported previously. The time-invariant solution contains three families of solutions, however, only one of these families contains stable solutions. The final values of the steady-state fluid velocity are determined by the initial conditions. After account of the Coriolis force the solutions become periodic in time and the family of solutions collapses to a unique solution. On the other hand, even with the Coriolis force the fluid motion remains two-dimensional in space and depends on a single spatial variable. The latter fact limits the scope of the AKA method to applications with pronounced 2D nature. In application to 3D models the method must be used with caution.[1] U. Frisch, Z.S. She and P. L. Sulem, &#8220;Large-Scale Flow Driven by the Anisotropic Kinetic Alpha Effect,&#8221; Physica D, Vol. 28, No. 3, 1987, pp. 382-392.

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Investigating Fast- and Slow-settling Phosphorus Fractions in Lakes using Steady-state Modeling

10.5194/egusphere-egu21-13910 ◽

2021 ◽

Author(s):

Hamed Khorasani ◽

Zhenduo Zhu

Keyword(s):

Steady State ◽

Mass Balance ◽

Large Scale ◽

Hydraulic Residence Time ◽

Simple Method ◽

Retention Models ◽

Mass Balance Models ◽

Limiting Nutrient ◽

Fast Settling ◽

P Retention

Phosphorus (P) is the key and limiting nutrient in the eutrophication of freshwater resources. Modeling P retention in lakes using steady-state mass balance models (i.e. Vollenweider-type models) provides insights into the lake P management and a simple method for large-scale assessments of P in lakes. One of the basic problems in the mass balance modeling of P in lakes is the removal of P from the lake water column by settling. A fraction of the incoming P into the lake from the watershed is associated with fast-settling particles (e.g. sediment particles) that result in the removal of that fraction of P quickly at the lake entrance. However, existing models considering a constant fraction of fast-settling TP for all lakes are shown to result in overestimation of the retention of P in lakes with short hydraulic residence time. In this study, we combine a hypothesis of the fast- and slow-settling P fractions into the steady-state mass balance models of P retention in lakes. We use a large database of lakes to calibrate the model and evaluate the hypothesis. The results of this work can be used for the improvement of the prediction power of P retention models in lakes and help to better understand the processes of P cycling in lakes.

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Artificial Intelligence Coreflooding Simulator for Special Core Data Analysis

SPE Reservoir Evaluation & Engineering ◽

10.2118/202700-pa ◽

2021 ◽

pp. 1-29

Author(s):

Eric Sonny Mathew ◽

Moussa Tembely ◽

Waleed AlAmeri ◽

Emad W. Al-Shalabi ◽

Abdul Ravoof Shaik

Keyword(s):

Artificial Intelligence ◽

Steady State ◽

History Matching ◽

Water Saturation ◽

Flow Behavior ◽

Model Performance ◽

Analysis Data ◽

Coefficient Of Determination ◽

Water Drainage ◽

Data Set

Two of the most critical properties for multiphase flow in a reservoir are relative permeability (Kr) and capillary pressure (Pc). To determine these parameters, careful interpretation of coreflooding and centrifuge experiments is necessary. In this work, a machine learning (ML) technique was incorporated to assist in the determination of these parameters quickly and synchronously for steady-state drainage coreflooding experiments. A state-of-the-art framework was developed in which a large database of Kr and Pc curves was generated based on existing mathematical models. This database was used to perform thousands of coreflood simulation runs representing oil-water drainage steady-state experiments. The results obtained from the corefloods including pressure drop and water saturation profile, along with other conventional core analysis data, were fed as features into the ML model. The entire data set was split into 70% for training, 15% for validation, and the remaining 15% for the blind testing of the model. The 70% of the data set for training teaches the model to capture fluid flow behavior inside the core, and then 15% of the data set was used to validate the trained model and to optimize the hyperparameters of the ML algorithm. The remaining 15% of the data set was used for testing the model and assessing the model performance scores. In addition, K-fold split technique was used to split the 15% testing data set to provide an unbiased estimate of the final model performance. The trained/tested model was thereby used to estimate Kr and Pc curves based on available experimental results. The values of the coefficient of determination (R2) were used to assess the accuracy and efficiency of the developed model. The respective crossplots indicate that the model is capable of making accurate predictions with an error percentage of less than 2% on history matching experimental data. This implies that the artificial-intelligence- (AI-) based model is capable of determining Kr and Pc curves. The present work could be an alternative approach to existing methods for interpreting Kr and Pc curves. In addition, the ML model can be adapted to produce results that include multiple options for Kr and Pc curves from which the best solution can be determined using engineering judgment. This is unlike solutions from some of the existing commercial codes, which usually provide only a single solution. The model currently focuses on the prediction of Kr and Pc curves for drainage steady-state experiments; however, the work can be extended to capture the imbibition cycle as well.

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Analytical Solution to Steady-State Heat-Conduction Problems With Irregularly Shaped Boundaries

Journal of Heat Transfer ◽

10.1115/1.3449844 ◽

1971 ◽

Vol 93 (4) ◽

pp. 449-454 ◽

Cited By ~ 9

Author(s):

D. M. France

Keyword(s):

Heat Conduction ◽

Steady State ◽

Analytical Solution ◽

Least Squares ◽

Series Solution ◽

Point Matching ◽

State Heat ◽

Temperature Heat ◽

Steady State Heat ◽

Least Squares Approach

A method of obtaining an analytical solution to two-dimensional steady-state heat-conduction problems with irregularly shaped boundaries is presented. The technique of obtaining the coefficients to the series solution via a direct least-squares approach is compared to the “point-matching” scheme. The two methods were applied to problems with known solutions involving the three heat-transfer boundary conditions, temperature, heat flux, and convection coefficient specified. Increased accuracy with substantially fewer terms in the series solution was obtained via the least-squares technique.

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