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1
Ursenbach, Charles P., and Robert R. Stewart. "Two-term AVO inversion: Equivalences and new methods." GEOPHYSICS 73, no. 6 (2008): C31—C38. http://dx.doi.org/10.1190/1.2978388.
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Most amplitude-variation-with-offset (AVO) studies use two-parameter inversion methods that are approximations of a more general three-parameter method based on the Aki-Richards approximation. Two-parameter methods are popular because the three-parameter inversion is often plagued by numerical instability. Reducing the dimensionality of the parameter space stabilizes the inversion. A variety of constraints can accomplish this, and these lead to the multiplicity of current two-parameter methods. It would be useful to understand relationships between various two-parameter methods. To this end, we derive formal expressions for inversion errors of each method. Using these expressions, conversion formulas are obtained that allow the flexibility to convert results of any two-parameter method to those of any other two-parameter method. The only requirement for the equivalence of methods is that the maximum angle of incidence be at least a few degrees less than the critical angle. In addition, error expressions result in a new formulation for a two-parameter AVO tool that combines strengths of two commonly used methods. The expressions also suggest a simple way to incorporate information from well-log calibration into legacy AVO inversions. These results should be helpful in resource exploration.
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Booth, Adam D., Ezgi Emir, and Anja Diez. "Approximations to seismic AVA responses: Validity and potential in glaciological applications." GEOPHYSICS 81, no. 1 (2016): WA1—WA11. http://dx.doi.org/10.1190/geo2015-0187.1.
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Amplitude-variation-with-angle (AVA) methods establish the seismic properties of material either side of a reflective interface, and their use is growing in glaciology. The AVA response of an interface is defined by the complex Knott-Zoeppritz (K-Z) equations, numerous approximations to which we typically assume weak interface contrasts and isotropic propagation, inconsistent with the strong contrasts at glacier beds and the vertically transverse isotropic (VTI) fabrics were associated with englacial reflectivity. We considered the validity of a suite of approximate K-Z equations for the exact P-wave reflectivity [Formula: see text] of ice overlying bedrock, sediment and water, and englacial interfaces between isotropic and VTI ice. We found that the approximations of Aki-Richards, Shuey, and Fatti match exact glacier bed reflectivity to within [Formula: see text], smaller than the uncertainty in typical glaciological AVA analyses, but only for maximum incident angle [Formula: see text] limited to 30°. A stricter limit of [Formula: see text] offered comparable accuracy to a hydrocarbon benchmark case of shale overlying gas-charged sand. The VTI-compliant Rüger approximation accurately described englacial reflectivity, to within [Formula: see text], and it can be modified to give a quadratic expression in [Formula: see text] suitable for curve-matching operations. Having shown the circumstances under which AVA approximations were valid for glaciological applications, we have suggested that their interpretative advantages can be exploited in the future AVA interpretations.
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Wang, Lingqian, Hui Zhou, Bo Yu, Yanxin Zhou, Wenling Liu, and Yukun Tian. "Inversion for Geofluid Discrimination Based on Poroelasticity and AVO Inversion." Geofluids 2019 (November 26, 2019): 1–17. http://dx.doi.org/10.1155/2019/2656747.
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Geofluid discrimination plays an important role in reservoir characterization and prospect identification. Compared with other fluid indicators, the effective pore-fluid bulk modulus is more sensitive to the property of fluid contained in reservoirs. We combine the empirical relations with deterministic models to form a new kind of linearized relationship between the mixed fluid/rock term and the fluid modulus. On the one hand, the linearized relationship can decouple the fluid bulk modulus from the mixed fluid/rock term; on the other hand, the decoupled terms are more stable especially in low-porosity situations compared with previous approaches. In terms of the new linearized equation of the fluid modulus, we derive a novel linearized amplitude variation with offset (AVO) approximation to avoid the complicated nonlinear relationship between the fluid modulus and the reflectivity series. Convoluting this linearized AVO approximation with seismic wavelets, the forward modeling is constructed to combine the prestack seismic records with the fluid modulus. Meanwhile, we introduce the Bayesian inference with multivariable Cauchy prior to the fluid modulus inversion for a stable and high-resolution solution. Model examples demonstrate the accuracy of the proposed linearized AVO approximation compared with the exact Zoeppritz equation and Aki-Richards approximate equation. The synthetic and field data tests illustrate the accuracy and feasibility of the proposed fluid modulus inversion approach for geofluid discrimination.
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Liu, Xiaobo, Jingyi Chen, Jing Zeng, et al. "An adaptive stratified joint PP and PS AVA inversion using accurate Jacobian matrix." GEOPHYSICS 86, no. 4 (2021): R447—R461. http://dx.doi.org/10.1190/geo2019-0785.1.
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Amplitude variation with incidence angle (AVA) analysis is an essential tool for discriminating lithology in hydrocarbon reservoirs. Compared to traditional AVA inversion using only compressional wave (P-wave) information, joint AVA inversion using PP and PS seismic data provides better estimation of rock properties (e.g., density, P- and shear wave [S-wave] velocities). Currently, the most used AVA inversions depend on the approximations of the Zoeppritz equations (e.g., the Shuey and Aki-Richards approximations), which are not suitable for formations with strong contrast interfaces and seismic data with large incidence angles. Based on the previous derivation of the accurate Jacobian matrix, we have found that the sign of each partial derivative of reflection coefficient with respect to the P-, S-wave velocities and density changes across the interface represents a good indicator for the reflection interfaces. Accordingly, we adopt an adaptive stratified joint PP and PS AVA inversion using the accurate Jacobian matrix that can automatically obtain the layer information and can be further used as a constraint in the inversion of in-layer rock properties (density and P- and S-wave velocities). Due to the use of the exact Zoeppritz equations and accurate Jacobian matrix, this proposed inversion method is more accurate than traditional AVA inversion methods, has higher computational efficiency, and can be applied to seismic wide-angle reflection data or seismic data acquired for formations with strong contrast interfaces. The model study shows that this proposed inversion method works better than the classic Shuey and Aki-Richards approximations at estimating reflection interfaces and in-layer rock properties. It also works well in handling a part of the complex Marmousi 2 model and real seismic data.
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Eladj, S., T. K. Lounissi, M. Z. Doghmane, and M. Djeddi. "Lithological Characterization by Simultaneous Seismic Inversion in Algerian South Eastern Field." Engineering, Technology & Applied Science Research 10, no. 1 (2020): 5251–58. https://doi.org/10.5281/zenodo.3659575.
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The main goal of this paper is to characterize a reservoir situated in the southeast of Algeria based on AVO seismic inversion. The seismic inversion model has been built by the iterative method of Aki and Richards’s approximation and it has been correlated with four-existing wells in the studied zone. The correlation rate between the inversion model and logging data is good (varying from 72% to 85%). Reservoir characterization of this field has been given in detail. The lithological description is used to construct a Geomechanical model that is useful for new wells’ drilling decisions. The high correlated results allowed us to have a vision on the horizontal variation of Petrophysical parameters such as density and lithological variation of three facies clay, tight limestone, and porous limestone. Moreover, this classification is used in the best way to determine the interesting zone with higher porosity values, so that the exploration strategy becomes more efficient with minimized uncertainties. Therefore, it is highly recommended to use the constructed model to propose new wells as well-5 in this study.
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Eladj, Said, Mohamed Zinelabidine Doghmane, Tanina Kenza Lounissi, Mabrouk Djeddi, Kong Fah Tee, and Sofiane Djezzar. "3D Geomechanical Model Construction for Wellbore Stability Analysis in Algerian Southeastern Petroleum Field." Energies 15, no. 20 (2022): 7455. http://dx.doi.org/10.3390/en15207455.
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The main objective of this research work was the wellbore stability evaluation of oil and gas wells based on a 3D geomechanical model, which as constructed using seismic inversion in a southeastern Algerian petroleum field. The seismic inversion model was obtained by using an iterative method and Aki and Richards approximation. Since the correlation between the inversion model and the log data was high at the wells, the reservoir was efficiently characterized and its lithology carefully discriminated in order to build a reliable 3D geomechanical model. The latter was further used to suggest the drilling mud weight window for the ongoing wells (well 5) and to examine the stability of four previously drilled wells. The main contribution of this study is providing a 3D geomechanical model that allows the optimization of drilling mud weight parameters so that a wellbore’s stability is guaranteed, on the one hand, and, on the other hand, so that the reservoir damage brought about by excessive surfactant use can be prevented. Indeed, the mud parameters are not just important for the drilling process’s effectiveness but also for logging operations. Since the tools have limited investigation diameters, with excessive use of surfactant, the invaded zone can become larger than the tools’ investigation diameter, which makes their logs unreliable. Hence, the 3D geomechanical model presented here is highly recommendable for the proposition of new wells, entailing less exploration uncertainty and more controllable productivity.
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Liu, Xiaobo, Jingyi Chen, Fuping Liu, and Zhencong Zhao. "An Accurate Jacobian Matrix with Exact Zoeppritz for Elastic Moduli of Dry Rock." Applied Sciences 9, no. 24 (2019): 5485. http://dx.doi.org/10.3390/app9245485.
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Seismic velocities are related to the solid matrices and the pore fluids. The bulk and shear moduli of dry rock are the primary parameters to characterize solid matrices. Amplitude variation with offset (AVO) or amplitude variation with incidence angle (AVA) is the most used inversion method to discriminate lithology in hydrocarbon reservoirs. The bulk and shear moduli of dry rock, however, cannot be inverted directly using seismic data and the conventional AVO/AVA inversions. The most important step to accurately invert these dry rock parameters is to derive the Jacobian matrix. The combination of exact Zoeppritz and Biot–Gassmann equations makes it possible to directly calculate the partial derivatives of seismic reflectivities (PP-and PS-waves) with respect to dry rock moduli. During this research, we successfully derive the accurate partial derivatives of the exact Zoeppritz equations with respect to bulk and shear moduli of dry rock. The characteristics of these partial derivatives are investigated in the numerical examples. Additionally, we compare the partial derivatives using this proposed algorithm with the classical Shuey and Aki–Richards approximations. The results show that this derived Jacobian matrix is more accurate and versatile. It can be used further in the conventional AVO/AVA inversions to invert bulk and shear moduli of dry rock directly.
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Graebner, Mark. "Plane‐wave reflection and transmission coefficients for a transversely isotropic solid." GEOPHYSICS 57, no. 11 (1992): 1512–19. http://dx.doi.org/10.1190/1.1443219.
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Numerous investigators have studied the P-SV reflection and transmission coefficients of an isotropic solid (Zoeppritz, 1919; Nafe, 1957; Frasier, 1970; Young and Braile, 1976; Kind, 1976; Aki and Richards, 1980).
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Kolesnykov, Valerii. "Richards-Klute Equation on Graphs." Modeling Control and Information Technologies, no. 6 (November 22, 2023): 70–72. http://dx.doi.org/10.31713/mcit.2023.018.
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This paper contains the formulation of the problem of mass transfer in a porous medium on a graph, on the edges of which the one-dimensional problem of mass transfer is modeled using the Richards-Klute equation. To combine separate Richards-Klute equations into a single system, auxiliary mass balance equations are introduced for the vertices of the graph. Problems of approximation of these equations at the vertices of the graph are also discussed.
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Li, H., M. W. Farthing, and C. T. Miller. "Adaptive local discontinuous Galerkin approximation to Richards’ equation." Advances in Water Resources 30, no. 9 (2007): 1883–901. http://dx.doi.org/10.1016/j.advwatres.2007.02.007.
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Bernstein, Herbert J., and Paul A. Craig. "Efficient molecular surface rendering by linear-time pseudo-Gaussian approximation to Lee–Richards surfaces (PGALRS)." Journal of Applied Crystallography 43, no. 2 (2010): 356–61. http://dx.doi.org/10.1107/s0021889809054326.
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ThePGALRS(pseudo-Gaussian approximation to Lee–Richards surfaces) algorithm is discussed. By modeling electron density with unphysical pseudo-Gaussian atoms, the Lee–Richards surface can be approximated by a contour level of that density in time approximately linear in the number of atoms. Having that contour level, the atoms and residues closest to that surface can be identified in average timeO[n2/3log(n)] using aNearTree-based nearest neighbor search. If a high-quality Lee–Richards surface is required, then, as a final stage, one of the standard Lee–Richards algorithms can be used but considering only the previously identified surface residues; the typical cost is thereby reduced toO[n2/3log(n)], making the overall average time for all the stepsO(n). For very large macromolecules, such a reduction in computational burden may be essential to being able to render a meaningful molecular surface. This approach extends the feasible range of application for existing molecular surface software, such asMSMS, to larger macromolecules, especially to macromolecules with more than 50 000 atoms, and can be used as a starting point for surface-based (as opposed to backbone-based) motif identification,e.g.usingProMol.
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Moradi, Shahpoor, and Kristopher A. Innanen. "Viscoelastic amplitude variation with offset equations with account taken of jumps in attenuation angle." GEOPHYSICS 81, no. 3 (2016): N17—N29. http://dx.doi.org/10.1190/geo2015-0366.1.
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Anelastic properties of reservoir rocks are important and sensitive indicators of fluid saturation and viscosity changes due (for instance) to steam injection. The description of seismic waves propagating through viscoelastic continua is quite complex, involving a range of unique homogeneous and inhomogeneous modes. This is true even in the relatively simple theoretical environment of amplitude variation with offset (AVO) analysis. For instance, a complete treatment of the problem of linearizing the solutions of the low-loss viscoelastic Zoeppritz equations to obtain an extended Aki-Richards equations (one that is in accord with the appropriate complex Snell’s law) is lacking in the literature. Also missing is a clear analytical path allowing such forms to be reconciled with more general volume scattering pictures of viscoelastic seismic wave propagation. Our analysis, which provides these two missing elements, leads to approximate reflection and transmission coefficients for the P- and type-I S-waves. These involve additional, complex terms alongside those of the standard isotropic-elastic Aki-Richards equations. The extra terms were shown to have a significant influence on reflection strengths, particularly when the degree of inhomogeneity was high. The particular AVO forms we evaluated were finally shown to be special cases of potentials for volume scattering from viscoelastic inclusions.
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Grzegorczyk, Andrzej. "Application of the Richards function to the description of leaf area growth in maize (Zea mays L.)." Acta Societatis Botanicorum Poloniae 63, no. 1 (2014): 5–7. http://dx.doi.org/10.5586/asbp.1994.001.
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The leaf area growth in maize was approximated basing on the Richards function in the form of: y=A[l+b exp(-kt)]<sup>1/(1-m)</sup> . The constant coefficients of the Richards function were found by means of the Marquardt's method. The initial values of parameters were given basing on results of the preliminary approximation of the growth process by means of logistic function y = A[l+b exp(-kt)]<sup>-1</sup>. The procedure of nonlinear regression was found to be useful (curvilinear determination coefficient R<sup>2</sup> = 0.995). The Richards curve precisely describes the course of changes of the leaf area in maize since sprouting to a tassel flowering phase.
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Lieth, J. H., P. R. Fisher, and R. D. Heins. "A Three-phase Model for the Analysis of Sigmoid Patterns of Growth." HortScience 30, no. 4 (1995): 761C—761. http://dx.doi.org/10.21273/hortsci.30.4.761c.
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A growth function was developed for describing the progression of shoot elongation over time. While existing functions, such as the logistic function or Richards function, can be fitted to most sigmoid data, we observed situations where distinct lag, linear, and saturation phases were observed but not well represented by these traditional functions. A function was developed that explicitly models three phases of growth as a curvilinear (exponential) phase, followed by a linear phase, and terminating in a saturation phase. This function was found to be as flexible as the Richards function and can be used for virtually any sigmoid data. The model behavior was an improvement over the Richards function in cases where distinct transitions between the three growth phases are evident. The model also lends itself well to simulation of growth using the differential equation approximation for the function.
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Al Nazer, Safaa, Carole Rosier, and Munkhgerel Tsegmid. "Mathematical analysis of a Dupuit-Richards model." Electronic Journal of Differential Equations 2022, no. 01-87 (2022): 06. http://dx.doi.org/10.58997/ejde.2022.06.
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This article concerns an alternative model to the 3D-Richards equation to describe the flow of water in shallow aquifers. The model couples the two dominant types of flow existing in the aquifer. The first is described by the classic Richards problem in the upper capillary fringe. The second results from Dupuit's approximation after vertical integration of the conservation laws between the bottom of the aquifer and the saturation interface. The final model consists of a strongly coupled system of parabolic-type partial differential equations that are defined in a time-dependent domain. First, we show how taking the low compressibility of the fluid into account eliminates the nonlinearity in the time derivative of the Richards equation. Then, the general framework of parabolic equations is used in non-cylindrical domains to give a global in time existence result to this problem.
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POP, IULIU SORIN, and BEN SCHWEIZER. "REGULARIZATION SCHEMES FOR DEGENERATE RICHARDS EQUATIONS AND OUTFLOW CONDITIONS." Mathematical Models and Methods in Applied Sciences 21, no. 08 (2011): 1685–712. http://dx.doi.org/10.1142/s0218202511005532.
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We analyze regularization schemes for the Richards equation and a time discrete numerical approximation. The original equations can be doubly degenerate, therefore they may exhibit fast and slow diffusion. In addition, we treat outflow conditions that model an interface separating the porous medium from a free flow domain. In both situations we provide a regularization with a non-degenerate equation and standard boundary conditions, and discuss the convergence rates of the approximations.
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Timsina, Ramesh Chandra. "Infiltration-Induced Landslide: An Application of Richards Equation." Journal of Nepal Mathematical Society 7, no. 1 (2024): 86–99. http://dx.doi.org/10.3126/jnms.v7i1.67490.
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In this work, we incorporate the solution of Richards equation in infinite slope model to locate the potential landslide hazards area and prediction of landslide hazards induced by heavy rainfall, continuously precipitation and redistribution. Firstly, we modeled the Richards equation in cylindrical coordinate with axial symmetry and use Kirchhoff ’s transformation to linearize it. With Kirchhoff ’s transformation the nonlinear axi-symmetric model is transformed into the nonlinear parabolic equation. Because of its high non-linear properties, analytical solutions of Richards equation are rare and limited for particular cases with hardly reliable. To solve the equation numerically, different approximation techniques as FDM, FVM are used on the prescribed model. Since, the landslide hazards problems are accelerated by safety factor which are related to the forces that restrain the surface from failure and endow the surface to smash. Hence to evaluate the safety factor we use the infinite slope model characterized with moisture content, pressure head in variably saturated (unsaturated) soils. The attachment of Richards equation along with the infinite slope model in the expression of safety factor which helps to explore the surface failure condition for different soils for their different physical characteristic including precipitation, infiltration, redistribution and moisture content.
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Koivusalo, H., T. Karvonen, and A. Lepistö. "A quasi-three-dimensional model for predicting rainfall-runoff processes in a forested catchment in Southern Finland." Hydrology and Earth System Sciences 4, no. 1 (2000): 65–78. http://dx.doi.org/10.5194/hess-4-65-2000.
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Abstract. Runoff generation in a forested catchment (0.18 km2) was simulated using a quasi-three-dimensional rainfall-runoff model. The model was formulated over a finite grid where water movement was assumed to be dominantly vertical in the unsaturated soil zone and horizontal in the saturated soil. The vertical soil moisture distribution at each grid cell was calculated using a conceptual approximation to the one-dimensional Richards equation. The approximation allowed the use of a simple soil surface boundary condition and an efficient solution to the water table elevation over the finite grid. The approximation was coupled with a two-dimensional ground water model to calculate lateral soil water movement between the grid cells and exfiltration over saturated areas, where runoff was produced by the saturation-excess mechanism. Runoff was an input to a channel network, which was modelled as a nonlinear reservoir. The proposed approximation for the vertical soil moisture distribution in unsaturated soil compared well to a numerical solution of the Richards equation during shallow water table conditions, but was less satisfactory during prolonged dry periods. The simulation of daily catchment outflow was successful with the exception of underprediction of extremely high peak flows. The calculated water table depth compared satisfactorily with the measurements. An overall comparison with the earlier results of tracer studies indicated that the modelled contribution of direct rainfall/snowmelt in streamflow was higher than the isotopically traced fraction of event-water in runoff. The seasonal variation in the modelled runoff-contributing areas was similar to that in the event-water-contributing areas from the tracer analysis.
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Sauquet, E., I. Krasovskaia, and E. Leblois. "Mapping mean monthly runoff pattern using EOF analysis." Hydrology and Earth System Sciences 4, no. 1 (2000): 79–93. http://dx.doi.org/10.5194/hess-4-79-2000.
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Abstract. Runoff generation in a forested catchment (0.18 km2) was simulated using a quasi-three-dimensional rainfall-runoff model. The model was formulated over a finite grid where water movement was assumed to be dominantly vertical in the unsaturated soil zone and horizontal in the saturated soil. The vertical soil moisture distribution at each grid cell was calculated using a conceptual approximation to the one-dimensional Richards equation. The approximation allowed the use of a simple soil surface boundary condition and an efficient solution to the water table elevation over the finite grid. The approximation was coupled with a two-dimensional ground water model to calculate lateral soil water movement between the grid cells and exfiltration over saturated areas, where runoff was produced by the saturation-excess mechanism. Runoff was an input to a channel network, which was modelled as a nonlinear reservoir. The proposed approximation for the vertical soil moisture distribution in unsaturated soil compared well to a numerical solution of the Richards equation during shallow water table conditions, but was less satisfactory during prolonged dry periods. The simulation of daily catchment outflow was successful with the exception of underprediction of extremely high peak flows. The calculated water table depth compared satisfactorily with the measurements. An overall comparison with the earlier results of tracer studies indicated that the modelled contribution of direct rainfall/snowmelt in streamflow was higher than the isotopically traced fraction of event-water in runoff. The seasonal variation in the modelled runoff-contributing areas was similar to that in the event-water-contributing areas from the tracer analysis.
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Chen, Xi, and Ying Dai. "Wetting Front Analysis of the Richards’ Equation with Impervious Boundary." International Journal of Nonlinear Sciences and Numerical Simulation 19, no. 6 (2018): 595–604. http://dx.doi.org/10.1515/ijnsns-2017-0084.
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AbstractIt is analyzed the wetting front of the Richards’ equation (RE) for horizontal infiltration problem with impervious layer in a finite medium, and obtained an approximate analytical solution by the series expansion technique. The present approximation is suitable for arbitrary diffusivity in RE and applied to simulate the changes of saturation after the front pass through the impervious point. Two examples about power law diffusivity are analyzed to confirm the accuracy of present solution.
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Parlange, J. Y., W. L. Hogarth, D. A. Barry, et al. "Analytical approximation to the solutions of Richards' equation with applications to infiltration, ponding, and time compression approximation." Advances in Water Resources 23, no. 2 (1999): 189–94. http://dx.doi.org/10.1016/s0309-1708(99)00022-6.
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Tregubov, Dmytro, Evgen Slepuzhnikov, Maryna Chyrkina, and Artem Maiboroda. "Cluster Mechanism of the Explosive Processes Initiation in the Matter." Key Engineering Materials 952 (August 18, 2023): 131–42. http://dx.doi.org/10.4028/p-lzz2hq.
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The relationship between substance characteristic temperatures: autoignition, melting, flash, boiling is demonstrated and analyzed. Based on the oscillatory and step changes presence, a conclusion was made about the supramolecular structures presence and periodicity in the n-alkanes homologous series. A method for modeling equivalent lengths of peroxide supramolecular structures for predicting the explosion and fire hazard parameters of n-alkanes is proposed. An approximation dependence was developed for predicting autoignition temperatures tai of n-alkanes. It is shown that stoichiometric concentrations of the various supramolecular peroxide structures formation accord to different flammability and explosion limits. A correlation between tai and Anti-Knock Index (AKI) was established. An approximation dependence was developed for predicting n-alkanes AKI. The detonation propensity index КD was introduced based on cluster supramolecular structures modeling and melting temperatures. It is shown that КD indicator correlates with the n-alkanes AKI and with the explosives detonation velocity. The possibility of taking into account during calculations the supramolecular structures presence at the combustion stage confirms their existence.
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Lyashko, S. I., N. I. Lyashko, D. A. Klyushin, and A. A. Tymoshenko. "METHOD FOR SOURCE POWER IDENTIFICATION IN RICHARDS EQUATION." Journal of Numerical and Applied Mathematics, no. 2 (2022): 67–75. http://dx.doi.org/10.17721/2706-9699.2022.2.08.
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In this paper a one-dimensional nonlinear Richards equation describing fluid flow in porous medium with inserted equalpowered sources is studied. An experimental iterational method is proposed to find source power to minimize the deviation of received humidity values from target values. Modeling was performed using numerical difference approximation of derivatives, resulting into a system of nonlinear equations with dependence from previous time step. The offered method allows to perform modeling for different source power values, and chooses the most suitable one.Iterations stop when they reach average modular difference value less than calculation error of numerical difference scheme. Here explicit scheme was used to save time, equations were tested for unsaturated medium only to avoid flooding the area, so source power is tested with given limitations. Results of simulations and choice for next source power approximations are described and compared until solution is found. This approach is considered as experimental so we plan to perform more analysis in the future.
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Barker, Joseph, Karl Smith-Byrne, Oliver Sayers, et al. "Electronic alerts for acute kidney injury across primary and secondary care." BMJ Open Quality 10, no. 2 (2021): e000956. http://dx.doi.org/10.1136/bmjoq-2020-000956.
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ProblemIn 2009 the National Confidential Enquiry into Patient Outcome and Death suggested only 50% of patients with acute kidney injury (AKI) receive good standards of care. In response National Health Service (NHS) England mandated the use of electronic AKI alerts within secondary care. However, we recognised AKI is not just a secondary care problem, where primary care has a crucial role to play in prevention, early detection and management as well as post-AKI care.MethodsAKI alerts were implemented in primary and secondary care services for a population of 480 000. Comparisons were made in AKI incidence, peak creatinine following AKI and renal recovery in the years before and after using Byar’s approximation (95% CI).InterventionA complex quality improvement initiative was implemented based on the design and integration of an AKI alerting system within laboratory information management systems for primary and secondary care, with an affixed URL for clinicians to access a care bundle of AKI guidelines on safe prescribing, patient advice and early contact with nephrology.ResultsThe intervention was associated with an 8% increase in creatinine testing (n=32 563). Hospital acquired AKI detection increased by 6%, while community acquired AKI detection increased by 3% and AKI stage 3 detected in primary care fell by 14%. The intervention overall had no effect on AKI severity but did improve follow-up testing and renal recovery. Importantly hospital AKI 3 recoveries improved by 22%. In a small number of AKI cases, the algorithm did not produce an alert resulting in a reduction in follow-up testing compared with preintervention levels.ConclusionThe introduction of AKI alerts in primary and secondary care, in conjunction with access to an AKI care bundle, was associated with higher rates of repeat blood sampling, AKI detection and renal recovery. Validating accuracy of alerts is required to avoid patient harm.
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Carrion, Philip, José Carcione, and Edson E. S. Sampaio. "Radiation patterns: Possibility for monitoring seismic sources." GEOPHYSICS 61, no. 1 (1996): 282–87. http://dx.doi.org/10.1190/1.1443950.
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Recent field measurements of the radiation in boreholes indicate that the radiation patterns of real seismic sources are not always in agreement with those corresponding to the point‐source excitation in unbounded homogeneous and isotropic acoustic or elastic media [we refer the reader to Aki and Richards (1980) for the basic discussion on the radiation patterns in homogeneous media]. This mismatch results from the fact that the point‐source radiation patterns corresponding to homogeneous media are too simplistic to satisfy any experiment in the more realistic Earth environment. A study of radiation patterns is certainly important not only to predict possible seismic events but also to analyze the source performance itself by recording seismic arrivals.
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Shanmugam, Mohanasundaram, G. Suresh Kumar, Balaji Narasimhan, and Sangam Shrestha. "Effective saturation-based weighting for interblock hydraulic conductivity in unsaturated zone soil water flow modelling using one-dimensional vertical finite-difference model." Journal of Hydroinformatics 22, no. 2 (2019): 423–39. http://dx.doi.org/10.2166/hydro.2019.239.
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Abstract Richards equation is solved for soil water flow modeling in the unsaturated zone continuum. Interblock hydraulic conductivities, while solving for Richards equation, are estimated by some sort of averaging process based on upstream and downstream nodes hydraulic conductivity values. The accuracy of the interblock hydraulic conductivity estimation methods mainly depends on the distance between two adjacent discretized nodes. In general, the accuracy of the numerical solution of the Richards equation decreases as nodal grid discretization increases. Conventional interblock hydraulic conductivity estimation methods are mostly mere approximation approaches while the Darcian-based interblock hydraulic conductivities involve complex calculations and require intensive computation under different flow regimes. Therefore, in this study, we proposed an effective saturation-based weighting approach in the soil hydraulic curve functions for estimating interblock hydraulic conductivity using a one-dimensional vertical finite-difference model which provides a parametric basis for interblock hydraulic conductivity estimation while reducing complexity in the calculation and computational processes. Furthermore, we compared four test case simulation results from different interblock hydraulic conductivity methods with the reference solutions. The comparison results show that the proposed method performance in terms of percentage reduction in root mean square and mean absolute error over other methods compared in this study were 59.5 and 60%, respectively.
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Corradini, C., and F. Melone. "Representation of Infiltration in Adaptive Rainfall – Runoff Models." Hydrology Research 23, no. 5 (1992): 291–304. http://dx.doi.org/10.2166/nh.1992.0020.
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The reliability of the extended Time Compression Approximation (TCA), commonly adopted in watershed models in order to represent the infiltration associated with erratic rainfalls, is investigated. This approximation is considered as a component of an adaptive real-time flood forecasting model. The forecasted flows are compared with those obtained replacing the extended TCA with the Complex Storm Point Infiltration Model (CSPIM) recently proposed by Smith et al. (1993). The discharge forecasted through the infiltration component based on the numerical solution of Richards' equation is used as a bench mark. The models were applied to situations representative of real areas in Central Italy. The CSPIM based watershed model was found to provide excellent results. The TCA based model, in spite of the adaptive component, yielded poor results for various rainfall patterns. However, it seems to be a reasonable approximation when a uniform rainfall spatial distribution is involved.
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Tura, Ali, and Margarita Corzo. "Introduction to this special section: Reservoir characterization Part I." Leading Edge 39, no. 2 (2020): 82–83. http://dx.doi.org/10.1190/tle39020082.1.
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In 1980, Aki and Richards published linearized formulations of the Zoeppritz equations from 1919. From then on, many flavors and variations of the P-P reflection mode so-called amplitude variation with offset (AVO) equations have been published and used. Assuming the earth is isotropic, these equations are used day in and day out in the industry for reservoir characterization and to find oil and gas in the subsurface. Some publications have shown that using the P-P and P-S reflections in a joint inversion can increase the accuracy of the inverted parameters. Technically, however, there has been little divergence from the linearized Zoeppritz equations until lately when full-waveform inversion started to gain traction, initially for velocity model estimation and imaging and more recently applied to reservoir characterization.
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Hopp, Luisa, Simone Fatichi, and Valeriy Y. Ivanov. "Simulating water flow in variably saturated soils: a comparison of a 3D model with approximation-based formulations." Hydrology Research 47, no. 2 (2015): 274–90. http://dx.doi.org/10.2166/nh.2015.126.
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In hydrological models, variably saturated flow is often described using the Richards equation, either in a fully three-dimensional (3D) implementation or using a quasi-3D framework based on the 1D Richards equation for vertical flow and a flow-approximation for the other two dimensions. However, it is unclear in which configuration or under which boundary conditions these approximations can produce adequate estimates. In this study, two formulations with a quasi-3D approach are benchmarked against a fully 3D model (HYDRUS-3D). The formulations are: the Real-time Integrated Basin Simulator + VEGetation Generator for Interactive Evolution (tRIBS + VEGGIE) model that uses the Dupuit–Forchheimer assumption and the Tethys & Chloris (T&C) model that implements the kinematic approach. Effects of domain slope, hillslope size, event size and initial moisture conditions on simulated runoff and soil moisture dynamics are examined in event-based simulations at the hillslope scale. The Dupuit–Forchheimer assumption (tRIBS-VEGGIE) produces deviations from the HYDRUS-3D solutions only for simulations with initially dry soil. Using the kinematic approach (T&C) results in deviations from the 3D solution primarily for the small hillslope domain in combination with a gentle slope angle. This applies especially to the partition between subsurface and surface runoff production, with T&C being biased towards the latter. For all other cases investigated, the simpler formulations provide reasonable approximations of the 3D model.
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Takenaka, H., M. Ohori, K. Koketsu, and B. L. N. Kennett. "An efficient approach to the seismogram synthesis for a basin structure using propagation invariants." Bulletin of the Seismological Society of America 86, no. 2 (1996): 379–88. http://dx.doi.org/10.1785/bssa0860020379.
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Abstract The Aki-Larner method is one of the cheapest methods for synthetic seismograms in irregularly layered media. In this article, we propose a new approach for a two-dimensional SH problem, solved originally by Aki and Larner (1970). This new approach is not only based on the Rayleigh ansatz used in the original Aki-Larner method but also uses further information on wave fields, i.e., the propagation invariants. We reduce two coupled integral equations formulated in the original Aki-Larner method to a single integral equation. Applying the trapezoidal rule for numerical integration and collocation matching, this integral equation is discretized to yield a set of simultaneous linear equations. Throughout the derivation of these linear equations, we do not assume the periodicity of the interface, unlike the original Aki-Larner method. But the final solution in the space domain implicitly includes it due to use of the same discretization of the horizontal wavenumber as the discrete wavenumber technique for the inverse Fourier transform from the wavenumber domain to the space domain. The scheme presented in this article is more efficient than the original Aki-Larner method. The computation time and memory required for our scheme are nearly half and one-fourth of those for the original Aki-Larner method. We demonstrate that the band-reduction technique, approximation by considering only coupling between nearby wavenumbers, can accelerate the efficiency of our scheme, although it may degrade the accuracy.
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Terleev, Vitaly, Wilfried Mirschel, Aleksandr Nikonorov, et al. "Estimating some hydrophysical properties of soil using mathematical modeling." MATEC Web of Conferences 193 (2018): 02035. http://dx.doi.org/10.1051/matecconf/201819302035.
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At substantiating land amelioration and land management designs, as well as during periods of operation and reconstruction of water facilities, information support plays an important role in relation to the hydrophysical properties of soil. Effective implementation of this support faces a number of challenges. Such problems include the very high laboriousness of carrying out the corresponding engineering surveys and laboratory studies. In this regard, the methods of indirect estimating the hydrophysical properties, the measurement of which requires considerable labor, are very in demand for land amelioration and land management practices. An equally acute problem is the problem of the functional representation of the coefficients of the Richards equation, which is widely used in engineering-hydrological calculations. The paper suggests: 1) the original method for assessment of the ratio of the values of the hydraulic conductivity function of soil to the moisture filtration coefficient using data from direct measurements of the water-retention capacity of soil carried out according to the standard procedure; 2) the mathematical model describing the hydrophysical properties of soil, and the system of functions with interpreted parameters that physically adequately describe the coefficients of the Richards equation. In carrying out the study, data on soils of different texture were used. A sufficiently low error in the dot approximation (fitting-procedure) of the experimental data confirms the physical adequacy of the proposed system that includes the functions describing the coefficients of the Richards equation.
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Miyama, Takeshi, Sung-mok Jung, Katsuma Hayashi, et al. "Phenomenological and mechanistic models for predicting early transmission data of COVID-19." Mathematical Biosciences and Engineering 19, no. 2 (2021): 2043–55. http://dx.doi.org/10.3934/mbe.2022096.
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<abstract> <p>Forecasting future epidemics helps inform policy decisions regarding interventions. During the early coronavirus disease 2019 epidemic period in January–February 2020, limited information was available, and it was too challenging to build detailed mechanistic models reflecting population behavior. This study compared the performance of phenomenological and mechanistic models for forecasting epidemics. For the former, we employed the Richards model and the approximate solution of the susceptible–infected–recovered (SIR) model. For the latter, we examined the exponential growth (with lockdown) model and SIR model with lockdown. The phenomenological models yielded higher root mean square error (RMSE) values than the mechanistic models. When using the numbers from reported data for February 1 and 5, the Richards model had the highest RMSE, whereas when using the February 9 data, the SIR approximation model was the highest. The exponential model with a lockdown effect had the lowest RMSE, except when using the February 9 data. Once interventions or other factors that influence transmission patterns are identified, they should be additionally taken into account to improve forecasting.</p> </abstract>
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Gąsiorowski, Dariusz, and Tomasz Kolerski. "Numerical Solution of the Two-Dimensional Richards Equation Using Alternate Splitting Methods for Dimensional Decomposition." Water 12, no. 6 (2020): 1780. http://dx.doi.org/10.3390/w12061780.
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Research on seepage flow in the vadose zone has largely been driven by engineering and environmental problems affecting many fields of geotechnics, hydrology, and agricultural science. Mathematical modeling of the subsurface flow under unsaturated conditions is an essential part of water resource management and planning. In order to determine such subsurface flow, the two-dimensional (2D) Richards equation can be used. However, the computation process is often hampered by a high spatial resolution and long simulation period as well as the non-linearity of the equation. A new highly efficient and accurate method for solving the 2D Richards equation has been proposed in the paper. The developed algorithm is based on dimensional splitting, the result of which means that 1D equations can be solved more efficiently than as is the case with unsplit 2D algorithms. Moreover, such a splitting approach allows any algorithm to be used for space as well as time approximation, which in turn increases the accuracy of the numerical solution. The robustness and advantages of the proposed algorithms have been proven by two numerical tests representing typical engineering problems and performed for typical properties of soil.
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Gregorczyk, Andrzej. "Error estimation in plant growth analysis." Acta Societatis Botanicorum Poloniae 65, no. 3-4 (2014): 207–12. http://dx.doi.org/10.5586/asbp.1996.033.
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The scheme is presented for calculation of errors of dry matter values which occur during approximation of data with growth curves, determined by the analytical method (logistic function) and by the numerical method (Richards function). Further formulae are shown, which describe absolute errors of growth characteristics: Growth rate (GR), Relative growth rate (RGR), Unit leaf rate (ULR) and Leaf area ratio (LAR). Calculation examples concerning the growth course of oats and maize plants are given. The critical analysis of the estimation of obtained results has been done. The purposefulness of joint application of statistical methods and error calculus in plant growth analysis has been ascertained.
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Zhang, Fanchang, Jingyang Yang, Chuanhui Li, Dong Li, and Yang Gao. "Direct inversion for reservoir parameters from prestack seismic data." Journal of Geophysics and Engineering 17, no. 6 (2020): 993–1004. http://dx.doi.org/10.1093/jge/gxaa058.
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Abstract Reliably estimating reservoir parameters is the final target in reservoir characterisation. Conventionally, estimating reservoir characters from seismic inversion is implemented by indirect approaches. The indirect estimation of reservoir parameters from inverted elastic parameters, however, will produce large bias due to the propagation of errors in the procedure of inversion. Therefore, directly obtaining reservoir parameters from prestack seismic data through a rock-physical model and prestack amplitude variation with offset (AVO) inversion is proposed. A generalised AVO equation in terms of oil-porosity (OP), sand indicator (SI) and density is derived by combining a physical rock model and the Aki–Richards equation in a whole system. This makes it possible to perform direct inversion for reservoir parameters. Next, under Bayesian theorem, we develop a robust prestack inversion approach based on the new AVO equation. Tests on synthetic seismic gathers show that it can dramatically reduce the prediction error of reservoir parameters. Furthermore, field data application illustrates that reliable reservoir parameters can be directly obtained from prestack inversion.
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EYMARD, R., T. GALLOUËT, R. HERBIN, M. GUTNIC, and D. HILHORST. "APPROXIMATION BY THE FINITE VOLUME METHOD OF AN ELLIPTIC-PARABOLIC EQUATION ARISING IN ENVIRONMENTAL STUDIES." Mathematical Models and Methods in Applied Sciences 11, no. 09 (2001): 1505–28. http://dx.doi.org/10.1142/s0218202501001446.
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We prove the convergence of a finite volume scheme for the Richards equation β(p)t- div (Λ(β(p))(∇p-ρg))=0 together with a Dirichlet boundary condition and an initial condition in a bounded domain Ω ×(0, T). We consider the hydraulic charge [Formula: see text] as the main unknown function so that no upwinding is necessary. The convergence proof is based on the strong convergence in L2 of the water saturation β(p), which one obtains by estimating differences of space and time translates and applying Kolmogorov's theorem. This implies the convergence in L2 of the approximate water mobility towards Λ(β(p)) as the time and mesh steps tend to 0, which in turn implies the convergence of the approximate pressure to a weak solution p of the continuous problem.
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Wever, N., C. Fierz, C. Mitterer, H. Hirashima, and M. Lehning. "Solving Richards Equation for snow improves snowpack meltwater runoff estimations." Cryosphere Discussions 7, no. 3 (2013): 2373–412. http://dx.doi.org/10.5194/tcd-7-2373-2013.
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Abstract. The runoff from the snow cover during spring snow melt or rain-on-snow events is an important factor in the hydrological cycle. In this study, water transport schemes for a 1-dimensional physical based snowpack model are compared to 14 yr of lysimeter measurements at a high alpine site. The schemes include a simple bucket-type approach, an approximation of Richards Equation (RE), and the full RE. The results show that daily sums of runoff are strongly related to a positive energy balance of the snow cover and therefore, all water transport schemes show very similar performance in terms of Nash–Sutcliffe efficiency (NSE) coefficients (around 0.59) and r2 values (around 0.77). Timing of the arrival of meltwater in spring at the bottom of the snowpack showed differences between the schemes, where especially in the bucket-type and approximated RE approach, meltwater release is slower than in the measurements. Overall, solving RE for the snow cover yields the best agreement between modelled and measured runoff. On sub-daily time scales, the water transport schemes behave very differently. Also here, solving RE provides the highest agreement between modelled and measured runoff in terms of NSE coefficient (0.48), where other water transport schemes loose any predictive power. This appears to be mainly due to bad timing of meltwater release during the day. Accordingly, solving RE for the snow cover improves several aspects of modelling snow cover runoff. The additional computational cost was found to be in the order of a factor of 1.5.
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Matthews, C. J., F. J. Cook, J. H. Knight, and R. D. Braddock. "Handling the water content discontinuity at the interface between layered soils within a numerical scheme." Soil Research 43, no. 8 (2005): 945. http://dx.doi.org/10.1071/sr05069.
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In general, the water content (θ) form of Richards’ equation is not used when modeling water flow through layered soil since θ is discontinuous across soil layers. Within the literature, there have been some examples of models developed for layered soils using the θ-form of Richards’ equation. However, these models usually rely on an approximation of the discontinuity at the soil layer interface. For the first time, we will develop an iterative scheme based on Newton’s method, to explicitly solve for θ at the interface between 2 soils within a numerical scheme. The numerical scheme used here is the Method of Lines (MoL); however, the principles of the iterative solution could be used in other numerical techniques. It will be shown that the iterative scheme is highly effective, converging within 1 to 2 iterations. To ensure the convergence behaviour holds, the numerical scheme will be tested on a fine-over-coarse and a coarse-over-fine soil with highly contrasting soil properties. For each case, the contrast between the soil types will be controlled artificially to extend and decrease the extent of the θ discontinuity. In addition, the numerical solution will be compared against a steady-state analytical solution and a numerical solution from the literature.
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Bohaienko, V. O., and A. V. Gladky. "MULTITHREADING PERFORMANCE SIMULATING FRACTIONAL-ORDER MOISTURE TRANSPORT ON AMD EPYC." Journal of Numerical and Applied Mathematics, no. 2 (2022): 174–82. http://dx.doi.org/10.17721/2706-9699.2022.2.20.
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The paper studies the performance of multithreaded parallel implementation of a finite-difference solver for a two-dimensional space-fractional generalization of Richards equation. For numerical solution we used implicit Crank-Nicholson scheme with L1-approximation of Caputo fractional derivative and TFQMR linear systems’ solver. OpenMP implementation was tested on three CPUs — server Intel Xeon Bronze 3104 and AMD EPYC 7542 along with laptop AMD Ryzen 3 5300U. Testing results show that the proposed implementation can give close-to-linear acceleration when executing on up to 8 cores. On high-performance AMD EPYC maximal acceleration was achieved when 32-64 cores were used showing limited scalability of the algorithms on such a CPU.
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Brkić, Iva, and Bojan Crnković. "Numerička simulacija prometnog toka." Zbornik radova 26, no. 1 (2023): 151–67. http://dx.doi.org/10.32762/zr.26.1.9.
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The paper discusses the concept of traffic flow described by hyperbolic differential equations. In this paper the Lighthill-Whitham-Richards model (LWR model) is used to describe traffic flow. The said model uses two parameters to describe the traffic flow – density and average speed of vehicles. Numerical approximation of the LWR model is formulated through scalar conservation laws. The finite volume method is used for numerical results. The term of shock wave and propagation of rarefaction wave in traffic flow are described. This paper focuses on numerical simulation of traffic flow via fluid dynamics model for a single road with a traffic light. The results obtained in this paper are compared with previous studies.
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Soylu, M. E., E. Istanbulluoglu, J. D. Lenters, and T. Wang. "Quantifying the impact of groundwater depth on evapotranspiration in a semi-arid grassland region." Hydrology and Earth System Sciences Discussions 7, no. 5 (2010): 6887–923. http://dx.doi.org/10.5194/hessd-7-6887-2010.
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Abstract. The interactions between shallow groundwater and land surface processes, mediated by capillary rise processes from groundwater, may play an important role in the ecohydrology of riparian zones in both humid and semi-arid ecosystems. Some recent land surface models (LSM) incorporate the contribution of groundwater to land surface processes with varying levels of complexity. In this paper, we examine the sensitivity of evapotranspiration at the land surface to the depth of groundwater using three models with different levels of complexity, two widely used representative soil hydraulic parameter sets, and four soil textures. The selected models are Hydrus-1D, which solves the Richards equation, the Integrated Biosphere Simulator (IBIS), which uses a multi-bucket approach with interactions between buckets, and a single-bucket model coupled with a classic simple capillary rise flux approximation. These models are first corroborated with field observations of soil moisture and groundwater elevation data from a site located in south-central Nebraska, USA. We then examine the sensitivity of the Richards equation to node spacing, as well as the relationship between groundwater depth and the ratio of actual to potential evapotranspiration (ET) for various soil textures and water table depths. The results show that selecting one representative soil parameter set over another may result in up to a 70% difference in actual ET (relative to the potential ET) when the depth to water table is in 0–5 m depending on the soil type. Moreover, solution type of the Richards equation and node spacing have also effect on surface ET up to 50% and 30% respectively depending on the depth-to-groundwater and node spacing. Therefore, further studies are needed to understand the sensitivities of land surface and atmospheric models to the existence of saturated layers, including studies with more field validation in regions with different climates and land cover types.
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Ercan, Ali, and M. Kavvas. "Numerical Evaluation of Fractional Vertical Soil Water Flow Equations." Water 13, no. 4 (2021): 511. http://dx.doi.org/10.3390/w13040511.
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Significant deviations from standard Boltzmann scaling, which corresponds to normal or Fickian diffusion, have been observed in the literature for water movement in porous media. However, as demonstrated by various researchers, the widely used conventional Richards equation cannot mimic anomalous diffusion and ignores the features of natural soils which are heterogeneous. Within this framework, governing equations of transient water flow in porous media in fractional time and multi-dimensional fractional soil space in anisotropic media were recently introduced by the authors by coupling Brooks–Corey constitutive relationships with the fractional continuity and motion equations. In this study, instead of utilizing Brooks–Corey relationships, empirical expressions, obtained by least square fits through hydraulic measurements, were utilized to show the suitability of the proposed fractional approach with other constitutive hydraulic relations in the literature. Next, a finite difference numerical method was proposed to solve the fractional governing equations. The applicability of the proposed fractional governing equations was investigated numerically in comparison to their conventional counterparts. In practice, cumulative infiltration values are observed to deviate from conventional infiltration approximation, or the wetting front through time may not be consistent with the traditional estimates of Richards equation. In such cases, fractional governing equations may be a better alternative for mimicking the physical process as they can capture sub-, super-, and normal-diffusive soil water flow processes during infiltration.
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Abaali, Mostafa. "Parameters correction of an elliptical equation using an a posteriori estimate." Boletim da Sociedade Paranaense de Matemática 42 (May 22, 2024): 1–12. http://dx.doi.org/10.5269/bspm.66435.
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In nature several phenomena touch humanity to act and control these phenomena we try to model their evolution. To simplify the study of the equations obtained, most of the time we try to use linear forms and in this way modelling errors are made which can influence the correct analysis of these phenomena. In this work we focus on the Richards' equation, where the coefficients changes their forms from a given value hs: This value is unknown then the coefficients are approximated. We prove an a priori and an a posteriori estimates on the modelling error. This estimates allows us, using local indicators, to build an adaptive algorithm to control the modelling error and automatically determine the "best" approximation of hs. Numerical results confirm theconvergence of this procedure and the interest of this approach.
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Anthony, L., and B. Fultz. "Kinetics of B2, DO3, and B32 ordering: Results from pair approximation calculations and Monte Carlo simulations." Journal of Materials Research 9, no. 2 (1994): 348–56. http://dx.doi.org/10.1557/jmr.1994.0348.
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A kinetic theory of ordering based on the path probability method was implemented in the pair (Bethe) approximation and used to study the kinetics of short- and long-range ordering in alloys with equilibrium states of B2, DO3, or B32 order. The theory was developed in a superposition approximation for a vacancy mechanism on a bcc lattice with first- (1nn) and second-nearest neighbor (2nn) pair interactions. Chained 1nn conditional probabilities were used to account for the entropy of 2nn pair configurations. Monte Carlo simulations of ordering were also performed and their results compared to predictions of the pair approximation. Comparisons are also made with predictions from an earlier kinetic theory implemented in the point (Bragg-Williams) approximation. For all three calculations (point, pair, and Monte Carlo), critical temperatures for B2 and DO3 ordering are reported for different 1nn and 2nn interaction strengths. The influence of annealing temperature on the kinetic paths through the space of B2, DO3, and B32 order parameters was found to be strong when the thermodynamic preferences for the ordered states were of similar strengths. Transient states of intermediate order were also studied. A transient formation of B32 order in an AB3 alloy was found when 2nn interactions were strong, even when B32 order was neither a Richards-Allen-Cahn ground state nor a stable equilibrium state at that temperature. The formation of this transient B32 order can be argued consistently from a thermodynamic perspective. However, a second example of transient B2 order in an AB alloy with equilibrium B32 order cannot be explained by the same thermodynamic argument, and we believe that its origin is primarily kinetic.
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Cheng, Yanyan, Guotao Cui, and Jianting Zhu. "Using time compression approximation to determine actual infiltration rate from variable rainfall events." Hydrology Research 50, no. 1 (2017): 155–65. http://dx.doi.org/10.2166/nh.2017.062.
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Abstract Understanding infiltration into soils from rainfall events is important for many practical applications. The idea of time compression approximation (TCA) was proposed to simulate infiltration rate, which only requires the relationship between the potential infiltration rate (PIR) and potential cumulative infiltration (PCI). The TCA-based method can be used in any rainfall–runoff models since the PIR vs. PCI relationship can be developed independent of actual rainfall patterns. The main objective of this study is to establish guidelines on when this method can be adequately applied. The results based on the TCA are compared with those from the field observations and the Richards equation numerical solver for observed rainfall events and randomly generated rainfall patterns with prescribed temporal variabilities and hiatuses. For continuous rainfall with potential ponding, the maximum error of infiltration amount using the TCA-based method is less than 5%. The TCA-based method, in general, underestimates the total infiltration amount from variable rainfall events. Variance in rainfall time series does not significantly affect the errors of using the TCA-based method to determine the actual infiltration rate. The TCA-based method can produce reasonable results in simulating the actual infiltration rate for rainfall events with a short hiatus.
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Yitong, Wang, Li Jingsheng, Sam Zandong Sun, et al. "Study of seismic attributes recognition method of high quality igneous rock reservoir." E3S Web of Conferences 329 (2021): 01058. http://dx.doi.org/10.1051/e3sconf/202132901058.
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Aimed target area is deeply buried, complex lithology, dual media, reservoir development degree is controlled by a variety of factors, meanwhile, lateral thickness and lithofacies change rapidly, and strata formation is poor. Therefore, igneous rock reservoir has difficulty in predicting, since seismic is complicated to track trace, reservoir attribute analysis is hard to determine the time window, and inversion modeling requires sophisticated. By analyzing, the basalt in the target research area accounts for the principal component of the igneous rock, however, the igneous rocks with relatively developed reservoirs are mostly distributed in the trachyte breccia which has good productivity. The results of petrophysical study indicate that frequency-dependent AVO inversion method is an important means to identify fluid and reservoir prediction, notwithstanding it is difficult to distinguish high-quality reservoirs barely by P-wave impedance. Consequently, AVOF inversion method is appropriately proposed to identify igneous rock reservoir. Foremost, eliminating the effects of algorithm,frequency, spectrum balancing and other factors, then put the improved three-term Aki&Richards frequency-dependent AVO inversion method applying to distinguish igneous reservoir fluid and lithology, for the purpose of carrying out the identification of high-quality reservoirs.
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Zou, Keshan. "S-Zero Stack: A converted wave processing to extract subsurface density information." GEOPHYSICS 79, no. 3 (2014): N1—N10. http://dx.doi.org/10.1190/geo2013-0029.1.
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Analyzing the Aki-Richards equation for converted waves, I found that it is possible to decouple the effect of density contrast from that of shear velocity contrast. The two terms were mixed when the P-wave incident angle was less than 30°, but they started to separate at a middle angle range (approximately 40°). The term related to S-wave velocity contrast reached zero at an incident angle around 60°. However, the other term, which was related to the density contrast, did not reverse polarity until 90°. Furthermore, this density term reached almost the maximum (magnitude) around 60°. Based on those characteristics, I designed a new method called “S-Zero Stack” to capture the density contrast reliably at the subsurface interface without going to inversion. S-Zero Stack captured subsurface density anomalies using a special stacking method. It is simple but robust, even when there is noise in the common-conversion-point gathers. Combined with the traditional P-wave amplitude-variation-with-offset technique, S-Zero Stack of PS-waves may help discriminate commercial gas from fizz in gas sand and could be a useful tool in shale gas exploration to locate lower-density anomalies (sweet spots).
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Watson, Maura A., Anna M. Howle, Oliver Lenz, et al. "Adapting an Objective Structured Clinical Examination (OSCE) on Conducting Difficult Conversations Between Nephrology Fellows and Patients to a Virtual Platform: A Research Letter." Canadian Journal of Kidney Health and Disease 10 (January 2023): 205435812211505. http://dx.doi.org/10.1177/20543581221150553.
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Background: We previously described a nephrology-specific “Breaking Bad News” Objective Structured Clinical Examination (OSCE) assessing nephrology fellow communication and counseling skills in 3 scenarios: kidney replacement therapy (KRT) in kidney failure, urgent KRT in acute kidney injury (AKI), and kidney biopsy (KBx). Objective: The main objectives of this study is to adapt the OSCE to a virtual platform, simulating nephrology patient telemedicine encounters involving difficult conversations, and to assess fellow and faculty satisfaction with the virtual format. Design: Description of a formative telemedicine simulation for nephrology fellows. Setting: Fully virtual simulation conducted by 2 academic medical simulation centers. Participants: Nephrology faculty and fellows at 3 urban/suburban training programs in the eastern United States. Measurements: Description of the virtual OSCE process. Fellow and faculty satisfaction overall and for each scenario. Faculty and fellow estimates of frequency of virtual patient encounters in the past year. Methods: The OSCE consisted of 3 scenarios: KRT in kidney failure, urgent KRT in AKI, and KBx. Objective Structured Clinical Examinations were administered in May 2021. Each scenario lasted 20 minutes. The AKI scenario was audio only. Fellows telephoned a simulated patient surrogate for urgent KRT consent. Kidney failure and KBx scenarios were video encounters. Faculty observed while muted/video off. Immediately after the OSCE, fellows and faculty were anonymously surveyed regarding their satisfaction with each scenario, the OSCE overall, and their estimate of outpatient encounters and inpatient KRT counseling done virtually in the preceding year. Results: Seventeen fellows completed the OSCE at 2 centers (3 programs). Sixteen (94%) completed the survey. Almost 94% rated the OSCE as a good/very good approximation of telemedicine encounters. Those satisfied/very satisfied with each scenario are as follow: 100% for AKI, 75% for kidney failure, and 75% for KBx. Two commented that they often did urgent KRT counseling by telephone. Fellows estimated a median 20% (interquartile range: 175, 50%) of counseling for acute inpatient KRT and a median 50% (IQR: 33.75, 70%) of outpatient encounters were virtual in the prior year. Two (regarding the kidney failure and KBx scenarios) indicated they would not have counseled similar outpatients virtually. Limitations: The 15-minute interactions may be too short to allow the encounter to be completed comfortably. A small number of programs and fellows participated, and programs were located in urban/suburban areas on the east coast of the United States. Conclusions: Overall, fellows felt that the OSCE was a good approximation of virtual encounters. The OSCE is an opportunity for fellows to practice telemedicine communication skills.
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Elbetch, Bilel. "Effect of dispersal in two-patch environment with Richards growth on population dynamics." Journal of Innovative Applied Mathematics and Computational Sciences 2, no. 3 (2022): 41–68. http://dx.doi.org/10.58205/jiamcs.v2i3.47.
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In this paper, we consider a two-patch model coupled by migration terms, where each patch follows a Richards law. First, we prove the global stability of the model. Second, in the case when the migration rate tends to infinity, the total carrying capacity is given, which in general is different from the sum of the two carrying capacities and depends on the parameters of the growth rate and also on the migration terms. Using the theory of singular perturbations, we give an approximation of the solutions of the system in this case. Finally, we determine the conditions under which fragmentation and migration can lead to a total equilibrium population which might be greater or smaller than the sum of two carrying capacities and we give a complete classification for all possible cases. The total equilibrium population formula for a large migration rate plays an important role in this classification. We show that this choice of local dynamics has an influence on the effect of dispersal. Comparing the dynamics of the total equilibrium population as a function of the migration rate with that of the logistic model, we obtain the same behavior. In particular, we have only three situations that the total equilibrium population can occur: it is always greater than the sum of two carrying capacities, always smaller, and a third case, where the effect of dispersal is beneficial for lower values of the migration rate and detrimental for the higher values. We end by examining the two-patch model where one growth rate is much larger than the second one, we compare the total equilibrium population with the sum of the two carrying capacities.
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Cloonan, Thomas F. "The Early history of Phenomenological Psychological Research in America." Journal of Phenomenological Psychology 26, no. 1 (1995): 46–126. http://dx.doi.org/10.1163/156916295x00033.
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AbstractThis article on the early history of phenomenological psychological research in the academic context in America focuses on the four approaches of the following respective psychologists: 1) Donald Snygg, Arthur W. Combs, and Anne C. Richards and Fred Richards; 2) Robert B. MacLeod; 3) Adrian L. van Kaam; and 4) Amedeo P. Giorgi. It begins by first addressing the "context" for this early history namely, the European origin of philosophical phenomenology and the connection of it with the psychology of its times in Europe, and then the American background for the development of a sensibility for phenomenology and an eventual connection of phenomenology with psychology. Each of the four positions was examined in terms of basic approach to the study of human experience and behavior. That is, examination was directed toward whether the respective position was under the aegis of psychology as a human science or as a natural science. Also examined were the research postures and the methodologies of the four positions in terms of their respective degrees of reflecting either the human science or the natural science approach, and in terms of their approximation to a phenomenological psychology. It was found that syncretism characterized the approaches of the first three positions, and that there was either an absence of phenomenological psychological method in the psychologies of those positions or, in the case of MacLeod, an undeveloped and non-worked-out method. Only the work of Amedeo Giorgi presented 1) a human science approach that was radical and not compromised by natural science syncretions, and 2) an articulated phenomenological psychological method based on Husserl's concept of intentionality and on mediation of Merleau-Ponty's philosophical phenomenological method.