Linear and nonlinear solutions for one-dimensional compaction flow in sedimentary basins

A new simulation-based site amplification model for shallow sites with thickness less than 30 m in Korea is developed. The site amplification model consists of linear and nonlinear components that are developed from one-dimensional linear and nonlinear site response analyses. A suite of measured shear wave velocity profiles is used to develop corresponding randomized profiles. A VS30 scaled linear amplification model and a model dependent on both VS30 and site period are developed. The proposed linear models compare well with the amplification equations developed for the western United States (WUS) at short periods but show a distinct curved bump between 0.1 and 0.5 s that corresponds to the range of site natural periods of shallow sites. The response at periods longer than 0.5 s is demonstrated to be lower than those of the WUS models. The functional form widely used in both WUS and central and eastern North America (CENA), for the nonlinear component of the site amplification model, is employed in this study. The slope of the proposed nonlinear component with respect to the input motion intensity is demonstrated to be higher than those of both the WUS and CENA models, particularly for soft sites with VS30 < 300 m/s and at periods shorter than 0.2 s. The nonlinear component deviates from the models for generic sites even at low ground motion intensities. The comparisons highlight the uniqueness of the amplification characteristics of shallow sites that a generic site amplification model is unable to capture.

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Land subsidence and hydrodynamic compaction of sedimentary basins

Hydrology and Earth System Sciences ◽

10.5194/hess-2-159-1998 ◽

1998 ◽

Vol 2 (2/3) ◽

pp. 159-171 ◽

Cited By ~ 29

Author(s):

H. Kooi ◽

J. J. de Vries

Keyword(s):

Response Time ◽

Land Subsidence ◽

Sedimentary Basins ◽

Sediment Loading ◽

Dimensional Model ◽

One Dimensional ◽

Model Equations ◽

Sediment Layers ◽

The Relationship

Abstract. A one-dimensional model is used to investigate the relationship between land subsidence and compaction of basin sediments in response to sediment loading. Analysis of the model equations and numerical experiments demonstrate quasi-linear systems behaviour and show that rates of land subsidence due to compaction: (i) can attain a significant fraction (>40%) of the long-term sedimentation rate; (ii) are hydrodynamically delayed with respect to sediment loading. The delay is controlled by a compaction response time τc that can reach values of 10-5-107 yr for thick shale sequences. Both the behaviour of single sediment layers and multiple-layer systems are analysed. Subsequently the model is applied to the coastal area of the Netherlands to illustrate that lateral variability in compaction-derived land subsidence in sedimentary basins largely reflects the spatial variability in both sediment loading and compaction response time. Typical rates of compaction-derived subsidence predicted by the model are of the order of 0.1 mm/yr but may reach values in excess of 1 mm/yr under favourable conditions.

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One-Dimensional Localization and Wave Propagation in Linear and Nonlinear Media

Springer Proceedings in Physics - Nonlinearity with Disorder ◽

10.1007/978-3-642-84774-5_13 ◽

1992 ◽

pp. 126-133

Author(s):

S. A. Gredeskul ◽

L. A. Pastur

Keyword(s):

Wave Propagation ◽

Nonlinear Media ◽

One Dimensional ◽

Linear And Nonlinear

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A Note on Double Conformable Laplace Transform Method and Singular One Dimensional Conformable Pseudohyperbolic Equations

Mathematics ◽

10.3390/math7100949 ◽

2019 ◽

Vol 7 (10) ◽

pp. 949 ◽

Cited By ~ 2

Author(s):

Hassan Eltayeb ◽

Said Mesloub ◽

Yahya T. Abdalla ◽

Adem Kılıçman

Keyword(s):

Present Method ◽

Decomposition Method ◽

Numerical Solutions ◽

High Accuracy ◽

Laplace Transform Method ◽

Transform Method ◽

Numerical Examples ◽

One Dimensional ◽

Linear And Nonlinear ◽

Laplace Decomposition Method

The purpose of this article is to obtain the exact and approximate numerical solutions of linear and nonlinear singular conformable pseudohyperbolic equations and conformable coupled pseudohyperbolic equations through the conformable double Laplace decomposition method. Further, the numerical examples were provided in order to demonstrate the efficiency, high accuracy, and the simplicity of present method.

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Quasi-one-dimensional photonic lattices and superlattices in lithium niobate: Linear and nonlinear discrete diffraction of light

Physics of Wave Phenomena ◽

10.3103/s1541308x10010012 ◽

2010 ◽

Vol 18 (1) ◽

pp. 1-6 ◽

Cited By ~ 5

Author(s):

S. A. Davydov ◽

P. A. Trenikhin ◽

V. M. Shandarov ◽

K. V. Shandarova ◽

D. Kip ◽

...

Keyword(s):

Lithium Niobate ◽

One Dimensional ◽

Photonic Lattices ◽

Diffraction Of Light ◽

Discrete Diffraction ◽

Linear And Nonlinear

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Absorbing Boundary Conditions for Solving N-Dimensional Stationary Schrödinger Equations with Unbounded Potentials and Nonlinearities

Communications in Computational Physics ◽

10.4208/cicp.251010.160211a ◽

2011 ◽

Vol 10 (5) ◽

pp. 1280-1304 ◽

Cited By ~ 9

Author(s):

Pauline Klein ◽

Xavier Antoine ◽

Christophe Besse ◽

Matthias Ehrhardt

Keyword(s):

Boundary Conditions ◽

Dirichlet Boundary ◽

Absorbing Boundary Conditions ◽

Schrodinger Equations ◽

Schrödinger Equations ◽

Absorbing Boundary ◽

One Dimensional ◽

Nonlinear Potential ◽

Linear And Nonlinear ◽

The One

AbstractWe propose a hierarchy of novel absorbing boundary conditions for the one-dimensional stationary Schrödinger equation with general (linear and nonlinear) potential. The accuracy of the new absorbing boundary conditions is investigated numerically for the computation of energies and ground-states for linear and nonlinear Schrödinger equations. It turns out that these absorbing boundary conditions and their variants lead to a higher accuracy than the usual Dirichlet boundary condition. Finally, we give the extension of these ABCs to N-dimensional stationary Schrödinger equations.

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Linear vs. nonlinear porosity estimation of NMR oil reservoir data

IIUM Engineering Journal ◽

10.31436/iiumej.v8i1.85 ◽

2010 ◽

Vol 8 (1) ◽

pp. 19-33

Author(s):

Mohsen Abdou Abou Mandour ◽

Mohamed Mohamed El-Affify ◽

Mohamed Hassan Hassan ◽

Amir Kamel Alramady

Keyword(s):

Nuclear Magnetic Resonance ◽

Regularization Parameter ◽

Least Square ◽

Oil Reservoir ◽

Tight Sandstone ◽

Linear Solution ◽

T2 Distribution ◽

Linear And Nonlinear ◽

Linear Least Square ◽

Nonlinear Solutions

Nuclear magnetic resonance is widely used to assess oil reservoir properties especially those that can not be evaluated using conventional techniques. In this regard, porosity determination and the related estimation of the oil present play a very important role in assessing the eco1nomic value of the oil wells. Nuclear Magnetic Resonance data is usually fit to the sum of decaying exponentials. The resulting distribution; i.e. T2 distribution; is directly related to porosity determination. In this work, three reservoir core samples (Tight Sandstone and two Carbonate samples) were analyzed. Linear Least Square method (LLS) and non-linear least square fitting using Levenberg-Marquardt method were used to calculate the T2 distribution and the resulting incremental porosity. Parametric analysis for the two methods was performed to evaluate the impact of number of exponentials, and effect of the regularization parameter (?) on the smoothing of the solution. Effect of the type of solution on porosity determination was carried out. It was found that 12 exponentials is the optimum number of exponentials for both the linear and nonlinear solutions. In the mean time, it was shown that the linear solution begins to be smooth at α = 0.5 which corresponds to the standard industrial value for the regularization parameter. The order of magnitude of time needed for the linear solution is in the range of few minutes while it is in the range of few hours for the nonlinear solution. Regardless of the fact that small differences exist between the linear and nonlinear solutions, these small values make an appreciable difference in porosity. The nonlinear solution predicts 12% less porosity for the tight sandstone sample and 4.5 % and 13 % more porosity in the two carbonate samples respectively.

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Application of Conformable Sumudu Decomposition Method for Solving Conformable Fractional Coupled Burger’s Equation

Journal of Function Spaces ◽

10.1155/2021/6613619 ◽

2021 ◽

Vol 2021 ◽

pp. 1-13

Author(s):

Hassan Eltayeb ◽

Said Mesloub

Keyword(s):

Partial Differential Equations ◽

Differential Equations ◽

Analytical Method ◽

Decomposition Method ◽

Nonlinear Partial Differential Equations ◽

One Dimensional ◽

Burger's Equation ◽

Burger’S Equation ◽

Sumudu Transform ◽

Linear And Nonlinear

The conformable double Sumudu decomposition method (CDSDM) is a combination of decomposition method (DM) and a conformable double Sumudu transform. It is an approximate analytical method, which can be used to solve linear and nonlinear partial differential equations. In this work, one-dimensional conformable functional Burger’s equation has been solved by applying conformable double Sumudu decomposition. Two examples are used to illustrate the method.

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The asymptotic response of three‐dimensional basin offsets to magnetotelluric fields at long periods: The effects of current channeling

Geophysics ◽

10.1190/1.1441306 ◽

1982 ◽

Vol 47 (11) ◽

pp. 1562-1573 ◽

Cited By ~ 36

Author(s):

John F. Hermance

Keyword(s):

Thin Sheet ◽

Three Dimensional ◽

Sedimentary Basins ◽

Transverse Magnetic ◽

Clear Correlation ◽

One Dimensional ◽

Skewness Coefficient ◽

Order Of Magnitude ◽

D Model ◽

Telluric Currents

A simple, inexpensive numerical algorithm is used to analyze the asymptotic long‐period behavior of magnetotelluric (MT) fields in the vicinity of lateral offsets in sedimentary basins. The model is based on the distortion or channeling of telluric currents in a horizontal thin sheet. Although a gross oversimplification of nature, the model represents a class of structures which, because of excessive computer costs, have been relatively unstudied previously. Within, and closely adjacent to, the region of the three‐dimensional (3-D) offset, significant distortion of the MT parameters occurs. Skewness coefficients vary from negligible values to over 0.7. Principal resistivities vary by an order of magnitude. On the other hand, there is not a clear correlation between the degree of distortion of the parameters usually evaluated during MT surveys and the magnitude of conventional 3-D indicators (e.g., the skewness coefficient). Calculations have simulated the technique of averaging resistivity parameters from a large number of field sites in order to arrive at a regionally representative one‐dimensional (1-D) model. The results indicate that unless care is taken in adapting the nature of the averaging algorithm to the class of distortions encountered, significant bias of the averaged parameters may result. Our results also suggest that for this class of structures grave problems may be associated with using the principal resistivity perpendicular to geologic strike, the so‐called transverse magnetic (TM) mode, to infer an equivalent two‐dimensional (2-D) model for the region. A 2-D model would likely show significant modulations in the physical character of the basement which are, in fact, an artifact of telluric distortion caused by current channeling in the surficial heterogeneity.

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