Higher‐order moveout spectra

Geophysics ◽  
1979 ◽  
Vol 44 (7) ◽  
pp. 1193-1207 ◽  
Author(s):  
Bruce T. May ◽  
Donald K. Straley
Keyword(s):  
Fourth Order ◽  
Seismic Reflection ◽  
Order Term ◽  
Higher Order ◽  
Second Order ◽  
Equation Modeling ◽  
Fourth Order Term ◽  
Higher Order Terms ◽  
Velocity Spectra

Higher‐order terms in the generalized seismic reflection moveout equation are usually neglected, resulting in the familiar second‐order, or hyperbolic, moveout equation. Modeling studies show that the higher‐order terms are often significant, and their neglect produces sizable traveltime residuals after correction for moveout in such cases as kinked‐ray models. Taner and Koehler (1969) introduced velocity spectra for estimating stacking velocity defined on the basis of second‐order moveout. Through the use of orthogonal polynomials, an iterative procedure is defined that permits computation of fourth‐order moveout spectra while simultaneously upgrading the previously computed, second‐order spectra. Emphasis is placed on the fourth‐order term, but the procedure is general and can be expanded to higher orders. When used with synthetic and field recorded common‐midpoint (CMP) trace data, this technique produces significant improvements in moveout determination affecting three areas: (1) resolution and interpretability of moveout spectra, (2) quality of CMP stacked sections, and (3) computation of velocity and depth for inverse modeling.

scholarly journals The Effect Of Randomness On The Stability Of Capillary Gravity Waves In The Presence Of Air Flowing Over Water

2015 ◽  
Vol 20 (4) ◽  
pp. 835-855
Author(s):  
D.P. Majumder ◽  
A.K. Dhar
Keyword(s):  
Growth Rate ◽  
Evolution Equation ◽  
Gravity Waves ◽  
Fourth Order ◽  
Order Term ◽  
Spectral Width ◽  
Higher Order ◽  
Order Contribution ◽  
Fourth Order Term ◽  
The Stability

Abstract A nonlinear spectral transport equation for the narrow band Gaussian random surface wave trains is derived from a fourth order nonlinear evolution equation, which is a good starting point for the study of nonlinear water waves. The effect of randomness on the stability of deep water capillary gravity waves in the presence of air flowing over water is investigated. The stability is then considered for an initial homogenous wave spectrum having a simple normal form to small oblique long wave length perturbations for a range of spectral widths. An expression for the growth rate of instability is obtained; in which a higher order contribution comes from the fourth order term in the evolution equation, which is responsible for wave induced mean flow. This higher order contribution produces a decrease in the growth rate. The growth rate of instability is found to decrease with the increase of spectral width and the instability disappears if the spectral width increases beyond a certain critical value, which is not influenced by the fourth order term in the evolution equation.

scholarly journals Higher order Hamiltonian Monte Carlo sampling for cosmological large-scale structure analysis

2021 ◽  
Vol 502 (3) ◽  
pp. 3976-3992
Author(s):  
Mónica Hernández-Sánchez ◽  
Francisco-Shu Kitaura ◽  
Metin Ata ◽  
Claudio Dalla Vecchia
Keyword(s):  
Fourth Order ◽  
Large Scale ◽  
Equations Of Motion ◽  
Large Scale Structure ◽  
Real Space ◽  
Higher Order ◽  
Second Order ◽  
Scale Structure ◽  
Integration Schemes ◽  
Reconstruction Methods

ABSTRACT We investigate higher order symplectic integration strategies within Bayesian cosmic density field reconstruction methods. In particular, we study the fourth-order discretization of Hamiltonian equations of motion (EoM). This is achieved by recursively applying the basic second-order leap-frog scheme (considering the single evaluation of the EoM) in a combination of even numbers of forward time integration steps with a single intermediate backward step. This largely reduces the number of evaluations and random gradient computations, as required in the usual second-order case for high-dimensional cases. We restrict this study to the lognormal-Poisson model, applied to a full volume halo catalogue in real space on a cubical mesh of 1250 h−1 Mpc side and 2563 cells. Hence, we neglect selection effects, redshift space distortions, and displacements. We note that those observational and cosmic evolution effects can be accounted for in subsequent Gibbs-sampling steps within the COSMIC BIRTH algorithm. We find that going from the usual second to fourth order in the leap-frog scheme shortens the burn-in phase by a factor of at least ∼30. This implies that 75–90 independent samples are obtained while the fastest second-order method converges. After convergence, the correlation lengths indicate an improvement factor of about 3.0 fewer gradient computations for meshes of 2563 cells. In the considered cosmological scenario, the traditional leap-frog scheme turns out to outperform higher order integration schemes only when considering lower dimensional problems, e.g. meshes with 643 cells. This gain in computational efficiency can help to go towards a full Bayesian analysis of the cosmological large-scale structure for upcoming galaxy surveys.

scholarly journals Effect of the turning characteristics of underfloor wheel lathes on the evolution of wheel polygonisation

2018 ◽  
Vol 233 (5) ◽  
pp. 479-488 ◽  
Author(s):  
Dabin Cui ◽  
Boyang An ◽  
Paul Allen ◽  
Ruichen Wang ◽  
Ping Wang ◽  
...  
Keyword(s):  
Fourth Order ◽  
High Speed ◽  
Higher Order ◽  
Ride Quality ◽  
Sustained Use ◽  
High Speed Trains ◽  
Cut Quality ◽  
Multiple Unit ◽  
Component Failures

During both running and wheel cut operations, wheels of railway vehicles and the friction rollers that support and drive the wheelset on a typical wheel cut lathe are subject to wear and hence are likely to develop out-of-round characteristics after sustained use. The resulting out-of-round wheels can significantly affect the ride quality and can potentially increase the incidence of fatigue-related component failures due to the resulting higher intensity loading cycles. Furthermore, the corresponding out-of-round characteristics of the lathe's friction rollers will continue to degrade the subsequent cut quality of wheels. For the analysis of the out-of-round characteristics caused by an underfloor wheel lathe used for the high-speed trains in China, a mathematical model based on a typical electric multiple unit (EMU) vehicle's wheelsets and their interactions with the wheel lathe friction rollers was established. Factors influencing the cut quality of the wheels, including the number of cuts, eccentricity forms of the friction rollers and the longitudinal spacing of the two rollers, have been analysed. The results show that two cuts can effectively remove the higher order polygon on the wheel surface. The eccentricity and phase angle of the friction rollers have no influence on the cut quality of higher order polygons, whereas they are the primary cause for the fourth-order polygons. The severity of the fourth-order polygon depends on the level and the phase of the eccentricity of the friction rollers. The space of the two rollers can also significantly affect the cut quality. Obtaining the theoretical and practical value for the maintenance of polygonised wheels using the underfloor lathe is the main outcome of this study.

Linking transformational leadership and “multi-dimensions” of project success

2019 ◽  
Vol 13 (1) ◽  
pp. 103-127 ◽  
Author(s):  
Umer Zaman ◽  
Shahid Nawaz ◽  
Sidra Tariq ◽  
Asad Afzal Humayoun
Keyword(s):  
Transformational Leadership ◽  
Structural Equation ◽  
Structural Model ◽  
Project Success ◽  
Higher Order ◽  
Project Managers ◽  
Second Order ◽  
Equation Modeling ◽  
Content Type ◽  
The Relationship

Purpose Transformational leadership, flexibility and visibility improves project responsiveness to highly unpredictable and impactful events referred as the ‘black swans’ in mega projects (Bloch et al., 2012; Raziq et al., 2018; Zailani et al., 2016). However, these concepts have never been empirically tested in a single framework to determine their significant impact on multi-dimensional project success. The purpose of this paper is to investigate the interactional effects of project flexibility and project visibility on the relationship between transformational leadership and “multi-dimensions” of project success including meeting design goals; impact on customers and benefits to project-based organization. Design/methodology/approach Empirical data derived from cross-sectional survey of 160 project managers from telecom intensive companies in Pakistan were used to test the conceptual framework developed from recent literature. Partial least squares-structural equation modeling (PLS-SEM) provided detailed analysis of the measurement and structural model. The most recent reflective–formative PLS-SEM approach for higher-order constructs has been introduced. Findings The results indicate that project managers’ transformational leadership (β = 0.348, p < 0.01), project flexibility (β = 0.221, p < 0.01) and project visibility (β = 0.366, p < 0.01) are positively related with the multi-dimensional project success (second-order formative) construct. Interestingly, the relationship between transformational leadership and project success is influenced by significantly negative moderations established through project flexibility (β = −0.100, p < 0.01) and project visibility (β = −0.093, p < 0.05). Research limitations/implications This study in the telecom sector examined the interactional effects of risk mitigating strategies (i.e. project flexibility and project visibility) on the relationship between transformational leadership and multi-dimensional project success. This study creates a basis for future investigations extending to various project types and relevant to different industries especially those involving higher-order (formative) assessments of project success. Practical implications The study findings assist project leaders to meet their escalating commitments in achieving project success from a multi-dimensional standpoint. Additionally, this study underscores a renewed perspective of transformational leadership and project outcomes. Despite prevailing understanding developed through prior research, transformational leadership may become less favorable for project success in conditions of increased flexibility and visibility in projects. Originality/value Earlier studies have overlooked the multi-dimensional nature of project success (second-order formative) construct, despite several attempts to examine the interplay between transformational leadership and project success. Based on the knowledge gap and non-existence of empirical evidence, the authors introduced and empirically tested the moderating role of project flexibility and project visibility in the relationship between transformational leadership and multi-dimensional project success.

scholarly journals Scale-invariant scalar spectrum from the nonminimal derivative coupling with fourth-order term

2015 ◽  
Vol 24 (14) ◽  
pp. 1550095 ◽  
Author(s):  
Yun Soo Myung ◽  
Taeyoon Moon
Keyword(s):  
Fourth Order ◽  
Order Term ◽  
Order Derivative ◽  
Scalar Perturbation ◽  
De Sitter ◽  
Scale Invariant ◽  
Derivative Coupling ◽  
Sitter Spacetime ◽  
Fourth Order Term ◽  
Derivative Term

In this paper, an exactly scale-invariant spectrum of scalar perturbation generated during de Sitter spacetime is found from the gravity model of the nonminimal derivative coupling with fourth-order term. The nonminimal derivative coupling term generates a healthy (ghost-free) fourth-order derivative term, while the fourth-order term provides an unhealthy (ghost) fourth-order derivative term. The Harrison–Zel’dovich spectrum obtained from Fourier transforming the fourth-order propagator in de Sitter space is recovered by computing the power spectrum in its momentum space directly. It shows that this model provides a truly scale-invariant spectrum, in addition to the Lee–Wick scalar theory.

scholarly journals GAUGED LIFSHITZ MODEL WITH CHERN–SIMONS TERM

2013 ◽  
Vol 28 (09) ◽  
pp. 1350025 ◽  
Author(s):  
GUSTAVO S. LOZANO ◽  
FIDEL A. SCHAPOSNIK ◽  
GIANNI TALLARITA
Keyword(s):  
Fourth Order ◽  
Order Term ◽  
Equations Of Motion ◽  
Nontrivial Solutions ◽  
Oscillatory Solutions ◽  
Modulated Phases ◽  
Fourth Order Term ◽  
Spatial Derivatives ◽  
Chern Simons ◽  
Derivatives Of

We present a gauged Lifshitz Lagrangian including second- and fourth-order spatial derivatives of the scalar field and a Chern–Simons term, and study nontrivial solutions of the classical equations of motion. While the coefficient β of the fourth-order term should be positive in order to guarantee positivity of the energy, the coefficient α of the quadratic one need not be. We investigate the parameter domains and find significant differences in the field behaviors. Apart from the usual vortex field behavior of the ordinary relativistic Chern–Simons–Higgs model, we find in certain parameter domains oscillatory solutions reminiscent of the modulated phases of Lifshitz systems.

Higher-Order Experimental Haptic Force Models of Mechanical Devices Using Moving Ridge Regression

2008 ◽  
Author(s):  
Mark A. Judd ◽  
Mark B. Colton
Keyword(s):  
Ridge Regression ◽  
Goodness Of Fit ◽  
Higher Order ◽  
Higher Order Terms ◽  
Haptic Simulations ◽  
Nonlinear Static ◽  
Mechanical Devices ◽  
Complex Mechanical Systems ◽  
Locally Linear

Accurate modeling of physical devices is one of the keys to improving the realism of haptic simulations. This paper presents general, locally linear haptic force models to describe the feel of complex mechanical systems that exhibit nonlinear static and dynamic behavior. The parameters of these models are estimated from experimental data using moving ridge regression. Nonlinear variations of the locally linear model are presented and analyzed, and the goodness-of-fit of these models is compared. Initial results suggest that higher-order terms do little to improve the quality of this class of haptic models, and that reduced-order models should be further investigated.

Accurate Description of Near-Crack-Tip Fields for the Estimation of Inelastic Zone Extent in Quasi-Brittle Materials

2012 ◽  
Vol 525-526 ◽  
pp. 529-532 ◽  
Author(s):  
Václav Veselý ◽  
Jakub Sobek ◽  
Lucie Šestáková ◽  
Stanislav Seitl
Keyword(s):  
Finite Element ◽  
Order Term ◽  
Higher Order ◽  
Fe Analysis ◽  
Displacement Fields ◽  
Deterministic Method ◽  
Stress And Displacement Fields ◽  
Higher Order Terms ◽  
Higher Order Term ◽  
Selection Of

A description of stress and displacement fields by means of the Williams power series using also higher-order terms is the focus of this paper. Coefficients of this series are determined via the over-deterministic method from the results of conventional finite element (FE) analysis. A study is conducted into the selection of the FE node set whose results are processed in this regression technique. Coefficients up to the twelfth term were determined with high precision. The effect of the position of the FE node set on the accuracy of the values of the higher-order term coefficients is reported.

THE NAMBU-JONA-LASINIO SOLITON WITH GENERALIZED SCALAR INTERACTIONS

1993 ◽  
Vol 08 (01) ◽  
pp. 79-88 ◽  
Author(s):  
C. WEISS ◽  
R. ALKOFER ◽  
H. WEIGEL
Keyword(s):  
Fourth Order ◽  
Scalar Meson ◽  
Order Term ◽  
Soliton Solutions ◽  
Meson Field ◽  
Scale Invariant ◽  
Scalar Glueball ◽  
Fourth Order Term ◽  
Scalar Meson Field

Soliton solutions are studied as a generalization of the bosonized Nambu-Jona-Lasinio model with a fourth order term in the scalar meson field. Such an interaction arises in the context of a scale-invariant modification of the Nambu-Jona-Lasinio action, in which the scalar meson field is coupled to a scalar glueball field. It is shown that a fourth order term in the scalar meson field is crucial for the existence of stable solitons. We investigate the dependence of soliton properties on the scalar-glueball coupling.

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