INTERVAL VELOCITIES FROM SURFACE MEASUREMENTS IN THE THREE‐DIMENSIONAL PLANE LAYER CASE

Geophysics ◽  
1976 ◽  
Vol 41 (2) ◽  
pp. 233-242 ◽  
Author(s):  
Peter Hubral
Keyword(s):  
Three Dimensional ◽  
Normal Incidence ◽  
Plane Layer ◽  
Three Dimensions ◽  
Seismic Parameters ◽  
Interval Velocity ◽  
Common Depth Point ◽  
Measured Time ◽  
Surface Measurements ◽  
Interval Velocities

The basic requirements to recover plane layers of constant interval velocity, arbitrary dip and strike from common depth point (CDP) recordings are the following four quantities related to the primary event of each reflector at the common midpoint of a CDP profile: a) Two‐way normal time b) Normal moveout velocity within one arbitrary CDP profile c) Time slope of normally reflected rays within the profile d) Time slope of normally reflected rays in some other direction. The solution of the inverse problem is obtained directly. The moveout velocity is expressed in terms of seismic parameters along the normal incidence path in three dimensions and the direction of the profile within the free surface. A formula connecting dip and strike of the emerging normal ray with the measured time gradients is given and discussed. The method includes, as a special case, the Dix formulas for plane parallel layers.

Inversion of reflection times in three dimensions

Geophysics ◽  
1981 ◽  
Vol 46 (7) ◽  
pp. 972-983 ◽  
Author(s):  
Håvar Gjøystdal ◽  
Bjørn Ursin
Keyword(s):  
Real Data ◽  
Normal Incidence ◽  
Thin Layers ◽  
Three Dimensions ◽  
Good Resolution ◽  
Inversion Algorithm ◽  
Linear Inversion ◽  
Seismic Reflection Data ◽  
Reflection Data ◽  
Interval Velocities

When reflection data are available from a grid of crossing seismic lines, it is possible to construct normal incidence time maps from interpreted stacked sections and then apply three‐dimensional (3-D) ray‐tracing techniques following the normal‐incidence raypaths down to the various reflectors. The main disadvantage of this well‐known “time map migration” procedure is that interval velocities must be known a priori, and they must be estimated in advance by some approximate method. A technique is presented here which combines the above procedure with an inversion algorithm, providing direct calculations of interval velocities from the additional use of nonzero offset traveltime observations. A generalized linear inversion scheme is used, making possible a complete calculation of interval velocities and reflection interfaces, the latter represented by bicubic spline functions. To test the method in practice, we have applied it to (1) synthetic data generated from a constructed model, and (2) real data obtained from marine seismic sections. In the latter case, velocities and reflector depths obtained were compared to those obtained directly from a well log in the area. These results show a reasonably good resolution for layers that are not too deep relative to the shot/receiver offsets used. For deep and/or thin layers, the results are not satisfactory. This indicates the general limitation of seismic reflection data to resolve interval velocity, even in the presence of horizontally layered structure.

Maximum uncertainty of interval velocity estimates

Geophysics ◽  
1981 ◽  
Vol 46 (11) ◽  
pp. 1543-1547 ◽  
Author(s):  
Z. Hajnal ◽  
I. T. Sereda
Keyword(s):  
Numerical Experiments ◽  
Normal Incidence ◽  
Mean Square ◽  
Order Error ◽  
First Order ◽  
Interval Velocity ◽  
Number Of Factors ◽  
Time Variables ◽  
Interval Velocities ◽  
Time Information

The Dix equation (Dix, 1955) is commonly used to estimate interval velocities from stacking velocity and travel‐time information. The errors in these estimates can result from a number of factors, including indiscriminate substitution of stacking velocities for root‐mean‐square (rms] velocities without compensating for the effects of spread‐length or dipping reflectors. A first‐order error equation has been developed which estimates the maximum uncertainty for Dix‐derived interval velocities when the accuracy of the input rms velocity and normal incidence time information is considered. Some simple numerical experiments using this equation indicate that the uncertainty in the calculated interval velocity increases with depth and is inversely proportional to layer thickness, even when the errors in the input velocity and time variables remain constant.

SEISMOGEOLOGIC EXPERIENCE IN THE BEAUFORT SEA

Geophysics ◽  
1972 ◽  
Vol 37 (4) ◽  
pp. 605-619 ◽  
Author(s):  
H. Hofer ◽  
W. Varga
Keyword(s):  
Common Ground ◽  
Beaufort Sea ◽  
Primary Energy ◽  
Velocity Control ◽  
Seismic Section ◽  
Interval Velocity ◽  
Common Depth Point ◽  
Analysis Package ◽  
Interval Velocities ◽  
Criterion Interval

Conventional seismic data processing was applied to 24‐fold airgun data acquired in the Liverpool and Mackenzie Bay areas of the Beaufort Sea. These data provided general indications of the regional geology and the types of structures present. A part of one line in each area was chosen on the basis of its geologic content and data quality for reprocessing through a velocity analysis package. The purpose was to establish velocity, particularly interval velocity, as the common ground between geology and the seismic section. The velocity package performs a continuous analysis for time and moveout as well as amplitude on all events present within a common‐depth‐point gather. Events are joined from depth point to depth point on the basis of similarity in time, moveout, amplitude, and polarity to yield a segment file. This file is statistically analyzed and sorted into two subsets, primary and nonprimary files, using segment velocity as the criterion. Interval velocities can be calculated between those segments that exhibit velocities characteristic of primary energy. The space‐variant velocity control derived from the data was used to correct it for moveout. A marked improvement in the interpretability of the data resulted on both lines. The data‐derived interval velocities give intriguing indications of lithology which can be correlated to acoustic logs on shore. Plausible hypotheses of offshore geology have been derived without the benefit of any offshore drilling.

On reconstruction of three-dimensional harmonic functions from discrete data

2010 ◽  
Vol 466 (2119) ◽  
pp. 1935-1955 ◽  
Author(s):  
A. N. Galybin ◽  
J. Irša
Keyword(s):  
Harmonic Functions ◽  
Three Dimensional ◽  
Three Dimensions ◽  
Data Types ◽  
Trefftz Method ◽  
Surface Measurements ◽  
Ill Posed ◽  
Element Type ◽  
Inverse Boundary Value Problems ◽  
Steady Heat Conduction

This study presents an approach for reconstruction of harmonic functions in three dimensions from the finite number of field and surface measurements. The approach, based on the Trefftz method, performs reconstruction as the best fit to the data and provides smoothness of the reconstructed function. Two particular algorithms are proposed; the first one uses specific radial basis functions and the second one is of finite element type. Either of them can be applied to analyse different data types but the latter can handle larger problems. The data types considered in this study also cover direct and inverse boundary value problems. Therefore, the proposed approach is universal and capable of dealing with both well-posed and ill-posed formulations. Examples from steady heat conduction and elastostatics are examined in order to investigate the efficiency of the approach.

convergent-beam diffraction from surfaces

1987 ◽  
Vol 45 ◽  
pp. 30-33
Author(s):  
J. A. Eades ◽  
A. E. Smith ◽  
D. F. Lynch
Keyword(s):  
Reciprocal Lattice ◽  
Three Dimensional ◽  
Grazing Incidence ◽  
Three Dimensions ◽  
Plane Figure ◽  
Transmission Electron ◽  
Convergent Beam ◽  
Beam Patterns ◽  
Beam Diffraction

It is quite simple (in the transmission electron microscope) to obtain convergent-beam patterns from the surface of a bulk crystal. The beam is focussed onto the surface at near grazing incidence (figure 1) and if the surface is flat the appropriate pattern is obtained in the diffraction plane (figure 2). Such patterns are potentially valuable for the characterization of surfaces just as normal convergent-beam patterns are valuable for the characterization of crystals.There are, however, several important ways in which reflection diffraction from surfaces differs from the more familiar electron diffraction in transmission.GeometryIn reflection diffraction, because of the surface, it is not possible to describe the specimen as periodic in three dimensions, nor is it possible to associate diffraction with a conventional three-dimensional reciprocal lattice.

Extension of the Spatial PDI Model to Three Dimensions

1997 ◽  
Vol 84 (1) ◽  
pp. 176-178
Author(s):  
Frank O'Brien
Keyword(s):  
Population Density ◽  
Dimensional Space ◽  
Finite Lattice ◽  
Three Dimensional ◽  
Upper Bounds ◽  
Three Dimensions ◽  
Lower And Upper Bounds ◽  
Density Index ◽  
Three Dimensional Space

The author's population density index ( PDI) model is extended to three-dimensional distributions. A derived formula is presented that allows for the calculation of the lower and upper bounds of density in three-dimensional space for any finite lattice.

scholarly journals Free partition functions and an averaged holographic duality

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Nima Afkhami-Jeddi ◽  
Henry Cohn ◽  
Thomas Hartman ◽  
Amirhossein Tajdini
Keyword(s):  
Partition Function ◽  
Spectral Gap ◽  
Central Charge ◽  
Three Dimensional ◽  
Two Dimensions ◽  
Three Dimensions ◽  
Partition Functions ◽  
General Constraints ◽  
Dimensional Gravity ◽  
Holographic Duality

Abstract We study the torus partition functions of free bosonic CFTs in two dimensions. Integrating over Narain moduli defines an ensemble-averaged free CFT. We calculate the averaged partition function and show that it can be reinterpreted as a sum over topologies in three dimensions. This result leads us to conjecture that an averaged free CFT in two dimensions is holographically dual to an exotic theory of three-dimensional gravity with U(1)c×U(1)c symmetry and a composite boundary graviton. Additionally, for small central charge c, we obtain general constraints on the spectral gap of free CFTs using the spinning modular bootstrap, construct examples of Narain compactifications with a large gap, and find an analytic bootstrap functional corresponding to a single self-dual boson.

Turbulent three-dimensional dielectric electrohydrodynamic convection between two plates

2012 ◽  
Vol 696 ◽  
pp. 228-262 ◽  
Author(s):  
A. Kourmatzis ◽  
J. S. Shrimpton
Keyword(s):  
Spatial Data ◽  
Three Dimensional ◽  
Reynolds Numbers ◽  
Two Dimensions ◽  
Three Dimensions ◽  
Energy Budgets ◽  
Turbulent Regime ◽  
Scalar Flux ◽  
Wide Range ◽  
Scalar Variance

AbstractThe fundamental mechanisms responsible for the creation of electrohydrodynamically driven roll structures in free electroconvection between two plates are analysed with reference to traditional Rayleigh–Bénard convection (RBC). Previously available knowledge limited to two dimensions is extended to three-dimensions, and a wide range of electric Reynolds numbers is analysed, extending into a fully inherently three-dimensional turbulent regime. Results reveal that structures appearing in three-dimensional electrohydrodynamics (EHD) are similar to those observed for RBC, and while two-dimensional EHD results bear some similarities with the three-dimensional results there are distinct differences. Analysis of two-point correlations and integral length scales show that full three-dimensional electroconvection is more chaotic than in two dimensions and this is also noted by qualitatively observing the roll structures that arise for both low (${\mathit{Re}}_{E} = 1$) and high electric Reynolds numbers (up to ${\mathit{Re}}_{E} = 120$). Furthermore, calculations of mean profiles and second-order moments along with energy budgets and spectra have examined the validity of neglecting the fluctuating electric field ${ E}_{i}^{\ensuremath{\prime} } $ in the Reynolds-averaged EHD equations and provide insight into the generation and transport mechanisms of turbulent EHD. Spectral and spatial data clearly indicate how fluctuating energy is transferred from electrical to hydrodynamic forms, on moving through the domain away from the charging electrode. It is shown that ${ E}_{i}^{\ensuremath{\prime} } $ is not negligible close to the walls and terms acting as sources and sinks in the turbulent kinetic energy, turbulent scalar flux and turbulent scalar variance equations are examined. Profiles of hydrodynamic terms in the budgets resemble those in the literature for RBC; however there are terms specific to EHD that are significant, indicating that the transfer of energy in EHD is also attributed to further electrodynamic terms and a strong coupling exists between the charge flux and variance, due to the ionic drift term.

scholarly journals The Everyday Life of Security: Capturing Space, Practice, and Affect

2021 ◽  
Author(s):  
Jonna Nyman
Keyword(s):  
Everyday Life ◽  
Research Methods ◽  
Lived Experiences ◽  
Three Dimensional ◽  
Three Dimensions ◽  
Conceptual Clarity ◽  
The Everyday ◽  
Participatory Photography ◽  
High Politics ◽  
Ordinary Citizens

Abstract Security shapes everyday life, but despite a growing literature on everyday security there is no consensus on the meaning of the “everyday.” At the same time, the research methods that dominate the field are designed to study elites and high politics. This paper does two things. First, it brings together and synthesizes the existing literature on everyday security to argue that we should think about the everyday life of security as constituted across three dimensions: space, practice, and affect. Thus, the paper adds conceptual clarity, demonstrating that the everyday life of security is multifaceted and exists in mundane spaces, routine practices, and affective/lived experiences. Second, it works through the methodological implications of a three-dimensional understanding of everyday security. In order to capture all three dimensions and the ways in which they interact, we need to explore different methods. The paper offers one such method, exploring the everyday life of security in contemporary China through a participatory photography project with six ordinary citizens in Beijing. The central contribution of the paper is capturing—conceptually and methodologically—all three dimensions, in order to develop our understanding of the everyday life of security.

scholarly journals Topological correlators and surface defects from equivariant cohomology

2020 ◽  
Vol 2020 (9) ◽  
Author(s):  
Rodolfo Panerai ◽  
Antonio Pittelli ◽  
Konstantina Polydorou
Keyword(s):  
Quantum Mechanics ◽  
Equivariant Cohomology ◽  
Surface Defects ◽  
Star Product ◽  
Three Dimensional ◽  
Three Dimensions ◽  
Dimensional System ◽  
The Novel ◽  
One Dimensional ◽  
Dual Quantum

Abstract We find a one-dimensional protected subsector of $$ \mathcal{N} $$ N = 4 matter theories on a general class of three-dimensional manifolds. By means of equivariant localization we identify a dual quantum mechanics computing BPS correlators of the original model in three dimensions. Specifically, applying the Atiyah-Bott-Berline-Vergne formula to the original action demonstrates that this localizes on a one-dimensional action with support on the fixed-point submanifold of suitable isometries. We first show that our approach reproduces previous results obtained on S3. Then, we apply it to the novel case of S2× S1 and show that the theory localizes on two noninteracting quantum mechanics with disjoint support. We prove that the BPS operators of such models are naturally associated with a noncom- mutative star product, while their correlation functions are essentially topological. Finally, we couple the three-dimensional theory to general $$ \mathcal{N} $$ N = (2, 2) surface defects and extend the localization computation to capture the full partition function and BPS correlators of the mixed-dimensional system.

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