Angle-domain common-image gathers from anisotropic migration

Geophysics ◽  
2007 ◽  
Vol 72 (2) ◽  
pp. S81-S91 ◽  
Author(s):  
Biondo Biondi
Keyword(s):  
Complex I ◽  
Theoretical Development ◽  
Isotropic Case ◽  
Data Set ◽  
Practical Applications ◽  
Wavefield Continuation ◽  
The Difference ◽  
Contrast Group ◽  
Vti Media ◽  
The Relationship

I present a general methodology for computing angle-domain common-image gathers (ADCIGs) in conjunction with anisotropic wavefield-continuation migration. The method is based on transforming the prestack image from the subsurface-offset domain to the angle domain using slant stacks. The processing sequence is the same as that for computing ADCIGs for the isotropic case, though the interpretation of the relationship between the slopes measured in the prestack image and the aperture angles is more complex. I demonstrate that the slopes measured by performing slant stacks along the subsurface-offset axis of the prestack image provide a good approximation of the phase aperture angles, and they are exactly equal to the phase aperture angles for flat reflectors in vertical transversly isotropic (VTI) media. In the general case of dipping reflectors, the angles computed using slant stacks can be easily corrected by applying the relationships that I present in this paper, and the accurate aperture angles can be determined as a function of the reflector dip and anisotropic slowness at the reflector. I derive these relationships from both plane-wave and ray viewpoints. This theoretical development links the kinematics in ADCIGs with migration-velocity errors. I apply the proposed method to compute ADCIGs from the prestack image obtained by anisotropic migration of a 2D line recorded in the Gulf of Mexico. I analyze the error introduced by neglecting the difference between the true phase aperture angle and the angle computed through slant stacks, showing that, at least for this data set, these errors are negligible and can be safely ignored. In contrast, group aperture angles can be quite different from phase aperture angles; thus, ignoring the distinction between these two angles can be detrimental to practical applications.

Calculation of Non-Homogeneous Anisotropic Rectangular Plates with Arbitrary Fixation on the Contur

2019 ◽  
Vol 968 ◽  
pp. 444-449
Author(s):  
Nikolay Zavrak
Keyword(s):  
Main Idea ◽  
Isotropic Case ◽  
Rectangular Plates ◽  
Orthotropic Plates ◽  
Anisotropic Plates ◽  
Practical Applications ◽  
Internal Forces ◽  
The Relationship ◽  
Difficult Cases ◽  
Anisotropic Rectangular Plates

The developing of the effective methodic of elastic orthotropic plates’ calculation and the research on the base of their state under different boundary conditions are of great importance nowadays. The representation of the received results in the form, convenient for practical use, is also important. For practical applications in engineering are important tables for determining deflections and internal forces of structures. Such tables for the isotropic case under various conditions of plate support on the contour are given in many works. As for the anisotropic plates, there are no such tables, with the exception of one Huber table compiled for a freely supported rectangular orthotropic plate, depending on the relationship between the stiffness values. Here is a method of calculating the non-homogeneous anisotropic rectangular plates with arbitrary fixation on the contour is set forth, which is reduced to a boundary value problem. The main idea of a calculated general methodic of linear marginal differential tasks calculation is based on underlying of the main part of a solution. Such approach is proved by means of development and some generalization of common positions of a variational method of marginal tasks of mathematical physics of self-conjugated tasks solution. To solve a system of equations in terms of displacements using finite difference method (FDM) in combination with different variations of analytical solutions. It is advisable to construct a numerical solution of the problem so that in difficult cases the support fixing and uploading solution sought, not directly, but in the form of amendments to the known solution for simple cases of reference to consolidate and uploading at finding the solutions which the analytical methods or the FDM with sparse mesh may be used. Given as examples are the results of calculation for a series of square orthotropic plates with a fixed boundary under the action of uniformly distributed load.

Residual moveout in anisotropic angle-domain common-image gathers

Geophysics ◽  
2007 ◽  
Vol 72 (2) ◽  
pp. S93-S103 ◽  
Author(s):  
Biondo Biondi
Keyword(s):  
Real Data ◽  
Velocity Estimation ◽  
Aperture Angle ◽  
Data Set ◽  
3D Data ◽  
Wavefield Continuation ◽  
Transverse Isotropic ◽  
Phase Angles ◽  
The Relationship ◽  
General Method

I develop the fundamental concepts for quantitatively relating perturbations in anisotropic parameters to the corresponding reflector movements in angle-domain common-image gathers (ADCIGs) after anisotropic wavefield-continuation migration. The proposed theory potentially enables the application of residual moveout (RMO) analysis of ADCIGs to velocity estimation in realistic anisotropic conditions. I demonstrate that linearization of the relationship between anisotropic velocity parameters and reflector movements can be derived by assuming stationary raypaths. This assumption leads to a fairly simple analytical derivation. I then apply the general method to the particular case of RMO analysis of reflections from flat reflectors in a vertical transverse isotropic (VTI) medium. This analysis yields expressions to predict RMO curves in migrated ADCIGs. These RMO expressions are functions of both the phase aperture angle and the group aperture angle. Several numerical examples demonstrate the accuracy of the RMO curves predicted by my kinematic analysis. The synthetic examples also show that approximating the group angles with the phase angles in the application of the RMO expressions may lead to substantial errors for events reflected at wide aperture angles. The results obtained by migrating a 2D line extracted from a Gulf of Mexico 3D data set confirm the accuracy of the proposed method. The RMO curves predicted by the theory match the RMO function observed in the ADCIGs computed from the real data.

Nominal Reference

2018 ◽  
Author(s):  
Donka Farkas
Keyword(s):  
Philosophy Of Language ◽  
Theoretical Development ◽  
Philosophical Investigations ◽  
Fine Grained ◽  
Pronominal Reference ◽  
Bare Nouns ◽  
Nominal Reference ◽  
The Difference ◽  
The Relationship ◽  
Theoretical Side

Nominal reference is central to both linguistic semantics and philosophy of language. On the theoretical side, both philosophers and linguists wrestle with the problem of how the link between nominal expressions and their referents is to be characterized, and what formal tools are most appropriate to deal with this issue. The problem is complex because nominal expression come in a large variety of forms, from simple proper names, pronouns, or bare nouns (Jennifer, they, books) to complex expressions involving determiners and various quantifiers (the/every/no/their answer). While the reference of such expressions is varied, their basic syntactic distribution as subjects or objects of various types, for instance, is homogeneous. Important advances in understanding this tension were made with the advent of the work of R. Montague and that of his successors. The problems involved in understanding the relationship between pronouns and their antecedents in discourse have led to another fundamental theoretical development, namely that of dynamic semantics. On the empirical side, issues at the center of both linguistic and philosophical investigations concern how to best characterize the difference between definite and indefinite nominals, and, more generally, how to understand the large variety of determiner types found both within a language and cross-linguistically. These considerations led to refining the definite/indefinite contrast to include fine-grained specificity distinctions that have been shown to be relevant to various morphosyntactic phenomena across the world’s languages. Considerations concerning nominal reference are thus relevant not only to semantics but also to morphology and syntax. Some questions within the domain of nominal reference have grown into rich subfields of inquiry. This is the case with generic reference, the study of pronominal reference, the study of quantifiers, and the study of the semantics of nominal number marking.

Mind the Gaps: How Organization Design Shapes the Sourcing of Inventions

2021 ◽  
Author(s):  
John Eklund ◽  
Rahul Kapoor
Keyword(s):  
New Products ◽  
Organization Design ◽  
Knowledge Flows ◽  
Managerial Decision ◽  
Data Set ◽  
Managerial Decision Making ◽  
Knowledge Based ◽  
It Impacts ◽  
The Difference ◽  
The Relationship

An important problem for many firms is sustaining their rate of innovation by launching new products on an ongoing basis. Accordingly, firms need to replenish their innovation pipelines with new inventions as existing inventions are weeded out or reach fruition. The replenishment can be done through internally generated inventions or through externally sourced inventions via licensing, alliance, or acquisition modes. Drawing on incentives- and knowledge-based views of the firm, we consider the difference in managerial decision making between centralized and decentralized research and development (R&D) organization designs and how it impacts firms’ propensities to draw on externally sourced inventions. As compared with centralized designs, decentralized designs are associated with greater incentives for managers to replenish their firms’ pipelines but are limited in terms of intraorganizational knowledge flows that can facilitate the creation of inventions. We explore these mechanisms using a novel data set of firms’ sourcing decisions within the pharmaceutical industry between 1996 and 2015. We find that firms with decentralized R&D designs replenish their pipelines with a higher proportion of externally sourced inventions than do firms with centralized designs. This difference is found to be mainly attributed to external sourcing via licensing and for inventions of moderate novelty. This study offers an important contribution to the question of how firms organize for innovation, highlighting the relationship between internal R&D organization design and the external sourcing of inventions. In so doing, it illustrates that the choice of organization design in terms of centralization or decentralization can shape a firm’s locus of innovation.

scholarly journals Application of time-lapse ERT imaging to watershed characterization

Geophysics ◽  
2008 ◽  
Vol 73 (3) ◽  
pp. G7-G17 ◽  
Author(s):  
Carlyle R. Miller ◽  
Partha S. Routh ◽  
Troy R. Brosten ◽  
James P. McNamara
Keyword(s):  
Reference Model ◽  
Time Lapse ◽  
Data Sets ◽  
Data Set ◽  
Resistivity Tomography ◽  
Practical Applications ◽  
Data Inversion ◽  
Time Periods ◽  
The Difference ◽  
Base Data

Time-lapse electrical resistivity tomography (ERT) has many practical applications to the study of subsurface properties and processes. When inverting time-lapse ERT data, it is useful to proceed beyond straightforward inversion of data differences and take advantage of the time-lapse nature of the data. We assess various approaches for inverting and interpreting time-lapse ERT data and determine that two approaches work well. The first approach is model subtraction after separate inversion of the data from two time periods, and the second approach is to use the inverted model from a base data set as the reference model or prior information for subsequent time periods. We prefer this second approach. Data inversion methodology should be consideredwhen designing data acquisition; i.e., to utilize the second approach, it is important to collect one or more data sets for which the bulk of the subsurface is in a background or relatively unperturbed state. A third and commonly used approach to time-lapse inversion, inverting the difference between two data sets, localizes the regions of the model in which change has occurred; however, varying noise levels between the two data sets can be problematic. To further assess the various time-lapse inversion approaches, we acquired field data from a catchment within the Dry Creek Experimental Watershed near Boise, Idaho, U.S.A. We combined the complimentary information from individual static ERT inversions, time-lapse ERT images, and available hydrologic data in a robust interpretation scheme to aid in quantifying seasonal variations in subsurface moisture content.

scholarly journals Relationship among Continuous Probability Distributions and Interpolation

2021 ◽  
pp. 196-210
Author(s):  
Kelachi P. Enwere ◽  
Uchenna P. Ogoke
Keyword(s):  
Probability Distribution ◽  
Probability Distributions ◽  
Linear Interpolation ◽  
Data Set ◽  
Statistical Probability ◽  
Practical Applications ◽  
Gamma Distributions ◽  
Chi Squared ◽  
Interpolation Techniques ◽  
The Difference

Aims: The Study seeks to determine the relationship that exists among Continuous Probability Distributions and the use of Interpolation Techniques to estimate unavailable but desired value of a given probability distribution. Study Design: Statistical Probability tables for Normal, Student t, Chi-squared, F and Gamma distributions were used to compare interpolated values with statistical tabulated values. Charts and Tables were used to represent the relationships among the five probability distributions. Methodology: Linear Interpolation Technique was employed to interpolate unavailable but desired values so as to obtain approximate values from the statistical tables. The data were analyzed for interpolation of unavailable but desired values at 95% a-level from the five continuous probability distribution. Results: Interpolated values are as close as possible to the exact values and the difference between the exact value and the interpolated value is not pronounced. The table and chart established showed that relationships do exist among the Normal, Student-t, Chi-squared, F and Gamma distributions. Conclusion: Interpolation techniques can be applied to obtain unavailable but desired information in a data set. Thus, uncertainty found in a data set can be discovered, then analyzed and interpreted to produce desired results. However, understanding of how these probability distributions are related to each other can inform how best these distributions can be used interchangeably by Statisticians and other Researchers who apply statistical methods employed in practical applications.

Difference Formulation and Slope Invariance in Spatially Varied Free Surface Flow

Volume 1 ◽  
2004 ◽  
Author(s):  
S. David Graber
Keyword(s):  
Free Surface ◽  
Pipe Flow ◽  
Free Surface Flow ◽  
Surface Flow ◽  
Reference Source ◽  
Practical Applications ◽  
Physical Reasoning ◽  
Difference Form ◽  
The Difference ◽  
The Relationship

The relationship for combined increasing and decreasing free surface flow is presented in difference form, and then particularized to spatially increasing and spatially decreasing flows. For spatially decreasing flow, a theoretical difference is noted between the writer’s version and that in a widely-used reference source. By investigating an application for uniformly decreasing, full-pipe flow, it is shown by physical reasoning and comparison of an available analytical solution to the alternate versions of the difference relationship that the writer’s difference relationship is the correct one. Free surface spatially varied flow relationships are specialized to pressure conduits to demonstrate conditions of slope invariance, which has important and somewhat counter-intuitive ramifications for certain practical applications encountered in environmental engineering.

scholarly journals The relationship between VHF radar auroral backscatter amplitude and Doppler velocity: a statistical study

1996 ◽  
Vol 14 (8) ◽  
pp. 803-810 ◽  
Author(s):  
B. A. Shand ◽  
M. Lester ◽  
T. K. Yeoman
Keyword(s):  
Solar Cycle ◽  
Intensity Variation ◽  
Statistical Investigation ◽  
Doppler Velocity ◽  
Data Set ◽  
Vhf Radar ◽  
Backscatter Intensity ◽  
The Difference ◽  
Scattering Volume ◽  
The Relationship

Abstract. A statistical investigation of the relationship between VHF radar auroral backscatter intensity and Doppler velocity has been undertaken with data collected from 8 years operation of the Wick site of the Sweden And Britain Radar-auroral Experiment (SABRE). The results indicate three different regimes within the statistical data set; firstly, for Doppler velocities <200 m s–1, the backscatter intensity (measured in decibels) remains relatively constant. Secondly, a linear relationship is observed between the backscatter intensity (in decibels) and Doppler velocity for velocities between 200 m s–1 and 700 m s–1. At velocities greater than 700 m s–1 the backscatter intensity saturates at a maximum value as the Doppler velocity increases. There are three possible geophysical mechanisms for the saturation in the backscatter intensity at high phase speeds: a saturation in the irregularity turbulence level, a maximisation of the scattering volume, and a modification of the local ambient electron density. There is also a difference in the dependence of the backscatter intensity on Doppler velocity for the flow towards and away from the radar. The results for flow towards the radar exhibit a consistent relationship between backscatter intensity and measured velocities throughout the solar cycle. For flow away from the radar, however, the relationship between backscatter intensity and Doppler velocity varies during the solar cycle. The geometry of the SABRE system ensures that flow towards the radar is predominantly associated with the eastward electrojet, and flow away is associated with the westward electrojet. The difference in the backscatter intensity variation as a function of Doppler velocity is attributed to asymmetries between the eastward and westward electrojets and the geophysical parameters controlling the backscatter amplitude.

scholarly journals Testing the Difference between School Level and Academic Mindset in the Classroom: Implications for Developing Student Psycho-Social Skills in Secondary School Classrooms

2017 ◽  
Vol 3 (1) ◽  
pp. 44 ◽  
Author(s):  
Janet Hanson
Keyword(s):  
Research Question ◽  
Elementary Classrooms ◽  
School Level ◽  
Secondary Classrooms ◽  
Social Construct ◽  
Practical Applications ◽  
Construct Theory ◽  
History Of ◽  
The Difference ◽  
The Relationship

This study explored the relationship between school level and the psychosocial construct of an academic mindset operationalized on the Likert-style Project for Educational Research That Scales (PERTS) instrument; widely used in testing academic mindset interventions at the classroom level. Analyses were conducted using existing school district data collected during the month of April, 2016, delivered to students, grades 3 through 8, (n = 2,908) in the classroom at three elementary schools and two middles schools. The overarching research question was, “Is there a relationship between school level and students’ academic mindset as measured by the PERTS scale?” Results revealed a significant decrease in the classroom PERTS scale mean scores between elementary classrooms (n = 70) and secondary classrooms (n = 50). A history of psycho-social construct theory and practical applications for the classroom are provided.

scholarly journals Low-dose CBCT reconstruction via joint non-local total variation denoising and cubic B-spline interpolation

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Ho Lee ◽  
Jiyoung Park ◽  
Yeonho Choi ◽  
Kyung Ran Park ◽  
Byung Jun Min ◽  
...  
Keyword(s):  
Total Variation ◽  
Low Dose ◽  
Spline Interpolation ◽  
Reconstruction Algorithm ◽  
Step Size ◽  
Data Set ◽  
B Spline ◽  
Practical Applications ◽  
Non Local ◽  
The Difference

AbstractThis study develops an improved Feldkamp–Davis–Kress (FDK) reconstruction algorithm using non-local total variation (NLTV) denoising and a cubic B-spline interpolation-based backprojector to enhance the image quality of low-dose cone-beam computed tomography (CBCT). The NLTV objective function is minimized on all log-transformed projections using steepest gradient descent optimization with an adaptive control of the step size to augment the difference between a real structure and noise. The proposed algorithm was evaluated using a phantom data set acquired from a low-dose protocol with lower milliampere-seconds (mAs).The combination of NLTV minimization and cubic B-spline interpolation rendered the enhanced reconstruction images with significantly reduced noise compared to conventional FDK and local total variation with anisotropic penalty. The artifacts were remarkably suppressed in the reconstructed images. Quantitative analysis of reconstruction images using low-dose projections acquired from low mAs showed a contrast-to-noise ratio with spatial resolution comparable to images reconstructed using projections acquired from high mAs. The proposed approach produced the lowest RMSE and the highest correlation. These results indicate that the proposed algorithm enables application of the conventional FDK algorithm for low mAs image reconstruction in low-dose CBCT imaging, thereby eliminating the need for more computationally demanding algorithms. The substantial reductions in radiation exposure associated with the low mAs projection acquisition may facilitate wider practical applications of daily online CBCT imaging.

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