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.

scholarly journals Spatial pattern and genetic diversity estimates are linked in stochastic models of population differentiation

2000 ◽  
Vol 23 (3) ◽  
pp. 541-544 ◽  
Author(s):  
José Alexandre Felizola Diniz-Filho ◽  
Mariana Pires de Campos Telles
Keyword(s):  
Genetic Diversity ◽  
Spatial Pattern ◽  
Stochastic Models ◽  
Population Differentiation ◽  
Real Data ◽  
Population Heterogeneity ◽  
Data Set ◽  
Mantel’S Test ◽  
The Relationship ◽  
Diversity Estimates

In the present study, we used both simulations and real data set analyses to show that, under stochastic processes of population differentiation, the concepts of spatial heterogeneity and spatial pattern overlap. In these processes, the proportion of variation among and within a population (measured by G ST and 1 - G ST, respectively) is correlated with the slope and intercept of a Mantel's test relating genetic and geographic distances. Beyond the conceptual interest, the inspection of the relationship between population heterogeneity and spatial pattern can be used to test departures from stochasticity in the study of population differentiation.

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.

scholarly journals A theory for non-linear prediction approach in the presence of vague variables: with application to BMI monitoring

2015 ◽  
Vol 3 (1) ◽  
Author(s):  
R. Pourmousa ◽  
M. Rezapour ◽  
M. Mashinchi
Keyword(s):  
Linear Prediction ◽  
Real Data ◽  
Continuous Data ◽  
Data Set ◽  
Truncated Data ◽  
Fault Inference ◽  
Prediction Approach ◽  
The Relationship ◽  
Threshold Point ◽  
Error Of Measurement

AbstractIn the statistical literature, truncated distributions can be used for modeling real data. Due to error of measurement in truncated continuous data, choosing a crisp trimmed point caucuses a fault inference, so using fuzzy sets to define a threshold pointmay leads us more efficient results with respect to crisp thresholds. Arellano-Valle et al. [2] defined a selection distribution for analysis of truncated data with crisp threshold. In this paper, we define fuzzy multivariate selection distribution that is an extension of the selection distributions using fuzzy threshold. A practical data set with a fuzzy threshold point is considered to investigate the relationship between high blood pressure and BMI.

Angle‐domain common‐image gathers for migration velocity analysis by wavefield‐continuation imaging

Geophysics ◽  
2004 ◽  
Vol 69 (5) ◽  
pp. 1283-1298 ◽  
Author(s):  
Biondo Biondi ◽  
William W. Symes
Keyword(s):  
Synthetic Data ◽  
Real Data ◽  
Migration Velocity ◽  
Image Point ◽  
Velocity Analysis ◽  
Data Set ◽  
The North ◽  
Migration Velocity Analysis ◽  
Wide Range ◽  
Wavefield Continuation

We analyze the kinematic properties of offset‐domain common image gathers (CIGs) and angle‐domain CIGs (ADCIGs) computed by wavefield‐continuation migration. Our results are valid regardless of whether the CIGs were obtained by using the correct migration velocity. They thus can be used as a theoretical basis for developing migration velocity analysis (MVA) methods that exploit the velocity information contained in ADCIGs. We demonstrate that in an ADCIG cube, the image point lies on the normal to the apparent reflector dip that passes through the point where the source ray intersects the receiver ray. The image‐point position on the normal depends on the velocity error; when the velocity is correct, the image point coincides with the point where the source ray intersects the receiver ray. Starting from this geometric result, we derive an analytical expression for the expected movements of the image points in ADCIGs as functions of the traveltime perturbation caused by velocity errors. By applying this analytical result and assuming stationary raypaths (i.e., small velocity errors), we then derive two expressions for the residual moveout (RMO) function in ADCIGs. We verify our theoretical results and test the accuracy of the proposed RMO functions by analyzing the migration results of a synthetic data set with a wide range of reflector dips. Our kinematic analysis leads also to the development of a new method for computing ADCIGs when significant geological dips cause strong artifacts in the ADCIGs computed by conventional methods. The proposed method is based on the computation of offset‐domain CIGs along the vertical‐offset axis and on the “optimal” combination of these new CIGs with conventional CIGs. We demonstrate the need for and the advantages of the proposed method on a real data set acquired in the North Sea.

Automatic nonhyperbolic velocity analysis by polynomial chaos expansion

Geophysics ◽  
2018 ◽  
Vol 83 (6) ◽  
pp. U79-U88 ◽  
Author(s):  
Mostafa Abbasi ◽  
Ali Gholami
Keyword(s):  
Seismic Data ◽  
Polynomial Chaos ◽  
Seismic Velocity ◽  
Real Data ◽  
Velocity Analysis ◽  
Data Set ◽  
New Approach ◽  
Transverse Isotropic ◽  
Two Parameters ◽  
Vti Media

Seismic velocity analysis is one of the most crucial and, at the same time, the most laborious tasks during seismic data processing. This becomes even more difficult and time-consuming when nonhyperbolicity has to be considered in the velocity analysis. Nonhyperbolic velocity analysis provides very useful information during the processing and interpretation of seismic data. The most common approach for considering anisotropy during velocity analysis is to describe the moveout based on a nonhyperbolic equation. The nonhyperbolic moveout equation in vertically transverse isotropic (VTI) media is defined by two parameters: normal moveout (NMO) velocity [Formula: see text] and anellipticity [Formula: see text] (or horizontal velocity [Formula: see text]). We have developed a new approach based on polynomial chaos (PC) expansion for automating nonhyperbolic velocity analysis of common-midpoint (CMP) data in VTI media. For this purpose, we use the PC expansion to approximate the nonhyperbolic semblance function with a very fast-to-simulate function in terms of [Formula: see text] and [Formula: see text]. Then, using particle swarm optimization, we stochastically look for the optimum NMO and horizontal velocities that provide the maximum semblance. In contrary to common approaches for nonhyperbolic velocity analysis in which the two parameters are estimated iteratively in an alternating fashion, we find [Formula: see text] and [Formula: see text] simultaneously. This approach is tested on various data including a simple convolutional model, an anisotropic benchmark model, and a real data set. In all cases, the new method provided acceptable results. Reflections in the CMP corrected using the optimum velocities are properly flattened, and almost no residual moveout is observed.

Engineering graphics’ knowledge: its persistence and application evaluation

2015 ◽  
Author(s):  
Zenonas Turskis ◽  
Birutė Juodagalvienė ◽  
Inga Garnytė Sapranavičienė
Keyword(s):  
Data Analysis ◽  
Civil Engineering ◽  
Real Data ◽  
Design Data ◽  
Data Set ◽  
Evaluation Data ◽  
Engineering Graphics ◽  
The Relationship ◽  
Constructional Design

The article deals with the knowledge of engineering graphics, obtained during studies and its application in architectural and constructional design. Data analysis was carried out and the relationship between the exams’ grades in lower and upper semesters was determined. The evaluations of the following subjects have been examined: General Engineering Graphics, Applied Engineering Graphics, Building Architecture and Structures 1, Building Architecture and Structures 2. The present paper describes the development of an approach that uses a real data set. The investigated data illustrates relevant concepts and methods in the application of introductory civil engineering. The creative use of students' scores evaluation data is recommended to facilitate the learning of civil engineering. The course has enrolments of approximately 250 students.

scholarly journals Relationship Between Performance Intelligence Quotient and Physical Characteristics

2020 ◽  
Vol 7 (11) ◽  
pp. 6256-6262
Author(s):  
Mahashweta Das ◽  
Chiranjib Ghosh
Keyword(s):  
Intelligence Quotient ◽  
Brain Size ◽  
Real Data ◽  
Random Variable ◽  
Physical Characteristics ◽  
Data Set ◽  
Constant Variance ◽  
And Gender ◽  
Performance Intelligence Quotient ◽  
The Relationship

Generally, it may be expected that physical characteristics such as brain size, height, weight, gender and body mass index (BMI) can be associated with the performance intelligence quotient (PIQ) score. The current report examines the relationship between PIQ and physical characteristics such as brain size, height, weight, gender and BMI based on a real data set. It is derived herein that PIQ is non-constant variance random variable, and its mean is positively associated with brain size (P=0.0002) and negatively associated with height (P=0.0046). Variance of PIQ is negatively partially associated with brain size (P=0.0903). It is also independent of weight, BMI and gender. PIQ is higher for the individuals with larger brain size, shorter height and irrespective of gender, body weight and BMI.

Spectroscopy-Based Mapping with Scanning Microwave Impedance Microscopy

2018 ◽  
Author(s):  
Peter De Wolf ◽  
Zhuangqun Huang ◽  
Bede Pittenger
Keyword(s):  
Single Point ◽  
Electrical Characterization ◽  
Principal Component ◽  
High Sensitivity ◽  
Data Cube ◽  
Nanometer Scale ◽  
Learning Approaches ◽  
Data Set ◽  
3D Data ◽  
Higher Dimensional

Abstract Methods are available to measure conductivity, charge, surface potential, carrier density, piezo-electric and other electrical properties with nanometer scale resolution. One of these methods, scanning microwave impedance microscopy (sMIM), has gained interest due to its capability to measure the full impedance (capacitance and resistive part) with high sensitivity and high spatial resolution. This paper introduces a novel data-cube approach that combines sMIM imaging and sMIM point spectroscopy, producing an integrated and complete 3D data set. This approach replaces the subjective approach of guessing locations of interest (for single point spectroscopy) with a big data approach resulting in higher dimensional data that can be sliced along any axis or plane and is conducive to principal component analysis or other machine learning approaches to data reduction. The data-cube approach is also applicable to other AFM-based electrical characterization modes.

EXPONENTIATED HALF-LOGISTIC LOMAX DISTRIBUTION WITH PROPERTIES AND APPLICATION

2019 ◽  
Vol XVI (2) ◽  
pp. 1-11
Author(s):  
Farrukh Jamal ◽  
Hesham Mohammed Reyad ◽  
Soha Othman Ahmed ◽  
Muhammad Akbar Ali Shah ◽  
Emrah Altun
Keyword(s):  
Real Data ◽  
Continuous Model ◽  
Model Parameters ◽  
Data Set ◽  
Lomax Distribution ◽  
Mathematical Properties ◽  
Proposed Model ◽  
Probability Weighted Moment ◽  
Record Statistics ◽  
Maximum Likelihood Criterion

A new three-parameter continuous model called the exponentiated half-logistic Lomax distribution is introduced in this paper. Basic mathematical properties for the proposed model were investigated which include raw and incomplete moments, skewness, kurtosis, generating functions, Rényi entropy, Lorenz, Bonferroni and Zenga curves, probability weighted moment, stress strength model, order statistics, and record statistics. The model parameters were estimated by using the maximum likelihood criterion and the behaviours of these estimates were examined by conducting a simulation study. The applicability of the new model is illustrated by applying it on a real data set.

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