Data‐matrix asymmetry and polarization changes from multicomponent surface seismics

Geophysics ◽  
1997 ◽  
Vol 62 (2) ◽  
pp. 630-643 ◽  
Author(s):  
Xiang‐Yang Li ◽  
Colin MacBeth
Keyword(s):  
Normal Incidence ◽  
Geological Structure ◽  
South Texas ◽  
Data Matrix ◽  
Reflection Coefficients ◽  
Incidence Plane ◽  
Degree Of Anisotropy ◽  
The Asymmetry ◽  
The Time Domain ◽  
Value Decomposition

We present methods for interpreting data‐matrix asymmetry and polarization changes with depth from multicomponent surface seismics. There are two main sources of data matrix asymmetry in four component shear‐wave seismics: that arising from the acquisition geometry caused by source and receiver misorientation, misalignment, imbalance, and cross‐coupling, and that arising from the medium caused by variations in the geological structure, lithology, or stress. The asymmetry caused by acquisition geometry is more significant than that from the medium. Two asymmetry indices are used to quantify these medium and acquisition asymmetries separately. Their behavior may be used to identify the origin of the asymmetry. The asymmetry caused by the medium is studied by deriving approximate normal‐incidence, plane‐wave reflection coefficients for an interface separating two anisotropic media with differenfly oriented symmetry axes. The degree of asymmetry in the reflectivity is proportional to the product of the degree of anisotropy in the layers above and below the reflector, and is thus small for most realistic cases. Consequently, the reflection coefficients can be approximated by a similarity transform of the principal reflection coefficients using the expected polarization difference. These equations can then be used to formulate a singular‐value decomposition (SVD) in the time‐domain to recover both the principal reflectivity and the changes of polarizations with depth. Applications to field data in south Texas reveal the potential of the technique, and zones of polarization changes in the Austin Chalk are identified that may be correlated with fracture swarms.

Migration velocity analysis based on focusing diffractions generated using the CRS wavefront attributes: Application to real land data

Geophysics ◽  
2021 ◽  
pp. 1-50
Author(s):  
German Garabito ◽  
José Silas dos Santos Silva ◽  
Williams Lima
Keyword(s):  
Time Domain ◽  
Real Data ◽  
Normal Incidence ◽  
Velocity Model ◽  
Migration Velocity ◽  
Velocity Analysis ◽  
Velocity Models ◽  
Time Migration ◽  
Migration Velocity Analysis ◽  
The Time Domain

In land seismic data processing, the prestack time migration (PSTM) image remains the standard imaging output, but a reliable migrated image of the subsurface depends on the accuracy of the migration velocity model. We have adopted two new algorithms for time-domain migration velocity analysis based on wavefield attributes of the common-reflection-surface (CRS) stack method. These attributes, extracted from multicoverage data, were successfully applied to build the velocity model in the depth domain through tomographic inversion of the normal-incidence-point (NIP) wave. However, there is no practical and reliable method for determining an accurate and geologically consistent time-migration velocity model from these CRS attributes. We introduce an interactive method to determine the migration velocity model in the time domain based on the application of NIP wave attributes and the CRS stacking operator for diffractions, to generate synthetic diffractions on the reflection events of the zero-offset (ZO) CRS stacked section. In the ZO data with diffractions, the poststack time migration (post-STM) is applied with a set of constant velocities, and the migration velocities are then selected through a focusing analysis of the simulated diffractions. We also introduce an algorithm to automatically calculate the migration velocity model from the CRS attributes picked for the main reflection events in the ZO data. We determine the precision of our diffraction focusing velocity analysis and the automatic velocity calculation algorithms using two synthetic models. We also applied them to real 2D land data with low quality and low fold to estimate the time-domain migration velocity model. The velocity models obtained through our methods were validated by applying them in the Kirchhoff PSTM of real data, in which the velocity model from the diffraction focusing analysis provided significant improvements in the quality of the migrated image compared to the legacy image and to the migrated image obtained using the automatically calculated velocity model.

A Fast, Memory-Efficient Discrete-Time Realization Algorithm for Reduced-Order Li-Ion Battery Models

2017 ◽  
Vol 14 (1) ◽  
Author(s):  
Krishnakumar Gopalakrishnan ◽  
Teng Zhang ◽  
Gregory J. Offer
Keyword(s):  
Discrete Time ◽  
Porous Electrode ◽  
Hankel Matrix ◽  
Lithium Ion ◽  
Computation Time ◽  
Power Sources ◽  
Reduced Order ◽  
The Time Domain ◽  
Computational Bottleneck ◽  
Value Decomposition

Research into reduced-order models (ROM) for Lithium-ion batteries is motivated by the need for a real-time embedded model possessing the accuracy of physics-based models, while retaining computational simplicity comparable to equivalent-circuit models. The discrete-time realization algorithm (DRA) proposed by Lee et al. (2012, “One-Dimensional Physics-Based Reduced-Order Model of Lithium-Ion Dynamics,” J. Power Sources, 220, pp. 430–448) can be used to obtain a physics-based ROM in standard state-space form, the time-domain simulation of which yields the evolution of all the electrochemical variables of the standard pseudo-2D porous-electrode battery model. An unresolved issue with this approach is the high computation requirement associated with the DRA, which needs to be repeated across multiple SoC and temperatures. In this paper, we analyze the computational bottleneck in the existing DRA and propose an improved scheme. Our analysis of the existing DRA reveals that singular value decomposition (SVD) of the large Block–Hankel matrix formed by the system's Markov parameters is a key inefficient step. A streamlined DRA approach that bypasses the redundant Block–Hankel matrix formation is presented as a drop-in replacement. Comparisons with existing DRA scheme highlight the significant reduction in computation time and memory usage brought about by the new method. Improved modeling accuracy afforded by our proposed scheme when deployed in a resource-constrained computing environment is also demonstrated.

The Effect of Inlet Grooves and Swirl on the Dynamics of Long Annular Seals in Centrifugal Pumps

1993 ◽  
Author(s):  
Mohamed Ismail ◽  
R. David Brown ◽  
David France
Keyword(s):  
Rolling Element Bearings ◽  
Rigid Rotor ◽  
Centrifugal Pumps ◽  
Test Rig ◽  
Singular Value Decomposition Method ◽  
Forcing Function ◽  
Rolling Element ◽  
The Time Domain ◽  
Value Decomposition ◽  
Annular Seals

Abstract This paper describes additional results from a continuing research program which aims to identify the dynamics of long annular seals in centrifugal pumps. A seal test rig designed to experimentally identify dynamic coefficients using a least-squares technique based on the singular value decomposition method. The analysis is carried out in the time domain using a multifrequency forcing function. The experimental method relies on the forced excitation of a flexibly supported stator by two hydraulic shakers. A rigid rotor supported in rolling element bearings runs through the stator. The only physical connection between shaft and stator is a pair of annular gaps filled with pressurised water discharged axially. The experimental coefficients obtained from the tests are compared with theoretical values.

scholarly journals SVD-based principal component analysis of geochemical data

2005 ◽  
Vol 3 (4) ◽  
pp. 731-741 ◽  
Author(s):  
Petr Praus
Keyword(s):  
Principal Component Analysis ◽  
Euclidean Distance ◽  
Principal Component ◽  
Component Analysis ◽  
Data Matrix ◽  
Geochemical Data ◽  
Average Group ◽  
Testing Data ◽  
Value Decomposition ◽  
Geochemical Variables

AbstractPrincipal Component Analysis (PCA) was used for the mapping of geochemical data. A testing data matrix was prepared from the chemical and physical analyses of the coals altered by thermal and oxidation effects. PCA based on Singular Value Decomposition (SVD) of the standardized (centered and scaled by the standard deviation) data matrix revealed three principal components explaining 85.2% of the variance. Combining the scatter and components weights plots with knowledge of the composition of tested samples, the coal samples were divided into seven groups depending on the degree of their oxidation and thermal alteration.The PCA findings were verified by other multivariate methods. The relationships among geochemical variables were successfully confirmed by Factor Analysis (FA). The data structure was also described by the Average Group dendrogram using Euclidean distance. The found sample clusters were not defined so clearly as in the case of PCA. It can be explained by the PCA filtration of the data noise.

REFLECTION COEFFICIENTS AND BOTTOM LOSSES AT NORMAL INCIDENCE COMPUTED FROM PACIFIC SEDIMENT PROPERTIES

Geophysics ◽  
1970 ◽  
Vol 35 (6) ◽  
pp. 995-1004 ◽  
Author(s):  
Edwin L. Hamilton
Keyword(s):  
Normal Incidence ◽  
Silty Sand ◽  
Reflection Coefficients ◽  
Silty Clay ◽  
Sediment Properties ◽  
Compressional Waves ◽  
Sea Floor ◽  
Sediment Types ◽  
The Pacific ◽  
Clayey Silt

Rayleigh reflection coefficients and bottom losses of compressional waves at normal incidence on the water‐sediment interface are computed with values of density and velocity measured in sea‐floor sediment samples; main sediment types in three major environments of the Pacific and adjacent areas are included. Some typical average computed values of acoustic bottom loss at normal incidence in db are (1) continental shelf: sands, 8; silty sand, 10; sandy silt, 14; silty clay, 16; (2) abyssal plain: clayey silt, 17; silty clay and clay, 21; and (3) abyssal hill: silty clay and clay, 17. Comparisons with actual measurements at sea by several investigators demonstrate the validity of the approach.

Identification of the Dynamic Characteristics of Long Annular Seals Using a Time Domain Technique

1998 ◽  
Vol 120 (3) ◽  
pp. 705-712 ◽  
Author(s):  
M. Ismail ◽  
R. D. Brown
Keyword(s):  
Dynamic Characteristics ◽  
Time Domain ◽  
Theoretical Models ◽  
Rotational Frequency ◽  
Singular Value Decomposition Method ◽  
Damping Coefficients ◽  
Theoretical Predictions ◽  
The Time Domain ◽  
Value Decomposition ◽  
Annular Seals

This paper describes experimental results from a research program aimed at a study of the static and dynamic characteristics of liquid long annular seals. A seal test rig permits the identification in the time domain of mass, stiffness, and damping coefficients using a least-squares technique based on the singular value decomposition method. The experimental method relies on the forced excitation of a flexibly supported stator by two hydraulic shakers. The forcing signal is composed from a small number of frequencies which are not related to the rotational frequency of the rigid shaft rotating inside the stator. The test data consisting of two inertia, four stiffness, and four damping coefficients is compared with theoretical predictions based on two theoretical models: (i) the model of Black et al. (1971 and 1981) and (ii) the model of Childs and Kim (1985).

Principal component transforms of triaxial recordings by singular value decomposition

Geophysics ◽  
1991 ◽  
Vol 56 (4) ◽  
pp. 528-533 ◽  
Author(s):  
G. M. Jackson ◽  
I. M. Mason ◽  
S. A. Greenhalgh
Keyword(s):  
Singular Value Decomposition ◽  
Time Window ◽  
Signal To Noise Ratio ◽  
Random Noise ◽  
Principal Component ◽  
Singular Value ◽  
Data Matrix ◽  
Single Station ◽  
Window Selection ◽  
Value Decomposition

Polarization analysis can be achieved efficiently by treating a time window of a single‐station triaxial recording as a matrix and doing a singular value decomposition (SVD) of this seismic data matrix. SVD of the triaxial data matrix produces an eigenanalysis of the data covariance (cross‐energy) matrix and a rotation of the data onto the directions given by the eigenanalysis (Karhunen‐Loève transform), all in one step. SVD provides a complete principal components analysis of the data in the analysis time window. Selection of this time window is crucial to the success of the analysis and is governed by three considerations: the window should contain only one arrival; the window should be such that the signal‐to‐noise ratio is maximized; and the window should be long enough to be able to discriminate random noise from signal. The SVD analysis provides estimates of signal, signal polarization directions, and noise. An F‐test is proposed which gives the confidence level for the hypothesis of rectilinear polarization. This paper illustrates the analysis and interpretation of synthetic rectilinearly and elliptically polarized arrivals at a single triaxial station by SVD.

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