Long-offset moveout for VTI using Padé approximation

Geophysics ◽  
2016 ◽  
Vol 81 (5) ◽  
pp. C219-C227 ◽  
Author(s):  
Hanjie Song ◽  
Yingjie Gao ◽  
Jinhai Zhang ◽  
Zhenxing Yao
Keyword(s):  
Padé Approximation ◽  
Pade Approximation ◽  
Practical Applications ◽  
Long Offset ◽  
Wide Range ◽  
Isotropic Media ◽  
Transversally Isotropic ◽  
Error Accumulation ◽  
Anisotropy Parameters ◽  
Vti Media

The approximation of normal moveout is essential for estimating the anisotropy parameters of the transversally isotropic media with vertical symmetry axis (VTI). We have approximated the long-offset moveout using the Padé approximation based on the higher order Taylor series coefficients for VTI media. For a given anellipticity parameter, we have the best accuracy when the numerator is one order higher than the denominator (i.e., [[Formula: see text]]); thus, we suggest using [4/3] and [7/6] orders for practical applications. A [7/6] Padé approximation can handle a much larger offset and stronger anellipticity parameter. We have further compared the relative traveltime errors between the Padé approximation and several approximations. Our method shows great superiority to most existing methods over a wide range of offset (normalized offset up to 2 or offset-to-depth ratio up to 4) and anellipticity parameter (0–0.5). The Padé approximation provides us with an attractive high-accuracy scheme with an error that is negligible within its convergence domain. This is important for reducing the error accumulation especially for deeper substructures.

Normal moveout for long offset in isotropic media using the Padé approximation

2016 ◽  
Vol 13 (4) ◽  
pp. 658-666 ◽  
Author(s):  
Han-Jie Song ◽  
Jin-Hai Zhang ◽  
Zhen-Xing Yao
Keyword(s):  
Padé Approximation ◽  
Pade Approximation ◽  
Long Offset ◽  
Isotropic Media

EFFICIENT COMPUTATION OF MULTI-FREQUENCY FAR-FIELD SOLUTIONS OF THE HELMHOLTZ EQUATION USING PADÉ APPROXIMATION

2000 ◽  
Vol 08 (01) ◽  
pp. 223-240 ◽  
Author(s):  
MANISH MALHOTRA ◽  
PETER M. PINSKY
Keyword(s):  
Transfer Function ◽  
Near Field ◽  
Padé Approximation ◽  
Linear Operators ◽  
Far Field ◽  
Efficient Computation ◽  
Pade Approximation ◽  
Wide Range ◽  
Multiple Frequencies ◽  
Element Matrix

For many problems in exterior structural acoustics, the solution is required to be computed over multiple frequencies. For some classes of these problems, however, it may be sufficient to evaluate the multiple frequency solutions over restricted regions of the spatial domain. Examples include optimization and inverse problems based on the minimization of a functional defined over a specified surface or sub-region. For such problems, which include both near-field and far-field computations, we recently proposed an efficient algorithm to compute the partial-field solutions at multiple frequencies simultaneously. In this paper, we consider the particular case of far-field computations and simplify the recently proposed algorithm by exploiting the symmetry of linear operators. The approach involves a reformulation of the Dirichlet-to-Neumann (DtN) map based finite-element matrix problem into a transfer-function form that can efficiently describe the far-field solution. A multi-frequency approximation of the transfer function is developed by constructing matrix-valued Padé approximation of the transfer function via a symmetric, banded Lanczos process. Numerical tests illustrate the accuracy of the approach for a wide range of frequencies and cost reductions of an order of magnitude when compared to commonly used factorization based methods.

Analytic study of the effective parameters for determination of the NMO velocity function in transversely isotropic media

Geophysics ◽  
1997 ◽  
Vol 62 (6) ◽  
pp. 1855-1866 ◽  
Author(s):  
Jack K. Cohen
Keyword(s):  
Transverse Isotropy ◽  
Transversely Isotropic ◽  
P Wave ◽  
Velocity Function ◽  
Transversely Isotropic Media ◽  
Wave Phase Velocity ◽  
Isotropic Media ◽  
Anisotropy Parameters ◽  
Vti Media ◽  
Ray Parameter

In their studies of transversely isotropic media with a vertical symmetry axis (VTI media), Alkhalifah and Tsvankin observed that, to a high numerical accuracy, the normal moveout (NMO) velocity for dipping reflectors as a function of ray parameter p depends mainly on just two parameters, each of which can be determined from surface P‐wave observations. They substantiated this result by using the weak‐anisotropy approximation and exploited it to develop a time‐domain processing sequence that takes into account vertical transverse isotropy. In this study, the two‐parameter Alkhalifah‐Tsvankin result was further examined analytically. It was found that although there is (as these authors already observed) some dependence on the remaining parameters of the problem, this dependence is weak, especially in the practically important regimes of weak to moderately strong transverse isotropy and small ray parameter. In each of these regimes, an analytic solution is derived for the anisotropy parameter η required for time‐domain P‐wave imaging in VTI media. In the case of elliptical anisotropy (η = 0), NMO velocity expressed through p is fully controlled just by the zero‐dip NMO velocity—one of the Alkhalifah‐ Tsvankin parameters. The two‐parameter representation of NMO velocity also was shown to be exact in another limit—that of the zero shear‐wave vertical velociy. The analytic results derived here are based on new representations for both the P‐wave phase velocity and normal moveout velocity in terms of the ray parameter, with explicit expressions given for the cases of vanishing onaxis shear speed, weak to moderate transverse isotropy, and small to moderate ray parameter. Using these formulas, I have rederived and, in some cases, extended in a uniform manner various results of Tsvankin, Alkhalifah, and others. Examples include second‐order expansions in the anisotropy parameters for both the P‐wave phase‐velocity function and NMO‐velocity function, as well as expansions in powers of the ray parameter for both of these functions. I have checked these expansions against the corresponding exact functions for several choices of the anisotropy parameters.

Reliability of the slowness and slowness-polarization methods for anisotropy estimation in VTI media from 3C walkaway VSP data

Geophysics ◽  
2013 ◽  
Vol 78 (5) ◽  
pp. WC93-WC102 ◽  
Author(s):  
Mehdi Asgharzadeh ◽  
Andrej Bóna ◽  
Roman Pevzner ◽  
Milovan Urosevic ◽  
Boris Gurevich
Keyword(s):  
Polarization Vector ◽  
Estimation Errors ◽  
Local Anisotropy ◽  
Weak Anisotropy ◽  
Polarization Measurements ◽  
Slowness Vector ◽  
Wide Range ◽  
Walkaway Vsp ◽  
Anisotropy Parameters ◽  
Vti Media

We studied the validity of qP-wave slowness and slowness-polarization methods for estimating local anisotropy parameters in transversely isotropic (TI) media by quantifying the estimation errors in a numerical exercise. We generated numerical slownesses and polarizations over two aperture ranges corresponding to a short offset walkaway vertical seismic profiling (VSP) and a long offset walkaway VSP for a range of TI models with vertical axis of symmetry (VTI). Synthetic data are equisampled over the phase angle range and contaminated with Gaussian noise. We inverted the data and compared the anisotropy parameters of the optimal model with the true model. We found that the selection of a proper methodology for VTI parameter estimation based on walkaway VSP measurements was mostly dependent on our ability to accurately estimate either horizontal components of qP-wave slowness vector or the polarization vector. With data contaminated with noise, methods that include the horizontal component of the slowness vector had greater accuracy than the methods that replace this information with polarization measurements. The estimations are particularly accurate when a wide range of propagation angle was available. For short offsets, only parameter [Formula: see text] could be reliably estimated. In the absence of long offsets, depending on the accuracy of polarization measurements, the method based on the weak anisotropy approximation for qP-wave velocity in VTI media or the method based on slowness and polarization vectors could be used to estimate [Formula: see text] and [Formula: see text]. If the horizontal components of the slowness vector were not available (a heterogeneous overburden), we used methods that were based on local measurements of the polarization vector. We found that, with accurate measurements of the polarization vector, the method based on exact relationship between vertical slowness and polarization dip could be used to estimate VTI parameters even for the cases in which the wide offset range was not available.

scholarly journals Reducing Residual Moveout for Long Offset Data in VTI Media Using Padé Approximation

2019 ◽  
Vol 125 ◽  
pp. 15005
Author(s):  
Indah Nur Pratiwi ◽  
Mohammad Syamsu Rosid ◽  
Humbang Purba
Keyword(s):  
Travel Time ◽  
Transverse Isotropy ◽  
Padé Approximation ◽  
Three Dimensional ◽  
Synthetic Data ◽  
Single Layer ◽  
Pade Approximation ◽  
Depth Ratio ◽  
Long Offset ◽  
Vertical Transverse Isotropy

Modification of the hyperbolic travel time equation into non-hyperbolic travel time equation is important to increase the reduction residual moveout for long offset data. Some researchers have modified hyperbolic travel time equation into a non-hyperbolic travel time equation to obtain a more accurate value NMO velocity and parameter an-ellipticity or etha on the large offset to depth ratio (ODR) so that the residual moveout value is smaller mainly in large offset to depth ratio. The aims of research is to increase the reduction value of error residue at long offset data using Padé approximation then compare with several approximations. The method used in this study is to conduct forward modeling of the subsurface coating structure. The results of the three-dimensional analysis show that the Padé approximation has the best accuracy compared to the other travel time equations for ODR value up to 4 with an-ellipticity parameter is varying from 0 to 0.5. Testing of synthetic data for single layer on vertical transverse isotropy (VTI) medium obtained the maximum residual error value produced by the Padé approximation is 0.25% in ODR=4. Therefore, Padé approximation is better than other methods for reducing residual moveout.

Semi-Adaptive Closed-Loop Control for Infusion of Medications With Transport Delay in Clinical Effects

2019 ◽  
Vol 14 (10) ◽  
Author(s):  
Xin Jin ◽  
Chang-Sei Kim ◽  
Steven T. Shipley ◽  
Guy A. Dumont ◽  
Jin-Oh Hahn
Keyword(s):  
Adaptive Control ◽  
Closed Loop ◽  
Padé Approximation ◽  
Control Design ◽  
Closed Loop Control ◽  
Clinical Effects ◽  
Pade Approximation ◽  
Loop Control ◽  
Transport Delay ◽  
Wide Range

Abstract This paper presents a semi-adaptive closed-loop control approach to autonomous infusion of medications exhibiting significant transport delay in clinical effects. The basic idea of the approach is to enable stable adaptive control of medication infusion by (1) incorporating transport delay explicitly into control design by way of a Padé approximation while (2) facilitating linear parameterization of control design model by desensitization of nonlinearly parameterized cooperativity constant associated with pharmacodynamics (PD). A novel dynamic dose–response model for control design is presented, in which the cooperativity constant exerts zero influence on the model output in the steady-state. Then, an adaptive pole placement control (APPC) technique was employed to fulfill adaptive control design in the presence of nonminimum phase dynamics associated with the Padé approximation of transport delay. The controller was evaluated in silico using a case study of regulating a cardiovascular variable with a sedative under a wide range of transport delay and pharmacological profiles. The results suggest that adaptation of transport delay and pharmacological characteristics may be beneficial in achieving consistent and robust regulation of medication-elicited clinical effects.

A New Detector System For The HB5 Stem Instrument

1985 ◽  
Vol 43 ◽  
pp. 134-135
Author(s):  
J.M. Cowley
Keyword(s):  
Dark Field ◽  
Detector System ◽  
Electron Holography ◽  
Small Specimen ◽  
Bright Field ◽  
Multiple Images ◽  
Practical Applications ◽  
Wide Range ◽  
Diffraction Patterns ◽  
Operational Modes

The HB5 STEM instrument at ASU has been modified previously to include an efficient two-dimensional detector incorporating an optical analyser device and also a digital system for the recording of multiple images. The detector system was built to explore a wide range of possibilities including in-line electron holography, the observation and recording of diffraction patterns from very small specimen regions (having diameters as small as 3Å) and the formation of both bright field and dark field images by detection of various portions of the diffraction pattern. Experience in the use of this system has shown that sane of its capabilities are unique and valuable. For other purposes it appears that, while the principles of the operational modes may be verified, the practical applications are limited by the details of the initial design.

Modeling of Rails Expressed using Pade Approximation Considering Frequency Dependent Effect

2017 ◽  
Vol 137 (2) ◽  
pp. 147-153
Author(s):  
Akinori Hori ◽  
Hiroki Tanaka ◽  
Yuichiro Hayakawa ◽  
Hiroshi Shida ◽  
Keiji Kawahara ◽  
...  
Keyword(s):  
Padé Approximation ◽  
Pade Approximation ◽  
Frequency Dependent ◽  
Dependent Effect

scholarly journals Ring-Forming Polymerization toward Perfluorocyclobutyl and Ortho-Diynylarene-Derived Materials: From Synthesis to Practical Applications

Materials ◽  
2021 ◽  
Vol 14 (6) ◽  
pp. 1486
Author(s):  
Eugene B. Caldona ◽  
Ernesto I. Borrego ◽  
Ketki E. Shelar ◽  
Karl M. Mukeba ◽  
Dennis W. Smith
Keyword(s):  
Chemical Resistance ◽  
Structural Features ◽  
Review Article ◽  
Aryl Ether ◽  
Aromatic Rings ◽  
Practical Applications ◽  
Repeat Units ◽  
Wide Range ◽  
Synthetic Routes ◽  
The Cost

Many desirable characteristics of polymers arise from the method of polymerization and structural features of their repeat units, which typically are responsible for the polymer’s performance at the cost of processability. While linear alternatives are popular, polymers composed of cyclic repeat units across their backbones have generally been shown to exhibit higher optical transparency, lower water absorption, and higher glass transition temperatures. These specifically include polymers built with either substituted alicyclic structures or aromatic rings, or both. In this review article, we highlight two useful ring-forming polymer groups, perfluorocyclobutyl (PFCB) aryl ether polymers and ortho-diynylarene- (ODA) based thermosets, both demonstrating outstanding thermal stability, chemical resistance, mechanical integrity, and improved processability. Different synthetic routes (with emphasis on ring-forming polymerization) and properties for these polymers are discussed, followed by their relevant applications in a wide range of aspects.

scholarly journals Sensing of Nickel(II) Ions by Immobilizing Ligands and Using Different SPEs

2021 ◽  
Vol 6 (1) ◽  
pp. 2
Author(s):  
Liliana Anchidin-Norocel ◽  
Sonia Amariei ◽  
Gheorghe Gutt
Keyword(s):  
Bismuth Oxide ◽  
Human Population ◽  
Raw Materials ◽  
Sensor Technology ◽  
Cyclic Voltammogram ◽  
Accurate Analysis ◽  
Nickel Allergy ◽  
Nickel Ions ◽  
Practical Applications ◽  
Wide Range

The aim of this paper is the development of a sensor for the quantification of nickel ions in food raw materials and foods. It is believed that about 15% of the human population suffers from nickel allergy. In addition to digestive manifestations, food intolerance to nickel may also have systemic manifestations, such as diffuse dermatitis, diffuse itching, fever, rhinitis, headache, altered general condition. Therefore, it is necessary to control this content of nickel ions for the health of the human population by developing a new method that offers the advantages of a fast, not expensive, in situ, and accurate analysis. For this purpose, bismuth oxide-screen-printed electrodes (SPEs) and graphene-modified SPEs were used with a very small amount of dimethylglyoxime and amino acid L-histidine that were deposited. A potentiostat that displays the response in the form of a cyclic voltammogram was used to study the electrochemical properties of nickel standard solution with different concentrations. The results were compared and the most sensitive sensor proved to be bismuth oxide-SPEs with dimethylglyoxime (Bi2O3/C-dmgH2) with a linear response over a wide range (0.1–10 ppm) of nickel concentrations. Furthermore, the sensor shows excellent selectivity in the presence of common interfering species. The Bi2O3/C-dmgH2 sensor showed good viability for nickel analysis in food samples (cocoa, spinach, cabbage, and red wine) and demonstrated significant advancement in sensor technology for practical applications.

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