Distribution by Scientific Domains

Kinds of Operator

  • differential operator
  • experience operator
  • integral operator
  • laplace operator
  • one operator
  • projection operator
  • schrödinger operator
  • selection operator
  • single operator
  • system operator
  • tangent operator

  • Terms modified by Operator

  • operator characteristic
  • operator characteristic curve
  • operator curve
  • operator curve analysis
  • operator dna
  • operator equation
  • operator error
  • operator experience
  • operator performance
  • operator splitting method

  • Selected Abstracts

    A new algorithm for reactive power management and pricing in an open access environment

    G. Reza Yousefi
    Abstract In deregulated electricity markets, reactive power is one of the ancillary services that is provided by the Independent System Operator (ISO). In this paper we propose a new algorithm to ,tune' reactive power resources with the objectives of minimizing active power losses and optimizing system voltage profile and stability. In our solution, we assume that reactive power resources are either owned by or are under long-term contracts with the ISO. The optimization problem is solved as an Extended Multi-objective Optimal Power Flow (EMOPF) problem using Lexico Graphic Method (LGM). Thereafter, using the concept of Fair Resource Allocation (FRA), the cost of reactive power is allocated to existing transactions. The application of the algorithm to a test system is also presented. Copyright © 2007 John Wiley & Sons, Ltd. [source]

    Electricity peak load forecasting with self-organizing map and support vector regression

    Shu Fan Non-member
    Abstract This paper aims to study the short-term peak load forecasting (PLF) by using Kohonen self-organizing maps (SOM) and support vector regression (SVR). We first adopt a SOM network to cluster the input data set into several subsets in an unsupervised learning strategy. Then, several SVRs for the next day's peak load are used to fit the training data of each subset in the second stage. In the numerical experiments, data of electricity demand from the New York Independent System Operator (ISO) are used to verify the effectiveness of the prediction for the proposed method. The simulation results show that the proposed model can predict the next day's peak load with a considerably high accuracy compared with the ISO forecasts. © 2006 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc. [source]

    Ventricular Septal Defect Repair by the Left-Handed Operator

    Po-Yuan Hu M.D.
    No abstract is available for this article. [source]

    Rhotacization and the ,Beijing Smooth Operator': The social meaning of a linguistic variable1

    Qing Zhang
    Recent sociolinguistic studies on style have focused much attention on the construction of social meaning in situated discursive practices. Despite a general recognition that the linguistic resources used are often already imbued with social meanings, little research has been done on what these meanings may be. Focusing on rhotacization, a sociolinguistic variable in Beijing Mandarin, this article explores its imbued social meanings and sociocultural associations. I demonstrate that rhotacization takes on semiotic saliency through co-occurrence with key Beijing cultural terms and frequent use in written representations of authentic Beijing-ness. Furthermore, this feature is associated with the ,Beijing Smooth Operator,' a salient male local character type, and is ideologically construed as reflecting its characterological attributes. The findings of this study shed light on the meaning potential of a linguistic variable, rhotacization in this case, which can enhance understanding of the possibilities and constraints for its use and meaning in new contexts. [source]

    Conformally invariant powers of the Dirac operator in Clifford analysis

    David Eelbode
    Abstract The paper deals with conformally invariant higher-order operators acting on spinor-valued functions, such that their symbols are given by powers of the Dirac operator. A general classification result proves that these are unique, up to a constant multiple. A general construction for such an invariant operators on manifolds with a given conformal spin structure was described in (Conformally Invariant Powers of the Ambient Dirac Operator. ArXiv math.DG/0112033, preprint), generalizing the case of powers of the Laplace operator from (J. London Math. Soc. 1992; 46:557,565). Although there is no hope to obtain explicit formulae for higher powers of the Laplace or Dirac operator on a general manifold, it is possible to write down an explicit formula on Einstein manifolds in case of the Laplace operator (see Laplacian Operators and Curvature on Conformally Einstein Manifolds. ArXiv: math/0506037, 2006). Here we shall treat the spinor case on the sphere. We shall compute the explicit form of such operators on the sphere, and we shall show that they coincide with operators studied in (J. Four. Anal. Appl. 2002; 8(6):535,563). The methods used are coming from representation theory combined with traditional Clifford analysis techniques. Copyright © 2010 John Wiley & Sons, Ltd. [source]

    Operator,valued Fourier multiplier theorems on Besov spaces

    Maria Girardi
    Presented is a general Fourier multiplier theorem for operator,valued multiplier functions on vector,valued Besov spaces where the required smoothness of the multiplier functions depends on the geometry of the underlying Banach space (specifically, its Fourier type). The main result covers many classical multiplier conditions, such as Mihlin and Hörmander conditions. [source]

    On-Line Parameter Identification of Systemic Circulation Using the Delta Operator

    ARTIFICIAL ORGANS, Issue 8 2002
    Ryo Kosaka
    Abstract: To develop effective medical care with the artificial heart, we propose a new method, on-line parameter identification of the systemic circulation using the delta operator which can calculate the time-varying and unmeasured hemodynamics of the internal human body from some measured data: aortic pressure and total flow in real time. This method consists of first, a dynamic physiological model which is configured with the physiological parameters Ca (aortic compliance) and Rp (total peripheral resistance); and second, a system identification method using the delta operator. In the computer simulation study, we could confirm the effectiveness to identify the physiological parameters. In animal experiments with a left ventricular assist system, the physiological parameters, Ca = 1.8 (ml/mm Hg) and Rp = 0.8 (mm Hg s/ml), could be identified on-line. [source]

    Failure Of ProFile NiTi Instruments Used By An Inexperienced Operator Under Access Limitations

    Article first published online: 11 FEB 2010
    No abstract is available for this article. [source]

    Rhotacization and the ,Beijing Smooth Operator': The social meaning of a linguistic variable1

    Qing Zhang
    Recent sociolinguistic studies on style have focused much attention on the construction of social meaning in situated discursive practices. Despite a general recognition that the linguistic resources used are often already imbued with social meanings, little research has been done on what these meanings may be. Focusing on rhotacization, a sociolinguistic variable in Beijing Mandarin, this article explores its imbued social meanings and sociocultural associations. I demonstrate that rhotacization takes on semiotic saliency through co-occurrence with key Beijing cultural terms and frequent use in written representations of authentic Beijing-ness. Furthermore, this feature is associated with the ,Beijing Smooth Operator,' a salient male local character type, and is ideologically construed as reflecting its characterological attributes. The findings of this study shed light on the meaning potential of a linguistic variable, rhotacization in this case, which can enhance understanding of the possibilities and constraints for its use and meaning in new contexts. [source]

    Adaptive and Feature-Preserving Subdivision for High-Quality Tetrahedral Meshes

    D. Burkhart
    I.3.5 [Computer Graphics]: Curve, surface, solid, and object representations Abstract We present an adaptive subdivision scheme for unstructured tetrahedral meshes inspired by the, -subdivision scheme for triangular meshes. Existing tetrahedral subdivision schemes do not support adaptive refinement and have traditionally been driven by the need to generate smooth three-dimensional deformations of solids. These schemes use edge bisections to subdivide tetrahedra, which generates octahedra in addition to tetrahedra. To split octahedra into tetrahedra one routinely chooses a direction for the diagonals for the subdivision step. We propose a new topology-based refinement operator that generates only tetrahedra and supports adaptive refinement. Our tetrahedral subdivision algorithm is motivated by the need to have one representation for the modeling, the simulation and the visualization and so to bridge the gap between CAD and CAE. Our subdivision algorithm design emphasizes on geometric quality of the tetrahedral meshes, local and adaptive refinement operations, and preservation of sharp geometric features on the boundary and in the interior of the physical domain. [source]

    Differential Representations for Mesh Processing

    Olga Sorkine
    Abstract Surface representation and processing is one of the key topics in computer graphics and geometric modeling, since it greatly affects the range of possible applications. In this paper we will present recent advances in geometry processing that are related to the Laplacian processing framework and differential representations. This framework is based on linear operators defined on polygonal meshes, and furnishes a variety of processing applications, such as shape approximation and compact representation, mesh editing, watermarking and morphing. The core of the framework is the definition of differential coordinates and new bases for efficient mesh geometry representation, based on the mesh Laplacian operator. [source]

    Multi-scale Feature Extraction on Point-Sampled Surfaces

    Mark Pauly
    We present a new technique for extracting line-type features on point-sampled geometry. Given an unstructuredpoint cloud as input, our method first applies principal component analysis on local neighborhoods toclassify points according to the likelihood that they belong to a feature. Using hysteresis thresholding, we thencompute a minimum spanning graph as an initial approximation of the feature lines. To smooth out the featureswhile maintaining a close connection to the underlying surface, we use an adaptation of active contour models.Central to our method is a multi-scale classification operator that allows feature analysis at multiplescales, using the size of the local neighborhoods as a discrete scale parameter. This significantly improves thereliability of the detection phase and makes our method more robust in the presence of noise. To illustrate theusefulness of our method, we have implemented a non-photorealistic point renderer to visualize point-sampledsurfaces as line drawings of their extracted feature curves. [source]

    CAD-Based Photogrammetry for Reverse Engineering of Industrial Installations

    Johan W. H. Tangelder
    For instance, in the case of a servicing plant, such a library contains descriptions of simple components such as straight pipes, elbows, and T-junctions. A new installation is constructed by selecting and connecting the appropriate components from the library. This article demonstrates that one can use the same approach for reverse engineering by photogrammetry. In our technique, the operator interprets images and selects the appropriate CAD component from a library. By aligning the edges of the component's wire frame to the visible edges in the images, we implicitly determine the position, orientation, and shape of the real component. For a fast object reconstruction the alignment process has been split in two parts. Initially, the operator approximately aligns a component to the images. In a second step a fitting algorithm is invoked for an automatic and precise alignment. Further improvement in the efficiency of the reconstruction is obtained by imposing geometric constraints on the CAD components of adjacent object parts. [source]

    Thermal relaxation and coherence dynamics of spin 3/2.


    Abstract The relaxation dynamics of the spin 3/2 density operator in the presence of fluctuating and static quadrupolar interactions is reviewed. The nuclear magnetic resonance (NMR) line shapes are analyzed for any value of the static quadrupolar interaction, ranging from isotropic systems to systems exhibiting large splitting far exceeding the line widths. Pulse sequences optimized for the elimination of line broadening due to an inhomogeneous static quadrupolar interaction and for the detection of nuclei involved in slow molecular motion and/or in anisotropic, liquid crystalline environment are discussed. In Part II, the dynamics of spin 3/2 in the presence of a (pulsed) radio frequency (RF) field is reviewed. © 2003 Wiley Periodicals, Inc. Concepts Magn Reson Part A 19A: 97,116, 2003. [source]

    A survey of interfacial forces used during filing of root canals

    J. D. Regan
    Abstract , The pattern of dentine removal during endodontic instrumentation is influenced by many factors including the interfacial forces applied by the operator. The aim of this study was to investigate the influence of operators and different sizes and types of instruments on the magnitude of these interfacial forces. Single-rooted teeth were mounted on a cantilevered aluminium beam to which two pairs of single element strain gauges were joined in a half-bridge configuration and mounted at right angles to each other. The strain gauges were connected to an analogue-to-digital converter fitted in a micro-computer via conditioning amplifiers. This enabled strains to be recorded over a period of time. Twenty operators instrumented root canals using a series of hand instruments for 1 min each. The mean interfacial forces used by operators demonstrated a wide variation ranging from 9.06 g to 149.42 g (range of forces from 0,331 g) but there was a consistency in the relative magnitude for each operator. The 20 operators could be divided into 13 groups which were significantly different (,=0.05) from each other. There were significant differences (,=0.05) between the forces used for each of the K-Flex files (15, 25, 35, 45, and 70), the force increasing with the file size. There was also a significant difference (,=0.05) in the forces used between the Flexofile (#25) and the #25 K-Flex and Hedström files. However, there was no significant difference between the K-Flex and Hedström files. [source]


    Kiichi Tamada
    When performing endoscopic retrograde cholangiopancreatography (ERCP), the smooth introduction of the duodenoscope into the papilla of Vater, an appropriate view of the papilla of Vater, and deep cannulation of the bile duct are essential. The operator must know the difference between the side-viewing endoscope and the forward-viewing endoscope. The rotation of the body and the left arm of the operator, switching with the left wrist, and dialing of the endoscope are essential for appropriately viewing the papilla of Vater. When training operators to do ERCP, a model is useful for helping them understand basic handling. The approach to deep cannulation of the bile duct should be selected based on the type of papilla (slit type, onion type, tongue protrusion type, flat type, and tumor type). Cannulation is more difficult in patients with the tongue protrusion-type of papilla than with a slit type, onion type, or tumor type. According to previous reports, therapeutic ERCP requires the ability to cannulate the common bile duct deeply 80% of the time; 180 to 200 supervised ERCP are necessary to achieve this success rate. [source]

    Comparison of LiDAR waveform processing methods for very shallow water bathymetry using Raman, near-infrared and green signals

    Tristan Allouis
    Abstract Airborne light detection and ranging (LiDAR) bathymetry appears to be a useful technology for bed topography mapping of non-navigable areas, offering high data density and a high acquisition rate. However, few studies have focused on continental waters, in particular, on very shallow waters (<2,m) where it is difficult to extract the surface and bottom positions that are typically mixed in the green LiDAR signal. This paper proposes two new processing methods for depth extraction based on the use of different LiDAR signals [green, near-infrared (NIR), Raman] of the SHOALS-1000T sensor. They have been tested on a very shallow coastal area (Golfe du Morbihan, France) as an analogy to very shallow rivers. The first method is based on a combination of mathematical and heuristic methods using the green and the NIR LiDAR signals to cross validate the information delivered by each signal. The second method extracts water depths from the Raman signal using statistical methods such as principal components analysis (PCA) and classification and regression tree (CART) analysis. The obtained results are then compared to the reference depths, and the performances of the different methods, as well as their advantages/disadvantages are evaluated. The green/NIR method supplies 42% more points compared to the operator process, with an equivalent mean error (,4·2,cm verusu ,4·5,cm) and a smaller standard deviation (25·3,cm verusu 33·5,cm). The Raman processing method provides very scattered results (standard deviation of 40·3,cm) with the lowest mean error (,3·1,cm) and 40% more points. The minimum detectable depth is also improved by the two presented methods, being around 1,m for the green/NIR approach and 0·5,m for the statistical approach, compared to 1·5,m for the data processed by the operator. Despite its ability to measure other parameters like water temperature, the Raman method needed a large amount of reference data to provide reliable depth measurements, as opposed to the green/NIR method. Copyright © 2010 John Wiley & Sons, Ltd. [source]

    Qualitative and quantitative fracture analyses of high-strength ceramics

    Marit Øilo
    The aims of this study were to assess the applicability and repeatability of qualitative and quantitative analyses of the fracture patterns of four different high-strength ceramics. Ten bar-shaped specimens of four high-strength ceramics with different material composition and fabrication methods had been fractured by three-point bending in water (n = 40). Commonly used fractographic patterns for brittle materials, such as mirror and mist, were used to characterize and quantify the fractured surfaces of these specimens. The analyses were performed twice, on separate occasions, by the same operator. Assessment of the association between fractographic patterns and fracture stress was carried out, and repeatability assessments of the measurements were performed. The fracture initiator site and the common fractographic markers surrounding this site were found in all specimens. Statistically significant correlations were found between certain fracture patterns and stress at fracture. The repeatability of the measurements of the different fractographic patterns varied among the materials. Fracture analyses seem applicable as a tool to determine the fracture initiation site and to estimate the force vectors involved in the fracture of dental high-strength ceramics. [source]

    Short-term scheduling of a wind generation and hydrogen storage in the electricity market

    G. Tina
    Abstract Intermittent renewable energy sources (RES) are promising to be the future of electricity generation. In particular wind generation, owing to its stochastic behaviour, has to be carefully managed. Its lack of sufficient predictability decreases the energy value in the current framework of electrical markets, therefore, beyond a certain threshold; this kind of generation into the electrical system represents a problem for the transmission system operator (TSO) during its despatching service. The coupling of wind energy conversion system (WECS) with a storage medium (i.e. hydrogen) could improve the programmability of such generation plants in electrical markets. In this paper, an economical optimization tool has been developed in order to find the short-term scheduling so as to maximize the economic revenues in the day-ahead electricity market of a storage plant coupled with a wind farm. This tool needs as input the forecasts of both wind generation power and market prices, obtained with the adoption of pre-processing input data algorithm based on different methods that involve both statistical and probabilistic approaches. Copyright © 2009 John Wiley & Sons, Ltd. [source]

    On-line dynamic security assessment to mitigate the risk of blackout in the Italian power system

    Diego Cirio
    Abstract This paper provides a comprehensive survey of the major initiatives and research projects recently carried out by the Italian system operator, Cesi Ricerca, and Universities on power system monitoring, defense, and security assessment. The technological and methodological features of an advanced wide area measurement system (WAMS) are described and the main aspects of an adaptive system for event-based automatic load shedding are presented. Then preventive and corrective security assessment, with particular emphasis to dynamic security assessment,DSA, is introduced. Results from an EU project, where the Italian power system served as a test site for on-line experimentation, are reported. Considering the need for very fast assessment by stability indices, a complementary approach to the above "conventional" DSA, currently under way, is described in further detail. The methodology relies on a correlation model relating significant power system measurements with local loadability margins. Results of some tests on the Italian power system are presented and discussed. Copyright © 2008 John Wiley & Sons, Ltd. [source]

    Strain-life approach in thermo-mechanical fatigue evaluation of complex structures


    ABSTRACT This paper is a contribution to strain-life approach evaluation of thermo-mechanically loaded structures. It takes into consideration the uncoupling of stress and damage evaluation and has the option of importing non-linear or linear stress results from finite element analysis (FEA). The multiaxiality is considered with the signed von Mises method. In the developed Damage Calculation Program (DCP) local temperature-stress-strain behaviour is modelled with an operator of the Prandtl type and damage is estimated by use of the strain-life approach and Skelton's energy criterion. Material data were obtained from standard isothermal strain-controlled low cycle fatigue (LCF) tests, with linear parameter interpolation or piecewise cubic Hermite interpolation being used to estimate values at unmeasured temperature points. The model is shown with examples of constant temperature loading and random force-temperature history. Additional research was done regarding the temperature dependency of the Kp used in the Neuber approximate formula for stress-strain estimation from linear FEA results. The proposed model enables computationally fast thermo-mechanical fatigue (TMF) damage estimations for random load and temperature histories. [source]

    Temperature,stress,strain trajectory modelling during thermo-mechanical fatigue

    ABSTRACT The isothermal strain-life approach is the most commonly used approach for determining fatigue damage, particularly when yielding occurs. Computationally it is extremely fast and generally requires elastic finite element analyses only. Therefore, it has been adapted for variable temperatures. Local temperature,stress,strain behaviour is modelled with an operator of the Prandtl type. The hysteresis loops are supposed to be stabilized and no creep is considered. The consequences of reversal point filtering are analysed. The approach is finally compared to several thermo-mechanical fatigue tests and the Skelton model. [source]

    Fast set-up of doxycycline-inducible protein expression in human cell lines with a single plasmid based on Epstein,Barr virus replication and the simple tetracycline repressor

    FEBS JOURNAL, Issue 3 2007
    Markus Bach
    We have developed a novel plasmid vector, pEBTetD, for full establishment of doxycycline-inducible protein expression by just a single transfection. pEBTetD contains an Epstein,Barr virus origin of replication for stable and efficient episomal propagation in human cell lines, a cassette for continuous expression of the simple tetracycline repressor, and a cytomegalovirus-type 2 tetracycline operator (tetO2)-tetO2 promoter. As there is no integration of vector into the genome, clonal isolation of transfected cells is not necessary. Cells are thus ready for use 1 week after transfection; this contrasts with 3,12 weeks for other systems. Adequate regulation of protein expression was accomplished by abrogation of mRNA polyadenylation. In northern analysis of seven cDNAs coding for transport proteins, pools of transfected human embryonic kidney 293 cells showed on/off mRNA ratios in the order of 100 : 1. Cell pools were also analyzed for regulation of protein function. With two transport proteins of the plasma membrane, the on/off activity ratios were 24 : 1 and 34 : 1, respectively. With enhanced green fluorescent protein, a 23 : 1 ratio was observed based on fluorescence intensity data from flow cytometry. The unique advantage of our system rests on the unmodified tetracycline repressor, which is less likely, by relocation upon binding of doxycycline, to cause cellular disturbances than chimera of tetracycline repressor and eukaryotic transactivation domains. Thus, in a comprehensive comparison of on- and off-states, a steady cellular background is provided. Finally, in contrast to a system based on Flp recombinase, the set-up of our system is inherently reliable. [source]

    Mimicry in plant-parasitic fungi

    Henry K. Ngugi
    Abstract Mimicry is the close resemblance of one living organism (the mimic) to another (the model), leading to misidentification by a third organism (the operator). Similar to other organism groups, certain species of plant-parasitic fungi are known to engage in mimetic relationships, thereby increasing their fitness. In some cases, fungal infection can lead to the formation of flower mimics (pseudoflowers) that attract insect pollinators via visual and/or olfactory cues; these insects then either transmit fungal gametes to accomplish outcrossing (e.g. in some heterothallic rust fungi belonging to the genera Puccinia and Uromyces) or vector infectious spores to healthy plants, thereby spreading disease (e.g. in the anther smut fungus Microbotryum violaceum and the mummy berry pathogen Monilinia vaccinii-corymbosi). In what is termed aggressive mimicry, some specialized plant-parasitic fungi are able to mimic host structures or host molecules to gain access to resources. An example is M. vaccinii-corymbosi, whose conidia and germ tubes, respectively, mimic host pollen grains and pollen tubes anatomically and physiologically, allowing the pathogen to gain entry into the host's ovary via stigma and style. We review these and other examples of mimicry by plant-parasitic fungi and some of the mechanisms, signals, and evolutionary implications. [source]

    Superalgebras of Dirac operators on manifolds with special Killing-Yano tensors

    I.I. Cot
    Abstract We present the properties of new Dirac-type operators generated by real or complex-valued special Killing-Yano tensors that are covariantly constant and represent roots of the metric tensor. In the real case these are just the so called complex or hyper-complex structures of the Kählerian manifolds. Such a Killing-Yano tensor produces simultaneously a Dirac-type operator and the generator of a one-parameter Lie group connecting this operator with the standard Dirac one. In this way the Dirac operators are related among themselves through continuous transformations associated with specific discrete ones. We show that the group of these continuous transformations can be only U(1) or SU(2). It is pointed out that the Dirac and Dirac-type operators can form ,, = 4 superalgebras whose automorphisms combine isometries with the SU(2) transformation generated by the Killing-Yano tensors. As an example we study the automorphisms of the superalgebras of Dirac operators on Minkowski spacetime. [source]

    A probabilistic approach to quantum mechanics based on ,tomograms'

    M. Caponigro
    It is usually believed that a picture of Quantum Mechanics in terms of true probabilities cannot be given due to the uncertainty relations. Here we discuss a tomographic approach to quantum states that leads to a probability representation of quantum states. This can be regarded as a classical-like formulation of quantum mechanics which avoids the counterintuitive concepts of wave function and density operator. The relevant concepts of quantum mechanics are then reconsidered and the epistemological implications of such approach discussed. [source]

    Lie Theory for Quantum Control

    GAMM - MITTEILUNGEN, Issue 1 2008
    G. Dirr
    Abstract One of the main theoretical challenges in quantum computing is the design of explicit schemes that enable one to effectively factorize a given final unitary operator into a product of basic unitary operators. As this is equivalent to a constructive controllability task on a Lie group of special unitary operators, one faces interesting classes of bilinear optimal control problems for which efficient numerical solution algorithms are sought for. In this paper we give a review on recent Lie-theoretical developments in finite-dimensional quantum control that play a key role for solving such factorization problems on a compact Lie group. After a brief introduction to basic terms and concepts from quantum mechanics, we address the fundamental control theoretic issues for bilinear control systems and survey standard techniques fromLie theory relevant for quantum control. Questions of controllability, accessibility and time optimal control of spin systems are in the center of our interest. Some remarks on computational aspects are included as well. The idea is to enable the potential reader to understand the problems in clear mathematical terms, to assess the current state of the art and get an overview on recent developments in quantum control-an emerging interdisciplinary field between physics, control and computation. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source]

    Recovering acoustic reflectivity using Dirichlet-to-Neumann maps and left- and right-operating adjoint propagators

    M. W. P. Dillen
    SUMMARY Constructing an image of the Earth subsurface from acoustic wave reflections has previously been described as a recursive downward redatuming of sources and receivers. Most of the methods that have been presented involve reflectivity and propagators associated with one-way wavefield components. In this paper, we consider the reflectivity relation between two-way wavefield components, each a solution of a Helmholtz equation. To construct forward and inverse propagators, and a reflection operator, the invariant-embedding technique is followed, using Dirichlet-to-Neumann maps. Employing bilinear and sesquilinear forms, the forward- and inverse-scattering problems, respectively, are treated analogously. Through these mathematical constructs, the relationship between a causality radiation condition and symmetry, with respect to a bilinear form, is associated with the requirement of an anticausality radiation condition with respect to a sesquilinear form. Using reciprocity, sources and receivers are redatumed recursively to the reflector, employing left- and right-operating adjoint propagators. The exposition of the proposed method is formal, that is numerical applications are not derived. The key to applications lies in the explicit representation, characterization and approximation of the relevant operators (symbols) and fundamental solutions (path integrals). Existing constructive work which could be applied to the proposed method are referred to in the text. [source]

    Upward continuation with topographic datuming operator: the integrated wave equation datuming scheme revised

    Kai Yang
    ABSTRACT The integrated wave equation datuming scheme is an integrated datuming method to implement the wave equation velocity replacement with a one-way extrapolator for overthrust data. The integrated wave equation datuming scheme is accomplished by downward continuing the data from the topography to a non-planar base of the weathering layer, followed by an upward continuation from the base of the weathering layer to a final planar datum. Both the downward and the upward continuation are accomplished by a one-way extrapolator by a classical ,two-step' implementation. The topographic datuming operator is a distinctive technique by which the shots and receivers are downward continued simultaneously. Although its inadaptability to non-planar datum and the strong lateral variation of the near-surface structure constrains its application to the downward continuation of the overthrust data, we found that the ,one-step' feature of the topographic datuming operator is extremely suitable for the upward continuation. In this paper, the topographic datuming operator is incorporated into the integrated wave equation datuming scheme to perform upward continuation instead of a one-way extrapolator , thus a revised integrated wave equation datuming scheme is constructed. Compared with the previous scheme, the computatiol cost of the revised integrated wave equation datuming scheme is greatly reduced, thus the applicability of the integrated wave equation datuming scheme is further improved. The synthetic and real data examples demonstrate its effectiveness and efficiency. [source]

    Operator-oriented CRS interpolation

    German Hoecht
    ABSTRACT In common-reflection-surface imaging the reflection arrival time field is parameterized by operators that are of higher dimension or order than in conventional methods. Using the common-reflection-surface approach locally in the unmigrated prestack data domain opens a potential for trace regularization and interpolation. In most data interpolation methods based on local coherency estimation, a single operator is designed for a target sample and the output amplitude is defined as a weighted average along the operator. This approach may fail in presence of interfering events or strong amplitude and phase variations. In this paper we introduce an alternative scheme in which there is no need for an operator to be defined at the target sample itself. Instead, the amplitude at a target sample is constructed from multiple operators estimated at different positions. In this case one operator may contribute to the construction of several target samples. Vice versa, a target sample might receive contributions from different operators. Operators are determined on a grid which can be sparser than the output grid. This allows to dramatically decrease the computational costs. In addition, the use of multiple operators for a single target sample stabilizes the interpolation results and implicitly allows several contributions in case of interfering events. Due to the considerable computational expense, common-reflection-surface interpolation is limited to work in subsets of the prestack data. We present the general workflow of a common-reflection-surface-based regularization/interpolation for 3D data volumes. This workflow has been applied to an OBC common-receiver volume and binned common-offset subsets of a 3D marine data set. The impact of a common-reflection-surface regularization is demonstrated by means of a subsequent time migration. In comparison to the time migrations of the original and DMO-interpolated data, the results show particular improvements in view of the continuity of reflections events. This gain is confirmed by an automatic picking of a horizon in the stacked time migrations. [source]