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Journal articles on the topic 'Extrapolation'

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Published: 4 June 2021
Last updated: 11 March 2023

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1

Zhu, X., and T. Wiegelmann. "Toward a fast and consistent approach to modeling solar magnetic fields in multiple layers." Astronomy & Astrophysics 658 (January 28, 2022): A37. http://dx.doi.org/10.1051/0004-6361/202141505.

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Aims. We aim to develop a fast and consistent extrapolation method for modeling multiple layers of the solar atmosphere. Methods. The new approach combines the magnetohydrostatic (MHS) extrapolation, which models the solar low atmosphere in a flat box, together with the nonlinear force-free field (NLFFF) extrapolation, which models the solar corona with a chromospheric vector magnetogram deduced from the MHS extrapolation. We tested our code with a snapshot of a radiative magnetohydrodynamic simulation of a solar flare and we conducted quantitative comparisons based on several metrics. Results. Following a number of test runs, we found an optimized configuration for the combination of two extrapolations with a 5.8-Mm-high box for the MHS extrapolation and a magnetogram at a height of 1 Mm for the NLFFF extrapolation. The new approach under this configuration has the capability to reconstruct the magnetic fields in multi-layers accurately and efficiently. Based on figures of merit that are used to assess the performance of different extrapolations (NLFFF extrapolation, MHS extrapolation, and the combined one), we find the combined extrapolation reaches the same level of accuracy as the MHS extrapolation and they are both better than the NLFFF extrapolation. The combined extrapolation is moderately efficient for application to magnetograms with high resolution.
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2

Norozi, Muhammad Ali. "Faster Ranking Using Extrapolation Techniques." International Journal of Computer Vision and Image Processing 1, no. 3 (July 2011): 35–52. http://dx.doi.org/10.4018/ijcvip.2011070103.

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Extrapolations are techniques in linear algebra that require little additional infrastructure that must be incorporated in the existing query-dependent Link Analysis Ranking (LAR) algorithms. Extrapolations in LAR settings relies on the prior knowledge of the (iterative) process that created the existing data points (iterates) to compute the new (improved) data point, which periodically leads to the desired solution faster than the original method. In this study, the author presents novel approaches using extrapolation techniques to speed-up the convergence of query-dependent iterative methods, link analysis based ranking methods, where hyperlink structures are used to determine relative importance of a document in the network of inter-connections. The author uses the framework defined in HITS and SALSA and proposes the use of different Extrapolation techniques for faster ranking. The paper improves algorithms like HITS and SALSA using Extrapolation techniques. With the proposed approaches it is possible to accelerate the iterative ranking algorithms in terms of reducing the number of iterations and increasing the rate of convergence.
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Cho, Doah, Saskia Cheyne, Sarah J. Lord, John Simes, and Chee Khoon Lee. "Extrapolating evidence for molecularly targeted therapies from common to rare cancers: a scoping review of methodological guidance." BMJ Open 12, no. 7 (July 2022): e058350. http://dx.doi.org/10.1136/bmjopen-2021-058350.

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ObjectivesCancer is increasingly classified according to biomarkers that drive tumour growth and therapies developed to target them. In rare biomarker-defined cancers, randomised controlled trials to adequately assess targeted therapies may be infeasible. Extrapolating existing evidence of targeted therapy from common cancers to rare cancers sharing the same biomarker may reduce evidence requirements for regulatory approval in rare cancers. It is unclear whether guidelines exist for extrapolation. We sought to identify methodological guidance for extrapolating evidence from targeted therapies used for common cancers to rare biomarker-defined cancers.DesignScoping review.Data sourcesWebsites of health technology assessment agencies, regulatory bodies, research groups, scientific societies and industry. EBM Reviews—Cochrane Methodology Register and Health Technology Assessment, Embase and MEDLINE databases (1946 to 11 May 2022).Eligibility criteriaPapers proposing a framework or recommendations for extrapolating evidence for rare cancers, small populations and biomarker-defined cancers.Data extraction and synthesisWe extracted framework details where available and guidance for components of extrapolation. We used these components to structure and summarise recommendations.ResultsWe identified 23 papers. One paper provided an extrapolation framework but was not cancer specific. Extrapolation recommendations addressed six distinct components: strategies for grouping cancers as the same biomarker-defined disease; analytical validation requirements of a biomarker test to use across cancer types; strategies to generate control data when a randomised concurrent control arm is infeasible; sources to inform biomarker clinical utility assessment in the absence of prospective clinical evidence; requirements for surrogate endpoints chosen for the rare cancer; and assessing and augmenting safety data in the rare cancer.ConclusionsIn the absence of an established framework, our recommendations for components of extrapolation can be used to guide discussions about interpreting evidence to support extrapolation. The review can inform the development of an extrapolation framework for biomarker-targeted therapies in rare cancers.
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Zhang, Jie, and George A. McMechan. "Turning wave migration by horizontal extrapolation." GEOPHYSICS 62, no. 1 (January 1997): 291–97. http://dx.doi.org/10.1190/1.1444130.

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Conventional migration based on depth stepping extrapolation fails to migrate turning wave energy because of its inability to propagate energy with dips beyond 90°. A viable strategy for imaging turning waves is to use horizontal, rather than depth, extrapolation. This can be implemented by a 90° rotation of the extrapolator so that the data are extrapolated horizontally rather than vertically. In this geometry, the energy associated with turned rays consistently moves in the same direction as the extrapolation, and so only one pass is necessary to image turned reflections. The viability of this strategy is demonstrated with both synthetic and field poststack data that include turned reflections from salt flanks. Depth extrapolation images the near‐horizontal structure and horizontal extrapolation images the near‐vertical structure, and combining them gives a full image containing all dips.
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5

Clewell, Harvey J., and Melvin E. Andersen. "Risk Assessment Extrapolations and Physiological Modeling." Toxicology and Industrial Health 1, no. 4 (October 1985): 111–34. http://dx.doi.org/10.1177/074823378500100408.

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The process of assessing the risk associated with human exposure to environmental chemicals inevitably relies on a number of assumptions, estimates and rationalizations. One of the more challenging aspects of risk assessment involves the need to extrapolate beyond the range of conditions used in experimental animal studies to predict anticipated human risks. The most obvious extrapolation required is that from the tested animal species to humans; but others are also generally required, including extrapolating from high dose to low dose, from one route of exposure to another and from one exposure timeframe to another. Several avenues are available for attempting these extrapolations, ranging from the assumption of strict correspondence of dose to the use of statistical correlations. One promising alternative for conducting more scientifically sound extrapolations is that of using physiologically based pharmacokinetic models that contain sufficient biological detail to allow pharmacokinetic behavior to be predicted for widely different exposure scenarios. In recent years, successful physiological models have been developed for a variety of volatile and nonvolatile chemicals, and their ability to perform the extrapolations needed in risk assessment has been demonstrated. Techniques for determining the necessary biochemical parameters are readily available, and the computational requirements are now within the scope of even a personal computer. In addition to providing a sound framework for extrapolation, the predictive power of a physiologically based pharmacokinetic model makes it a useful tool for more reliable dose selection before beginning large-scale studies, as well as for the retrospective analysis of experimental results.
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6

Zhou, Hongbo, and George A. McMechan. "Rigorous absorbing boundary conditions for 3-D one‐way wave extrapolation." GEOPHYSICS 65, no. 2 (March 2000): 638–45. http://dx.doi.org/10.1190/1.1444760.

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Absorbing boundary conditions play an important role in one‐way wave extrapolations by reducing reflections at grid edges. Clayton and Engquist’s 2-D absorbing boundary conditions for one‐way wave extrapolation by depth stepping in the frequency domain are extended to three dimensions using paraxial approximations of the scalar wave equation. Internal consistency is retained by incorporating the interior extrapolation equation with the absorbing boundary conditions. Numerical schemes are designed to make the proposed absorbing boundary conditions both mathematically correct and efficient with negligible extra cost. Synthetic examples illustrate the effectiveness of the algorithm for extrapolation with the 3-D 45° one‐way wave equation.
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7

Kodell, Ralph L., and David W. Gaylor. "Uncertainty of Estimates of Cancer Risks Derived by Extrapolation from High to Low Doses and from Animals to Humans." International Journal of Toxicology 16, no. 4-5 (July 1997): 449–60. http://dx.doi.org/10.1080/109158197227062.

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The uncertainties associated with extrapolating model-based cancer risks from high to low doses and animal-based cancer risks to humans are examined. It is argued that low-dose linear extrapolation based on statistical confidence limits calculated from animal data is designed to account for data uncertainty, model-selection uncertainty, and model-fitting instability. The intent is to err on the side of safety, that is, overstating rather than understating the true risk. The tendency toward conservatism in predicting human cancer risks from animal data based on linear extrapolation is confirmed by a real-data analysis of the various sources of uncertainty involved in extrapolating from animals to humans. Along with the tendency toward conservatism, a high degree of overall uncertainty in the interspecies extrapolation process is demonstrated. It is concluded that human cancer risk estimates based on animal data may underestimate the true risk by a factor of 10 or may overestimate that risk by a factor of 1,000.
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8

Jing, J. R., Q. Li, X. Y. Ding, N. L. Sun, R. Tang, and Y. L. Cai. "AENN: A GENERATIVE ADVERSARIAL NEURAL NETWORK FOR WEATHER RADAR ECHO EXTRAPOLATION." ISPRS - International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences XLII-3/W9 (October 25, 2019): 89–94. http://dx.doi.org/10.5194/isprs-archives-xlii-3-w9-89-2019.

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Abstract. Weather radar echo is one of the fundamental data for meteorological workers to weather systems identification and classification. Through the technique of weather radar echo extrapolation, the future short-term weather conditions can be predicted and severe convection storms can be warned. However, traditional extrapolation methods cannot offer accurate enough extrapolation results since their modeling capacity is limited, the recent deep learning based methods make some progress but still remains a problem of blurry prediction when making deeper extrapolation, which may due to they choose the mean square error as their loss function and that will lead to losing echo details. To address this problem and make a more realistic and accurate extrapolation, we propose a deep learning model called Adversarial Extrapolation Neural Network (AENN), which is a Generative Adversarial Network (GAN) structure and consist of a conditional generator and two discriminators, echo-frame discriminator and echo-sequence discriminator. The generator and discriminators are trained alternately in an adversarial way to make the final extrapolation results be realistic and accurate. To evaluate the model, we conduct experiments on extrapolating 0.5h, 1h, and 1.5h imminent future echoes, the results show that our proposed AENN can achieve the expected effect and outperforms other models significantly, which has a powerful potential application value for short-term weather forecasting.
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9

Mousa, Wail A., Mirko van der Baan, Said Boussakta, and Desmond C. McLernon. "Designing stable extrapolators for explicit depth extrapolation of 2D and 3D wavefields using projections onto convex sets." GEOPHYSICS 74, no. 2 (March 2009): S33—S45. http://dx.doi.org/10.1190/1.3077621.

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We have developed a robust algorithm for designing explicit depth extrapolation operators using the projections-onto-convex-sets (POCS) method. The operators are optimal in the sense that they satisfy all required extrapolation design characteristics. In addition, we propose a simple modification of the POCS algorithm (modified POCS, or MPOCS) that further enhances the stability of extrapolated wavefields and reduces the number of iterations required to design such operators to approximately 2% of that required for the basic POCS design algorithm. Various synthetic tests show that 25-coefficient 1D extrapolation operators, which have 13 unique coefficients, can accommodate dip angles up to 70°. We migrated the SEG/EAGE salt model data with the operators and compare our results with images obtained via extrapolators based on modified Taylor series and with wavefield extrapolation techniques such as phase shift plus interpolation (PSPI) and split-step Fourier. The MPOCS algorithm provides practically stable depth extrapolators. The resulting migrated section is comparable in quality to an expensive PSPI result and visibly outperforms the other two techniques. Strong dips and subsalt structures are imaged clearly. Finally, we extended the 1D extrapolator design algorithm, using MPOCS for 2D extrapolation, to the 2D case to perform 3D extrapolation; the result is a perfect circularly symmetric migration impulse response.
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10

Suominen, Arho, and Marko Seppänen. "Bibliometric data and actual development in technology life cycles: flaws in assumptions." Foresight 16, no. 1 (March 4, 2014): 37–53. http://dx.doi.org/10.1108/fs-03-2013-0007.

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Purpose – Motivated with the ever growing number of bibliometric trend extrapolation studies, the purpose of this paper is to demonstrate through two technologies how the selection of an upper limit of growth affects the correlation and causality of technology development measured with bibliometric data. Design/methodology/approach – The paper uses Gompertz and Fisher-Pry curves to model the technological development of white light emitting diodes and flash memory, and show with extrapolation results from several bibliometric sources how a typical bias is caused in trend extrapolations. Findings – The paper shows how drastic an effect the decision to set an upper bound has on trend extrapolations, to be used as a reference for applications. The paper recommends carefully examining the interconnection of actual development and bibliometric activity. Originality/value – Despite increasing interest in modelling technological data using this method, reports rarely discuss basic assumptions and their effects on outcomes. Since trend extrapolations are applied more widely in different disciplines, the basic limitations of methods should be explicitly expressed.
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11

Vassallo, Daniel, Raghavendra Krishnamurthy, and Harindra J. S. Fernando. "Decreasing wind speed extrapolation error via domain-specific feature extraction and selection." Wind Energy Science 5, no. 3 (July 26, 2020): 959–75. http://dx.doi.org/10.5194/wes-5-959-2020.

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Abstract. Model uncertainty is a significant challenge in the wind energy industry and can lead to mischaracterization of millions of dollars' worth of wind resources. Machine learning methods, notably deep artificial neural networks (ANNs), are capable of modeling turbulent and chaotic systems and offer a promising tool to produce high-accuracy wind speed forecasts and extrapolations. This paper uses data collected by profiling Doppler lidars over three field campaigns to investigate the efficacy of using ANNs for wind speed vertical extrapolation in a variety of terrains, and it quantifies the role of domain knowledge in ANN extrapolation accuracy. A series of 11 meteorological parameters (features) are used as ANN inputs, and the resulting output accuracy is compared with that of both standard log-law and power-law extrapolations. It is found that extracted nondimensional inputs, namely turbulence intensity, current wind speed, and previous wind speed, are the features that most reliably improve the ANN's accuracy, providing up to a 65 % and 52 % increase in extrapolation accuracy over log-law and power-law predictions, respectively. The volume of input data is also deemed important for achieving robust results. One test case is analyzed in depth using dimensional and nondimensional features, showing that the feature nondimensionalization drastically improves network accuracy and robustness for sparsely sampled atmospheric cases.
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Varandas, A. J. C. "Extrapolation in quantum chemistry: Insights on energetics and reaction dynamics." Journal of Theoretical and Computational Chemistry 19, no. 07 (September 2, 2020): 2030001. http://dx.doi.org/10.1142/s0219633620300013.

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Since there is no exact solution for problems in physics and chemistry, extrapolation methods may assume a key role in quantitative quantum chemistry. Two topics where it bears considerable impact are addressed, both at the heart of computational quantum chemistry: electronic structure and reaction dynamics. In the first, the problem of extrapolating the energy obtained by solving the electronic Schrödinger equation to the limit of the complete one-electron basis set is addressed. With the uniform-singlet-and-triplet-extrapolation (USTE) scheme at the focal point, the emphasis is on recent updates covering from the energy itself to other molecular properties. The second topic refers to extrapolation of quantum mechanical reactive scattering probabilities from zero total angular momentum to any of the values that it may assume when running quasiclassical trajectories, QCT/QM-[Formula: see text]J. With the extrapolation guided in both cases by physically motivated asymptotic theories, realism is seeked by avoiding unsecure jumps into the unknown. Although, mostly review oriented, a few issues are addressed for the first time here and there. Prospects for future work conclude the overview.
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Gallacher, Daniel, Peter Kimani, and Nigel Stallard. "Extrapolating Parametric Survival Models in Health Technology Assessment Using Model Averaging: A Simulation Study." Medical Decision Making 41, no. 4 (February 25, 2021): 476–84. http://dx.doi.org/10.1177/0272989x21992297.

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Previous work examined the suitability of relying on routine methods of model selection when extrapolating survival data in a health technology appraisal setting. Here we explore solutions to improve reliability of restricted mean survival time (RMST) estimates from trial data by assessing model plausibility and implementing model averaging. We compare our previous methods of selecting a model for extrapolation using the Akaike information criterion (AIC) and Bayesian information criterion (BIC). Our methods of model averaging include using equal weighting across models falling within established threshold ranges for AIC and BIC and using BIC-based weighted averages. We apply our plausibility assessment and implement model averaging to the output of our previous simulations, where 10,000 runs of 12 trial-based scenarios were examined. We demonstrate that removing implausible models from consideration reduces the mean squared error associated with the restricted mean survival time (RMST) estimate from each selection method and increases the percentage of RMST estimates that were within 10% of the RMST from the parameters of the sampling distribution. The methods of averaging were superior to selecting a single optimal extrapolation, aside from some of the exponential scenarios where BIC already selected the exponential model. The averaging methods with wide criterion-based thresholds outperformed BIC-weighted averaging in the majority of scenarios. We conclude that model averaging approaches should feature more widely in the appraisal of health technologies where extrapolation is influential and considerable uncertainty is present. Where data demonstrate complicated underlying hazard rates, funders should account for the additional uncertainty associated with these extrapolations in their decision making. Extended follow-up from trials should be encouraged and used to review prices of therapies to ensure a fair price is paid.
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14

Cerrini, Angela, P. Johannesson, and Stefano Beretta. "Superposition of Manoeuvres and Load Spectra Extrapolation." Applied Mechanics and Materials 5-6 (October 2006): 255–62. http://dx.doi.org/10.4028/www.scientific.net/amm.5-6.255.

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To face the increasing demand for long lasting, versatile and performing machines, a detailed analysis of the load conditions is required especially when structural integrity assessment has to be achieved. Usually acquisitions of load histories are shorter than the machine working life and an extrapolation of the signal for the total service life is needed. Traditional methods for load spectra extrapolation are based on conservative choices in terms of worst case scenario. Methods based on extreme value statistics have been developed. The problem addressed in this paper concerns the extrapolation of load histories on a welded boom in which different manoeuvres are superimposed. Different ways of extrapolating the load measurement have been derived, both in time domain and in Markov domain, in order to account for the superposition of bigger and more damaging cycles and smaller cycles caused by two different service operations.
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Wu, Zedong, and Tariq Alkhalifah. "The optimized expansion based low-rank method for wavefield extrapolation." GEOPHYSICS 79, no. 2 (March 1, 2014): T51—T60. http://dx.doi.org/10.1190/geo2013-0174.1.

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Spectral methods are fast becoming an indispensable tool for wavefield extrapolation, especially in anisotropic media because it tends to be dispersion and artifact free as well as highly accurate when solving the wave equation. However, for inhomogeneous media, we face difficulties in dealing with the mixed space-wavenumber domain extrapolation operator efficiently. To solve this problem, we evaluated an optimized expansion method that can approximate this operator with a low-rank variable separation representation. The rank defines the number of inverse Fourier transforms for each time extrapolation step, and thus, the lower the rank, the faster the extrapolation. The method uses optimization instead of matrix decomposition to find the optimal wavenumbers and velocities needed to approximate the full operator with its explicit low-rank representation. As a result, we obtain lower rank representations compared with the standard low-rank method within reasonable accuracy and thus cheaper extrapolations. Additional bounds set on the range of propagated wavenumbers to adhere to the physical wave limits yield unconditionally stable extrapolations regardless of the time step. An application on the BP model provided superior results compared to those obtained using the decomposition approach. For transversely isotopic media, because we used the pure P-wave dispersion relation, we obtained solutions that were free of the shear wave artifacts, and the algorithm does not require that [Formula: see text]. In addition, the required rank for the optimization approach to obtain high accuracy in anisotropic media was lower than that obtained by the decomposition approach, and thus, it was more efficient. A reverse time migration result for the BP tilted transverse isotropy model using this method as a wave propagator demonstrated the ability of the algorithm.
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Whitney, David. "Visuomotor extrapolation." Behavioral and Brain Sciences 31, no. 2 (April 2008): 220–21. http://dx.doi.org/10.1017/s0140525x08004044.

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AbstractAccurate perception of moving objects would be useful; accurate visually guided action is crucial. Visual motion across the scene influences perceived object location and the trajectory of reaching movements to objects. In this commentary, I propose that the visual system assigns the position of any object based on the predominant motion present in the scene, and that this is used to guide reaching movements to compensate for delays in visuomotor processing.
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Keating, Mike. "Extrapolation nation." New Scientist 204, no. 2737 (December 2009): 30. http://dx.doi.org/10.1016/s0262-4079(09)63194-8.

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Supp, Georg, Richard Rosedale, and Mark Werneke. "Unjustified extrapolation." Scandinavian Journal of Pain 16, no. 1 (July 1, 2017): 189–90. http://dx.doi.org/10.1016/j.sjpain.2017.03.008.

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Makai, Mihály. "Richardson Extrapolation." Nuclear Science and Engineering 89, no. 4 (April 1985): 382–83. http://dx.doi.org/10.13182/nse85-a18631.

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Vishwanathan, S. V. N., Karsten M. Borgwardt, Omri Guttman, and Alex Smola. "Kernel extrapolation." Neurocomputing 69, no. 7-9 (March 2006): 721–29. http://dx.doi.org/10.1016/j.neucom.2005.12.113.

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Quinlan, Christina. "Extrapolation warning." Canadian Medical Association Journal 189, no. 36 (September 10, 2017): E1151. http://dx.doi.org/10.1503/cmaj.733233.

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Guala, Francesco. "Emphasising Extrapolation." Metascience 18, no. 2 (May 12, 2009): 331–33. http://dx.doi.org/10.1007/s11016-009-9286-6.

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23

Brezinski, C., and M. Redivo-Zaglia. "Extrapolation methods." Applied Numerical Mathematics 15, no. 2 (September 1994): 123–31. http://dx.doi.org/10.1016/0168-9274(94)00015-8.

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Martín, Joaquim, and Mario Milman. "Extrapolation methods and Rubio de Francia's extrapolation theorem." Advances in Mathematics 201, no. 1 (March 2006): 209–62. http://dx.doi.org/10.1016/j.aim.2005.02.006.

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Li, Ren, Yanan Cao, Qiannan Zhu, Guanqun Bi, Fang Fang, Yi Liu, and Qian Li. "How Does Knowledge Graph Embedding Extrapolate to Unseen Data: A Semantic Evidence View." Proceedings of the AAAI Conference on Artificial Intelligence 36, no. 5 (June 28, 2022): 5781–91. http://dx.doi.org/10.1609/aaai.v36i5.20521.

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Knowledge Graph Embedding (KGE) aims to learn representations for entities and relations. Most KGE models have gained great success, especially on extrapolation scenarios. Specifically, given an unseen triple (h, r, t), a trained model can still correctly predict t from (h, r, ?), or h from (?, r, t), such extrapolation ability is impressive. However, most existing KGE works focus on the design of delicate triple modeling function, which mainly tells us how to measure the plausibility of observed triples, but offers limited explanation of why the methods can extrapolate to unseen data, and what are the important factors to help KGE extrapolate. Therefore in this work, we attempt to study the KGE extrapolation of two problems: 1. How does KGE extrapolate to unseen data? 2. How to design the KGE model with better extrapolation ability? For the problem 1, we first discuss the impact factors for extrapolation and from relation, entity and triple level respectively, propose three Semantic Evidences (SEs), which can be observed from train set and provide important semantic information for extrapolation. Then we verify the effectiveness of SEs through extensive experiments on several typical KGE methods. For the problem 2, to make better use of the three levels of SE, we propose a novel GNN-based KGE model, called Semantic Evidence aware Graph Neural Network (SE-GNN). In SE-GNN, each level of SE is modeled explicitly by the corresponding neighbor pattern, and merged sufficiently by the multi-layer aggregation, which contributes to obtaining more extrapolative knowledge representation. Finally, through extensive experiments on FB15k-237 and WN18RR datasets, we show that SE-GNN achieves state-of-the-art performance on Knowledge Graph Completion task and performs a better extrapolation ability. Our code is available at https://github.com/renli1024/SE-GNN.
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Hale, Dave. "Stable explicit depth extrapolation of seismic wavefields." GEOPHYSICS 56, no. 11 (November 1991): 1770–77. http://dx.doi.org/10.1190/1.1442989.

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Stability has traditionally been one of the most compelling advantages of implicit methods for seismic wavefield extrapolation. The common 45-degree, finite‐difference migration algorithm, for example, is based on an implicit wavefield extrapolation that is guaranteed to be stable. Specifically, wavefield energy will not grow exponentially with depth as the wavefield is extrapolated downwards into the subsurface. Explicit methods, in contrast, tend to be unstable. Without special care in their implementation, explicit extrapolation methods cause wavefield energy to grow exponentially with depth, contrary to physical expectations. The Taylor series method may be used to design finite‐length, explicit, extrapolation filters. In the usual Taylor series method, N coefficients of a finite‐length filter are chosen to match N terms in a truncated Taylor series approximation of the desired filter’s Fourier transform. Unfortunately, this method yields unstable extrapolation filters. However, a simple modification of the Taylor series method yields extrapolators that are stable. The accuracy of stable explicit extrapolators is determined by their length—longer extrapolators yield accurate extrapolation for a wider range of propagation angles than do shorter filters. Because a very long extrapolator is required to extrapolate waves propagating at angles approaching 90 degrees, stable explicit extrapolators may be less efficient than implicit extrapolators for high propagation angles. For more modest propagation angles of 50 degrees of less, stable explicit extrapolators are likely to be more efficient than current implicit extrapolators. Furthermore, unlike implicit extrapolators, stable explicit extrapolators naturally attenuate waves propagating at high angles for which the extrapolators are inaccurate.
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van Eerden, Ruben A. G., Esther Oomen-de Hoop, Aad Noordam, Ron H. J. Mathijssen, and Stijn L. W. Koolen. "Feasibility of Extrapolating Randomly Taken Plasma Samples to Trough Levels for Therapeutic Drug Monitoring Purposes of Small Molecule Kinase Inhibitors." Pharmaceuticals 14, no. 2 (February 4, 2021): 119. http://dx.doi.org/10.3390/ph14020119.

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Small molecule kinase inhibitors (SMKIs) are widely used in oncology. Therapeutic drug monitoring (TDM) for SMKIs could reduce underexposure or overexposure. However, logistical issues such as timing of blood withdrawals hamper its implementation into clinical practice. Extrapolating a random concentration to a trough concentration using the elimination half-life could be a simple and easy way to overcome this problem. In our study plasma concentrations observed during 24 h blood sampling were used for extrapolation to trough levels. The objective was to demonstrate that extrapolation of randomly taken blood samples will lead to equivalent estimated trough samples compared to measured Cmin values. In total 2241 blood samples were analyzed. The estimated Ctrough levels of afatinib and sunitinib fulfilled the equivalence criteria if the samples were drawn after Tmax. The calculated Ctrough levels of erlotinib, imatinib and sorafenib met the equivalence criteria if they were taken, respectively, 12 h, 3 h and 10 h after drug intake. For regorafenib extrapolation was not feasible. In conclusion, extrapolation of randomly taken drug concentrations to a trough concentration using the mean elimination half-life is feasible for multiple SMKIs. Therefore, this simple method could positively contribute to the implementation of TDM in oncology.
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Khosrowi, Donal. "When Experiments Need Models." Philosophy of the Social Sciences 51, no. 4 (April 21, 2021): 400–424. http://dx.doi.org/10.1177/00483931211008542.

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This paper argues that an important type of experiment-target inference, extrapolating causal effects, requires models to be successful. Focusing on extrapolation in Evidence-Based Policy, it is argued that extrapolation should be understood not as an inference from an experiment to a target directly, but as a hybrid inference that involves experiments and models. A general framework, METI, is proposed to capture this role of models, and several benefits are outlined: (1) METI highlights epistemically significant interactions between experiments and models, (2) reconciles some differences among existing accounts of experiment-target relationships, and (3) facilitates critical appraisal of inferential practices from experiments.
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Mittet, Rune, Roger Sollie, and Ketil Hokstad. "Prestack depth migration with compensation for absorption and dispersion." GEOPHYSICS 60, no. 5 (September 1995): 1485–94. http://dx.doi.org/10.1190/1.1443882.

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In prestack depth migration using explicit extrapolators, the attenuation and dispersion of the seismic wave has been neglected so far. We present a method for accommodating absorption and dispersion effects in depth migration schemes. Extrapolation operators that compensate for absorption and dispersion are designed using an optimization algorithm. The design criterion is that the wavenumber response of the operator should equal the true extrapolator. Both phase velocity and absorption macro models are used in the wavefield extrapolation. In a model with medium to high absorption, the images obtained are superior to those obtained using extrapolators without compensation for absorption.
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Gallacher, Daniel, Peter Auguste, and Martin Connock. "How Do Pharmaceutical Companies Model Survival of Cancer Patients? A Review of NICE Single Technology Appraisals in 2017." International Journal of Technology Assessment in Health Care 35, no. 2 (2019): 160–67. http://dx.doi.org/10.1017/s0266462319000175.

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AbstractObjectivesBefore an intervention is publicly funded within the United Kingdom, the cost-effectiveness is assessed by the National Institute of Health and Care Excellence (NICE). The efficacy of an intervention across the patients’ lifetime is often influential of the cost-effectiveness analyses, but is associated with large uncertainties. We reviewed committee documents containing company submissions and evidence review group (ERG) reports to establish the methods used when extrapolating survival data, whether these adhered to NICE Technical Support Document (TSD) 14, and how uncertainty was addressed.MethodsA systematic search was completed on the NHS Evidence Search webpage limited to single technology appraisals of cancer interventions published in 2017, with information obtained from the NICE Web site.ResultsTwenty-eight appraisals were identified, covering twenty-two interventions across eighteen diseases. Every economic model used parametric curves to model survival. All submissions used goodness-of-fit statistics and plausibility of extrapolations when selecting a parametric curve. Twenty-five submissions considered alternate parametric curves in scenario analyses. Six submissions reported including the parameters of the survival curves in the probabilistic sensitivity analysis. ERGs agreed with the company's choice of parametric curve in nine appraisals, and agreed with all major survival-related assumptions in two appraisals.ConclusionsTSD 14 on survival extrapolation was followed in all appraisals. Despite this, the choice of parametric curve remains subjective. Recent developments in Bayesian approaches to extrapolation are not implemented. More precise guidance on the selection of curves and modelling of uncertainty may reduce subjectivity, accelerating the appraisal process.
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Damoiseaux, David, Wenlong Li, Alejandra Martínez-Chávez, Jos H. Beijnen, Alfred H. Schinkel, Alwin D. R. Huitema, and Thomas P. C. Dorlo. "Predictiveness of the Human-CYP3A4-Transgenic Mouse Model (Cyp3aXAV) for Human Drug Exposure of CYP3A4-Metabolized Drugs." Pharmaceuticals 15, no. 7 (July 13, 2022): 860. http://dx.doi.org/10.3390/ph15070860.

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The extrapolation of drug exposure between species remains a challenging step in drug development, contributing to the low success rate of drug approval. As a consequence, extrapolation of toxicology from animal models to humans to evaluate safe, first-in-human (FIH) doses requires high safety margins. We hypothesized that a human-CYP3A4-expressing transgenic (Cyp3aXAV) mouse is a more predictive model for human drug exposure of CYP3A4-metabolized small-molecule drugs. Population pharmacokinetic models based on wild-type (WT) and Cyp3aXAV mouse pharmacokinetic data of oral lorlatinib, brigatinib, ribociclib and fisogatinib were allometrically scaled and compared to human exposure. Extrapolation of the Cyp3aXAV mouse model closely predicted the observed human exposure for lorlatinib and brigatinib with a 1.1-fold and 1.0-fold difference, respectively, compared to a 2.1-fold and 1.9-fold deviation for WT-based extrapolations of lorlatinib and brigatinib, respectively. For ribociclib, the extrapolated WT mouse model gave better predictions with a 1.0-fold deviation compared to a 0.3-fold deviation for the extrapolated Cyp3aXAV mouse model. Due to the lack of a human population pharmacokinetic model for fisogatinib, only median maximum concentration ratios were calculated, resulting in ratios of 1.0 and 0.6 for WT and Cyp3aXAV mice extrapolations, respectively. The more accurate predictions of human exposure in preclinical research based on the Cyp3aXAV mouse model can ultimately result in FIH doses associated with improved safety and efficacy and in higher success rates in drug development.
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Jing, Jinrui, Qian Li, and Xuan Peng. "MLC-LSTM: Exploiting the Spatiotemporal Correlation between Multi-Level Weather Radar Echoes for Echo Sequence Extrapolation." Sensors 19, no. 18 (September 15, 2019): 3988. http://dx.doi.org/10.3390/s19183988.

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Weather radar echo is the data detected by the weather radar sensor and reflects the intensity of meteorological targets. Using the technique of radar echo extrapolation, which is the prediction of future echoes based on historical echo observations, the approaching short-term weather conditions can be forecasted, and warnings can be raised with regard to disastrous weather. Recently, deep learning based extrapolation methods have been proposed and show significant application potential. However, there are two limitations of existing extrapolation methods which should be considered. First, few methods have investigated the impact of the evolutionary process of weather systems on extrapolation accuracy. Second, current deep learning methods usually encounter the problem of blurry echo prediction as extrapolation goes deeper. In this paper, we aim to address the two problems by proposing a Multi-Level Correlation Long Short-Term Memory (MLC-LSTM) and integrate the adversarial training into our approach. The MLC-LSTM can exploit the spatiotemporal correlation between multi-level radar echoes and model their evolution, while the adversarial training can help the model extrapolate realistic and sharp echoes. To train and test our model, we build a real-life multi-level weather radar echoes dataset based on raw CINRAD/SA radar observations provided by the National Meteorological Information Center, China. Extrapolation experiments show that our model can accurately forecast the motion and evolution of an echo while keeping the predicted echo looking realistic and fine-grained. For quantitative evaluation on probability of detection (POD), false alarm rate (FAR), critical success index (CSI), and Heidke skill score (HSS) metrics, our model can reach average scores of 0.6538 POD, 0.2818 FAR, 0.5348 CSI, and 0.6298 HSS, respectively when extrapolating 15 echoes into the future, which outperforms the current state-of-the-art extrapolation methods. Both the qualitative and quantitative experimental results demonstrate the effectiveness of our model, suggesting that it can be effectively applied to operational weather forecasting practice.
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Zhou, Wen, and Jisheng Kou. "Third-Order Newton-Type Methods Combined with Vector Extrapolation for Solving Nonlinear Systems." Abstract and Applied Analysis 2014 (2014): 1–8. http://dx.doi.org/10.1155/2014/601745.

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We present a third-order method for solving the systems of nonlinear equations. This method is a Newton-type scheme with the vector extrapolation. We establish the local and semilocal convergence of this method. Numerical results show that the composite method is more robust and efficient than a number of Newton-type methods with the other vector extrapolations.
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Mousa, Wail A., Said Boussakta, Desmond C. McLernon, and Mirko Van der Baan. "Implementation of 2D explicit depth extrapolation FIR digital filters for 3D seismic volumes using singular value decomposition." GEOPHYSICS 75, no. 1 (January 2010): V1—V12. http://dx.doi.org/10.1190/1.3294424.

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We propose a new scheme for implementing predesigned 2D complex-valued wavefield extrapolation finite impulse response (FIR) digital filters, which are used for extrapolating 3D seismic wavefields. The implementation is based on singular value decomposition (SVD) of quadrantally symmetric 2D FIR filters (extrapolators). To simplify the SVD computations for such a filter impulse response structure, we apply a special matrix transformation on the extrapolation FIR filter impulse responses where we guarantee the retention of their wavenumber phase response. Unlike the existing 2D FIR filter implementation methods that are used for this geophysical application such as the McClellan transformation or its improved version, this implementation via SVD results in perfect circularly symmetrical magnitude and phase wavenumber responses. In this paper, we also demonstrate that the SVD method can save (depending on the filter size) more than 23% of the number of multiplications per output sample and approximately 62% of the number of additions per output sample when compared to direct implementation with quadrantal symmetry via true 2D convolution. Finally, an application to extrapolation of a seismic impulse is shown to prove our theoretical conclusions.
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Xu, Zhi Qiang, Hong Jian Wang, and Ming Yao Yao. "Load Spectrum Compilation Based on Nonparametric Statistical Extrapolation." Advanced Materials Research 694-697 (May 2013): 271–77. http://dx.doi.org/10.4028/www.scientific.net/amr.694-697.271.

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Considering the special load characteristics of the wheel loader, thispaper focus on compiling the load spectrum of the transmission of the wheelloader using the nonparametric statistical extrapolation method (NSEM). In thisprocess, the determination of the kernel function shape is the critical issue,which has been discussed in detail. Before extrapolating the sample loadspectrum, the signal denoising of the field-tested time-history load signals isperformed. After that, the sample load cycles are obtained using the rainflowcounting method and the corresponding kernel function shape is determined. Thenthe NSEM of rainflow matrix is proposed, by which the whole-life load spectrumis estimated. The proposed extrapolation method can well realize the estimationof the load cycles that do not appear in sample load cycles but may exist inthe whole-life load history.
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Coon, Sidney A., and Michael K. G. Kruse. "Properties of infrared extrapolations in a harmonic oscillator basis." International Journal of Modern Physics E 25, no. 05 (May 2016): 1641011. http://dx.doi.org/10.1142/s0218301316410111.

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The success and utility of effective field theory (EFT) in explaining the structure and reactions of few-nucleon systems has prompted the initiation of EFT-inspired extrapolations to larger model spaces in ab initio methods such as the no-core shell model (NCSM). In this contribution, we review and continue our studies of infrared (ir) and ultraviolet (uv) regulators of NCSM calculations in which the input is phenomenological [Formula: see text] and [Formula: see text] interactions fitted to data. We extend our previous findings that an extrapolation in the ir cutoff with the uv cutoff above the intrinsic uv scale of the interaction is quite successful, not only for the eigenstates of the Hamiltonian but also for expectation values of operators, such as [Formula: see text], considered long range. The latter results are obtained with Hamiltonians transformed by the similarity renormalization group (SRG) evolution. On the other hand, a possible extrapolation of ground state energies in the uv cutoff when the ir cutoff is below the intrinsic ir scale is not robust and does not agree with the ir extrapolation of the same data or with independent calculations using other methods.
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37

Du, Xiang, Paul J. Fowler, and Robin P. Fletcher. "Recursive integral time-extrapolation methods for waves: A comparative review." GEOPHYSICS 79, no. 1 (January 1, 2014): T9—T26. http://dx.doi.org/10.1190/geo2013-0115.1.

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We compared several families of algorithms for recursive integral time-extrapolation (RITE) algorithms for waves in isotropic and anisotropic media. These methods allow simulating accurate wave extrapolation with little numerical dispersion even when using larger time steps than are usually possible for conventional finite-difference methods. These various RITE algorithms all share the use of mixed space/wavenumber-domain operators derived from Fourier integral solutions of single-mode wave equations. We evaluated a taxonomy for RITE methods based on how they approximated the influence of medium heterogeneity. One family of methods uses mixed-domain series expansions to provide accurate approximations to heterogeneous extrapolators even for large time steps. We compared several methods for deriving coefficients for such series approximations. Another family of methods uses interpolation between different homogeneous extrapolations to approximate heterogeneous time extrapolation. Such methods can be based on interpolating either the extrapolators themselves or interpolating between reference wavefields extrapolated using different homogeneous parameters. Interpolation methods work well for smooth media, but can suffer from oscillatory artifacts at large velocity discontinuities unless the time step is small. We tested numerical examples of the various families of RITE algorithms to determine their relative strengths and limitations.
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Al-Saleh, Saleh M., Gary F. Margrave, and Sam H. Gray. "Direct downward continuation from topography using explicit wavefield extrapolation." GEOPHYSICS 74, no. 6 (November 2009): S105—S112. http://dx.doi.org/10.1190/1.3263914.

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Downward-continuation migration algorithms are powerful tools for imaging complicated subsurface structures. However, they usually assume that extrapolation proceeds from a flat surface, whereas most land surveys are acquired over irregular surfaces. Our method downward continues data directly from topography using a recursive space-frequency explicit wavefield-extrapolation method. The algorithm typically handles strong lateral velocity variations by using the velocity value at each spatial position to build the wavefield extrapolator in which the depth step usually is kept fixed. To accommodate topographic variations, we build space-frequency wavefield extrapolators with laterally variable depth steps (LVDS). At each spatial location, the difference between topography and extrapolation depth is used to determine the depth step. We use the velocity and topographic values at each spatial lateral position to build extrapolators. The LVDS approach does not add more data nor does it require preprocessing prior to extrapolation. We implemented the LVDS method and applied it to a source profile prestack migration technique. We also implemented the previously developed zero-velocity layer approach to use for comparison. For both algorithms, we modeled the acoustic source as an approximate free-space Green’s function, not as a simple extrapolated spatial impulse. Tests on a synthetic data set modeled from rough topography and comparisons with the zero-velocity layer approach confirm the method’s effectiveness in imaging shallow and deep structures beneath rugged topography.
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Clareson, Alice S. "Carry On, Extrapolation!" Extrapolation 40, no. 4 (January 1999): 271–76. http://dx.doi.org/10.3828/extr.1999.40.4.271.

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Levy, David. "Extrapolation and Speculation." ICGA Journal 18, no. 3 (September 1, 1995): 171–74. http://dx.doi.org/10.3233/icg-1995-18308.

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41

Hobbs, Sandy. "Barriers to Extrapolation?" Behavior and Social Issues 13, no. 2 (October 2004): 116–18. http://dx.doi.org/10.5210/bsi.v13i2.18.

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42

Li, Xiaochun, and Nancy E. Heckman. "Local linear extrapolation." Journal of Nonparametric Statistics 15, no. 4-5 (August 2003): 565–78. http://dx.doi.org/10.1080/10485250310001605432.

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43

Bangalore, S., and F. H. Messerli. "Assumptions and extrapolation." BMJ 338, jun29 1 (June 29, 2009): b2600. http://dx.doi.org/10.1136/bmj.b2600.

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44

Berezhnoi, E. I. "Extremal Extrapolation Spaces." Functional Analysis and Its Applications 54, no. 1 (January 2020): 1–6. http://dx.doi.org/10.1134/s0016266320010013.

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Sava, Paul, and Sergey Fomel. "Riemannian wavefield extrapolation." GEOPHYSICS 70, no. 3 (May 2005): T45—T56. http://dx.doi.org/10.1190/1.1925748.

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Riemannian spaces are described by nonorthogonal curvilinear coordinates. We generalize one-way wavefield extrapolation to semiorthogonal Riemannian coordinate systems that include, but are not limited to, ray coordinate systems. We obtain a one-way wavefield extrapolation method that can be used for waves propagating in arbitrary directions, in contrast to downward continuation, which is used for waves propagating mainly in the vertical direction. Ray coordinate systems can be initiated in many different ways; for example, from point sources or from plane waves incident at various angles. Since wavefield propagation happens mostly along the extrapolation direction, we can use inexpensive finite-difference or mixed-domain extrapolators to achieve high angle accuracy. The main applications of our method include imaging of steeply dipping or overturning reflections.
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Lin, Tim T., and Felix J. Herrmann. "Compressed wavefield extrapolation." GEOPHYSICS 72, no. 5 (September 2007): SM77—SM93. http://dx.doi.org/10.1190/1.2750716.

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An explicit algorithm for the extrapolation of one-way wavefields is proposed that combines recent developments in information theory and theoretical signal processing with the physics of wave propagation. Because of excessive memory requirements, explicit formulations for wave propagation have proven to be a challenge in 3D. By using ideas from compressed sensing, we are able to formulate the (inverse) wavefield extrapolation problem on small subsets of the data volume, thereby reducing the size of the operators. Compressed sensing entails a new paradigm for signal recovery that provides conditions under which signals can be recovered from incomplete samplings by nonlinear recovery methods that promote sparsity of the to-be-recovered signal. According to this theory, signals can be successfully recovered when the measurement basis is incoherent with the representa-tion in which the wavefield is sparse. In this new approach, the eigenfunctions of the Helmholtz operator are recognized as a basis that is incoherent with curvelets that are known to compress seismic wavefields. By casting the wavefield extrapolation problem in this framework, wavefields can be successfully extrapolated in the modal domain, despite evanescent wave modes. The degree to which the wavefield can be recovered depends on the number of missing (evanescent) wavemodes and on the complexity of the wavefield. A proof of principle for the compressed sensing method is given for inverse wavefield extrapolation in 2D, together with a pathway to 3D during which the multiscale and multiangular properties of curvelets, in relation to the Helmholz operator, are exploited. The results show that our method is stable, has reduced dip limitations, and handles evanescent waves in inverse extrapolation.
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Müller, J. W., V. E. Lewis, D. Smith, J. G. V. Taylor, and G. Winkler. "9. Extrapolation Techniques." Reports of the International Commission on Radiation Units and Measurements os-27, no. 1 (November 1994): 56–60. http://dx.doi.org/10.1093/jicru_os27.1.56.

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48

Messaoudi, A. "Matrix extrapolation algorithms." Linear Algebra and its Applications 256 (April 1997): 49–73. http://dx.doi.org/10.1016/s0024-3795(97)81112-3.

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49

van der Hoeven, Joris. "On asymptotic extrapolation." Journal of Symbolic Computation 44, no. 8 (August 2009): 1000–1016. http://dx.doi.org/10.1016/j.jsc.2009.01.001.

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50

Truhlar, Donald G. "Basis-set extrapolation." Chemical Physics Letters 294, no. 1-3 (September 1998): 45–48. http://dx.doi.org/10.1016/s0009-2614(98)00866-5.

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