Log in

Relevant bibliographies by topics / Born approximations

Contents

Journal articles

Academic literature on the topic 'Born approximations'

Author: Grafiati

Published: 4 June 2021

Last updated: 17 February 2022

Create a spot-on reference in APA, MLA, Chicago, Harvard, and other styles

Select a source type:

Consult the lists of relevant articles, books, theses, conference reports, and other scholarly sources on the topic 'Born approximations.'

Next to every source in the list of references, there is an 'Add to bibliography' button. Press on it, and we will generate automatically the bibliographic reference to the chosen work in the citation style you need: APA, MLA, Harvard, Chicago, Vancouver, etc.

You can also download the full text of the academic publication as pdf and read online its abstract whenever available in the metadata.

Journal articles on the topic "Born approximations"

1

Wei, Jia, Zengxi Ge, Mianshui Rong, and Zhenning Ba. "Preconditioned Splitting Series Approximation for 2D Rough Surface Scattering." Bulletin of the Seismological Society of America 110, no. 3 (2020): 1149–61. http://dx.doi.org/10.1785/0120190309.

Full text

Abstract:

ABSTRACT Scattering sensitivity of waves to surface roughness has been widely observed in many fields. Some series approximations for rough surface scattering, such as the general Born, the splitting, and the preconditioned splitting series, are presented for a numerical description of rough surface scattering by multiscale surfaces. In fact, the splitting series approximation is a specific form of the preconditioned splitting series. Numerical tests with several benchmark models are compared with the full-waveform numerical solution and the general Born series approximation to investigate the range of validity of the splitting and the preconditioned splitting series approximations. The splitting and the preconditioned splitting series approximations to multiscale surfaces are not subject to the strict limit applied to the general Born series approximation. Each order of the splitting series represents an increase of multiple scatterings between surface points. Therefore, higher-order splitting series approximation accounts for stronger surface scattering. A suitable preconditioned splitting and the splitting series approximations improve the general Born series approximation for the convergence of high-incident angle scattering, and, therefore, become realistic methods for multiscale surfaces with infinite gradients and extremely large surface heights. This series approximation mathematically provides a unified framework for rough surface scattering, which contains Born or Rytov series approximation as specific cases.

APA, Harvard, Vancouver, ISO, and other styles

2

Friar, J. L., and G. L. Payne. "Configuration-Space-Faddeev Born Approximations." Few-Body Systems 33, no. 4 (2003): 233–40. http://dx.doi.org/10.1007/s00601-003-0016-0.

Full text

APA, Harvard, Vancouver, ISO, and other styles

3

Zaidi, H. R. "Green's function equations of motion for driven two-level atoms." Canadian Journal of Physics 63, no. 3 (1985): 314–26. http://dx.doi.org/10.1139/p85-049.

Full text

Abstract:

Using a diagram technique, equations of motion for N coherently driven two-level atoms are obtained from Green's functions. The longitudinal (Coulomb) dipole–dipole interaction is neglected. Three approximations (Born approximation, extended Born approximation, and screened interaction approximation) are considered. The existing theories are shown to be equivalent to the extended Born approximation. For a small sample, the equations of motion exhibit S conservation in this case. The screened interaction model predicts a different behaviour; in particular, S-breaking terms appear in the equations of motion for a small sample.

APA, Harvard, Vancouver, ISO, and other styles

4

Yang, Kai, and Jianfeng Zhang. "Comparison between Born and Kirchhoff operators for least-squares reverse time migration and the constraint of the propagation of the background wavefield." GEOPHYSICS 84, no. 5 (2019): R725—R739. http://dx.doi.org/10.1190/geo2018-0438.1.

Full text

Abstract:

The Born approximation and the Kirchhoff approximation are two frameworks that are extensively used in solving seismic migration/inversion problems. Both approximations assume a linear relationship between the primary reflected/scattered data to the corresponding physical model. However, different approximations result in different behaviors. For least-squares reverse time migration (LSRTM), most of the algorithms are constructed based on Born approximation. We have constructed a pair of Kirchhoff modeling and migration operators based on the Born modeling operator and the connection between the perturbation model and the reflectivity model, and then we compared the different performances between Born and Kirchhoff operators for LSRTM. Numerical examples on Marmousi model and SEAM 2D salt model indicate that LSRTM with Kirchhoff operators is a better alternative to that with Born operators for imaging complex structures. To reduce the computational cost, we also investigate a strategy by restricting the propagation of the background wavefield to a stopping time rather than the maximum recording time. And this stopping time can be chosen as half of the maximum recording time. This computational strategy can be used in LSRTM procedures of predicting the primary reflected data, calculating the step length, and computing the gradient. Theoretical analyses and numerical experiments are given to justify this computational strategy for LSRTM.

APA, Harvard, Vancouver, ISO, and other styles

5

Rajan, Subramaniam D., and George V. Frisk. "A comparison between the Born and Rytov approximations for the inverse backscattering problem." GEOPHYSICS 54, no. 7 (1989): 864–71. http://dx.doi.org/10.1190/1.1442715.

Full text

Abstract:

We compare the Born and Rytov approximations in solving the inverse acoustic backscattering problem, i.e., determining medium properties from reflections. For the one‐dimensional problem, we show that the Rytov approximation is generally better than the Born approximation in predicting sound speed changes, while both methods have the same error in determining the positions of reflectors. This is shown analytically for simple models and numerically for more general models. The performance of the Rytov approximation is degraded when low‐velocity regions are present in the medium being probed. The accuracy of the inversion depends on the manner in which the sound speed perturbation is linearized. The location of the receiver affects the accuracy of the inversion, and, in the case of the Rytov approximation, best results are obtained when the receiver is at the interface between the known and unknown regions. Furthermore, the Rytov method is less sensitive to the choice of reference sound speed used in the inversion than is the Born approximation.

APA, Harvard, Vancouver, ISO, and other styles

6

Lo, Tien‐when, M. Nafi Toksöz, Shao‐hui Xu, and Ru‐Shan Wu. "Ultrasonic laboratory tests of geophysical tomographic reconstruction." GEOPHYSICS 53, no. 7 (1988): 947–56. http://dx.doi.org/10.1190/1.1442531.

Full text

Abstract:

In this study, we test geophysical ray tomography and geophysical diffraction tomography by scaled model ultrasonics experiments. First, we compare the performance of these two methods under limited view‐angle conditions. Second, we compare the adaptabilities of these two methods to objects of various sizes and acoustic properties. Finally, for diffraction tomography, we compare the Born and Rytov approximations based on the induced image distortion by using these two approximation methods. Our experimental results indicate the following: (1) When the scattered field can be obtained, geophysical diffraction tomography is in general superior to ray tomography because diffraction tomography is less sensitive to the limited view‐angle problem and can image small objects of size comparable to a wavelength. (2) The advantage of using ray tomography is that reconstruction can be done using the first arrivals only, the most easily measurable quantity; and there is no restriction on the properties of the object being imaged. (3) For geophysical diffraction tomography, the Rytov approximation is valid over a wider frequency range than the Born approximation in the cross‐borehole experiment. In the VSP and the surface reflection tomography experiments, no substantial difference between the Born and Rytov approximations is observed.

APA, Harvard, Vancouver, ISO, and other styles

7

Moy, G., J. Hope, and C. Savage. "Born and Markov approximations for atom lasers." Physical Review A 59, no. 1 (1999): 667–75. http://dx.doi.org/10.1103/physreva.59.667.

Full text

APA, Harvard, Vancouver, ISO, and other styles

8

McCarthy, IE. "The Electron - Atom Ionisation Problem." Australian Journal of Physics 49, no. 2 (1996): 219. http://dx.doi.org/10.1071/ph960219.

Full text

Abstract:

Methods of calculating electron–atom ionisation as a three-body problem with Coulomb boundary conditions are considered. In the absence of a fully-valid computational method for a time-independent experiment the approximation is made that the incident electron experiences a screened potential. Approximations involving a final state that obeys the three-body Coulomb boundary condition are compared with the distorted-wave Born approximation and the convergent close-coupling method.

APA, Harvard, Vancouver, ISO, and other styles

9

Beylkin, G., and M. L. Oristaglio. "Distorted-wave born and distorted-wave rytov approximations." Optics Communications 53, no. 4 (1985): 213–16. http://dx.doi.org/10.1016/0030-4018(85)90157-9.

Full text

APA, Harvard, Vancouver, ISO, and other styles

10

Birch, A. C., and A. G. Kosovichev. "Towards a Wave Theory Interpretation of Time-Distance Helioseismology Data." Symposium - International Astronomical Union 203 (2001): 180–82. http://dx.doi.org/10.1017/s0074180900219025.

Full text

Abstract:

Time-distance helioseismology, which measures the time for acoustic waves to travel between points on the solar surface, has been used to study small-scale three-dimensional features in the sun, for example active regions, as well as large-scale features, such as meridional flow, that are not accessible by standard global helioseismology. Traditionally, travel times have been interpreted using geometrical ray theory, which is not always a good approximation. In order to develop a wave interpretation of time-distance data we employ the first Born approximation, which takes into account finite-wavelength effects and is expected to provide more accurate inversion results. In the Born approximation, in contrast with ray theory, travel times are sensitive to perturbations to sound speed which are located off the ray path. In an example calculation of travel time perturbations due to sound speed perturbations that are functions only of depth, we see that that the Born and ray approximations agree when applied to perturbations with large spatial scale and that the ray approximation fails when applied to perturbations with small spatial scale.

APA, Harvard, Vancouver, ISO, and other styles

More sources

We offer discounts on all premium plans for authors whose works are included in thematic literature selections. Contact us to get a unique promo code!