### Abstract

We present the application of the theory of Padé approximants to extending the perturbative solutions of acoustic wave equation for a three dimensional vertically varying medium with one interface. These type of solutions have limited convergence properties depending on either the degree of contrast between the actual and the reference medium or the angle of incidence of a plane wave component. We show that the sequence of Padé approximants to the partial sums in the forward scattering series for the 3D wave equation is convergent for any contrast and any incidence angle. This allows the construction of any reflected waves including phase-shifted post-critical plane waves and, for a point-source problem, refracted events or headwaves, and it also provides interesting interpretations of these solutions in the scattering theory formalism.

Original language | English |
---|---|

Pages (from-to) | 180-202 |

Number of pages | 23 |

Journal | Communications in Computational Physics |

Volume | 3 |

Issue number | 1 |

State | Published - 1 Jan 2008 |

### Fingerprint

### Keywords

- Acoustic wave modeling
- Forward scattering series
- Padé approximants

### Cite this

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*Communications in Computational Physics*, vol. 3, no. 1, pp. 180-202.

**Forward scattering series and Padé approximants for acoustic wavefield propagation in a vertically varying medium.** / Nita, Bogdan.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Forward scattering series and Padé approximants for acoustic wavefield propagation in a vertically varying medium

AU - Nita, Bogdan

PY - 2008/1/1

Y1 - 2008/1/1

N2 - We present the application of the theory of Padé approximants to extending the perturbative solutions of acoustic wave equation for a three dimensional vertically varying medium with one interface. These type of solutions have limited convergence properties depending on either the degree of contrast between the actual and the reference medium or the angle of incidence of a plane wave component. We show that the sequence of Padé approximants to the partial sums in the forward scattering series for the 3D wave equation is convergent for any contrast and any incidence angle. This allows the construction of any reflected waves including phase-shifted post-critical plane waves and, for a point-source problem, refracted events or headwaves, and it also provides interesting interpretations of these solutions in the scattering theory formalism.

AB - We present the application of the theory of Padé approximants to extending the perturbative solutions of acoustic wave equation for a three dimensional vertically varying medium with one interface. These type of solutions have limited convergence properties depending on either the degree of contrast between the actual and the reference medium or the angle of incidence of a plane wave component. We show that the sequence of Padé approximants to the partial sums in the forward scattering series for the 3D wave equation is convergent for any contrast and any incidence angle. This allows the construction of any reflected waves including phase-shifted post-critical plane waves and, for a point-source problem, refracted events or headwaves, and it also provides interesting interpretations of these solutions in the scattering theory formalism.

KW - Acoustic wave modeling

KW - Forward scattering series

KW - Padé approximants

UR - http://www.scopus.com/inward/record.url?scp=38849132847&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:38849132847

VL - 3

SP - 180

EP - 202

JO - Communications in Computational Physics

JF - Communications in Computational Physics

SN - 1815-2406

IS - 1

ER -