A pseudodifferential equation with damping for one-way wave propagation in inhomogeneous acoustic media

C.C. Stolk

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    22 Citations (Scopus)
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    Abstract

    A one-way wave equation is an evolution equation in one of the space directions that describes (approximately) a wave field. The exact wave field is approximated in a high frequency, microlocal sense. Here we derive the pseudodifferential one-way wave equation for an inhomogeneous acoustic medium using a known factorization argument. We give explicitly the two highest order terms, that are necessary for approximating the solution. A wave front (singularity) whose propagation velocity has non-zero component in the special direction is correctly described. The equation cannot describe singularities propagating along turning rays, i.e. rays along which the velocity component in the special direction changes sign. We show that incorrectly propagated singularities are suppressed if a suitable dissipative term is added to the equation.
    Original languageEnglish
    Pages (from-to)111-121
    Number of pages11
    JournalWave motion
    Volume40
    Issue number2
    DOIs
    Publication statusPublished - 2004

    Fingerprint

    Wave propagation
    Wave Propagation
    wave propagation
    Damping
    Acoustics
    damping
    Singularity
    Wave equations
    wave equations
    acoustics
    Half line
    Wave equation
    rays
    propagation velocity
    Sign Change
    Term
    wave fronts
    Factorization
    factorization
    Wave Front

    Keywords

    • Acoustic equation
    • One-way wave equation
    • Pseudodifferential calculus
    • MSC-35L05
    • MSC-35S10

    Cite this

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    title = "A pseudodifferential equation with damping for one-way wave propagation in inhomogeneous acoustic media",
    abstract = "A one-way wave equation is an evolution equation in one of the space directions that describes (approximately) a wave field. The exact wave field is approximated in a high frequency, microlocal sense. Here we derive the pseudodifferential one-way wave equation for an inhomogeneous acoustic medium using a known factorization argument. We give explicitly the two highest order terms, that are necessary for approximating the solution. A wave front (singularity) whose propagation velocity has non-zero component in the special direction is correctly described. The equation cannot describe singularities propagating along turning rays, i.e. rays along which the velocity component in the special direction changes sign. We show that incorrectly propagated singularities are suppressed if a suitable dissipative term is added to the equation.",
    keywords = "Acoustic equation, One-way wave equation, Pseudodifferential calculus, MSC-35L05, MSC-35S10",
    author = "C.C. Stolk",
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    A pseudodifferential equation with damping for one-way wave propagation in inhomogeneous acoustic media. / Stolk, C.C.

    In: Wave motion, Vol. 40, No. 2, 2004, p. 111-121.

    Research output: Contribution to journalArticleAcademicpeer-review

    TY - JOUR

    T1 - A pseudodifferential equation with damping for one-way wave propagation in inhomogeneous acoustic media

    AU - Stolk, C.C.

    PY - 2004

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    N2 - A one-way wave equation is an evolution equation in one of the space directions that describes (approximately) a wave field. The exact wave field is approximated in a high frequency, microlocal sense. Here we derive the pseudodifferential one-way wave equation for an inhomogeneous acoustic medium using a known factorization argument. We give explicitly the two highest order terms, that are necessary for approximating the solution. A wave front (singularity) whose propagation velocity has non-zero component in the special direction is correctly described. The equation cannot describe singularities propagating along turning rays, i.e. rays along which the velocity component in the special direction changes sign. We show that incorrectly propagated singularities are suppressed if a suitable dissipative term is added to the equation.

    AB - A one-way wave equation is an evolution equation in one of the space directions that describes (approximately) a wave field. The exact wave field is approximated in a high frequency, microlocal sense. Here we derive the pseudodifferential one-way wave equation for an inhomogeneous acoustic medium using a known factorization argument. We give explicitly the two highest order terms, that are necessary for approximating the solution. A wave front (singularity) whose propagation velocity has non-zero component in the special direction is correctly described. The equation cannot describe singularities propagating along turning rays, i.e. rays along which the velocity component in the special direction changes sign. We show that incorrectly propagated singularities are suppressed if a suitable dissipative term is added to the equation.

    KW - Acoustic equation

    KW - One-way wave equation

    KW - Pseudodifferential calculus

    KW - MSC-35L05

    KW - MSC-35S10

    U2 - 10.1016/j.wavemoti.2003.12.016

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    JF - Wave motion

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