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Wavelet-Based Integral Formula for Solving the Wave Equation and Its Application

Author

Listed:
  • Maria V. Perel

    (St. Petersburg State University, Department of Mathematical Physics, Physics Faculty)

  • Evgeny A. Gorodnitskiy

    (St. Petersburg State University, Department of Mathematical Physics, Physics Faculty)

Abstract

A representation of the solution of the initial-boundary value problem for the wave equation in a half-plane is given as an integral superposition of parameter-dependent packets (localized solutions). The parameters of each packet have the meaning of a coordinate on the boundary from which the packet is emitted, the direction in which it is emitted, the time of its emission, and its characteristic frequency. The excitation coefficient of an individual packet is a wavelet transform of the boundary data, which depends on the parameters and processes the boundary data. The resulting representation is applied to seismic migration.

Suggested Citation

  • Maria V. Perel & Evgeny A. Gorodnitskiy, 2026. "Wavelet-Based Integral Formula for Solving the Wave Equation and Its Application," Springer Books,, Springer.
    • Handle: RePEc:spr:sprchp:978-3-032-04458-7_21
    DOI: 10.1007/978-3-032-04458-7_21
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