Journal : Acta Geophysica
Article : Numerical analysis of one-dimensional nonlinear acoustic wave

Authors :
Domański, B.M.
Institute of Geophysics, Polish Academy of Sciences, Warszawa, Poland,,
Gnyp, A.
Carpathian Branch of Subbotin Institute of Geophysics, National Academy of Sciences of Ukraine, Lviv, Ukraine,,
Shanker, D.
Department of Earthquake Engineering, Indian Institute of Technology Roorkee, Roorkee, India,,
Zheng, H.
Geological Science Department, University of Saskatchewan, Saskatoon, Canada,,
Abstract : Numerical investigations on one-dimensional nonlinear acoustic wave with third and fourth order nonlinearities are presented using high-order finite-difference (HFD) operators with a simple flux-limiter (SFL) algorithm. As shown by our nu-merical tests, the HFDSFL method is able to produce more stable, accurate and conservative solutions to the nonlinear acoustic waves than those computed by finite-difference combined with the flux-corrected-transport algorithm. Unlike the linear acoustic waves, the nonlinear acoustic waves have variable phase velocity and waveform both in time-space (t-x) domain and frequency-wavenumber (f-k) domain; of our special interest is the behaviour during the propagation of nonlinear acoustic waves: the waveforms are strongly linked to the type of medium nonlinearities, generation of harmonics, frequency and wavenumber peak shifts. In seismic sense, these characteristics of nonlinear wave will introduce new issues during such seismic processing as Normal Moveout and f-k filter. Moreover, as shown by our numerical experiment for a four-layer model, the nonlinearities of media will introduce extra velocity errors in seismic velocity inversion.

Keywords : nonlinear acoustic wave, high-order finite difference, flux limiter,
Publishing house : Instytut Geofizyki PAN
Publication date : 2007
Number : Vol. 55, no. 3
Page : 313 – 323

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Qute : Domański, B.M. ,Gnyp, A. ,Shanker, D. ,Zheng, H. ,Zheng, H. , Numerical analysis of one-dimensional nonlinear acoustic wave. Acta Geophysica Vol. 55, no. 3/2007