Numerical analysis of one-dimensional nonlinear acoustic wave |
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| Authors: | Haishan Zheng Igor B Morozov Zhongjie Zhang |
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| Institution: | (1) Geological Science Department, University of Saskatchewan, Saskatoon, Canada;(2) Institute of Geology and Geophysics, Chinese Academy of Sciences, Beijing, China |
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| 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 numerical 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. |
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| Keywords: | nonlinear acoustic wave high-order finite difference flux limiter |
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