Highly-accurate stability-preserving optimization of the Zener viscoelastic model, with application to wave propagation in the presence of strong attenuation

Abstract : This article concerns the numerical modeling of time-domain mechanical waves in vis-coelastic media based on a generalized Zener model. To do so, classically in the literature relaxation mechanisms are introduced, resulting in a set of so-called memory variables and thus in large computational arrays that need to be stored. A challenge is thus to accurately mimic a given attenuation law using a minimal set of relaxation mechanisms. For this purpose, we replace the classical linear approach of Emmerich & Korn (1987) with a nonlinear optimization approach with constraints of positivity. We show that this technique is significantly more accurate than the linear approach. Moreover it ensures that physically-meaningful relaxation times that always honor the constraint of decay of total energy with time are obtained. As a result these relaxation times can always be used in a stable way in a modeling algorithm, even in the case of very strong attenuation for which the classical linear approach may provide some negative and thus unusable coefficients.
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Submitted on : Monday, January 18, 2016 - 4:32:13 PM
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Emilie Blanc, Dimitri Komatitsch, Emmanuel Chaljub, Bruno Lombard, Zhinan Xie. Highly-accurate stability-preserving optimization of the Zener viscoelastic model, with application to wave propagation in the presence of strong attenuation. Geophysical Journal International, Oxford University Press (OUP), 2016, 205, pp.427-439. ⟨10.1093/gji/ggw024⟩. ⟨hal-01228901v2⟩

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