Abstract
Earth medium is not completely elastic, with its viscosity resulting in attenuation and dispersion of seismic waves. Most viscoelastic numerical simulations are based on the finite-difference and finite-element methods. Targeted at viscoelastic numerical modeling for multilayered media, the constant-Q acoustic wave equation is transformed into the corresponding wave integral representation with its Green’s function accounting for viscoelastic coefficients. An efficient alternative for full-waveform solution to the integral equation is proposed in this article by extending conventional frequency-domain boundary element methods to viscoelastic media. The viscoelastic boundary element method enjoys a distinct characteristic of the explicit use of boundary continuity conditions of displacement and traction, leading to a semi-analytical solution with sufficient accuracy for simulating the viscoelastic effect across irregular interfaces. Numerical experiments to study the viscoelastic absorption of different Q values demonstrate the accuracy and applicability of the method.
Highlights
The viscoelastic absorption causes energy loss during the wave propagation in real Earth media
Most viscoelastic numerical simulations are based on the finite-difference and finite-element methods
We present an efficient alternative for full-waveform method to simulate wave propagation in multilayered viscoelastic media
Summary
The viscoelastic absorption causes energy loss during the wave propagation in real Earth media. The time-domain methods use a series of viscous parameters (i.e., the standard linear body) to describe the medium viscosity These methods are based on various approximate constant-Q models, such as Kelvin-Voigt model, Maxwell model, and standard linear solid model (SLS). The SLS model (Carcione 2007) can describe both the elasticity creep and the stress relaxation, more closely approximating the real law of seismic wave propagation in viscoelastic. Viscoelastic seismic imaging of viscosity acoustic media can compensate viscoelastic dispersion and attenuation and has been widely used to improve seismic imaging quality (Zhu 2014; Zhu et al 2014). Targeted at numerical wave propagation in layered viscoelastic media with an explicit use of boundary continuity conditions, an efficient alternative for fullwaveform viscoelastic numerical modeling is proposed in this article by extending conventional frequency-domain BEMs to viscoelastic media. To show the applicability of the method, we present numerical examples with viscoelastic media to study the viscoelastic effect of different Q values on wave propagation
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