Scattering of plane SH waves by a cylindrical canyon of circular-arc cross-section

Yuan, Xiaoming; Liao, Zhenpeng

doi:10.1016/0267-7261(94)90011-6

Cited by 61 publications

(14 citation statements)

References 4 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In fact, the series solutions of wavefunctions for a semi‐circular canyon (Trifunac 1973) and for a semi‐elliptical canyon (Wong & Trifunac 1974) have been frequently used to validate numerical methods (Wong & Jennings 1975; Sills 1978; Sanchez‐Sesma & Rosenblueth 1979; England et al 1980; Shah et al 1982; Hirai 1988; Zhang & Zhao 1988; Takemiya & Fujiwara 1994; Lee & Wu 1994; Bouchon 1985; Kawase 1988; Zhou & Chen 2006). Later, a few series solutions of wavefunctions for concave topographies (Lee 1982, 1990; Cao & Lee 1989; Yuan & Liao 1994; Tsaur & Chang 2008, 2009a; Tsaur et al 2010) and for convex topographies (Yuan & Men 1992; Yuan & Liao 1996; Lee et al 2006; Tsaur & Chang 2009b) in a half‐space under incident SH waves were proposed. Wedge‐shaped space problems include, but not limit to, propagation of SH waves in wedges (Sanchez‐Sesma 1985) and diffraction of SH waves by a circular canyon in a wedge space (Lee & Sherif 1996).…”

Section: Introductionmentioning

confidence: 99%

Scattering of SH waves induced by a non-symmetrical V-shaped canyon

Zhang¹,

Gao²,

Cai³

et al. 2012

Geophysical Journal International

View full text Add to dashboard Cite

SUMMARY Topographies have significant effects on seismic waves. The wavefunction expansion method has been frequently employed to study the topographic effect because this method can reveal the physics of the wave scattering and can testify the accuracy of numerical methods. The 2‐D scattering and diffraction of plane SH waves induced by a non‐symmetrical V‐shaped canyon is examined here by using the wavefunction expansion method. Through a new domain decomposition strategy, the half‐space containing a V‐shaped canyon is divided into three subregions. Then the wavefield for every subregion is constructed in terms of an infinite series of wavefunctions with unknown coefficients in three coordinate systems, respectively. After that, three wavefields are all represented in the same coordinate system using the Graf addition theorem. The unknown coefficients are obtained by satisfying the continuity conditions of the auxiliary boundary. The proposed series solution of wavefunctions for a non‐symmetrical V‐shaped canyon can be reduced to a symmetrical case. Results in this study for the symmetrical case agree very well with those in the published literature. To show the effects of the non‐symmetrical‐geometry topography on the surface ground motion, a parametric study is carried out in the frequency domain. Surface and subsurface transient responses in the time domain demonstrate the phenomenon of wave propagating and scattering. Finally, the proposed model is successfully applied to two idealized cross sections of Pacoima canyon and Feitsui canyon.

show abstract

Section: Introductionmentioning

confidence: 99%

Scattering of SH waves induced by a non-symmetrical V-shaped canyon

Zhang¹,

Gao²,

Cai³

et al. 2012

Geophysical Journal International

View full text Add to dashboard Cite

show abstract

“…Regarding SH‐ wave scattering problems by the alluvial valley and canyon, Trifunac derived analytical solutions for semi‐circular cases with alluvial and without alluvial in 1971 (Trifunac 1971, 1973)), respectively. Later, Yuan & Liao (1994) employed the approach of wavefunction expansion to deal with problems of SH‐ waves scattered by a cylindrical canyon of circular‐arc cross‐section. Wong and Trifunac extended a circular case to a semi‐elliptical canyon (Wong & Trifunac 1974a) and alluvial (Wong & Trifunac 1974b).…”

Section: Introductionmentioning

confidence: 99%

SH-wave scattering by a semi-elliptical hill using a null-field boundary integral equation method and a hybrid method

Chen

Lee

Shyu

2011

Geophysical Journal International

View full text Add to dashboard Cite

S U M M A R YFollowing the success of seismic analysis of a semi-circular hill, the problem of SH-wave scattering by a semi-elliptical hill is revisited by using the null-field boundary integral equation method (BIEM). To fully use the analytical property in the null-field boundary integral equation approach in conjunction with degenerate kernels for solving the semi-elliptical hill scattering problem, the problem is decomposed to two regions to produce elliptical boundaries by using the technique of taking free body. One is the half-plane problem containing a semi-elliptical boundary. This semi-infinite problem is imbedded in an infinite plane with an artificial elliptical boundary such that degenerate kernel can be fully applied. The other is an interior problem bounded by an elliptical boundary. The degenerate kernel in the elliptic coordinates for two subdomains is used to expand the closed-form fundamental solution. The semi-analytical formulation in companion with matching boundary conditions yields six constraint equations. Instead of finding admissible wave-expansion bases, our null-field BIEM in conjunction with degenerate kernels has the five features over the conventional BIEM/BEM, (1) free of calculating principal values, (2) exponential convergence, (3) elimination of boundary-layer effect, (4) meshless and (5) well-posed system. All numerical results are compared well with those of using the hybrid method which is also described in this paper. It is interesting to find that a focusing phenomenon is also observed in this study.

show abstract

“…The analytical method that provides a series of solutions for several simple geometric shapes in a homogenous half-space is valuable for revealing the nature of the topographic effect and for testing the accuracy of numerical methods. For example, analytical solutions for incident SH-waves include the semi-cylindrical canyon (Trifunac, 1973), semielliptical canyon (Wong, 1974), shallow circular-arc canyon (Lee, 1990;Todorovska and Lee, 1991;Yuan and Liao, 1994;Liang et al, 2000Liang et al, , 2003, V-shaped canyon (Tsaur and Chang, 2008;Tsaur et al, 2010;Gao et al, 2012), U-shaped canyon , truncated semicircular canyon (Tsaur and Chang, 2009) and circular sectorial canyon (Chang et al, 2013). Numerical methods are more fl exible than the analytical approach and modern high-speed computers make various numerical schemes more powerful to account for complex conditions and material nonlinear problems.…”

Section: Introductionmentioning

confidence: 99%

Scattering and diffraction of plane SH-waves by periodically distributed canyons

Liang

Zhang

2016

Earthq. Eng. Eng. Vib.

View full text Add to dashboard Cite

A new method is presented to study the scattering and diffraction of plane SH-waves by periodically distributed canyons in a layered half-space. This method uses the indirect boundary element method combined with Green's functions of uniformly distributed loads acting on periodically distributed inclined lines. The periodicity feature of the canyons is exploited to limit the discretization effort to a single canyon, which avoids errors induced by the truncation of the infi nite boundary, and the computational complexity and the demand on memory can be signifi cantly reduced. Furthermore, the total wave fi elds are decomposed into the free fi eld and scattered fi eld in the process of calculation, which means that the method has defi nite physical meaning. The implementation of the method is described in detail and its accuracy is verifi ed. Parametric studies are performed in the frequency domain by taking periodically distributed canyons of semi-circular and semi-elliptic cross-sections as examples. Numerical results show that the dynamic responses of periodically distributed canyons can be quite different from those for a single canyon and signifi cant dynamic interactions exist between the canyons.

show abstract

Scattering of plane SH waves by a cylindrical canyon of circular-arc cross-section

Cited by 61 publications

References 4 publications

Scattering of SH waves induced by a non-symmetrical V-shaped canyon

Scattering of SH waves induced by a non-symmetrical V-shaped canyon

SH-wave scattering by a semi-elliptical hill using a null-field boundary integral equation method and a hybrid method

Scattering and diffraction of plane SH-waves by periodically distributed canyons

Contact Info

Product

Resources

About