Surface Motion of a Half-Space with Triangular and Semicircular Hills under Incident SH Waves

Liu, Gang; Chen, Haitao; Dian-kui, Liu; Khoo, Boo Cheong

doi:10.1785/0120090273

Cited by 31 publications

(7 citation statements)

References 20 publications

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“…Chen et al (2008, 2011) presented a null‐field boundary integral equation method. Other boundary methods (England et al 1980; Sanchez‐Sesma et al 1982; Moeen‐Vaziri & Trifunac 1988; Eshraghi & Dravinski 1989; Liu & Han 1991; Lee & Wu 1994; Liu et al 2010) have been developed as well.…”

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

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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.

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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

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“…For instance, the scattering of incident P and SV waves by a semicircular canyon was only recently found by Lee and Liu [3] using a wave function expansion approach, while in the case of horizontally polarized shear waves there is only a handful of contributions: an important work was conducted by Trifunac [4], who found the frequency domain solution to the scattering of plane SH waves by a semicircular canyon and a semicircular valley using a separation of variables approach. Similar solutions for the scattering of SH waves by irregularities of various shapes constructed in terms of wave function expansions have also been developed by a region matching technique in Tsaur and Chang [5]; Tsaur et al [6]; Tsaur [7]; Liu et al [8]; Tsaur [9]; 2 International Journal of Geophysics Han et al [10]; Gao et al [11]; Zhang et al [12]; Gao and Zhang [13]; Chang et al [14]; and Tsaur and Hsu [15]. In all of these works the solutions take the form of infinite series or expansions with an infinite number of terms and despite the fact that they correspond to the simplest cases of scattering of scalar waves by strongly idealized geometries, these solutions shed light on conceptual understanding of the problem of site-specific response.…”

Section: Introductionmentioning

confidence: 97%

A Superposition Based Diffraction Technique to Study Site Effects in Earthquake Engineering

Gómez

Jaramillo

Sáenz

et al. 2016

International Journal of Geophysics

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A method to study the response of surface topographies submitted to incidentSHwaves is presented. The method is based on the superposition of diffracted sources described in Jaramillo et al. (2013). Since the technique proceeds in the frequency domain in terms of the superposition of incident, reflected, and diffracted waves, it has been termed like a superposition based diffraction approach. The final solution resulting from the superposition approach takes the form of a series of infinite terms, where each term corresponds to diffractions of increasing order and of decreasing amplitude generated by the interactions between the geometric singularities of the scatterer. A detailed, step-by-step algorithm to apply the method is presented with regard to the simple problem of scattering by a V-shaped canyon. In order to show the accuracy of the method we compare our time and frequency domain results with those obtained from a direct Green’s function approach. We show that fast solutions with an error of the order of 6.0% are obtained.

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“…Chen [27] studied the surface motion of multiple alluvial valleys for incident plane SH waves by using a semianalytical approach. Liu [28] studied the multiple scattering of SH waves by two hills of different geometries (a triangle and a semicircle) on a solid half-space. Du [29] studied the surface displacement function of two isosceles triangular hills during the incidence of SH wave by using wave function expanding.…”

Section: Introductionmentioning

confidence: 99%

Scattering of Antiplane SH Waves by Complex Landforms

Sun

2021

Shock and Vibration

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The multiple scattering of SH waves by isosceles triangular hill, semicircle depression, and isosceles trapezoidal hill in the solid half-space is studied. The complex model is divided into multiple subdomains by using the region matching method, then the wave functions in each subdomain are constructed by using the fractional-order Bessel function, and finally, the infinite algebraic equations for solving the unknown coefficients in the wave function are established by using the multipolar coordinate technique and the complex function method according to the boundary conditions. Fourier series is used to solve the unknown undetermined coefficients. The results show that due to the multiple reflections of the incident wave between complex landforms, surface displacement amplitude is affected by the incident angle, incident frequency, and the distance between the isosceles triangular hill, semicircle depression, and isosceles trapezoidal hill. It is found that when the incident frequency increases, there is a certain amplification effect between the hills and the depression. When the wave is incident horizontally, there is a certain “barrier” effect between hills and depression, and when the distance between the hills and depression reaches a certain level, the “barrier” effect will reach a stable value.

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Surface Motion of a Half-Space with Triangular and Semicircular Hills under Incident SH Waves

Cited by 31 publications

References 20 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

A Superposition Based Diffraction Technique to Study Site Effects in Earthquake Engineering

Scattering of Antiplane SH Waves by Complex Landforms

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