SH waves scattering from a partially filled semi-elliptic alluvial valley

Tsaur, Deng‐How; Hsu, Ming-Sheng

doi:10.1093/gji/ggt106

Cited by 18 publications

(4 citation statements)

References 25 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…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: 96%

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

Gómez

Jaramillo

Sáenz

et al. 2016

International Journal of Geophysics

View full text Add to dashboard Cite

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.

show abstract

Section: Introductionmentioning

confidence: 96%

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

Gómez

Jaramillo

Sáenz

et al. 2016

International Journal of Geophysics

View full text Add to dashboard Cite

show abstract

“…While maintaining conceptual and analytical simplicity, the wave function expansion method has been widely used to investigate the site effects in elastodynamics [Trifunac, 1971[Trifunac, , 1973Wong and Trifunac, 1974;Lee, 1982Lee, , 1990Yuan and Men, 1992;Liao, 1994, 1996;Lee and Sherif, 1996;Lee et al, 2006;Tsaur and Chang, 2008, 2009a, 2009bTsaur et al, 2010;Tsaur, 2011;Amornwongpaibun and Lee, 2013;Gao et al, 2012;Lee and Amornwongpaibun, 2012;Zhang et al, 2012;Chang et al, 2013;Tsaur and Hsu, 2013;Lee and Zhu, 2014]. In contrast to the numerical methods, the wave function expansion method can only treat problems of linear elastic medium with regular and simple geometry.…”

Section: Introductionmentioning

confidence: 99%

“…The key treatment of the present method is the introduction of the regionmatching technique with a semicircular auxiliary boundary. The auxiliary condition is probably first used by Yuan et al [Yuan and Men, 1992;Liao, 1994, 1996], then by Tsaur et al [Tsaur and Chang, 2008, 2009a, 2009bTsaur et al, 2010;Tsaur, 2011;Tsaur and Hsu, 2013] to study the topographic effect of the surface canyons. Following the idea of a circular auxiliary boundary, the Helmholtz equations with the geometry conditions of two obliquely straight walls are solved with the method of separation of variables initially in this study.…”

Section: Introductionmentioning

confidence: 99%

Antiplane Scattering of SH Waves by a Trapezoidal Valley with a Circular-Arc Alluvium in an Elastic Half Space

Zhang

Liu

Deng

2015

J. Earthquake and Tsunami

View full text Add to dashboard Cite

Both lithologic and topographic irregularities may trigger significant scattering phenomenon of seismic waves. In this study, a series solution is presented for the analysis of scattering of SH waves induced by a trapezoidal valley during earthquakes. An appropriate region matching technique is utilized to divide the physical region into four computational subregions. The wave motions of each subregion are obtained as an infinite series of wave functions with unknown coefficients in the respective cylindrical coordinates through wave function expansion method. The Graf's addition theorem is applied to transform the wave potentials of each subregion into the global coordinate. The mixed boundary conditions are solved by truncating the obtained infinite equations into a finite set. The effects of geometrical topographies and sedimentary properties on the amplification are analyzed and discussed in terms of steady-state and transient response analysis.

show abstract

“…Subsequently, the conceptual model was extended by Tsaur and Hsu (2013) to study alluvial valleys with semi-elliptic cross sections. Thus, this article continues along this path, looking closely at the spatial and temporal fluctuations in ground motions near a semicircular valley partially filled with an inclined alluvial layer.…”

Section: Introductionmentioning

confidence: 99%

Ground motions around a semi-circular valley partially filled with an inclined alluvial layer under SH-polarized excitation

Chang¹,

Tsaur

2014

Earth Planet Sp

Self Cite

View full text Add to dashboard Cite

A simplified mathematical model, composed of a semi-circular valley partially filled with an inclined alluvial layer under plane SH-wave incidence, is presented. To evaluate the site response theoretically, a rigorous series solution is derived via the region-matching technique. For angular wavefunctions constrained by an inclined free surface, the original form of Graf's addition formula is recast to arbitrarily shift the local coordinate system. The valley geometry, filling material, angle of incidence, and wave frequency are taken as significant parameters in exploring the site effect on ground motions. Also included are the frequency-and time-domain computations. Two canonical cases, the semi-circular vacant canyon and the fully filled semi-circular alluvial valley, with exact analytical solutions, and the partly horizontally filled case previously studied, are taken to be particular cases of the proposed general model. Steady-state results show that the peak amplitudes of motion may increase at low frequencies when the filling layer inclines to the illuminated region. At low-grazing incidence, the phenomenon of wave focusing becomes evident on the shadow side of the filling layer. Transient-state simulations elucidate how a sequence of surface waves travel on the topmost alluvium along opposite directions and interfere with multiple reflected waves within the filling layer.

show abstract

SH waves scattering from a partially filled semi-elliptic alluvial valley

Cited by 18 publications

References 25 publications

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

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

Antiplane Scattering of SH Waves by a Trapezoidal Valley with a Circular-Arc Alluvium in an Elastic Half Space

Ground motions around a semi-circular valley partially filled with an inclined alluvial layer under SH-polarized excitation

Contact Info

Product

Resources

About