Topographic effects on ground motion for incident P waves: a model study

Rogers, A.M.; Katz, Lewis J.; Bennett, Theron J.

doi:10.1016/0148-9062(74)91167-x

Cited by 7 publications

(12 citation statements)

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“…Bouchon (1973) observed amplification (100% amplification in horizontal displacement) of incident SH, P, and SV waves at the crest of a mountain ridge and attenuation (30% reduction in horizontal displacement) near the bottom of a depression using a single frequency method developed by Aki and Larner (1970). Similar results were obtained by Rogers et al (1974) based on two-dimensional scale models for incident P waves. A systematic review on topography effects was made by Geli et al (1988), who compared theoretical and experimental results and found qualitative agreement about the amplification at mountaintops.…”

Section: Introductionsupporting

confidence: 81%

Response of High-Strength Rock Slope to Seismic Waves in a Shaking Table Test

Liu

Li³

et al. 2013

Bulletin of the Seismological Society of America

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Studies on landslides by the 2008 Wenchuan earthquake showed that the topography is of great importance in amplifying the seismic shaking. The present study carried out experiments on rock slopes by means of a shaking table. The recorded Wenchuan earthquake waves are scaled to excite the model slopes. Measurements from accelerometers installed on free surface of the model slope simulating high-strength rocks are analyzed, with much effort on acceleration responses to both horizontal and vertical components of seismic shaking. It is found that the amplification factor of peak horizontal acceleration (PHA) is increasing with elevation of the model slope, though the upper and lower halves of the slope exhibit different increasing patterns. The amplification factor of peak vertical acceleration (PVA) exhibits a lying S-shaped changing trend with the elevation, indicating attenuations of PVAs at the toe and top of a slope. In addition, the XZ-direction shaking produces a horizontal and vertical response stronger than X-direction and Z-direction shaking alone. Both PHA and PVA increase with the excitation intensity. However, the corresponding amplification factors generally decrease, indicating the acceleration response of a slope weakens with the excitation intensity of shaking. Finally the statistic of ratio of PVA to PHA indicates that 85% of the slope height, especially the upper middle part, is likely subject to PVAs greater than or equal to 2=3 of PHA and 32% of the slope height to PVAs greater than or equal to PHA. This indicates the nonignorable role of PVA in responses of a slope to an earthquake and necessity of considering during design work.

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Section: Introductionsupporting

confidence: 81%

Response of High-Strength Rock Slope to Seismic Waves in a Shaking Table Test

Liu

Li³

et al. 2013

Bulletin of the Seismological Society of America

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“…In other respects, all available theoretical results seem to underestimate the observed effects of topography on surface motion, as reported by Davis &West (1973), andGriffiths &Bollinger (1979). Since the model study values corroborate those obtained by numerical methods (Rogers et at. 1974;Ilan et af.…”

supporting

confidence: 82%

“…Besides field studies (Davis & West 1973;Griffiths & Bollinger 1979), or model studies (Rogers, Katz & Bennett 1974;Ilan, Bond & Spivack 1979), the theoretical investigations have focused more on numerical solution rather than on a detailed study of the effects of topography on surface motion. A lot of numerical methods have been developed to investigate the scattered far-field (small perturbations: Gilbert & Knopoff 1960;Hudson & Knopoff 1967;Hudson 1967;MacIvor 1969; small perturbations and finite difference: Aboudi 1971;Alterman & Aboudi 1971), or the displacement field over the topography itself (analytical models : Trifunac 1973;Wong & Trifunac 1974;Singh & Sabina 1977;finite differences: Boore 1972;Alterman & Nathaniel 1975;Ilan 1977;Ilan et af.…”

mentioning

confidence: 99%

Diffracted waves and displacement field over two-dimensional elevated topographies

Bard

1982

Geophysical Journal International

137

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The Aki-Larner technique is used to perform, in both the time and frequency domains, an analysis of the effects of two-dimensional elevated topography on ground motion. Incident plane SH-, SVand P-waves are considered and the respective influences of surface geometry, elastic parameters and the incident wave characteristics, as long as they remain within the limits of applicability of the A-L technique, are investigated in some detail.Besides the well-known amplification/deamplfication effect related to the surface curvature, wave scattering phenomena on the convex parts of the surface are shown to contribute significantly to the disturbances in the displacement field around the topographic structure. These scattered waves are SH in the case of incident SH-waves, and mainly Rayleigh waves in the P case, while both Rayleigh and horizontal P-waves, sometimes of large amplitude, develop in the SV case. The frequency dependence of this scattering, though complex, seems to be mainly controlled by the horizontal scale of the topographic structure. The parameter study points out the regular and intuitive behaviour of this wave scattering in both SH and P cases, while it exhibits a puzzling complexity for incident SV-waves, which is interpreted as resulting from the importance of the S-P reflections on mountain slopes in that case.As to the ground motion, some general features may be pointed out. The amplification on mountain tops, which is systematically greater for incident S-waves than for P-waves, generally decreases as the average slope decreases or as the angle of incidence increases. Mountain slopes undergo either amplification or deamplification depending on site location, frequency and incidence angle, but they always undergo strong differential motion due to the lateral propagation of the scattered waves and their interference with the primary wave. Finally, all these effects may be greatly enhanced in the case of complex topographies, which moreover give rise to a significant prolongation of ground motion because of the large number of scattered waves.

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“…The interest originally incited by the San Fernando earthquake recordings has since continued. Field experiments have been performed on hills and mountain ridges [Davis' and West, 1973;Rogers et al, 1974;Gr{ffiths and Bollinger, 1979 2000 120 shattered earth at the top of prominences [Muir, 1912;Hadley, 1964;Nason, 1971] and the disruptions of rocks and boulders. near hill crests [Oldham, 1899;Clark, 1972;Bolt and Hansen, 1977;Urneda, 1992] also indicate the occurrence of intense shaking in elevated areas of rugged topography.…”

Section: Introductionmentioning

confidence: 99%

Effect of three‐dimensional topography on seismic motion

Bouchon¹,

Schultz²,

Toksöz³

1996

J. Geophys. Res.

198

121

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We present a semianalytical, seminumerical method to calculate the diffraction of elastic waves by an irregular topography of arbitrary shape. The method is a straightforward extension to three dimensions of the approach originally developed to study the diffraction of S.H waves [Bouchon, 1985] and P-SV waves [Gaffer and Bouchon, 1989] by two-dimensional topographies. It relies on a boundary integral equation scheme formulated in •he frequency domain where the Green functions are evaluated by the discrete wavenumber method. The principle of the method is simple. The diffracted wave field is represented as the integral over the topographic surface of an unknown source density function times the medium Green functions. The Green functions are expressed as integrals over the horizontal wavenumbers. The introduction of a spatial periodicity of the t0pogr,aphy combined with the discretization of the surface at equal intervals results in a discretization of the wavenumber integrals and in a periodicity in the horizontal wavenumber space. As a result, the Green functions are expressed as finite sums of analytical terms. The writing of the boundary conditions of free stress at the surface yields a linear system of equations where the unknowns are the source density functions representing the diffracted wave field. Finally, this system is solved iteratively using the conjugate gradient approach. We use this method to investigate the effect of a hill on the ground motion produced during an earthquake. The hill considered is 120 rn high and has an elliptical base and ratios of height-to-half-width of 0.2 and 0.4 along its major and minor axes. The results obtained show that amplification occurs at and near the top of the hill over a broad range of frequencies. For incident shear waves polarized along the short dimension of the hill the amplification at the top reaches 100% around 10 Hz and stays above 50% for frequencies between 1.5 Hz and 20 Hz. For incident shear waves polarized along the direction of elongation of the topography, the maximum amplification Occurs between 2 Hz and 5 Hz with values ranging from 50% to 75%. The results also' show that the geometry of the topography exe..rts a very strong directivity on the wave field diffracted away from the hill and thai' at some distance from the hill this diffracted wave field consists mostly of Rayleigh waves.

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Topographic effects on ground motion for incident P waves: a model study

Cited by 7 publications

References 0 publications

Response of High-Strength Rock Slope to Seismic Waves in a Shaking Table Test

Response of High-Strength Rock Slope to Seismic Waves in a Shaking Table Test

Diffracted waves and displacement field over two-dimensional elevated topographies

Effect of three‐dimensional topography on seismic motion

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