Vincent W. Lee

Rocking strong earthquake accelerations

In this paper, the method presented by Lee and Trifunac (1985) for generating synthetic torsional accelerograms has been extended to the estimation of synthetic rocking accelerograms and of their response spectra. Results from our previous regression analyses for the characterization of strong shaking in terms of (1) earthquake magnitude and epicentral distance, or (2) Modified Mercalli Intensity at the site are utilized here again. The effects of geologic environment, in terms of site parameters or the representative depth of sediments, which influence amplification, and the dispersive properties of ground motion are also included. The synthetic rocking accelerogram is then constructed from the horizontal and vertical acceleration components.

Diffraction of SV waves by underground, circular, cylindrical cavities

The scattering and diffraction of plane SV waves underground, circular, cylindrical cavities at various depths in an elastic half space is studied in this paper. The cavities, studied here, are at depths of two to five cavity radii, measured from the surface to the center of the cavity. Fourier-Bessel series are used to satisfy the wave equation and the boundary conditions. When the angle of incidence of the plane SV wave exceeds the critical angle, surface waves are generated, which are expanded in terms of Fourier series, which also involve Bessel functions. The surface displacement amplitudes and phases that are presented show that the results depend on the following parameters: (1) The angle of incidence, θβ; (2) the ratio cavity depth to the cavity radius, ha; (3) the dimensionless frequency of the incident SV wave, η; and (4) Poissons ratio, v. The presence of the cavity in the half space results in significant deviation of both the displacement amplitudes and phases on the nearby half space surface from that of a uniform half space.

Frequency dependent attenuation of strong earthquake ground motion

New shape for the frequency dependent attenuation function of Fourier amplitude spectra of recorded strong earthquake ground acceleration has been developed. It has been found that for distances less than about 100 km there is clear frequency dependent variation of the attenuation functions, with high frequency amplitudes attenuating faster with distance.

Empirical models for scaling pseudo relative velocity spectra of strong earthquake accelerations in terms of magnitude, distance, site intensity and recording site conditions

Our previous empirical scaling model for Pseudo Relative Velocity (PSV) spectrum amplitudes has been refined here by introducing the frequency dependent attenuation of amplitudes with distance 9 . The new model also considers the depth of earthquake focus and the approximate characterization of the source size to compute the ‘representative’ source to station distances in addition to all other scaling parameters used previously 4 . The form of the probability distribution function of spectral amplitudes proposed by Trifunac and Anderson 4 to describe the distribution of the residuals about the chosen regression model has been confirmed by this analysis.

A note on the scattering of elastic plane waves by a hemispherical canyon

Abstract The three-dimensional scattering and diffraction of plane waves by a hemispherical canyon in the homogeneous elastic half-space has been analyzed. Using the series solution for a general angle of wave incidence, ground motion near the canyon has been studied. The nature of ground motion has been found to depend on three key parameters: 1. (1) γ, the angle of incidence, 2. (2) ν, a dimensionless frequency of wave number proportional to the ratio of the diameter of the canyon to wavelength of the incident P-wave, and 3. (3) κ, the ratio of longitudinal to transverse wave speeds. The displacement amplitudes and phases on nearby ground surface show significant departure from the uniform half-space motions. The angle of incidence γ determines the overall trends of motion amplitudes. For oblique incidence, for example, considerable amplification is observed in front of the canyon, and a prominent shadow zone is relaized behind the canyon.

Empirical models for scaling Fourier amplitude spectra of strong ground acceleration in terms of earthquake magnitude source to station distance, site intensity and recording site conditions

In this paper, we present the current improvements in empirical scaling of Fourier spectrum amplitudes of strong earthquake accelerations by introducing the frequency dependent attenuation function which has been developed13 from the same data base. This function replaces the Richters empirical attenuation function which we previously used together with a linear term in R, the epicentral distance. By using the new attenuation function, the scaling model has the additional flexibility for estimating the Fourier spectral amplitudes from earthquakes of given source dimensions and focal depths.

Application of the weighted residual method to diffraction by 2-D canyons of arbitrary shape: I. Incident SH waves

Abstract A solution for the two-dimensional scattering and diffraction of plane SH waves by canyons of arbitrary shape in an elastic half space is presented. The wave field for arbitrary geometry in this paper is computed numerically by the method of weighted residues (moment method). The wave displacement field computed by the present residual method for the case of a semi-circular canyon was shown to agree analytically and numerically with that computed by the exact closed form series solution. The same observations about ground amplifications, their dependence on frequencies and orientations of the incident waves, can be stated here for canyons of arbitrary shape as previously made for circular canyons.

Peak surface strains during strong earthquake motion

Abstract Peak amplitudes of surface strains during strong earthquake ground motion can be approximated by ϵ = Aν max β 1 , where νmax is the corresponding peak particle velocity, β1 is the velocity of shear waves in the surface layer, and A is a site specific scaling function. In a 50 m thick layer with shear wave velocity β1 ∼ 300 m/s, A ∼ 0·4 for the radial strain ϵrr, A ∼ 0·2 for the tangential strain ϵrθ, and A ∼ 1·0 for the vertical strain, ϵz. These results are site specific and representative of strike slip faulting and of soil in Westmoreland, in Imperial Valley, California. Similar equations can be derived for other sites with known shear wave velocity profile versus depth.

Application of the weighted residual method to diffraction by 2-D canyons of arbitrary shape: II. Incident P, SV and Rayleigh waves

Abstract A solution for the two-dimensional scattering and diffraction of plane P and SV waves by canyons of arbitrary shape in an elastic half space is presented. Numerical computation of the wave field is carried out on and near the canyon surfaces using the method of weighted residues (moment method). The wave displacement fields computed by the residual method for the cases of shallow to semi-circular canyons were shown to agree with those from the analytic solutions. As in the SH wave case, the same observations about ground amplifications, their dependence on frequencies and orientation of the incident waves, can be stated for canyons of arbitrary shape as for those of regular shape.

The Rinaldi Strong Motion Accelerogram of the Northridge, California Earthquake of 17 January 1994

The Rinaldi record of the 1994 Northridge earthquake is one of the most important strong motion records in earthquake engineering (largest recorded horizontal peak ground velocity in the western United States, ∼170 cm/s). Digitization of this record was not straightforward because of numerous stalls and malfunction of the half-second pulse relays. It was digitized and processed for the Los Angeles Department of Water and Power soon after the earthquake, and was recently redigitized and reprocessed. This paper presents the results of the recent digitization and processing and a comparison of the two digital versions of the record. The “new” version differs from the “old” version in the number of stalls corrected for (17 versus one stall), total length of digitized traces (∼20 s versus ∼15 s), and amplitudes of some high frequency acceleration peaks (in the “old” version, some high frequency peaks have been underestimated). The peak amplitudes of corrected acceleration, velocity and displacement, and the linear response spectrum amplitudes are not significantly different. However, the two digital interpretations have different time scales, because of the difference in the number of stalls accounted for.