Singularities of compressional wave propagation in hard rock masses

1988 ◽  
Vol 24 (3) ◽  
pp. 234-238 ◽  
Author(s):  
V. A. Virchenko ◽  
S. V. Krasavin ◽  
S. V. Tsirel
Keyword(s):  
Wave Propagation ◽  
Hard Rock ◽  
Compressional Wave ◽  
Rock Masses

Polarization and coherence of 5 to 30 Hz seismic wave fields at a hard-rock site and their relevance to velocity heterogeneities in the crust

1990 ◽  
Vol 80 (2) ◽  
pp. 430-449 ◽  
Author(s):  
William Menke ◽  
Arthur L. Lerner-Lam ◽  
Bruce Dubendorff ◽  
Javier Pacheco
Keyword(s):  
Hard Rock ◽  
Scale Effects ◽  
Spatial Coherence ◽  
Compressional Wave ◽  
P Wave ◽  
Transverse Motion ◽  
S Wave ◽  
Chemical Explosions ◽  
Aperture Arrays ◽  
The Waves

Abstract Except for its very onset, the P wave of earthquakes and chemical explosions observed at two narrow-aperture arrays on hard-rock sites in the Adirondack Mountains have a nearly random polarization. The amount of energy on the vertical, radial, and transverse components is about equal over the frequency range 5 to 30 Hz, for the entire seismogram. The spatial coherence of the seismograms is approximately exp(−cfΔx), where c is in the range 0.4 to 0.7 km−1Hz−1, f is frequency and Δx is the distance between array elements. Vertical, radial, and transverse components were quite coherent over the aperture of the array, indicating that the transverse motion of the compressional wave is a property of relatively large (106 m3) volumes of rock, and not just an anomaly caused by a malfunctioning instrument, poor instrument-rock coupling, or out-crop-scale effects. The spatial coherence is approximately independent of component, epicentral azimuth and range, and whether P- or S-wave coda is being considered, at least for propagation distances between 5 and 170 km. These results imply a strongly and three-dimensionally heterogeneous crust, with near-receiver scattering in the uppermost crust controlling the coherence properties of the waves.

scholarly journals Wave Propagation Across Acoustic/Biot’s Media: A Finite-Difference Method

2013 ◽  
Vol 13 (4) ◽  
pp. 985-1012 ◽  
Author(s):  
Guillaume Chiavassa ◽  
Bruno Lombard
Keyword(s):  
Wave Propagation ◽  
Numerical Methods ◽  
Heterogeneous Media ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Compressional Wave ◽  
Interface Conditions ◽  
Immersed Interface Method ◽  
Fluid Medium ◽  
Strang Splitting

AbstractNumerical methods are developed to simulate the wave propagation in heterogeneous 2D fluid/poroelastic media. Wave propagation is described by the usual acoustics equations (in the fluid medium) and by the low-frequency Biot’s equations (in the porous medium). Interface conditions are introduced to model various hydraulic contacts between the two media: open pores, sealed pores, and imperfect pores. Well-posedness of the initial-boundary value problem is proven. Cartesian grid numerical methods previously developed in porous heterogeneous media are adapted to the present context: a fourth-order ADER scheme with Strang splitting for time- marching; a space-time mesh-refinement to capture the slow compressional wave predicted by Biot’s theory; and an immersed interface method to discretize the interface conditions and to introduce a subcell resolution. Numerical experiments and comparisons with exact solutions are proposed for the three types of interface conditions, demonstrating the accuracy of the approach.

Direct P-wave anisotropy measurements at Homestake Mine: implications for wave propagation in continental crust

2020 ◽  
Vol 224 (1) ◽  
pp. 121-137
Author(s):  
James Atterholt ◽  
Sarah J Brownlee ◽  
Gary L Pavlis
Keyword(s):  
Wave Propagation ◽  
Particle Motion ◽  
Bootstrap Method ◽  
Estimation Method ◽  
Principal Component ◽  
Compressional Wave ◽  
P Wave ◽  
Longitudinal Motion ◽  
Angular Deviation ◽  
Homestake Mine

SUMMARY We measured anisotropic seismic properties of schists of the Homestake Formation located at a depth of 1478 m in the Sanford Underground Research Facility (SURF) in the Black Hills of South Dakota, USA. We deployed a 24-element linear array of three-component geophones in an area in the Homestake Mine called 19-ledge. An airless jackhammer source was used to shoot two profiles: (1) a walkaway survey to appraise any distance dependence and (2) a fan shot profile to measure variations with azimuth. Slowness estimates from the fan shot profile show a statistically significant deviation with azimuth with the expected 180° variation with azimuth. We measured P-wave particle motion deviations from data rotated to ray coordinates using three methods: (1) a conventional principal component method, (2) a novel grid search method that maximized longitudinal motion over a range of search angles and (3) the multiwavelet method. The multiwavelet results were computed in two frequency bands of 200–600 and 100–300 Hz. Results were binned by azimuth and averaged with a robust estimation method with error bars estimated by a bootstrap method. The particle motion results show large, statistically significant variations with azimuth with a 180° cyclicity. We modelled the azimuthal variations in compressional wave speed and angular deviation from purely longitudinal particle motion of P-waves using an elastic tensor method to appraise the relative importance of crystalline fabric relative to fracturing parallel to foliation. The model used bulk averages of crystal fabric measured for an analogous schist sample from southeast Vermont rotated to the Homestake Formation foliation directions supplied by SURF from old mine records. We found with average crustal crack densities crack induced anisotropy had only a small effect on the observables. We found strong agreement in the traveltime data. The observed amplitudes of deviations of P particle motion showed significantly larger variation than the model predictions and a 20° phase shift in azimuth. We attribute the inadequacies of the model fit to the particle motion data to inadequacies in the analogue rock and/or near receiver distortions from smaller scale heterogeneity. We discuss the surprising variability of signals recorded in this experimental data. We show clear examples of unexplained resonances and unexpected variations on a scale much smaller than a wavelength that has broad implications for wave propagation in real rocks.

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