scholarly journals ANALYSIS OF TF-SF BOUNDARY FOR 2D-FDTD WITH PLANE P-WAVE PROPAGATION IN LAYERED DISPERSIVE AND LOSSY MEDIA

2008 ◽  
Vol 83 ◽  
pp. 157-172 ◽  
Author(s):  
Yan-Nan Jiang ◽  
De-Biao Ge ◽  
Shi-Jing Ding
Keyword(s):  
Wave Propagation ◽  
P Wave ◽  
Lossy Media ◽  
2D Fdtd ◽  
Plane P Wave

scholarly journals Recording seismic reflections using rigidly interconnected geophones

Geophysics ◽  
2001 ◽  
Vol 66 (6) ◽  
pp. 1838-1842 ◽  
Author(s):  
C. M. Schmeissner ◽  
K. T. Spikes ◽  
D. W. Steeples
Keyword(s):  
Wave Propagation ◽  
Data Acquisition ◽  
Seismic Reflection ◽  
Spatial Sampling ◽  
P Wave ◽  
Signal Distortion ◽  
Reflection And Refraction ◽  
First Arrival ◽  
The Cost ◽  
Seismic Reflections

Ultrashallow seismic reflection surveys require dense spatial sampling during data acquisition, which increases their cost. In previous efforts to find ways to reduce these costs, we connected geophones rigidly to pieces of channel iron attached to a farm implement. This method allowed us to plant the geophones in the ground quickly and automatically. The rigidly interconnected geophones used in these earlier studies detected first‐arrival energy along with minor interfering seismic modes, but they did not detect seismic reflections. To examine further the feasibility of developing rigid geophone emplacement systems to detect seismic reflections, we experimented with four pieces of channel iron, each 2.7 m long and 10 cm wide. Each segment was equipped with 18 geophones rigidly attached to the channel iron at 15‐cm intervals, and the spikes attached to all 18 geophones were pushed into the ground simultaneously. The geophones detected both refracted and reflected energy; however, no significant signal distortion or interference attributable to the rigid coupling of the geophones to the channel iron was observed in the data. The interfering seismic modes mentioned from the previous experiments were not detected, nor was any P‐wave propagation noted within the channel iron. These results show promise for automating and reducing the cost of ultrashallow seismic reflection and refraction surveys.

Rise times of attenuated seismic pulses detected in both empty and fluid‐filled cylindrical boreholes

Geophysics ◽  
1984 ◽  
Vol 49 (4) ◽  
pp. 398-410 ◽  
Author(s):  
D. P. Blair
Keyword(s):  
Stress Wave ◽  
Particle Motion ◽  
P Wave ◽  
Wave Incident ◽  
Stress Wave Propagation ◽  
Linear Phase ◽  
Phase Filter ◽  
Mathematical Expressions ◽  
Plane P Wave ◽  
Theory And Experiment

Fourier‐Bessel theory is used to derive filters representing the influence of both empty and fluid‐filled cylindrical boreholes on particle motion induced in rock by a plane P-wave incident perpendicular to the borehole axis. For wavelengths greater than 10 times the borehole circumference, the effect of the borehole on particle motions is shown to be negligible; thus the results have little relevance for the long wavelengths commonly encountered in earthquake seismology. The results are, however, relevant to the study of stress wave propagation at ultrasonic frequencies in rock masses. For small wavelengths (αa > 3.0) the filter representing particle motion on the wave incident site of an empty borehole reduces to a linear phase filter which increases all amplitudes by a factor of 2 while the filter representing fluid stress at the center of a fluid‐filled borehole may be reduced to simple mathematical expressions. Experimental results were obtained for the interaction of a stress wave with either accelerometers mounted in an empty borehole or a hydrophone located centrally in a fluid‐filled borehole. Both theory and experiment show a similar distortion in the rise time of the pulse traveling past the borehole.

Effect of Fluids on the Elastic Properties of 3D-Printed Anisotropic Rock Models

2021 ◽  
Vol 62 (5) ◽  
pp. 537-552
Author(s):  
Suresh Dande ◽  
◽  
Robert R. Stewart ◽  
Nikolay Dyaur ◽  
◽  
...  
Keyword(s):  
Wave Propagation ◽  
Elastic Properties ◽  
P Wave ◽  
Engine Oil ◽  
Rock Properties ◽  
Anisotropic Rock ◽  
Wave Velocities ◽  
Inclusion Model ◽  
3D Printed ◽  
Primary Porosity

Laboratory physical models play an important role in understanding rock properties and wave propagation, both theoretically and at the field scale. In some cases, 3D-printing technology can be adopted to construct complex rock models faster, more inexpensively, and with more specific features than previous model-building techniques. In this study, we use 3D-printed rock models to assist in understanding the effects of various fluids (air, water, engine oil, crude oil, and glycerol) on the models’ elastic properties. We first used a 3D-printed, 1-in. cube-shaped layered model. This model was created with a 6% primary porosity and a bulk density of 0.98 g/cc with VTI anisotropy. We next employed a similar cube but with horizontal inclusions embedded in the layered background, which contributed to its total 24% porosity (including primary porosity). For air to liquid saturation, P-velocities increased for all liquids in both models, with the highest increase being with glycerol (57%) and an approximately 45% increase for other fluids in the inclusion model. For the inclusion model (dry and saturated), we observed a greater difference between two orthogonally polarized S-wave velocities (Vs1 and Vs2) than between two P-wave velocities (VP0 and VP90). We attribute this to the S2-wave (polarized normal to both the layering and the plane of horizontal inclusions), which appears more sensitive to horizontal inclusions than the P-wave. For the inclusion model, Thomsen’s P-wave anisotropic parameter (ɛ) decreased from 26% for the air case to 4% for the water-saturated cube and to 1% for glycerol saturation. The small difference between the bulk modulus of the frame and the pore fluid significantly reduces the velocity anisotropy of the medium, making it almost isotropic. We compared our experimental results with theory and found that predictions using Schoenberg’s linear slip theory combined with Gassmann’s anisotropic equation were closer to actual measurements than Hudson’s isotropic calculations. This work provides insights into the usefulness of 3D-printed models to understand elastic rock properties and wave propagation under various fluid saturations.

Analytical Study of Cylindrical P-Wave Propagation across Jointed Rock Masses

2014 ◽  
Vol 988 ◽  
pp. 502-507 ◽  
Author(s):  
Shao Bo Chai ◽  
Jian Chun Li ◽  
Hai Bo Li ◽  
Ya Qun Liu
Keyword(s):  
Wave Propagation ◽  
Rock Joint ◽  
Jointed Rock ◽  
P Wave ◽  
Displacement Discontinuity ◽  
Linear Elastic ◽  
Transmission And Reflection Coefficients ◽  
Conservation Of Momentum ◽  
Elastic Rock ◽  
Transmission And Reflection

According to the displacement discontinuity method and the conservation of momentum at the wave fronts, analysis for cylindrical P-wave propagation across a linear elastic rock joint is carried out. Considering the energy variation for wave propagation in one medium, the wave propagation equation was derived and expressed in an iterative form. The transmission and reflection coefficients are then obtained from the equation. By verification, the results agree very well with those from the existing results.

A hybrid method to calculate teleseismic body waves in a regional 3D model using GEMINI and SPECFEM.

2021 ◽  
Author(s):  
Thomas Möller ◽  
Wolfgang Friederich
Keyword(s):  
Wave Propagation ◽  
Hybrid Method ◽  
Velocity Model ◽  
Absorbing Boundary Conditions ◽  
Body Waves ◽  
P Wave ◽  
Spherically Symmetric ◽  
Target Region ◽  
3D Simulations ◽  
Earth Models

<p>Modeling waveforms of teleseismic body waves requires the solution of the seismic wave equation in the entire Earth. Since fully-numerical 3D simulations on a global scale with periods of a few seconds are far too computationally expensive, we resort to a hybrid approach in which fully-numerical 3D simulations are performed only within the target region and wave propagation through the rest of the Earth is modeled using methods that are much faster but apply only to spherically symmetric Earth models.</p><p>We present a hybrid method that uses GEMINI to compute wave fields for a spherically symmetric Earth model up to the boundaries of a regional box. The wavefield is injected at the boundaries, where wave propagation is continued using SPECFEM-Cartesian. Inside the box, local heterogeneities in the velocity distribution are allowed, which can cause scattered and reflected waves. To prevent these waves from reflecting off the edges of the box absorbing boundary conditions are specifically applied to these parts of the wavefields. They are identified as the difference between the wavefield calculated with SPECFEM at the edges and the incident wavefield.</p><p>The hybrid method is applied to a target region in and around the Alps as a test case. The region covers an area of 1800 by 1350 km centered at 46.2°N and 10.87°E and includes crust and mantle to a depth of 600 km. We compare seismograms with a period of up to ten seconds calculated with the hybrid method to those calculated using GEMINI only for identical 1D earth models. The comparison of the seismograms shows only very small differences and thus validates the hybrid method. In addition, we demonstrate the potential of the method by calculating seismograms where the 1D velocity model inside the box is replaced by a velocity model generated using P-wave traveltime tomography.</p>

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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