P-SV wave propagation in heterogeneous media: Velocity‐stress finite‐difference method

Geophysics ◽  
1986 ◽  
Vol 51 (4) ◽  
pp. 889-901 ◽  
Author(s):  
Jean Virieux
Keyword(s):  
Wave Propagation ◽  
Poisson’S Ratio ◽  
Heterogeneous Media ◽  
Velocity Dispersion ◽  
Poisson's Ratio ◽  
S Wave ◽  
Phase Velocity Dispersion ◽  
Wave Phase Velocity ◽  
Converted Phases ◽  
Phase Velocity Dispersion Curve

I present a finite‐difference method for modeling P-SV wave propagation in heterogeneous media. This is an extension of the method I previously proposed for modeling SH-wave propagation by using velocity and stress in a discrete grid. The two components of the velocity cannot be defined at the same node for a complete staggered grid: the stability condition and the P-wave phase velocity dispersion curve do not depend on the Poisson’s ratio, while the S-wave phase velocity dispersion curve behavior is rather insensitive to the Poisson’s ratio. Therefore, the same code used for elastic media can be used for liquid media, where S-wave velocity goes to zero, and no special treatment is needed for a liquid‐solid interface. Typical physical phenomena arising with P-SV modeling, such as surface waves, are in agreement with analytical results. The weathered‐layer and corner‐edge models show in seismograms the same converted phases obtained by previous authors. This method gives stable results for step discontinuities, as shown for a liquid layer above an elastic half‐space. The head wave preserves the correct amplitude. Finally, the corner‐edge model illustrates a more complex geometry for the liquid‐solid interface. As the Poisson’s ratio v increases from 0.25 to 0.5, the shear converted phases are removed from seismograms and from the time section of the wave field.

An average-derivative optimal scheme for modeling of the frequency-domain 3D elastic wave equation

Geophysics ◽  
2018 ◽  
Vol 83 (4) ◽  
pp. T209-T234 ◽  
Author(s):  
Jing-Bo Chen ◽  
Jian Cao
Keyword(s):  
Wave Equation ◽  
Elastic Wave ◽  
Frequency Domain ◽  
Poisson’S Ratio ◽  
Poisson's Ratio ◽  
S Wave ◽  
Elastic Wave Equation ◽  
Wave Phase Velocity ◽  
Point Scheme ◽  
Grid Points

Because of its high computational cost, we needed to develop an efficient numerical scheme for the frequency-domain 3D elastic wave equation. In addition, the numerical scheme should be applicable to media with a liquid-solid interface. To address these two issues, we have developed a new average-derivative optimal 27-point scheme with arbitrary directional grid intervals and a corresponding numerical dispersion analysis for the frequency-domain 3D elastic wave equation. The novelty of this scheme is that its optimal coefficients depend on the ratio of the directional grid intervals and Poisson’s ratio. In this way, this scheme can be applied to media with a liquid-solid interface and a computational grid with arbitrary directional grid intervals. For media with a variable Poisson’s ratio, we have developed an effective and stable interpolation method for optimization coefficients. Compared with the classic 19-point scheme, this new scheme reduces the required number of grid points per wavelength for equal and unequal directional grid intervals. The reduction of the number of grid points increases as the Poisson’s ratio becomes larger. In particular, the numerical S-wave phase velocity of this new scheme becomes zero, whereas the classic 19-point scheme produces a spurious numerical S-wave phase velocity, as Poisson’s ratio reaches 0.5. We have performed numerical examples to develop the theoretical analysis.

Seismic velocities and Poisson’s ratio of shallow unconsolidated sands

Geophysics ◽  
2000 ◽  
Vol 65 (2) ◽  
pp. 559-564 ◽  
Author(s):  
Ran Bachrach ◽  
Jack Dvorkin ◽  
Amos M. Nur
Keyword(s):  
Wave Velocity ◽  
Poisson’S Ratio ◽  
Tangential Component ◽  
Poisson's Ratio ◽  
Contact Theory ◽  
Beach Sand ◽  
Contact Radius ◽  
Seismic Velocities ◽  
S Wave ◽  
Unconsolidated Sands

We determined P- and S-wave velocity depth profiles in shallow, unconsolidated beach sand by analyzing three‐component surface seismic data. P- and S-wave velocity profiles were calculated from traveltime measurements of vertical and tangential component seismograms, respectively. The results reveal two discrepancies between theory and data. Whereas both velocities were found to be proportional to the pressure raised to the power of 1/6, as predicted by the Hertz‐Mindlin contact theory, the actual values of the velocities are less than half of those calculated from this theory. We attribute this discrepancy to the angularity of the sand grains. Assuming that the average radii of curvature at the grain contacts are smaller than the average radii of the grains, we modify the Hertz‐Mindlin theory accordingly. We found that the ratio of the contact radius to the grain radius is about 0.086. The second disparity is between the observed Poisson’s ratio of 0.15 and the theoretical value (0.008 for random pack of quartz spheres). This discrepancy can be reconciled by assuming slip at the grain contacts. Because slip decreases the shearing between grains, Poisson’s ratio increases.

scholarly journals The Passive Surface Wave Methods for Shallow Engineering Exploration Based on the ESPAC Technology

2019 ◽  
Vol 131 ◽  
pp. 01041
Author(s):  
Tong Wu ◽  
Kezhu Song ◽  
Zhengyang Sun ◽  
Hongwei Zhao ◽  
Xin Hu
Keyword(s):  
Surface Wave ◽  
Phase Velocity ◽  
Velocity Dispersion ◽  
Vertical Component ◽  
Original Data ◽  
Phase Velocity Dispersion ◽  
Wave Phase Velocity ◽  
Wave Methods ◽  
Rayleigh Wave Phase Velocity ◽  
Selection Of

ESPAC method is a rapidly emerging field of seismological research, which can reflect the physical properties of the Earth’s medium. In the process of using the ESPAC method, sometimes the noise of the original data is relatively large, and the raw data of each seismometer needs to be preprocessed, including operations such as de-averaging, de-trending, re-sampling, normalization, and filtering. The selection of the normalized method and the selection of the bandwidth of the filter are particularly important, and it will produce the wrong result if not handled properly. This article attempts to use the extended spatial autocorrelation (ESPAC) method to extract Rayleigh-wave phase velocity dispersion curves from the vertical component of the seismic stations’ microtremors, and proposes feasible and effective solutions to the selection of the normalized method and bandwidth of bandpass filtering.

Effect of longitudinal stress on wave propagation in width-constrained elastic plates with arbitrary Poisson's ratio

2015 ◽  
Vol 252 (7) ◽  
pp. 1615-1619 ◽  
Author(s):  
Paweł Sobieszczyk ◽  
Marcin Majka ◽  
Dominika Kuźma ◽  
Teik-Cheng Lim ◽  
Piotr Zieliński
Keyword(s):  
Wave Propagation ◽  
Poisson’S Ratio ◽  
Poisson's Ratio ◽  
Elastic Plates ◽  
Longitudinal Stress

scholarly journals Estimation of S-Wave Velocity Profiles at Lima City, Peru Using Microtremor Arrays

2014 ◽  
Vol 9 (6) ◽  
pp. 931-938 ◽  
Author(s):  
Selene Quispe ◽  
◽  
Kosuke Chimoto ◽  
Hiroaki Yamanaka ◽  
Hernando Tavera ◽  
...  
Keyword(s):  
Wave Velocity ◽  
Velocity Structure ◽  
Site Effect ◽  
Site Amplification ◽  
Velocity Profiles ◽  
S Wave ◽  
Phase Velocity Dispersion ◽  
Seismic Recording ◽  
Phase Velocity Dispersion Curve ◽  
Alluvial Material

Microtremor exploration was performed around seismic recording stations at five sites in Lima city, Peru in order to know the site amplification at these sites. The Spatial Autocorrelation (SPAC) method was applied to determine the observed phase velocity dispersion curve, which was subsequently inverted in order to estimate the 1-D S-wave velocity structure. From these results, the theoretical amplification factor was calculated to evaluate the site effect at each site. S-wave velocity profiles at alluvial gravel sites have S-wave velocities ranging from ∼500 to ∼1500 m/s which gradually increase with depth, while Vs profiles at sites located on fine alluvial material such as sand and silt have Swave velocities that vary between ∼200 and ∼500 m/s. The site responses of all Vs profiles show relatively high amplification levels at frequencies larger than 3 Hz. The average transfer function was calculated to make a comparison with values within the existing amplification map of Lima city. These calculations agreed with the proposed site amplification ranges.

scholarly journals Wave-equation based traveltime seismic tomography – Part 2: Application to the 1992 Landers earthquake (<i>M</i><sub>w</sub> 7.3) area

2014 ◽  
Vol 6 (2) ◽  
pp. 2567-2613 ◽  
Author(s):  
P. Tong ◽  
D. Zhao ◽  
D. Yang ◽  
X. Yang ◽  
J. Chen ◽  
...  
Keyword(s):  
Wave Equation ◽  
High Resolution ◽  
Seismic Tomography ◽  
Lower Crust ◽  
Poisson’S Ratio ◽  
Arrival Time ◽  
Poisson's Ratio ◽  
S Wave ◽  
Landers Earthquake ◽  
1992 Landers Earthquake

Abstract. High-resolution 3-D P and S wave crustal velocity and Poisson's ratio models of the 1992 Landers earthquake (Mw 7.3) area are determined iteratively by a wave-equation based traveltime seismic tomography (WETST) technique as developed in the first paper. The details of data selection, synthetic arrival-time determination, and trade-off analysis of damping and smoothing parameters are presented to show the performance of this new tomographic inversion method. A total of 78 523 P wave and 46 999 S wave high-quality arrival-time data from 2041 local earthquakes recorded by 275 stations during the period of 1992–2013 is used to obtain the final tomographic models which costs around 10 000 CPU h. Checkerboard resolution tests are conducted to verify the reliability of inversion results for the chosen seismic data and the wave-equation based traveltime seismic tomography method. Significant structural heterogeneities are revealed in the crust of the 1992 Lander earthquake area which may be closely related to the local seismic activities. Strong variations of velocity and Poisson's ratio exist in the source regions of the Landers and three other strong earthquakes in this area. Most seismicity occurs in areas with high-velocity and low Poisson's ratio, which may be associated with the seismogenic layer. Pronounced low-velocity anomalies revealed in the lower crust along the Elsinore, the San Jacinto and the San Andreas faults may reflect the existence of fluids in the lower crust. The recovery of these strong heterogeneous structures are facilitated by the use of full wave equation solvers and WETST and verifies their ability in generating high-resolution tomographic models.

scholarly journals On the Effect of CO2 on Seismic and Ultrasonic Properties: A Novel Shale Experiment

Energies ◽  
2021 ◽  
Vol 14 (16) ◽  
pp. 5007
Author(s):  
Stian Rørheim ◽  
Mohammad Hossain Bhuiyan ◽  
Andreas Bauer ◽  
Pierre Rolf Cerasi
Keyword(s):  
Young’S Modulus ◽  
Wave Velocity ◽  
Poisson’S Ratio ◽  
Young's Modulus ◽  
Co2 Storage ◽  
Poisson's Ratio ◽  
Rock Properties ◽  
S Wave ◽  
Velocity Changes ◽  
4D Seismic

Carbon capture and storage (CCS) by geological sequestration comprises a permeable formation (reservoir) for CO2 storage topped by an impermeable formation (caprock). Time-lapse (4D) seismic is used to map CO2 movement in the subsurface: CO2 migration into the caprock might change its properties and thus impact its integrity. Simultaneous forced-oscillation and pulse-transmission measurements are combined to quantify Young’s modulus and Poisson’s ratio as well as P- and S-wave velocity changes in the absence and in the presence of CO2 at constant seismic and ultrasonic frequencies. This combination is the laboratory proxy to 4D seismic because rock properties are monitored over time. It also improves the understanding of frequency-dependent (dispersive) properties needed for comparing in-situ and laboratory measurements. To verify our method, Draupne Shale is monitored during three consecutive fluid exposure phases. This shale appears to be resilient to CO2 exposure as its integrity is neither compromised by notable Young’s modulus and Poisson’s ratio nor P- and S-wave velocity changes. No significant changes in Young’s modulus and Poisson’s ratio seismic dispersion are observed. This absence of notable changes in rock properties is attributed to Draupne being a calcite-poor shale resilient to acidic CO2-bearing brine that may be a suitable candidate for CCS.

Combining surface-wave phase-velocity dispersion curves and full microtremor horizontal-to-vertical spectral ratio for subsurface sedimentary site characterization

2016 ◽  
Vol 4 (4) ◽  
pp. SQ41-SQ49 ◽  
Author(s):  
Agostiny Marrios Lontsi ◽  
Matthias Ohrnberger ◽  
Frank Krüger ◽  
Francisco José Sánchez-Sesma
Keyword(s):  
Surface Wave ◽  
Phase Velocity ◽  
Velocity Dispersion ◽  
Spectral Ratio ◽  
Test Site ◽  
Dispersion Curves ◽  
Surface Velocity ◽  
Wave Phase ◽  
Phase Velocity Dispersion ◽  
Wave Phase Velocity

We compute seismic velocity profiles by a combined inversion of surface-wave phase-velocity dispersion curves together with the full spectrum of the microtremor horizontal-to-vertical (H/V) spectral ratio at two sediment-covered sites in Germany. The sediment deposits are approximately 100 m thick at the first test site and approximately 400 m thick at the second test site. We have used an extended physical model based on the diffuse wavefield assumption for the interpretation of the observed microtremor H/V spectral ratio. The extension includes the interpretation of the microtremor H/V spectral ratio observed at depth (in boreholes). This full-wavefield approach accounts for the energy contribution from the body and surface waves, and thus it allows for inverting the properties of the shallow subsurface. We have obtained the multimode phase velocity dispersion curves from an independent study, and a description of the extracted branches and their interpretation was developed. The inversion results indicate that the combined approach using seismic ambient noise and actively generated surface-wave data will improve the accuracy of the reconstructed near-surface velocity model, a key step in microzonation, geotechnical engineering, seismic statics corrections, and reservoir imaging.

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