Exact solutions of SH wave equation for inhomogeneous media

1970 ◽  
Vol 60 (6) ◽  
pp. 1847-1859
Author(s):  
S. N. Bhattacharya
Keyword(s):  
Wave Equation ◽  
Exact Solutions ◽  
Elastic Medium ◽  
Shear Wave ◽  
Wave Velocity ◽  
Shear Wave Velocity ◽  
Sh Wave ◽  
Exponential Functions ◽  
Transcendental Functions ◽  
Inhomogeneous Elastic Medium

Abstract The SH wave equation in a vertically inhomogeneous elastic medium has been considered. It is possible to determine all vertical inhomogeneities for which the SH wave equation can be solved in terms of standard transcendental functions. The inhomogeneities where either shear-wave velocity, modulus of rigidity, or density is constant have also been considered. A few simple inhomogeneities and their solutions in terms of hypergeometric, Whittaker, Bessel and exponential functions have been given.

Effect of Rotation, Gravity, Primary Stress and Magnetic Field on Shear Waves Spreading in an Anisotropic Incompressible Sandy Elastic Medium

2019 ◽  
Vol 16 (11) ◽  
pp. 4443-4454
Author(s):  
S. H. Elhag ◽  
F. S. Bayones
Keyword(s):  
Magnetic Field ◽  
Elastic Medium ◽  
Gravity Field ◽  
Shear Wave ◽  
Wave Velocity ◽  
Shear Wave Velocity ◽  
Incompressible Medium ◽  
Primary Stress ◽  
Dry Sand ◽  
Inhomogeneous Elastic Medium

In this paper, we investigated the spreading of shear wave in an anisotropic non-homogeneous elastic medium under effect of dry sand, rotation, gravity, primary stress, and magnetic field. We have reached equation of variation of shear wave velocity c1 in an anisotropic incompressible medium according to sand, rotation, gravity, primary stress, and magnetic field, then we used graphs to illustrate to show the effect of direction of spreading of shear wave. The results indicate that the effect of dry sand, rotation, gravity, primary stress, and magnetic field on the spreading of shear wave in an anisotropic inhomogeneous elastic medium are very pronounced. The results have been obtained are discussed and presented visually, the results demonstrate that the effect of sand, gravity field, primary stress, magnetic field, anisotropy and rotation are noticeable.

scholarly journals Calibrating a new attenuation curve for the Dead Sea region using surface wave dispersion surveys in sites damaged by the 1927 Jericho earthquake

Solid Earth ◽  
2019 ◽  
Vol 10 (2) ◽  
pp. 379-390 ◽  
Author(s):  
Yaniv Darvasi ◽  
Amotz Agnon
Keyword(s):  
Shear Wave ◽  
Wave Velocity ◽  
Shear Wave Velocity ◽  
Dead Sea ◽  
Attenuation Curve ◽  
Surface Wave Dispersion ◽  
Near Surface ◽  
Moderate Seismicity ◽  
Local Point ◽  
The Dead

Abstract. Instrumental strong motion data are not common around the Dead Sea region. Therefore, calibrating a new attenuation equation is a considerable challenge. However, the Holy Land has a remarkable historical archive, attesting to numerous regional and local earthquakes. Combining the historical record with new seismic measurements will improve the regional equation. On 11 July 1927, a rupture, in the crust in proximity to the northern Dead Sea, generated a moderate 6.2 ML earthquake. Up to 500 people were killed, and extensive destruction was recorded, even as far as 150 km from the focus. We consider local near-surface properties, in particular, the shear-wave velocity, as an amplification factor. Where the shear-wave velocity is low, the seismic intensity far from the focus would likely be greater than expected from a standard attenuation curve. In this work, we used the multichannel analysis of surface waves (MASW) method to estimate seismic wave velocity at anomalous sites in Israel in order to calibrate a new attenuation equation for the Dead Sea region. Our new attenuation equation contains a term which quantifies only lithological effects, while factors such as building quality, foundation depth, topography, earthquake directivity, type of fault, etc. remain out of our scope. Nonetheless, about 60 % of the measured anomalous sites fit expectations; therefore, this new ground-motion prediction equation (GMPE) is statistically better than the old ones. From our local point of view, this is the first time that integration of the 1927 historical data and modern shear-wave velocity profile measurements improved the attenuation equation (sometimes referred to as the attenuation relation) for the Dead Sea region. In the wider context, regions of low-to-moderate seismicity should use macroseismic earthquake data, together with modern measurements, in order to better estimate the peak ground acceleration or the seismic intensities to be caused by future earthquakes. This integration will conceivably lead to a better mitigation of damage from future earthquakes and should improve maps of seismic hazard.

scholarly journals Multi-method site characterization to verify the hard rock (Site Class A) assumption at 25 seismograph stations across Eastern Canada

2021 ◽  
pp. 875529302110010
Author(s):  
Sameer Ladak ◽  
Sheri Molnar ◽  
Samantha Palmer
Keyword(s):  
Shear Wave ◽  
Wave Velocity ◽  
Shear Wave Velocity ◽  
Hard Rock ◽  
Site Characterization ◽  
Eastern Canada ◽  
Site Class ◽  
Paleozoic Rock ◽  
Rock Types ◽  
Site Period

Site characterization is a crucial component in assessing seismic hazard, typically involving in situ shear-wave velocity ( VS) depth profiling, and measurement of site amplification including site period. Noninvasive methods are ideal for soil sites and become challenging in terms of field logistics and interpretation in more complex geologic settings including rock sites. Multiple noninvasive active- and passive-seismic techniques are applied at 25 seismograph stations across Eastern Canada. It is typically assumed that these stations are installed on hard rock. We investigate which site characterization methods are suitable at rock sites as well as confirm the hard rock assumption by providing VS profiles. Active-source compression-wave refraction and surface wave array techniques consistently provide velocity measurements at rock sites; passive-source array testing is less consistent but it is our most suitable method in constraining the rock VS. Bayesian inversion of Rayleigh wave dispersion curves provides quantitative uncertainty in the rock VS. We succeed in estimating rock VS at 16 stations, with constrained rock VS estimates at 7 stations that are consistent with previous estimates for Precambrian and Paleozoic rock types. The National Building Code of Canada uses solely the time-averaged shear-wave velocity of the upper 30 m ( VS30) to classify rock sites. We determine a mean VS30 of ∼ 1600 m/s for 16 Eastern Canada stations; the hard rock assumption is correct (>1500 m/s) but not as hard as often assumed (∼2000 m/s). Mean variability in VS30 is ∼400 m/s and can lead to softer rock classifications, in particular, for Paleozoic rock types with lower average rock VS near the hard/soft rock boundary. Microtremor and earthquake horizontal-to-vertical spectral ratios are obtained and provide site period classifications as an alternative to VS30.

scholarly journals The Polito Surface Wave flat-file Database (PSWD): statistical properties of test results and some inter-method comparisons

2021 ◽  
Vol 19 (6) ◽  
pp. 2343-2370
Author(s):  
Federico Passeri ◽  
Cesare Comina ◽  
Sebastiano Foti ◽  
Laura Valentina Socco
Keyword(s):  
Surface Wave ◽  
Shear Wave ◽  
Wave Velocity ◽  
Shear Wave Velocity ◽  
Active Surface ◽  
Statistical Properties ◽  
Test Results ◽  
Flat File ◽  
Research Fields ◽  
Database Content

AbstractThe compilation and maintenance of experimental databases are of crucial importance in all research fields, allowing for researchers to develop and test new methodologies. In this work, we present a flat-file database of experimental dispersion curves and shear wave velocity profiles, mainly from active surface wave testing, but including also data from passive surface wave testing and invasive methods. The Polito Surface Wave flat-file Database (PSWD) is a gathering of experimental measurements collected within the past 25 years at different Italian sites. Discussion on the database content is reported in this paper to evaluate some statistical properties of surface wave test results. Comparisons with other methods for shear wave velocity measurements are also considered. The main novelty of this work is the homogeneity of the PSWD in terms of processing and interpretation methods. A common processing strategy and a new inversion approach were applied to all the data in the PSWD to guarantee consistency. The PSWD can be useful for further correlation studies and is made available as a reference benchmark for the validation and verification of novel interpretation procedures by other researchers.

Shear Strength Monitoring System Based on Measurement of Shear Wave Velocity and Moisture Content

2014 ◽  
Vol 635-637 ◽  
pp. 750-754
Author(s):  
Peng Hu ◽  
Qing Li ◽  
Yi Wei Xu ◽  
Nan Ying Shentu ◽  
Quan Yuan Peng
Keyword(s):  
Shear Strength ◽  
Moisture Content ◽  
Shear Wave ◽  
Monitoring System ◽  
Wave Velocity ◽  
Shear Wave Velocity ◽  
Bender Elements ◽  
Strength Measurement ◽  
Soil Shear Strength ◽  
The Relationship

Expound the importance of soil shear strength measurement at mudslide hidden point to release the loss caused by the disaster, explain the relationship between shear wave velocity, moisture content and shear strength, design the shear strength monitoring system combining the shear wave velocity measured by Piezoelectric bender elements and moisture content.

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