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Geophysical investigation techniques: seismic
Published in Ian Acworth, Investigating Groundwater, 2019
Rayleigh waves are a type of surface wave confined to the near surface of the ground. Rayleigh waves include both longitudinal and transverse motions that decrease exponentially in amplitude as distance from the surface increases. There is also a phase difference between these component motions. The speed of the Rayleigh wave is a little less than the shear wave and can be approximated from Equation 8.16: VRayleigh=0.862+1.14μ1+μ
Miscellaneous topics
Published in Michael Talbot-Smith, Audio Engineer's Reference Book, 2013
Steven Dixon, Vivian Weeks, John Ratcliff
(a) Scratches and cracks. The presence of scratches or cracks on or just under the surface can be detected using ultrasonic techniques. Rayleigh waves are localized at a surface but do extend into the bulk of the material. The amplitude of the wave decays exponentially into the sample and falls to a fraction 1/e (e = 2.7183) of its amplitude at the surface at a depth equal to one wavelength in the material. Because the depth to which a surface wave extends is dependent on frequency, an indication of the depth of the crack or scratch can be obtained. Thus the limiting factor in detecting the depth of the scratch or crack is the highest frequency of Rayleigh waves that can be generated or detected. When using a broadband Rayleigh wave, the same argument applies, i.e. there must be a significant magnitude of frequency component with a wavelength comparable to the size of the structure to be detected.
Gravimetric Humidity Sensors
Published in Ghenadii Korotcenkov, Handbook of Humidity Measurement, 2019
The SAW devices also utilize piezoelectric crystal resonators to generate AWs (Afzal and Dickert 2011; Fanget et al. 2011). A SAW is a kind of AW that propagates along the surface of a material. In other words, a SAW is a mechanical wave in which acoustic energy is confined to the surface of an isotropic single crystal. For the first time, the possibility of propagation of AWs along a solid surface was predicted by Rayleigh in 1885 (Ristic 1983; Grate et al. 1993). These waves, which are sometimes called Rayleigh waves, have considerable importance in the areas as diverse as structural testing, telecommunications, and signal processing.
Total seismic analysis of slope considering logarithmic spiral failure surface
Published in Geomechanics and Geoengineering, 2021
Suman Hazari, Sima Ghosh, Richi Prasad Sharma
All the above pseudo-dynamic methods seismic analyses consider only the effect of primary and shear waves. It is seen in the literature (Choudhury and Katdare 2013, Chanda et al. 2017) that about 67% of the total seismic energy is carried by the Rayleigh waves. The Rayleigh wave decreases exponentially in amplitude as the distance from the surface increase. Hence, the effect of the Rayleigh wave on the surface structure is important. Navarro and Samartin (1989) have given an approximation procedure considering the effect of Rayleigh waves for studying harmonic solid–structure interaction problems in the time domain. Uenishi (2010) has investigated the dynamic behaviour of a two-dimensional linear elastic slope and suggested that the amplitude and phase changes of the surface waves strongly depend on the slope inclination and superimposition of reflected waves. Later, Choudhury and Katdare (2013) and Choudhury et al. (2014) have analysed the earth retaining structure considering the effect of Rayleigh waves along with primary and shear waves. Chanda et al. (2017) have analysed the slope considering the effect of the Rayleigh wave in which the failure surface is assumed as circular. Qin and Chian (2018) provide a procedure to calculate the bearing capacity of a soil slope using discretisation-based kinematic analysis considering the effect of Rayleigh waves.
Eigenfunction expansion method to characterize Rayleigh wave propagation in orthotropic medium with phase lags
Published in Waves in Random and Complex Media, 2019
Siddhartha Biswas, Basudeb Mukhopadhyay
The study of elastic waves and the nature of earthquakes remained as paramount interest to the geophysicists. The primary work on elastic waves received it impetus from the earlier studies by the scientists around the middle of the nineteenth century. Owing to slower attenuation of energy compare to the body waves, Rayleigh type surface waves are the most destructive seismic surface waves that can unobstructedly transmit along the stress-free surface with the phase velocities lying within the seismic range and its amplitude decaying exponentially with depth from the surface. Rayleigh waves are generally non-dispersive in nature but exhibit dispersion in case of stratified semi-infinite medium. It is well established that Rayleigh waves travel along the surface of relatively thicker solid materials penetrating to a depth of one wave length and therefore, the study of these waves is very useful because of their sensitivity of surface defects. Moreover, since they follow the surface around, so these waves can also be used to inspect areas that other waves might have difficulty in reaching.
Explicit secular equation and H/V ratio formula of Rayleigh waves in orthotropic micropolar elastic half-spaces
Published in Waves in Random and Complex Media, 2022
Pham Chi Vinh, Truong Thi Thuy Dung, Pham Thi Ha Giang, Tran Thanh Tuan
It is well-known that studies on Rayleigh waves have found wide range of applications in seismology, acoustics, geophysics, telecommunications industry, for example. Especially, Rayleigh waves are a convenient tool for nondestructively evaluating the mechanical characteristics of structures during loading [1]. When they are used for this task, their explicit secular equations are used as mathematical base to formulate inverse problems: determining the mechanical characteristics of structures from experimentally measured valued of Rayleigh wave velocity. Therefore, finding the secular equations in explicit form is always the first object of all investigations on Rayleigh waves.