Physics
Love Waves
Love waves are a type of surface seismic wave that travel along the Earth's surface. They are the fastest surface wave and cause the ground to move in a side-to-side, horizontal motion. Love waves are particularly significant in seismology for their ability to cause damage during earthquakes.
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eBook - PDFSurface Waves
New Trends and Developments
- Farzad Ebrahimi(Author)
- 2018(Publication Date)
- IntechOpen(Publisher)
Surface Waves - New Trends and Developments 24 Propagation of Love surface waves on the Earth’s surface is made possible by layered struc-ture of the Earth. The outermost layer of the Earth, the crust, is made of solid rocks composed of lighter elements. Thickness of the crust varies from 5 to 10 km under oceans (oceanic crust) to 30–70 km under continents (continental crust). The crust sits on mantle, which in turn cov-ers the outer and inner core. The destructive power of earthquakes is mainly due to waves traveling in this thin crustal layer [23]. As predicted by Love, the velocity of SH bulk waves increases with depth [24], i.e., as a func-tion of distance from the free surface of the Earth. The frequency of Love Waves generated by earthquakes is rather low comparing to that used in sensor technology and ranges typically from 10 mHz to 10 Hz. 3.1. Investigation of the Earth’s interior with Love surface waves Love and Rayleigh surface waves travel along great circle paths around the globe. Surface waves from strong earthquakes may travel several times around the Earth without a signifi -cant attenuation. They are termed global Rayleigh wave impulses [25]. An example of surface waves traveling multiply around the Earth [26] is given in Figure 4 . Seismic waves, generated both by natural earthquakes and by man-made sources, have deliv-ered an enormous amount of information about the Earth’s interior (subsurface properties of Earth’s crust). In classical seismology, Earth is modeled as a sequence of uniform horizontal layers (or spherical shells) having different elastic properties and one determines these prop -erties from travel times and dispersion of seismic waves [27]. Love surface waves have been successfully employed in a tomographic reconstruction of the physical properties of Earth’s upper mantle [28] as well as in diamond, gold, and copper exploration in Australia, South America, and South Africa [29].
- Roberto Villaverde(Author)
- 2009(Publication Date)
- CRC Press(Publisher)
Note, therefore, that the motion generated by Love Waves occurs mostly near the surface and thus they are of the surface type. That is, Love Waves are surface waves. Note, too, that the most significant part of the motion is concentrated in the surficial layer. For this reason, Love Waves are often thought of as SH waves trapped by multiple reflections within this surficial layer. Note, further, that the particle motion generated by a Love wave occurs only along the direction of the y -axis when one assumes that the wave travels along the direction of the x -axis. Hence, it may be concluded that, in general, Love Waves induce a horizontal motion that is perpendicular to the direction along which the wave propagates. This type of motion may indeed be seen in actual earthquake ground motion records such as that shown in Figure 4.26, where one can observe the arrival of the Love wave in the north–south record but not in the other two. The general nature of the motion generated by Love Waves is depicted in Figure 4.19d. 4.8.5 D ISPERSION OF L OVE W AVES It was mentioned earlier and may be seen from the inspection of Equation 4.249 that the propaga-tion velocity of Love Waves depends on their wavelength. This means that Love Waves with different FIGURE 4.25 Variation with depth of particle displacements generated by Love Waves. H v ( z ) z Exponential function Sinusoidal function 114 Fundamental Concepts of Earthquake Engineering wavelengths (or different frequencies) will travel with different velocities and arrive at a particular site at different times. It also means that, as in the case of waves in a flexural beam (see Sec-tion 4.5.2), Love Waves undergo dispersion and are therefore considered to be dispersive. Because of dispersion, Love Waves with different wavelengths may interfere with one another, form an apparent wave, and give the impression that they travel with a different velocity, the group velocity discussed in Section 4.5.3.
No longer available |Learn more- (Author)
- 2014(Publication Date)
- Academic Studio(Publisher)
Note that these Rayleigh waves have a much higher frequency than Rayleigh waves generated by earthquakes. After the 2004 Indian Ocean Earthquake, some people have speculated that Rayleigh waves served as a warning to animals to seek higher ground, allowing them to escape the more slowly-traveling tsunami. At this time, evidence for this is mostly anecdotal. Another animal early warning systems may rely on an ability to sense infrasonic waves traveling through the air. ________________________ WORLD TECHNOLOGIES ________________________ L waves or Love Waves How Love Waves work In elastodynamics, Love Waves are essentially horizontally polarized shear waves (SH waves) guided by an elastic layer, which is welded to an elastic half space on one side while bordering a vacuum on the other side. In seismology, Love Waves (also named Q waves ( Q uer: German for lateral)) are surface seismic waves that cause horizontal shifting of the earth during an earthquake. A.E.H. Love predicted the existence of Love Waves mathematically in 1911; the name comes from him (Chapter 11 from Love's book Some problems of geodynamics, first published in 1911). They form a distinct class, different from other types of seismic waves, such as P-waves and S-waves (both body waves), or Rayleigh waves (another type of surface wave). Love Waves travel with a slower velocity than P- or S- waves, but faster than Rayleigh waves. Description The particle motion of a Love wave forms a horizontal line perpendicular to the direction of propagation (i.e. are transverse waves). Moving deeper into the material, motion can decrease to a node and then alternately increase and decrease as one examines deeper layers of particles. The amplitude, or maximum particle motion, often decreases rapidly with depth. Since Love Waves travel on the Earth's surface, the ability (or amplitude) of the waves decrease exponentially with the depth of an earthquake.
eBook - PDF- Peter M. Shearer(Author)
- 2019(Publication Date)
- Cambridge University Press(Publisher)
8 Surface Waves and Normal Modes Our treatment to this point has been limited to body waves, solutions to the seismic wave equation that exist in whole spaces. However, when free sur- faces exist in a medium, other solutions are possible and are given the name surface waves. There are two types of surface waves that propagate along Earth’s surface, Rayleigh waves and Love Waves. For laterally homogeneous models, Rayleigh waves are radially polarized (P-SV ) and exist at any free surface, whereas Love Waves are transversely polarized and require some veloc- ity increase with depth (or a spherical geometry). Surface waves are generally the strongest arrivals recorded at teleseismic distances and they provide some of the best constraints on Earth’s shallow structure and low-frequency source properties. They differ from body waves in many respects – they travel more slowly, their amplitude decay with range is generally much less, and their velocities are strongly frequency dependent. Surface waves from large earth- quakes are observable for many hours, during which time they circle the Earth multiple times. Constructive interference among these orbiting surface waves, together with analogous reverberations of body waves, form the normal modes, or free oscillations of the Earth. Surface waves and normal modes are generally observed at periods longer than about 10 s, in contrast to the much shorter periods seen in many body wave observations. 8.1 Love Waves Love Waves are formed through the constructive interference of high-order SH surface multiples (i.e., SSS, SSSS, SSSSS, etc.). Thus, it is possible to model Love Waves as a sum of body waves. To see this, consider monochromatic plane wave propagation for the case of a vertical velocity gradient in a laterally homogeneous model, a situation we previously examined in Section 6.4. In this case, a plane wave defined by ray parameter p will turn at the depth where β = 1/p.
eBook - PDFElasticity and Fluid Dynamics
Volume 3 of Modern Classical Physics
- Kip S. Thorne, Roger D. Blandford(Authors)
- 2021(Publication Date)
- Princeton University Press(Publisher)
(12.62) Equation (12.62) represents a backward rotating, elliptical motion for each fluid element near the surface (as depicted in Fig. 12.7), reversing to a forward rotation at depths where the sign of ξ x has flipped. Rayleigh waves propagate around the surface of Earth rather than penetrate its interior. However, our treatment is inadequate, because their wavelengths—typically 1–10 km if generated by an earthquake—are not necessarily small compared with the scale heights in the outer crust over which C S and C T vary. Our wave equation has to be modified to include these vertical gradients. 12.4 Body Waves and Surface Waves—Seismology and Ultrasound 657 This vertical stratification has an important additional consequence. Ignoring these gradients, if we attempt to find an orthogonal surface mode just involving SH waves, we find that we cannot simultaneously satisfy the surface boundary conditions on displacement and stress with a single evanescent wave. We need two modes to do this. However, when we allow for stratification, the strong refraction allows an SH surface wave to propagate. This is known as a Love wave. The reason for its Love Waves practical importance is that seismic waves are also created by underground nuclear explosions, and it is important to be able to distinguish explosion-generated waves from earthquake waves. An earthquake is usually caused by the transverse slippage of two blocks of crust across a fault line. It is therefore an efficient generator of shear modes, including Love Waves. By contrast, explosions involve radial motions away from the point of explosion and are inefficient emitters of Love Waves. This allows these two sources of seismic disturbance to be distinguished. EXERCISES Exercise 12.11 Example: Earthquakes The magnitude M of an earthquake, on modern variants of the Richter scale , is a quantitative measure of the strength of the seismic waves it creates.
eBook - PDF- William Lowrie, Andreas Fichtner(Authors)
- 2020(Publication Date)
- Cambridge University Press(Publisher)
Love Waves are intrinsically dispersive < V < Love wave (L ) (a) (b) 2 β 1 β β 1 2 β 1 β > depth surface surface layer semi-infinite half-space reflected SH-wave SH particle motion direction of propagation surface Q LQ Fig. 6.7 (a) A Love wave results from constructive interference among SH-waves that are reflected at the top and bottom of the surface layer and become trapped in the layer. (b) The particle motion in a Love wave is horizontal and perpendicular to the direction of propagation. The amplitude of the wave decreases with depth below the free surface. P SV V = 0.92 β direction of propagation Rayleigh wave (L ) R depth particle motion surface LR Fig. 6.6 The particle motion of a Rayleigh wave consists of a combination of P- and SV-vibrations in the vertical plane. The particles move in retrograde sense around an ellipse that has its major axis vertical and minor axis in the direction of wave propagation. 154 6 Seismology even when the surface layer and underlying half-space are uniform. Rayleigh waves over a uniform half-space are non- dispersive. However, horizontal layers with different veloci- ties are usually present or there is a vertical velocity gradient. Rayleigh waves with long wavelengths penetrate more deeply into the Earth than those with short wavelengths. The speed of Rayleigh waves is proportional to the shear- wave velocity (V R ≈ 0.92β), and in the crust and uppermost mantle β generally increases with depth. Thus, the deeper penetrating long wavelengths travel with faster seismic velo- cities than the short wavelengths. As a result, the Rayleigh waves are dispersive. The packet of energy that propagates as a surface wave contains a spectrum of wavelengths. The energy in the wave propagates as the envelope of the wave packet (Fig. 6.8a), at a speed that is called the group velocity (U). The individual waves that make up the wave packet travel with phase velo- city (c), as defined in Eq.
- Sebastiano Foti, Carlo Lai, Glenn J. Rix, Claudio Strobbia(Authors)
- 2014(Publication Date)
- CRC Press(Publisher)
Love Waves can be acquired, processed, and inverted with methods that are similar to those used for Rayleigh waves. In the next section, the basic properties of the Love Waves are sum-marized, the experimental configuration to be used for the acquisition is discussed, and an example of joint Love and Rayleigh wave testing is presented. 394 Surface wave methods for near-surface site characterization 8.1.1 The nature of Love Waves Love Waves are surface waves containing only Shear, Horizontally polarised (SH) motion, while Rayleigh waves have coupled P and SV potentials (see Chapter 2). Although Rayleigh waves exist in a homogeneous half-space because of the interference between evanescent P-waves and phase shifted SV-waves, the Love Waves do not exist in a homogeneous half-space. The simplest model in which Love Waves can exist is a low-velocity layer over a stiff half-space. The supercritical energy, impinging on the half-space with an angle larger than the critical angle, is totally reflected up and reaches the free surface where it is totally reflected down. Energy is then trapped in the low-velocity layer. In this case, the Love wave kinematics can be easily explained in terms of total internal reflections in the waveguide, interfering constructively and destructively as a function of the wavelength (Ewing et al. 1957). Like Rayleigh waves, Love Waves are modal and, in simple cases, they have simple modal shapes. In Figure 8.2, the displacement eigenfunctions Figure 8.1 Schematic representation of Love wave propagation and their acquisition with horizontal sources and receivers on the ground surface. Advanced surface wave methods 395 are plotted as a function of depth for the first five modes at the frequency of 80 Hz for a simple model of a single-layer waveguide (4 m with a shear wave velocity of 100 m/s) over a half-space (with a shear wave velocity of 300 m/s). The modal curves are plotted in Figure 8.3 and compared to the Rayleigh wave modal curves.
eBook - PDFPhysics and Chemistry of the Earth
Progress Series, Volume 6
- L. H. Ahrens, Frank Press, S. K. Runcorn(Authors)
- 2013(Publication Date)
- Pergamon(Publisher)
In the preceding volume of this series, ANDERSON (1963) has given an excellent review concerning the structure and composition of the Earth's mantle and the numerical techniques for calculating theoretical surface wave dispersion for multi-layered media. Because of the installation of long-period seismograph systems in many parts of the world, much new surface wave data is rapidly accumulating and many new investigators will engage in surface wave studies. It is the purpose of this review to attempt to summarize much of the observed seismic surface wave data that has accumulated in the past 30 years so that investigators can obtain a clear picture of the state-of-the-art. The data are discussed by seismic wave type and by major geographic areas. Except for the Antarctic region, data from mixed continental and oceanic paths are mostly avoided, not be-cause mixed paths do not contain valuable information but because it is felt that a clearer insight into the use of surface waves for studying internal structure can be attained by discussing continental and oceanic data separately. Much of the progress in the study of surface waves has been made because of improvements in long-period seismographs. A brief discussion of recent de-velopments in seismometer instrumentation is given in Section 2. This is followed in Sections 3-6 by a discussion of most of the observed fundamental mode Love and Rayleigh wave data. A large portion of the theory and observed data on higher mode Love and Rayleigh waves presented in Section 7 is new. Many phases on a seismogram can be explained by broad plateaus on the higher mode Love and Rayleigh wave group velocity curves and a detailed study of the channel waves Lgl, Lg2, Li, and Sa has been made in an endeavor to fit these phases into a unified higher mode theory. Higher mode surface waves are very diagnostic of the structure of the upper mantle and important inferences can be made concerning this region from higher mode data.
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