Basic Geophysics Surface Waves

On March 11, 2011, the Great Tohoku Earthquake took place off the coast of Japan, which also gave rise to a devastating tsunami. The quake was recorded on seismometers around the world, such as the one here at the BFO seismic observatory in the Black Forest. The arrival of various waves can be seen just barely here, and stronger waves can be seen here. Finally, we see the surface waves here, which have the greatest amplitude - these waves are responsible for the damage that occurs during major earthquakes. When these seismic waves are made audible, it sounds like this. Listen to how the arrival of the surface waves is louder than the earlier components, and how the pitch increases at the end. Hello and welcome. In this video, I will be showing you what characterizes seismic surface waves and how they differ from seismic body waves. At the same time, we will also address the question of why in the audio example, the low-pitched sounds arrive first, followed by the high- pitched ones. Unlike body waves, surface waves do not travel through the earth's interior, but instead along the earth's surface, much like water waves on the surface of water. In the seismogram, you saw that surface waves have a higher amplitude; that means their oscillations are greater than those of body waves, which arrive earlier - which means that they cause the ground to move more and possess a higher destructive force. This is due primarily to what we call geometrical spreading. This process describes the different forms of attenuation of both wave types along their path. Surface waves are radiated two- dimensionally with a penetration depth d. Hence, their energy is distributed over a cylinder with a surface area of “two pi times d times the radius r” - which means they attenuate linearly with distance. Body waves, on the other hand, spread out in three dimensions. Hence, their energy is distributed over the surface of a sphere of the size “two times pi times r squared” - which means the amplitude decreases proportionally to the square of the distance, making it lower at greater distances than it is the case for surface waves. Let's return to the seismogram of the Tohoku quake we saw at the beginning. You can clearly see the greater amplitudes of the surface waves which were recorded at a distance of over 9,000 km away. The seismogram shown here indicates the horizontal ground motion, that is the earth's surface moving back and forth. Generally, a seismometer measures the motion of the ground in three spatial dimensions. The two horizontal directions are measured in a north-south and east-west direction. For the evaluation of individual earthquakes, they are rotated via calculations and labeled with an R for radial and T for transverse. Shown here is the transverse direction T, which oscillates orthogonally to the direction from which the earthquake waves arrive. You can see the radial component here. It indicates the direction of oscillation parallel to the direction of propagation of the waves. Clearly, the surface waves are arriving later here. Before we speak about this difference, let me show you the third component of the records: the vertically oriented Z- component. This is especially where the P- wave, which is the first body wave to arrive, can be seen. The reason for the later arrival of the surface waves on the radial component is the existence of two types of seismic surface waves. Rayleigh waves and Love waves. They are named after their discoverers Lord Rayleigh and August Love. Rayleigh waves are a combination of longitudinal and vertically polarized transverse waves. They oscillate in a manner similar to water waves. In this animation, you can see the particle movement of water waves, which describe vertically oriented elliptical movements. The movement takes place in the direction of wave propagation - we call this prograde. However, in Rayleigh waves it is the other way around. In this other representational form, you see the same elliptical movement, but this time against the direction of propagation - we call this retrograde. The reason for this difference is the corresponding restoring force acting on it. While waves in water are restored to equilibrium by the force of gravity, in Rayleigh waves, this restoring force is the elasticity of the affected ground layers. The second type of seismic surface waves are Love waves, which are composed of horizontally oscillating transverse waves. The animation shows the shear movement perpendicular to the direction of propagation. In both Rayleigh and Love waves, the amplitude diminishes with depth. Unlike Rayleigh waves, however, Love waves only travel through one layer of the earth lying on top of another deeper layer with a higher propagation velocity. One can imagine them to be much like light trapped in a fiber optic cable. Both are kept inside their propagation channel via supercritical reflection. Let me now show you another analogy relating surface waves to light. A rainbow shows different colors because different frequencies are refracted to varying degrees by raindrops. But not only is the refraction of light frequency-dependent, the propagation velocity is as well. This is called dispersion. Without dispersion, there would be no rainbows... Surface waves are also dispersive. We can visualize this qualitatively using a Love wave in a simple homogeneous layer on top of the half-space as an example. The wave is composed of various horizontally oscillating S-waves which are reflected within the layer. Now, in order to interfere constructively, the oscillation on one wavefront must be in phase, that means all parts of the wavefront must oscillate simultaneously. Hence, in the drawing, the path marked in red must concurrently contain one or multiple full oscillations. We can now imagine that for this to be the case, the oscillation frequency must perfectly match the propagation velocity on the surface so that this constructive superposition occurs. This “matching” corresponds to a wave velocity that changes along with the frequency of the Love wave, that is dispersive. Rayleigh waves in the earth are also dispersive, but body waves are not. Let's return to the audio example we heard in the beginning. Dispersion is indicated by the fact that we first hear the low and then the high-pitched tones of the surface waves. This graph shows specific values for the propagation velocity. What you are seeing is the propagation velocity as a function of its period of oscillation, which is the reciprocal of the frequency. We see that Love waves are generally faster than Rayleigh waves. Both types of surface waves travel at a velocity of approximately 4-5 km/s and are hence slightly slower than S-waves. Hence, they only arrive after the weaker body waves. This is of great importance for earthquake early warning systems: Namely, body waves can automatically trigger early warning systems shortly before the arrival of destructive surface waves. These systems can stop trains or shut off gas lines, for instance. From a scientific perspective, surface waves are highly useful for investigating large structures in the earth's crust and the upper mantle. Penetration depths correspond to the range of the wavelengths, and are between 40 and 1,000 km. In this video, you learned about the two seismic surface wave types that travel along the earth's surface. Love waves oscillate in a transverse fashion and are the faster wave type. They only occur in ground layers which overlie a layer with a higher propagation velocity. Rayleigh waves, on the other hand, oscillate much like water waves in elliptical movements, even in homogeneous media. Unlike water waves, they do so in a retrograde direction. Both wave types are dispersive; that means their propagation velocity is frequency-dependent. In general, they travel at a slower velocity than body waves. Because surface waves have a higher amplitude than body waves and cause the greatest damage during major earthquakes, it is important to know and understand their propagation and oscillation characteristics.

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