What Is a Seismic Wave?

Seismic waves are vibrations that travel from the source of an earthquake to all directions, and refer to elastic waves that radiate from the source to the surroundings. According to the propagation mode, it can be divided into three types: longitudinal wave (P wave), transverse wave (S wave) (both longitudinal and transverse waves are body waves) and surface wave (L wave). When an earthquake occurs, the medium in the source area undergoes rapid rupture and movement, and this disturbance constitutes a wave source. Due to the continuity of the earth's medium, this wave propagates to the interior of the earth and everywhere on the surface, forming elastic waves in the continuous medium.

One of the main contents of seismology is studying the information brought by seismic waves. Seismic waves are a transmission of mechanical motion that arise from the elasticity of the earth's medium. Its nature is very close to the sound wave, so it is also called geoacoustic wave. But ordinary sound waves propagate in the fluid, and seismic waves propagate in the earth's medium, so it is much more complicated. There are some similarities between seismic waves and light waves in calculation. Wave optics can transition to geometric optics in the case of short waves, which simplifies calculations. Similarly, under certain conditions, the concept of seismic waves can be replaced with seismic rays to form geometric seismology. However, light waves are only transverse waves, while seismic waves have both vertical and horizontal parts. Therefore, in specific calculations, seismic waves are much more complicated. ^[1]

Chinese name: Earthquake wave
Foreign name: seismic waves
Principle: The source of the medium in the earthquake source area constitutes the wave source

Media: Earth medium
Propagation mode: P-wave, S-wave, and surface-wave
Species: Solid wave, surface wave
measuring instrument: Seismometer, geophone

Overview of Seismic Wave Physics

Earthquake wave Seismic waves are divided into three types according to the propagation mode: longitudinal waves, transverse waves, and surface waves. P-waves are propulsion waves. The propagation velocity in the crust is 5.5 ~ 7 km / s. The first to reach the epicenter, also known as the P-wave, causes the ground to vibrate up and down and is less destructive. Shear waves are shear waves: the propagation velocity in the earth's crust is 3.2 to 4.0 km / s, and the second one reaches the epicenter, also known as the S wave, which causes the ground to shake back and forth, left and right, and is highly destructive. Surface waves, also known as L-waves, are mixed waves generated by the excitation of longitudinal and transverse waves on the ground. Its large wavelength and strong amplitude can only propagate along the ground surface, which is the main factor causing strong damage to buildings. ^[2]

Seismic wave impact range

Review of Seismic Waves

When a water wave encounters an interface, such as a steep shore, it will be reflected back from the boundary, forming a series of water waves coming out of the shore, overlapping with those coming inward. When an ocean wave enters a shallow bank obliquely, the wave travels slower when the depth of the seawater becomes shallower, and falls behind the wave deeper in the seawater. As a result, the wave bends in shallow water. So the wavefronts turned more and more parallel to the beach before they hit the shore. The term refraction describes the phenomenon that the direction of the wavefront changes due to conditions on the propagation path during wave propagation. Reflection and refraction are also well-known properties as light passes through lenses and prisms.

Derivation of seismic wave properties

Modulus of elasticity and wave velocity

Homogeneous and isotropic solids can be described by two constants: k and , and both constants can be expressed as forces per unit area.

k is the bulk modulus and represents incompressibility.

Granite: k is about 27 × 1010 dyne /

;

Water: k is about 2 × 1010 dyne /

is the shear modulus and indicates its rigidity.

Granite: about 1.6 × 1010 dyne /

;

Water: is 0.

In an elastic solid with a density of , two kinds of elastic waves can be propagated.

P wave, velocity vP = (k + 4 / 3) / .

Granite: vP = 5.5 km / s;

Water: vP = 1.5 km / s.

S wave, speed vS = / .

Granite: vS = 3.0 km / s;

Water: vS = 0 km / s.

Seismic wave phenomenon introduction

Like acoustic, light, or water waves, seismic waves can also be reflected or refracted on a boundary, but they are different from other waves in that when a seismic wave is incident on a reflecting surface in the earth, for example, a P wave strikes the side at an angle At the interface, it is not only divided into a reflected P wave and a refracted P wave, but also generates a reflected S wave and a refracted S wave. The reason is that the rock at the boundary of the incident point is not only squeezed but also sheared. .

In other words, an incident P wave generates 4 types of converted waves. The multiplication of the wave pattern from one wave pattern to another wave pattern also occurs when the SV wave is incident obliquely on the internal boundary, and it will generate reflected and refracted P waves and SV waves. In this case, the reflected and refracted S waves are always of the SV type, because when the incident SV waves arrive, the rock mass moves laterally in an incident plane perpendicular to the ground. Conversely, if the incident S wave is a horizontally polarized SH type, the particle moves back and forth in a direction perpendicular to the incident plane and parallel to the boundary surface, and there is no extrusion or deformation in the vertical direction on the discontinuous interface. Corresponding new P-waves and SV-waves are generated, with only one reflected wave and one refracted wave of the SH type. Visually analyzing from the physical image, the vertically incident P wave has no shear component on the reflection interface, only the reflected P wave, and no reflected SV wave or SH wave at all. The limitations of the wave pattern conversion discussed above are crucial in fully understanding the complexity of ground motion and interpreting various images of seismic waves in seismic maps.

Buildings built on thick soil, such as sediments in alluvial valleys along rivers, are susceptible to severe damage during earthquakes, and the reason is also the amplification and enhancement of waves. When we vibrate two springs connected together, a weak spring will have a larger vibration amplitude. Similarly, when the S wave is transmitted from deep underground and passes through deeper rigid rocks to less rigid alluvium, weak rock and soil with less rigidity in the alluvial river valley will increase the amplitude by 4 times or more. Depends on the frequency of the wave and the thickness of the alluvial layer. During the Loma Pritt earthquake in California in 1989, homes built on the sand and scoured San Francisco waterfront were more damaged than similar homes built on solid foundations not far away.

Application field of seismic wave

Seismic and geophysicists and engineers use seismometers and geophones to record seismic waves. Early instruments used pendulum principles and analog signals to record seismic waves. Modern instruments use piezo-transistors and digital signals to process seismic waves. Seismic waves will have different transmission speeds when the medium changes, and will produce refraction and reflection behaviors at the interface. These characteristics are used to understand the internal structure of the earth.

In March 2015, U.S. scientists used a simulation map drawn by the speed of seismic waves to reveal underground structures. This simulation shows the mantle below the Pacific Ocean, with slower seismic waves in red and orange and faster seismic waves in green and blue. A 3D simulation of the Earth's interior was drawn by a research team led by Princeton Professor Jeron Troup. The goal of their research is to map the entire mantle by the end of the year. The depth of the mantle reaches 1865 miles.

Seismic wave seismic resonance

Seismic wave concept explained

Earthquake wave The reflection and refraction of seismic waves can sometimes cause seismic energy to be concentrated in a geological structure, such as an alluvial river valley, where there are softer rocks or soil near the surface. The special distribution areas severely damaged during the 1985 Mexico City and 1989 Loma Pritt earthquakes, which will be discussed later, can be explained by this reason (Figure 2.7). The effect is the same as that in a room where sound waves can be reflected multiple times by walls to form echoes to pool energy. During an earthquake, P waves and S waves came from a distance and refracted into the valley. Their speed was reduced in the rock with low rigidity. When they propagated under the valley and approached the edge of the valley, part of the energy was refracted back into the basin. In this way, waves begin to travel back and forth, similar to water waves in a pond. Different P waves and S waves are intertwined, and the turning peaks are superimposed on the incoming peaks, causing a change in amplitude. At this time, the phase of each superimposed wave is the key, because the energy will be strengthened when the wave phases of the intersection are the same. Through this "positive interference", seismic energy is pooled in certain frequency bands. Without the geometrical diffusion and frictional dissipation of waves, that is, the vibrating rocks and soils convert some wave energy into heat, the amplitude increase caused by wave interference can really have disastrous consequences.

The effect of seismic waves in a limited geological structure can be understood from another perspective. Like the cross-water waves seen in a pond, the interfering seismic waves can generate standing waves. On the surface, the interfering waves seem to be standing still, and the ground seems to be purely up and down. Similarly, standing strings are produced when strings of a stringed instrument such as a harp are plucked. In general, during earthquakes, many P waves and S waves of different frequencies and amplitudes are often excited in a river valley or similar structure. Soft soil can enhance the movement in many frequency bands, as in the case of music. Overtone or higher order mode. If sufficient seismic wave recording equipment is deployed, such overtones can sometimes be identified.

Specific case of seismic wave

Since the 18th century, mathematicians have analyzed the vibration of an elastic ball. In 1911, the British mathematician Love predicted that a steel ball as big as the earth would have a basic vibration with a period of about one hour and a harmonic with a smaller period. However, more than half a century after Loew's prediction, seismologists are still not sure whether even the largest earthquakes really have enough energy to shake the earth and produce deep earthquake music. It is not hard to imagine how secluded scientists were when they first observed the free oscillation of the earth. During the Chilean earthquake in May 1960, it was clearly recorded on the only few long-period seismometers around the world that the extremely long-period earthquake wave lasted for many days, and the longest period of vibration measured was 53 minutes. This is about the same as Loew's 60 points. The analysis of these ground motion records gave for the first time clear evidence that the theoretically predicted free oscillations of the Earth were indeed observed.

Summary of seismic waves

Vibration state of elastic rope When a seismic source releases energy, the earth s resonance vibrations continue in a way that they are no longer under stress. At this time, the vibration frequency depends only on the nature of the elastic earth. The exact basic principles of mathematical simulation are still similar to the analysis of plucked stringed instruments. The Greeks recognized more than 2,000 years ago that the harmonics of music depend only on the length, density, and tension of the strings (Figure 2.8). This free vibration is called intrinsic vibration. In the same way, the intrinsic vibrations of the earth that are plunged depend on the size, density, and elastic modulus of the entire interior.

Elastic spheres have only two different types of intrinsic vibrations. One type is called T-shaped or ring-shaped oscillation, which only includes the horizontal movement of the earth's rocks; the particles of the rock reciprocate on the spherical surface of the earth or some internal interfaces. The second type is called S-type or spherical oscillation. The motion components of spherical oscillation are both in the radial direction and the horizontal direction.

Seismic wave

Movement of near-surface rocks during the propagation of Love waves and Rayleigh waves When P and S waves reach the free surface of the earth or at the interface of layered geological structures, other types of seismic waves will be generated under certain conditions. The most important of these waves are Rayleigh waves and Love waves. These two types of waves propagate along the surface of the earth; the amplitude of rock vibrations gradually decreases to zero with increasing depth. Because the energy of these surface waves is captured on the surface to propagate along or near the surface, otherwise these waves will reflect down into the earth and have only a short life on the surface. These waves are similar to the sound waves captured on the wall of the Whispering Promenade in St. Paul's Cathedral in London. The whispers from the opposite wall can only be heard when the ear is close to the wall. Luff waves are the simplest type of seismic surface waves. They were named after Lov, who first described them in 1912. As shown in Figure 2.9, this type of wave makes rock particles move similarly to SH waves, with no vertical displacement. Rock movement from side to side in the horizontal plane perpendicular to the direction of propagation. Although Luff waves do not include waves of vertical ground motion, they can be the most destructive in earthquakes because they often have large amplitudes and can cause horizontal shear below the foundation of a building.

In contrast, Rayleigh surface waves have quite different ground motions. First described by Lord Rayleigh in 1885, they are the closest water waves to seismic waves. Rock particles move forward, upward, backward, and downward, making a vertical plane along the wave's propagation direction, and the particles move in this plane, depicting an ellipse. The speeds of Love waves and Rayleigh waves are always smaller than those of P waves and equal to or smaller than those of S waves. From the similarity of ground motion, the spherical (S-shaped) free oscillation is a standing wave of the Rayleigh wave, and the ring-shaped (T-shaped) free oscillation corresponds to the Love wave.

Seismic wave sequence

Due to the different velocities of different types of seismic waves, their arrival times are different, forming a series of sequences that explain the feeling we experience after the ground starts to shake during an earthquake.

The first wave from the source to a certain place is the "Push and Pull" P wave. They generally exit the ground at a steep inclination angle, thus causing vertical ground motion. Vertical shaking is generally easier to withstand than horizontal shaking, so they are generally not the most destructive waves. Because the S wave travels at about half the speed of the P wave, the relatively strong S wave arrives later. It includes SH and SV fluctuations: the former is in the horizontal plane, and the latter is in the vertical plane. S waves last longer than P waves. Earthquakes mainly shake buildings up and down through the action of P waves, and shake laterally through the action of S waves.

Just after or at the same time as the S wave, the Love wave began to arrive. The ground began to shake laterally perpendicular to the direction of wave propagation. Although eyewitnesses often claim that the direction of the source can be determined based on the direction of shaking, Luff waves make it difficult to determine the direction of the source based on the feeling of shaking on the ground. The next is a Rayleigh wave that propagates across the surface of the earth, which causes the ground to shake both vertically and vertically. These waves may last for many cycles, causing what is known as a "rock movement" during a large earthquake. Because they decay at a slower rate than P or S waves with distance, they are mainly surface waves that are perceived or recorded for long periods of time from the source.

Similar to the last verse of the musical composition, the surface wave train forms an important part of the seismic record, which is called the seismic coda. The tail of the seismic wave actually contains a mixture of P-waves, S-waves, Love waves, and Rayleigh waves that pass through complex rock structures along scattered paths. Continued wave cycles in the coda waves may play a role in the destruction of buildings, prompting the collapse of buildings that have been weakened by the stronger S waves that arrived earlier.

Surface wave expansion into a long tail wave is an example of wave dispersion. This effect occurs when various types of waves pass through a medium whose physical properties or scale changes. A closer look at the water waves in the pond shows that ripples with short wavelengths travel in front of ripples with longer wavelengths. The velocity of the peak is not constant and depends on the wavelength of the wave. After a stone hits the water, over time, the original wave begins to be distinguished according to different wavelengths. Later, shorter ridges and grooves spread more and more in front of long waves, and similarities in the propagation of seismic surface waves phenomenon.

The wavelength of different seismic waves varies greatly, ranging from several kilometers to as short as tens of meters, so that the seismic waves are likely to be scattered. Figure 2.11 shows the variation of a typical surface wave from ground to deeper rock particles with depth. Since it is a surface wave, most of the energy of the wave is captured near the surface. After a certain depth, the rock is not affected by the surface wave. This depth depends on the wavelength. The longer the wavelength, the more the wave penetrates the earth. deep. Generally speaking, the deeper the rocks in the earth, the faster the seismic wave velocity passing through them, so long-period (long-wavelength) surface waves generally propagate faster than short-period (short-wavelength) waves. This difference in wave speed causes the surface waves to disperse, which opens up a long wave train. But in contrast to water waves, longer surface waves arrive first.

As the depth increases, the ellipse becomes smaller and eventually disappears. The elliptical movement may be clockwise or counterclockwise.

We also need to understand another nature of waves in order to complete all the understanding of the marvelous world of seismic wave motion. This is the phenomenon of diffraction (diffraction) of waves. When a line of water waves encounters an obstacle, such as a vertical pipe protruding from the water surface, most of the energy of the wave energy is reflected away, but some waves will enter the shadow around the pipe, so the water behind the pipe is not completely calm. Diffraction of virtually all types of waves, whether water, sound or seismic waves, cause them to deviate from a straight path, dimly illuminating the area behind the obstacle.

The theory and observations are consistent: Long waves deflection more towards the calm zone than shorter waves. That is, diffraction, like dispersion, is a function of wavelength. The most important point for geological interpretation is that P waves and S waves and surface waves are not completely blocked by anomalous rock inclusions. Some seismic energy bypasses the geological structure and is refracted by them.

Types of seismic waves

Seismic waves are mainly divided into two types, one is a surface wave and the other is a solid wave. Surface waves pass only on the surface, and solid waves can pass through the interior of the earth.

Body Wave (Body Wave): It is transmitted inside the Earth and is divided into P wave and S wave.

P wave : P stands for Primary or Pressure. It is a type of longitudinal wave. The direction of particle vibration is parallel to the wave advancing side. Among all seismic waves, the advancing speed is the fastest and it is the earliest arrival. P waves can be transmitted in solid, liquid or gas.
S wave : S means Secondary or Shear, the speed of advance is second only to P wave, and the direction of particle vibration is perpendicular to the direction of wave advance, which is a type of transverse wave. S waves can only travel in solids and cannot pass through liquid foreign cores.

Using P-waves and S-waves with different transmission speeds, and using the time difference between the two, simple seismic positioning can be performed.

Surface Wave: Surface waves caused by shallow source earthquakes are the most obvious. Surface waves have the characteristics of low frequency, high amplitude, and dispersion. They are transmitted only near the surface and are the most powerful seismic waves.

Love Wave: The particle vibration direction is perpendicular to the wave's advancing direction, but the vibration only occurs in the horizontal direction. There is no vertical component, similar to the S wave. The difference is that the amplitude of the lateral vibration decreases with increasing depth.
Rayleigh wave: Also known as ground rolling wave, particles move in a manner similar to ocean waves. On the vertical plane, particles vibrate in a counterclockwise elliptical shape, and the amplitude of vibration will decrease with increasing depth.