Topic of Discussion : Seismology
- Why earthquake happens ?
- What are seismic waves ?
- How theory of seismology developed ?
- Is theoretical seismology enough to understand earth ?
- How to get observational data sets ?
- Types of seismic waves ?
- Body wave
- Surface waves
- Types of Surface wave
- Rayleigh wave
- What is dispersion ?
- What is Seismic wave attenuation ?
- Geometrical spreading
- Does body wave and surface wave attenuates equally ?
- Anelastic attenuation
- Dispersive nature of seismic waves
What is seismology ?
Seismology is the study of earthquakes, its devastation, causes and prediction. It further leads to detailed study in terms of earth structure and imaging. As it is impossible to look into the earth directly. So indirect method is used to know about the planet earth and what is going in the deep down. In seismology, seismic waves carries wealth of information when it reaches the earth surface. Seismic waves being mechanical in nature highly depends on the medium through which it travels. Thus, physical properties of the medium can be extracted. In-situ physical properties is immensely important as temperature and pressure severely affects these indirect measurements.
Who are Seismologists ?
Those who investigates Earthquake related Seismology studies are “Seismologist“. It can be associated with Earthquake forecasting, understanding the earth structure using seismogram, finding the earthquake source ( Epicentre and Hypocentre) , developing artificial earth models from the seismic wave physics to mimic the real earth as far as possible. It also involves studying past earthquakes to understand the earthquake mechanism and for early warning system if another earthquake is imminent.
A instrument is used for ground motions, such as caused by earthquakes, volcanic eruptions, and explosions.
Why earthquake happens ?
Lithopsheric part of the earth is underlain by the Asthenosphere. Ashtenosphere, in geological time scale, creeps i.e. it moves very slowly despite being solid ( Earth’s interior is considered to be elastic solid as evident from seismic waves ). The lithospheric plate sitting on it undergo motion in return. As the plate boundaries are locked with respect to each other, the moving plate constantly force them to move. A stage is reached when plate undergo motion overcoming friction against each other releasing the stress stored. This phenomenon is called Earthquake. Hence, the energy gets released in the form of seismic waves and is recorded on the seismometers.
What are seismic waves ?
Earthquake or any vibration that occurs within the earth acts as an energy source. The energy travels the entire earth in the form of waves. These mechanical waves are called seismic waves. They behave differently in various parts of the earth and hence considered to be the characteristic property of the medium through which it travels. Whenever earthquake happens, it radiates waves with period ranging from one-tenth of a second to several minutes. Within this period ( or frequency) range rocks behave like elastic solids. As elastic solids allow variety of waves, thus making the ground motion quite complex after event takes place.
Another way of representing the ground motion is in terms of Normal modes. After a large earthquake event, earth rings like a ‘bell’. The period of ringing is identifiable when it is large i.e. greater than 40 second or so. The lowest frequency has a period of around one hour.
How theory of seismology developed ?
Whenever earthquake happens it emits waves of multiple frequency. Frequency range of interest enables the rocks to behave elastically. The propagation of sound waves in elastic media is a proven science and is beyond the scope of present discussion. Seismology inherited that concept. For mathematical formalism, media is considered to be homogeneous and isotropic, thus coining the term ‘simple media’ in Seismology sometimes.
The wave that emanates from the source forms spherical wave front provided the source of disturbance is a point source ( Huygen’s principle). However, as the wave travels to a significant distance, It turns out to behave as a plane wave. Plane wave approximation is thus used for further theoretical calculations. For simplicity, considering a ray path is convenient and good amount of theoretical calculations has been accomplished using ray theory.
Is theoretical seismology enough to understand earth ?
No. theoretical seismology simply helps us simplify wave propagation by turning into the physics having well driven rules. However, observation is quintessential. As simple approximation doesn’t mimic the earth’s interior. Observational datasets are obtained from the instruments and then it is matched with the theoretical datasets for the similar geological conditions. Appraisals are made in the theoretical data and the background physics unless it matches with the observations to a good extent. This act of minimizing the error is called as optimization. This topic needs further explanation in detail. Obtaining the theoretical model parameter from the observed data is called seismological inversion.
How to get observational data sets ?
In seismology, we place seismometer on the ground. It is a highly sensitive instrument that measures the time dependence of ground displacement. However, it is not as direct as it seems. The basic principle lies in the ‘inertia’. The mass is attached to the spring vertically and is housed in cage like structure that is kept on the ground. Because of the vibration, there begins the differential motion between the hanging mass and the cage.
This in turn sense the motion which can further be quantitatively interpreted. The instrument used is called seismometer. These days digital seismometers are into existence. The recorded data is called seismogram. A typical seismogram records vibrations in three direction. East-west, North-South and Vertical component are the directions of vibration.
Types of seismic waves
Seismic waves are broadly divided into
- Body waves
- Surface wave.
Body wave arises due to body force, this is a volume force field given by , where f is force per unit volume acting on an infinitesimal volume.
Body waves are further divided into :
Primary waves / P waves : These waves travel by elastic displacements in the medium. They travel by compressions and rarefactions of the particles of the elastic medium in the direction of wave propagation. This makes it longitudinal in nature. In this way the particles of the medium undergo simple harmonic motion and seismic wave gets transmitted as a complex set of wave motions. This helps understand the seismology behavior the wave as it can be put into mathematical formulations.
Primary waves are the fastest wave so far and reaches the earth surface first. On the seismogram, first arrival is the P wave. As the particle medium vibrates in the same direction as wave propagation, P waves are mostly identified on the vertical component of seismogram. The speed of the P wave is given by . and are the elastic parameter ( called Lame’s parameter) that controls the velocity. is the density.
Secondary waves / S wave : From the energy source itself, another kind of disturbance gets produced that displaces the particle in the direction perpendicular to the wave motion. This makes them transverse in nature. The transverse motion of the particles leads to shear distortion in medium. These waves are isovolumic, means volume of a given unit remains unchanged while wave propagation. The speed of the shear wave is given by . The only elastic parameter that controls the speed of shear wave is shear modulus.
The top image represents S-wave where particle motion is perpendicular to the wave propagation while the bottom image is P-wave where particle motion is back and forth in the direction of wave propagation. One major difference between P and S wave is P wave can travel in all the media such as solid, liquid and gas whereas shear wave cannot travel in fluid. Thus in the outer core of the earth, S-wave is seen to be nowhere. Only P wave exists.
Surface waves :
The surface waves are the manifestation of body waves. They are like ripples on the water body formed when stones are thrown. Their origin is considered to be from surface force which is represented by where f is force acting per unit area.
Types of Surface wave :
Surface waves are further divided into :
Rayleigh wave :
It arises from the superposition of P wave with the vertical component of S wave i.e SV wave. As P and SV are polarised in perpendicular direction with respect to each other. Their superposition leads to elliptical polarization of Rayleigh wave.
Rayleigh wave in uniform half-space : In uniform half-space Rayleigh waves are non-dispersive in nature. However, in reality the medium itself is non-uniform resulting in the dispersive nature of Rayleigh wave.
What is dispersion ?
Dispersion refers to the frequency dependence of velocity. This means waves with different frequencies travel with different velocities. As seismic waves emanating from the source contains all the frequency component ranging from 0.001 Hz to 100 Hz.
This is a broad frequency range that carries wealth of information regarding the structure from the surface to the centre of the earth. As frequency is inversely proportional to the time period. Part of the wave with low frequency will have high period and hence greater penetration depth and vice-versa. Also wave with higher time period will be sensitive towards the structure of same size. Hence, if we are interested in imaging the bigger structure within the earth we should choose waveform with higher period. For thin layer imaging waves with lower period ( higher frequency) should be chosen.
Love wave :
It is the superposition of horizontal component of shear waves i.e SH. It arises under the condition when shear wave gets stuck in a layer whose velocity is greater than the free surface ( upper surface ) and lesser than those of semi – infinite half space. In that case superposed SH waves that got reflected at supercritical angle interferes constructively to form love waves. Love waves travels horizontally. They are most destructive.
What is Seismic wave attenuation ?
While transmitting within the earth seismic wave gets attenuated by various ways.
Geometrical spreading :
As the wave propagates away from the the source energy gets spread over a larger surface area so that the amount of energy per unit area keeps on diminishing. It is universal with all kinds of wave.
Does body wave and surface wave attenuates equally ?
No, in geometrical spreading body wave attenuates as while surface waves attenuates as .
2. Anelastic attenuation :
In reality earth is not perfectly elastic for propagating seismic waves. The anelastic component leads to the absorption of seismic waves to some extent, this is called as anelastic attenuation.
Dispersive nature of seismic waves :
Body waves are non-dispersive in nature. Whereas surface waves are dispersive under certain condition. Rayleigh wave when passing through a homogeneous medium are non-dispersive. While Love waves are inherently dispersive. The dispersion of surface waves plays a key role in understanding the earth structure. Waves with higher period ( lower frequency) travels faster and travels deeper within the earth and vice versa. This is true for normal dispersion. However, in some cases opposite happens. In this waves with shorter period travels faster and reaches the sensor prior to long period waves.
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