P Wave

To understand P waves, we have to first get into the basics of seismology and seismic waves. Seismic waves are waves of energy which passes through the earth and they are the reason for earthquakes and related phenomena.

They are the energy waves that pass through the Earth's layers, and that’s resulting in earthquakes, magma movement, volcanic eruptions, large landslides and huge man-made explosions that give out low-frequency audio energy. Many other anthropogenic and natural causes create low-amplitude waves generally referred to as ambient vibrations. Seismic waves are studied by geophysicists who are known, seismologists. Seismic wave fields are recorded by a seismometer, accelerometer, or hydrophone (in water).

The circulation speed of the waves depends on the density and elasticity of the medium. Speed tends to rise with depth and ranges from about 3 to 8 km/s in the Earth's crust, up to 13-14 km/s in the deep mantle.

Earthquakes generate distinct kinds of waves which travel at different speeds; when reaching seismic laboratories, their different passing times help scientists to locate the source of the hypocenter. In geophysics, the reflection or refraction of seismic waves is used for research into the arrangement of the Earth's interior, and vibrations caused by humans are often produced to investigate shallow, subsurface structures.

Types of waves

1. Body waves

2. A. Primary waves (P- waves)

B. Secondary waves (S- waves) 

3. Surface waves

4. Rayleigh waves

5. Love waves

6. Stoneley waves

1. Body Waves

Body waves pass through the inner side of the Earth along paths controlled by the material properties in terms of density and stiffness. The density and stiffness, in turn, vary according to temperature, material phase, and composition. This effect resembles the refraction of light waves. There are two types of particle motion result in two types of body waves: 

Primary (P) and Secondary waves(S)

a. Primary Wave

Primary waves (P-waves) are longitudinal and compressional waves by nature. Primary waves are pressure waves that travel much faster than any other waves through the earth to reach at seismograph stations first, therefore the name "Primary". These waves can travel through any kind of material, including fluids, and can travel nearly 1.8 times faster than the Secondary waves. In the air, they take the form of sound waves, so they travel at the speed of sound. Usual speeds are 334 m/s in the air, 1455 m/s in water and about 5001 m/s in granite.

b. Secondary wave

Secondary waves (S-waves) are transverse and shear waves in nature. Resulting in an earthquake event, Secondary waves which arrive at seismograph posts after the faster-moving P-waves and displace the ground perpendicular to the direction of transmission. Depending on the transmission direction, the wave can take on different surface properties; for example, in the case of parallel polarized S waves, the ground moves consecutively to one side and then the other. S-waves can travel only through solids, and also through liquids and gases do not support shear stresses. S-waves are pretty slower than P-waves, and speeds are normally around 65% of that of P-waves in any given material.

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2. Surface Waves

Seismic surface waves pass along the surface of the earth. They can be classified in a form of mechanical surface waves hence they are called surface waves, as they shrink as they get far from the surface. They travel slower than seismic body waves (P and S). In heavy earthquakes, surface waves can have an amplitude of some centimeters

3. Rayleigh Waves

Rayleigh waves, also known as ground roll, are surface waves that pass as waves with motions that are parallel to those of waves on the surface of water (even though the related particle motion at shallow depths is retrograde, and the reinstating force in Rayleigh and in other seismic waves is flexible, not gravitational as for water waves). 

4. Love Waves

Love waves are waves which are horizontally polarized and shear (SH waves), standing only in the presence of a semi-infinite medium covered by an upper layer of limited thickness.

5. Stoneley waves

A Stoneley wave is an interface wave or boundary wave that transmits along a solid-fluid boundary or, under specific conditions, also along a solid-solid border. Scales of Stoneley waves have their maximum values at the boundary between the two contacting points and decay exponentially at the depth of each of them. These waves can be produced along the walls of a fluid-filled well, being a vital source of coherent noise in VSPs and building up the low-frequency component of the source in sonic logging.

P and S Waves on Earth's Mantle and Core

When an earthquake takes place, seismographs which are near the epicenter are able to record both P and S waves, but those which are far from the distance make detection harder for the high frequencies of the first S wave. Since shear waves cannot pass from liquids, this process was original evidence for the now well-established thought that the Earth has a liquid external core, as proven by Richard Dixon Oldham. 

How will P Waves and S Waves give Information About the Structure of the Earth?

Due to the transverse nature of S waves they cannot travel through the liquid outer core. They can pass through the mantle because the mantle it acts more like a solid than a liquid. The S waves curve as they are passing through the mantle due to refraction as the mass of the mantle changes. There is a huge part of the planet surface where no S waves are detected or measured. This proves that the outer core is liquid because it prevents S waves. It also shows how huge the outer core is. The longitudinal P waves can pass through the whole planet. They also curve with the changing mass of both the mantle and the core except the wave traveling through the center, which passes in a straight line, normal to the boundary. The P waves change direction rapidly at the boundary among the different layers of the Earth. This is due to refraction produced by the different densities of the layers. The P waves show how huge the solid inner core is.

Nomenclature of P- Waves

A P-wave is one of the two main forms of elastic body waves, called are seismic waves in seismology. P-waves travel sooner than other seismic waves and therefore are the first signal from an earthquake to reach at any affected place or at a seismograph. P-waves can be transmitted through, liquids, gases or solids. The name P-wave can be either for pressure wave (as it is made from alternating densities and rarefactions) or primary wave (as it has high speed and is, therefore, a seismograph measures the first wave).

In isotropic and similar solids, the mode of transmission of a P-wave has always been longitudinal; hence, the particles in the solid vibrate along the axis of transmission (the direction of motion) of the wave energy.

P-Wave Shadow Zone

Almost all the data available on the structure of the Earth's deep inside and is derived from observations of the passing times, refractions, reflections and phase shifts of seismic body waves, or normal modes. P-waves passes through the fluid layers of the Earth's interior, and yet they are refracted somewhat when they travel through the transition among the semisolid mantle and the liquid outer core. Due to which, P-wave is in "shadow zone" between 105° and 140° from the earthquake's center, where the starting of P-waves are not registered on seismometers. In compare to, S-waves which do not travel through liquids, rather, they are attenuated. In the picture below P, waves are shown in blue and S waves are in red. The earthquake has taken place on the left side of the planet, the waves are passing from left to right.

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Seismic Wave in the Earth

Primary and secondary waves are body waves that travel inside the Earth. The behavior and motion of both P-type and S-type in the Earth are watched to probe the interior structure of the Earth. Discontinuities in speed as a function of depth are indicative of changes in composition or phase. Differences in coming times of waves originating in a seismic event like an earthquake as a result of waves taking different routes help in the mapping of the Earth's inner structure.

Properties of P- Waves

The Velocity of P Waves

The velocity of P-waves in a standardized isotropic medium is given by

\[V_{p} \sqrt{\frac{K + \frac{4}{3}\mu}{P}} = \sqrt{\frac{\lambda + 2\mu}{P}}\]

where K is the bulk modulus (the modulus of incompressibility),µ {\displaystyle \mu }is for shear modulus (modulus of rigidity, sometimes it is denoted as G and also known as the second Lamé parameter), {\displaystyle \rho }𝞺 is the density of the material through which the wave transmits, and {\displaystyle \lambda }𝞴 is the first Lamé parameter.

Of these, density shows the minimum variation, so the speed is mostly controlled by K and μ.

The elastic moduli P-wave modulus, M is well-defined so that M=k+4µ/3 and, therefore.

\[V_{p} = \sqrt{M + \rho}\]

Typical values for P-wave speed in earthquakes are in the range7 to 9 km/s. The precise velocity differs according to the region of the Earth's interior, from less than 8 km/s in the Earth's crust to 15.5 km/s in the lower mantle, and 13 km/s through the inner core.

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seismic waves’ velocity in the Earth versus depth.