What are the boundary conditions for Navier’s Equations of motion in seismic?

Asked by: Shawn Wade

What is seismic wave equation?

3.1. Seismic wave equation. The 1D time-dependent seismic wave equation in an isotropic and homogeneous medium can be expressed by (Sheriff and Geldart, 1995):(24) ∂ 2 u ( x , t ) ∂ t 2 − V 2 ∂ 2 u ( x , t ) ∂ x 2 = 0 where u ( x , t ) is the displacement in point at time .

What are the different types of seismic waves?

There are three basic types of seismic waves – P-waves, S-waves and surface waves. P-waves and S-waves are sometimes collectively called body waves.

What is elastic wave equation?

β = √µ ρ Page 22 The Elastic Wave Equation P- and S- wave properties The oscillatory variable (u = ∇φ) of P-waves or compressional waves is volumetric change, which is directly related to pressure. In contrast, the oscillatory variable u = ∇ × Ψ of S-waves implies a shear disturbance with no volume change (∇·∇× Ψ = 0).

How do you find the speed of a seismic wave?

The velocity of the wave is determined by the physical properties of the material through which it propagates. In the case of a vibrating string, c2 = F/ρ where F is the string tension force and ρ is the density.

How do you find the amplitude of a seismic wave?

The amplitude is measured from the seismogram, as is the time difference between the arrival of the P- and S-waves. A line connecting the two values on the graph gives the magnitude of the earthquakes.

What does the speed of a seismic wave depend on?

Ultimately, seismic velocity depends on the density and elastic properties of the material, whatever its composition. Specifically, Compressional-wave velocity depends on the “incompressibility” of the material, as embodied in the bulk modulus.

What are the characteristics of seismic waves?

Seismic waves can be distinguished by a number of properties including the speed the waves travel, the direction that the waves move particles as they pass by, where and where they don’t propagate. We’ll go through each wave type individually to expound upon the differences.

What is the main cause of seismic wave?

Earthquakes are the result of sudden movement along faults within the Earth. The movement releases stored-up ‘elastic strain’ energy in the form of seismic waves, which propagate through the Earth and cause the ground surface to shake.

What type of seismic waves have particle motion?

Surface Waves, as the name implies, travel primarily along the ground surface; amplitudes decrease rapidly with depth. There are two types of surface waves. Like body waves, they are characterized by particle motion.

What are the applications of wave equation?

Wave equation is usually used to investigate bearing capacity resistance of pile foundation. There are many reasons a geotechnical engineer would recommend a deep foundation over a shallow foundation, but some of the common reasons are very large design loads, a poor soil at shallow depth, or site constraints.

Why wave equation is hyperbolic?

The wave equation utt − uxx = 0 is hyperbolic. The Laplace equation uxx + uyy = 0 is elliptic. The heat equation ut − uxx = 0 is parabolic.

What is the importance of wave equation?

The wave equation is one of the most important equations in mechanics. It describes not only the movement of strings and wires, but also the movement of fluid surfaces, e.g., water waves. The wave equation is surprisingly simple to derive and not very complicated to solve although it is a second-order PDE.

Which factor affects the seismic wave amplitude?

The amplitude of seismic energy varies over a tremendous range. Some of the factors responsible for such variation do not contain subsurface information; these include source strength and coupling, geophone sensitivity, array directivity, instrument balance, scattering in the near-surface, for example.

How is seismic polarity calculated?

Determination polarity



When marine seismic data, the polarity is identified by reflector of sea water and seabed. The reflector appears from low to high AI, if red is negative amplitude and reflector between sea water and seabed is red.

What are the three components of each seismogram?

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What are the formula for P and S velocity?

The velocity of a P wave can be expressed as: Velocity P wave = ((B + 1.3G)/Density)^1/2, where: B = the bulk modulus – the resistance to change in volume. G = the Shear modulus – the resistance to change in shape.

What is Helmholtz wave equation?

Helmholtz’s equation, named after Hermann von Helmholtz, is used in Physics and Mathematics. It is a partial differential equation and its mathematical formula is: ▽ 2 A + k 2 A = 0.

What is the S wave of an earthquake?

An S wave, or shear wave, is a seismic body wave that shakes the ground back and forth perpendicular to the direction the wave is moving.

What is caused by seismic waves?

Seismic waves are caused by the sudden movement of materials within the Earth, such as slip along a fault during an earthquake. Volcanic eruptions, explosions, landslides, avalanches, and even rushing rivers can also cause seismic waves.

What are the characteristics of seismic waves?

Seismic waves can be distinguished by a number of properties including the speed the waves travel, the direction that the waves move particles as they pass by, where and where they don’t propagate. We’ll go through each wave type individually to expound upon the differences.

Why earthquake is called as seismic activity?

When an earthquake occurs, the violent breaking of rock releases energy that travels through the earth in the form of vibrations called seismic waves. These seismic waves move out from the hypocentre in all directions and when they travel long distance from the hypocentre, they become weaker.