What is the relationship between rock density and the velocity of seismic waves?
It appears that the seismic velocity and density are inversely related, but the denser rocks are characterized by higher velocities compared to lighter rocks because the density also depends on κ and μ.
What is the relationship between density and wave velocity?
The wave velocity is defined theoretically by the Newton-Laplace equation, which relates the wave velocity, V, to the square root of the ratio of the rock’s elastic modulus, M, and its density, [rho] (Bourvie et al., 1987). Therefore, the equation indicates that the velocity is inversely proportional to density.
What happens to the velocity of waves as density of rocks increase?
“… The speeds vР and vS are inversely proportional to the square root density but in fact, as numerous measurements show, for rocks, the opposite relationship takes place, with increasing density, the speed increases.
How do you calculate the velocity of a shear wave?
To find shear wave velocity:
- Divide the shear modulus by the density of the material.
- Find the square root of this ratio. Mathematically, that’s: Vs = √(G / ρ)
Is density inversely proportional to velocity?
Hence, velocity of sound in a medium is inversely proportional to the square root of its density.
What is seismic velocity of rocks?
seismic velocity: The speed with which an elastic wave propagates through a medium. For non-dispersive body waves, the seismic velocity is equal to both the phase and group velocities; for dispersive surface waves, the seismic velocity is usually taken to be the phase velocity.
How do you find velocity with density?
First you need to use this ṁ / ρ = Q tool to calculate the volume flow rate by entering each mass flow rate and density value. Then you need to use this Q / (π · (ø / 2)²) = v tool to calculate the velocity by entering the previously calculated volume flow rate, and the diameter of the pipe.
What is shear wave velocity?
The velocity (ν) of a shear wave is equal to the square root of the ratio of shear modulus (G), a constant of the medium, to density (ρ) of the medium, ν = Square root of√G/ρ.
How does density of the material affect the speed of seismic waves?
Seismic velocities depend on the material properties such as composition, mineral phase and packing structure, temperature, and pressure of the media through which seismic waves pass. Seismic waves travel more quickly through denser materials and therefore generally travel more quickly with depth.
What is shear wave velocity used for?
The shear wave velocity of soil and rock is one of the key components in establishing the design response spectra, and therefore the seismic design forces, for a building, bridge, or other structure. The shear wave velocity can be measured from in-situ field tests, such as cross-hole or downhole testing.
Is speed directly proportional to density?
This implies that speed of sound must be proportional to density of the medium. But in the expression v=sqrt (gP/r) speed of sound ‘v’ is inversely proportional to the density ‘r’ of the medium, and directly proportional to ‘g'(gamma) and pressure. Therefore,speed of the sound is inversely proportional to density.
What is density proportional to?
Density is mass per unit volume. The relation between density and volume is directly proportional. That is any change in volume will result in the change in its density and vise-versa.
What is the shear wave velocity of a rock?
The shear wave velocity and bulk density values for the rock data varied from between 130–4000 m s -1 and 1.26–3.05 g cc -1. This data was added to the densities and shear wave velocities from the study area, and a new correlation was developed, as given in equation ( 9 ).
How many shear wave velocity and density data are there?
Here, the shear wave velocity, density and depth at 22 locations have been considered in order to develop the correlations. These 22 locations comprise 354 Vs and density data sets, which consist of 225 fine-grained soil data sets and 129 coarse-grained data sets.
What is the in situ density of shear waves?
As per the procedure of Boore ( 2007 ), a density of 1.8 g cc -1 can be obtained for a shear wave velocity of 0.1 km s -1. A review of the literature shows that very limited direct correlations are available for the prediction of in situ density.
How is shear velocity deduced in line with depth?
Variation in velocity in line with frequency, referred to as dispersion curve, enables shear velocity to be deduced in line with depth via inversion [AKI 75]. This complex step is not systematically used. As such, operators merely provide phase velocity values for wavelengths given for mapping or continual monitoring purposes.