# Density and Seismic Velocity

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Why are density and seismic velocity inversely proportional to one another? Seems counterintuitive....

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If it helps, the relationships are given by:

VP = √{(E/ρ)((1-μ)/((1-2μ)(1+μ)))}

VS = √{(E/ρ)(1/(2(1+μ)))}

where

VP = P-wave velocity

VS = S-wave velocity

E = Young's Modulus

ρ = density

μ = Poisson's Ratio

I just cannot find the reason that an increase in density causes a decrease in seismic velocity.

Just at first glance, it seemed to me that an object with higher density would propagate a seismic wave more easily than an object with lower density; i.e. that more atomic matter would allow for a better transmission of a wave.

I was thinking of this problem macroscopically...part of me assumed that lower density (in this case) meant higher porosity (geologically speaking, porosity is almost always relevant)...and since I already happened to know that air has a lower seismic velocity (~330 m/s) than most consolidated rocks (~1000-7000 m/s), an inverse relationship between density and seismic velocity seemed counterintuitive, because it seemed that the presence of more empty space (which I equated with air) would slow seismic wave propagation.

After doing a bit more research, I finally started thinking about this problem at an atomic scale...it now seems more logical (and almost obvious) that more matter per volume means that more matter must be undulated by any given seismic event. If there are two rock bodies of equivalent volume, identical porosity, but body A has a higher density than body B...the wave will logically travel through body B more quickly, simply because there is less matter to undulate in body B....no?

Objections? Concurrences?

Not sure if anyone actually cares or not...I just had a whole conversation with myself today

Edited by OSHMUNNIES

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Why are density and seismic velocity inversely proportional to one another? Seems counterintuitive....

I do believe you are correct in the first case, higher propagation through denser material. It is when the wave reaches a more liquified medium, that the propagating wave is dampened.

Damping effect. In the first case you may have trust type quake, because the energy has someplace to go, and that is a more sever Earth quake.

Seismic wave

The S-wave moves as a shear or transverse wave, so motion is perpendicular to the direction of wave propagation: S-waves are like waves in a rope, as opposed to waves moving

Wikki "through a slinky, the P-wave. The wave moves through elastic media, and the main restoring force comes from shear effects. These waves do not diverge, and they obey the continuity equation for incompressible media: The shadow zone of a P-wave. S-waves don't penetrate the outer core, so they're shadowed everywhere more than 104° away from the epicenter (from USGS) Its name, S for secondary, comes from the fact that it is the second direct arrival on an earthquake seismogram, after the compressional primary wave, or P-wave, because S-waves travel slower in rock. Unlike the P-wave, the S-wave cannot travel through the molten outer core

Edited by superball

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I agree it is counterintuitve. I am accustomed to working with sonic travel times through formations in oil and gas wells as a means of determining compressive strength of the rock. The sonic travel times are generally lower, i.e. the velocities are higher, in the rocks with a greater density. But that density difference is due to a difference in porosity. Sometimes you can't see the woods for the trees.

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think in terms of masses and springs

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