Thank you, David! That is an excellent addition to Ernie (and others)
explanation! The Geo-Tectonics community has saved my day!
Thanks,
Greg
Quoting David Pedreira <[log in to unmask]>:
> Dear Gregory,
>
> Just to make a minor addition to the excellent explanation by Ernie
> Rutter: if you look at the P-wave velocity equation you will realize
> that it also contains the bulk modulus in the numerator, so the fact
> that denser rocks are also more incompressible than less dense
> rocks, also helps to increase the P-wave velocity. The increase in
> density has less "weight" in the formula than the parallel increase
> in stiffness and incompressibility, and final the empirical
> observation is that denser rocks have higher velocities. This is not
> obviously the case for S-waves because their velocity depends only
> on the stiffness (in the numerator) and density (in the denominator).
>
> Best regards,
> David
>
>
>
>> It is a fact that velocity increases with the density of a suite of
>> (different) rocks, but for constant elasticity velocity decreases
>> with density. It is just that going from say, granite to
>> peridotite, the increase in density is more than offset by the
>> increase in stiffness. Denser rocks tend to be stiffer. Hotter
>> rocks have lower densities AND lower stiffnesses. Stiffness is a
>> much more variable property than density, so you can have denser
>> rocks being faster than less dense rocks.
>>
>> Ernie Rutter
>>
>> -----Original Message-----
>> From: Tectonics & structural geology discussion list
>> [mailto:[log in to unmask]] On Behalf Of Gregory Dumond
>> Sent: 17 March 2011 16:45
>> To: [log in to unmask]
>> Subject: P-wave velocity, Density, and Modulus
>>
>> There is a lot of remarkable work being done in North America,
>> Tibet, and all over the globe using seismic tomography!
>> Consequently, I receive questions from many students that are
>> similar to "What do the red and blue colors mean?!"
>>
>> I first admit my unfortunate lack of anything but a basic education
>> in geophysics. In my non-expert opinion, the equation for P-wave
>> velocity (e.g., in Fowler (2005-2nd ed. on p. 102) appears at first
>> to be nonintuitive, based on the following:
>>
>> (1) Classic experiments by Christensen and Mooney (1995: JGR-Solid
>> Earth) and others demonstrate a general trend of P-wave velocity
>> increase with increasing density. One of my illustrations for
>> students is to hand them similarly-sized hand samples of basalt and
>> eclogite to convey to them a sense of how phase changes and
>> densification can occur in a fixed bulk composition.
>> Coincidentally, the average P-wave velocity and density for mafic
>> eclogite (7.984 km/s for a density of 3515 kg/m3) is greater than
>> basalt (5.873 km/s for a density of 2926 kg/km3), at 762C and
>> 50-km-depths (Christensen and Mooney, 1995).
>>
>> (2) The density term is in the denominator of the P-wave velocity
>> equation, implying that density is (by definition) inversely
>> proportional with seismic velocity. Yet, Birch's Law tells us that
>> denser rocks DO have higher seismic velocities. This inspired me to
>> look for references that have plotted Modulus as a function of
>> Density. Web of Science provided few results. The most intriguing
>> one involve a 2007 publication in Nature Materials on the direct
>> relationship between modulus and density in bone and some
>> nanomaterials (Fan et al., 2007).
>>
>> I really like Professor Fowler's explanations on pp. 102-104 in her
>> awesome "The Solid Earth..." textbook, but I have still encountered
>> difficulties with regards to getting junior-senior undergraduate
>> students (and some colleagues) to fully understand these
>> relationships.
>>
>> I would sincerely appreciate any advice or guidance on this topic.
>>
>> With warmest regards,
>> Gregory Dumond
>> Department of Geosciences
>> University of Arkansas, USA
>
>
> --
>
> David Pedreira
> Area de Geodinamica
> Departamento de Geologia
> Universidad de Oviedo
> C/ J. Arias de Velasco, s/n
> 33005 OVIEDO
> SPAIN
>
> New phone number: +34 985 10 31 79
> Fax: +34 985 10 31 03
> http://www.geol.uniovi.es/~david/home.html
>
--
Gregory Dumond
Assistant Professor
Department of Geosciences
University of Arkansas
18 Ozark Hall
Fayetteville, AR 72701, USA
http://geosciences.uark.edu/3858.php
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