Dear All,
As a magmatist, I would also translate "stiffness" in term of composition
and thus in term of melting temperature. The red/blue colors can be due to
difference of temperature but also to different melting temperature of the
mantle part considered, the mantle being highly heterogeneous. If a mantle
area is more fusible because of its composition, for a same P-T ambiance,
lower velocities will be seen and it will appear "more red" than adjacent
areas (if red is adopted for lower velocities of course, the inverse is also
used).
I think that this is a fundamental issue.
Best regards,
Jean-Paul Liégeois
Head of Division
Isotope Geology
Royal Museum for Central Africa
B-3080 Tervuren Belgium
Tel/Fax: + 32 2 650 2252
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-----Message d'origine-----
De : Tectonics & structural geology discussion list
[mailto:[log in to unmask]] De la part de David Pedreira
Envoyé : vendredi 18 mars 2011 10:09
À : [log in to unmask]
Objet : Re: P-wave velocity, Density, and Modulus
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
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