Dear Jean Paul and others,
In the mantle difference in melting temperature is not the source of variations in seismic waves velocity. Variation in Tm is an effect, as variation in seismic velociies, of the Fe-Mg contents of olivine. Olivine reacher in Mg is less dense (with almost similar elastic moduli) and therefore seismic waves propagates faster, and they are also more refractory, as you pointed out. This is, togeter with a lower geotherm, the reason why cratonic domains are characterized by positive velocity anomalies ("blue").
Cheers
Alain
÷÷÷÷÷÷÷÷÷÷÷÷÷÷÷÷÷÷÷
Dr. Alain Vauchez
Géosciences Montpellier
CNRS -Universite de Montpellier II - UMR 5243
Place E. Bataillon - cc 060
34095 - MONTPELLIER cedex 05 - FRANCE
Tel. 33 - (0)467 14 38 95 (0: only from France)
Fax 33 - (0)467 14 36 03
http://www.gm.univ-montp2.fr/PERSO/vauchez/
Le 18 mars 2011 à 10:34, Jean-Paul Liegeois a écrit :
> 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
> [log in to unmask] (max 4 Mb)
> [log in to unmask] (max 10 Mb)
> [log in to unmask]
> http://www.africamuseum.be/museum/home/contact/staff/LIEGEOIS_Jean-Paul
>
> -----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
>
