Sorry, I should have also said that Q particularly affects S-waves.

> One thing that is perhaps being swept under the rug here is attenuation
> (or Q). If there is melt, fluid of any sort, anisotropy and all these good
> things that we know are there (but generally choose to ignore), then we
> have to learn to deal with wave attenuation and this can cause BIG
> problems in determining an accurate velocity model whither by tomography
> or by wide-angle data. Since many, if not most, of our assumptions about
> crustal, especially lower crustal, and mantle composition comes from
> inverting velocity models to lithologies and then to chemical composition,
> the errors involved by not taking Q into account can be quite big. So, a
> few percent melt has a much more complex effect on seismic velocities than
> just a few % change.
>
> Dennis
>
>
>> Dear Alain,
>>
>>
>>
>> OK, I agree that basically this is the composition that is important.
>>
>> But, in the case there is a few % melting, isn’t it a additional source
>> of
>> change in velocity?
>>
>>
>>
>> All the best,
>>
>>
>>
>> Jean-Paul
>>
>>
>>
>>
>>
>>   _____
>>
>> De : Tectonics & structural geology discussion list
>> [mailto:[log in to unmask]] De la part de Alain Vauchez
>> Envoyé : vendredi 18 mars 2011 10:58
>> À : [log in to unmask]
>> Objet : Re: P-wave velocity, Density, and Modulus
>>
>>
>>
>> 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
>>
>>
>>
>>
>