Awesome answer! Thank you, Ernie! That is just what I was looking for!
On 3/17/2011 11:58 AM, Ernest Rutter wrote:
> 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
Department of Geosciences
University of Arkansas
18 Ozark Hall
Fayetteville, AR 72701
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