Message from discussion
Seismic waves, density and temperature.
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Newsgroups: sci.geo.geology
Subject: Seismic waves, density and temperature.
From: auxotectonics_deletethis@nachon_andthis.net (Florian)
Date: Sun, 30 Mar 2008 14:28:19 +0200
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Stuart <bigdak...@aol.com> wrote:
> (Florian) wrote:
> > Not without full eclogitization. Eclogitization occurs only at depth >45
> > km and is only partial.
>
> The lithosphere gets to be about 100km think.
Hu? Only basalt and gabbro Eclogitized, so it concerns only 5-8 km not
the whole lithosphere!
> Also, it is on average roughly 600-700K
> cooler than the upper mantle. That buys you another 1.5%- 2%.
> > See Doglioni et al "What moves slabs":
> >
> > <http://tetide.geo.uniroma1.it/sciterra/sezioni/doglioni/Publ_download/W
> > hatMovesSlabs.pdf>
> >
>
> Some things in here may make sense, but then...
> Statements like the below give me pause with respect to this paper.
>
> "The high velocity of slab detected by tomography could be related not
> to its higher density but to its higher rigidity and viscosity"
Indeed, that statement looks incorrect.
>
> For starters tomography of slabs is done using P-waves.
Nowadays, tomography is done using S-waves and P-waves.
> The celerity of a P-wave is given by [ (K+4/3U)/R) ]^1/2 where U is the
> shear rigidity, K is the incompressibility and R is the density.
Just a reminder, the celerity of S-waves is given by [U/R]^1/2.
> So one wonders how in the world high velocity of the slab could *ever* be
> do to a simple change in density? Greater density by itself means slower.
So actually, the higher velocity in the slab could mean that the slab is
simply less dense than surrounding material. Interesting.
Doglioni argues that oceanic basalt is depleted and serpentinized which
support this interpretation but is at odd with the quote above.
> Indeed, the speed of seismic waves increases in slabs because they are
> stiffer; temperature has a greater effect on rigidity than it does on
> density. You'll also notice that there is no term for viscosity in the
> wave speed formula. The slab has higher viscosity because it is cooler.
> The viscosity increases with decreasing temperature. It is the higher
> stiffness that allows one to
> ( That should read "larger rigidity", for that matter the
> incompressibility also increases with decreasing temp.)
> put bounds on the density through an appropriate equation of state. There
> is simply no question that the slab is cooler than the surrounding mantle
> and hence more dense. How much more may be arguable, but there is no
> question that it is more.
Not so sure. Don L. Anderson has a discussion about tomography problems,
and notably the tendancy to wrongly use it as a kind of thermometer:
See paragraph: "Seismic velocity is not a thermometer"
<http://www.mantleplumes.org/TomographyProblems.html>
By the way, I note the same confusion, i.e., denser material <=>higher
velocity:
"Nevertheless, tomographic images are often interpreted assuming that a
simple velocity-density-temperature correlation exists. High velocity
(blue) is generally attributed to cold, dense, sinking material, and low
velocity (red) as hot, low-density, rising material (Figures 4 & 5)."
Weird, isn't it?
Especially, that a few lines further:
"The African and south Pacific "superplumes" are vast, low-velocity
bodies in the lower mantle whose low velocities have been shown to
result from anomalously high density and not to high temperature
(Trampert et al., 2004)"
thus suggesting again that low velocities region are associated to high
density.
>
> Maybe they meant to say "lower temperature" and "not higher density" but
> it still wouldn't make sense. What would imbue these roughly tabular
> regions with special stiffness and viscosity?
>
> I also take issue with his statement that mantle densities are "quite
> speculative". I disagree, they are well constrained by modeling the
> earth's free oscillations. In fact people are using free oscillations to
> work out some of the three dimensional structure of density variations in
> the mantle. As far as I know, the mean radial density profile for the
> Earth is known to a couple of percent if not better.
Actually, the density profile raises another issue according to Stavros:
"Then seismology tells us that the velocity of both P and S waves
increases with depth in the mantle. Density also increases
with depth. So, if it was only for density the velocity of
seismic waves should decrease with depth. There is no other physically
possible way for seismic wave velocity to increase with depth but for
the elastic moduli to increase with depth at a faster rate than density.
This is impossible though if temperature increases with depth.
Experiment has shown that the elastic moduli are very sensitive to
temperature; rigidity decreases as temperature increases, and vice
versa, and at temperatures above 800 oC rigidity diminishes rapidly.
This decrease cannot in any way be compensated by pressure-depth,
because the pressure at any depth is below the rigidity and
incompressibility thresholds. For example according to the Preliminary
Reference Earth Model - PREM the density of crustal rocks at ~10 km
depth, is ~2900 kg/m3, the pressure ~0.3 GPa, whereas rigidity mu, and
incompressibility K, are ~26.6 and ~52 GPa, respectively. At 77 km the
density is ~3375 kg/m3, the static stress ~2.45 GPa, the rigidity ~67.4
GPa, and the incompressibility modulus ~130 GPa. At the depth of 667 km
the corresponding values for density rho, pressure, rigidity mu, and
incompressibility K are ~4381 kg/m3, ~23.8, ~155 and ~300 GPa, and at
2888 km they are ~5566 kg/m3, ~136, ~294, ~656 GPa."
"The implication is quite clear: Depth and therefore static
stress-pressure has no effect on elastic moduli. For seismic wave
velocity to increase with depth in the mantle rigidity has to increase
with depth; as a result temperature cannot increase with depth.
Therefore the seismic wave velocity profile is an approximation of the
actual, whereas the conventional temperature profile is not based on
observation, experiment and logic, i.e., it is not an approximation of
the actual."
So, where is the flaw?
[...]
--
Florian
"Toute vérité passe par trois phases. D'abord, elle est ridiculisée;
ensuite, elle rencontre une vive opposition avant d'être acceptée comme
une totale évidence" - Arthur Schopenhauer
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