Robert:
I'm posting my comments to the list in case anyone else wants to comment also.
>Dear Dave,
>
>Thanks for the pointer to Ague's boot-strap method. The maths in
>this paper put me off a bit because I was wanting to try my data
>with a method that is most widely used, so that I had some idea of
>geochemical shifts that were reasonable, as against shifts that were
>outrageous.
I used Ague and van Haren's method without much complicated math and
was able to calculate almost everything except the variances limited
by a minimum of zero, thus my calculated variances were overestimates.
>
>As I understand it from reading so far, (especially the Leitch and
>Lentz chapter in GAC short course 11), the Gresens method involves
>the following operations. Queries are where I don't follow the nuts
>and bolts of the method:
>
>1) Choose your fresh protolith (single sample rather than an
>average of a set of samples).
You could do Gresens calculations using one parent sample or an
average of several or do it several times using different parents for
each altered sample and then assessing which parent gave results most
consistent with other comparisons. If you can precisely match parents
and altered rocks, e.g., you are comparing alteration adjacent to a
vein to a parent farther from the vein but definitely in the same
unit (flow, pillow, phase, etc) then the one to one comparisons are
best. However, if you are comparing a suite of altered samples to
parents that are quite similar, but may have some compositional range
themselves, then using an average composition and accounting for the
variability of the parents may be the best way to go. Ague and van
Haren's method may be better because it will reveal when you have
addition or subtraction that is within the variability of the parent
sample population and that should not be attributed to alteration.
>
>2) Plot X-Y plot where X axis = weakly altered majors/traces and Y
>axis = protolith majors/traces (using assorted factors to get the
>majors and traces conveniently spread out). Elements generally
>assumed to be immobile (Al, Zr, Ti) should be scattered along a
>line through the origin. Mobile elements all over the place.
It is those 'assorted factors to get the majors and traces
conveniently spread out' that Ague and van Haren argue cause problems
and produce the lever effect. Re-arranging those factors can produce
lines with different slopes in some cases, and thus different volume
factors.
Ague and van Haren's approach is like plotting normalized REE
diagrams. In a sense the Y axis is altered-rock/parent ( instead of
rock/chondrite) and the X axis is element. Elements that were
immobile should line up on one horizontal line, whereas mobile
elements would plot above or below that.
>3) If immobile element slope = 1 through the origin, there is no
>volume change (Fv=1). If slope not = 1 then Fv can be calculated
>for the sample (How? Fv = slope?).
Leitch & Lentz p.172:
Slope inverted gives mass change, R super(A/B), which when multiplied
by ratio of densities (altered/original, SB/SA) gives volume change
Fv.
>4) Plot X-Y plot of Fv vs loss/gain for individual samples . This
>"composition-volume" diagram (in above reference p. 163, fig. 2)
>really puzzles me:
>
>a) For one of my samples, each element would be represented by a
>single Fv value (from 3) and a loss/gain value (which I do not yet
>know). Hence how are lines for each element plotted. They imply
>multiple determinations of Fv and loss/gain. How can these come
>from one sample?
This is an alternative to your step 3) not a subsequent proceedure.
In this proceedure plot all possible log Fv against all possible log
loss/gain factors. If the lines for several possibly immobile
elements intersect the zero loss/gain axis at the same point (as
Al2O3, TiO2 and Zr do in Fig. 2, p.163) then the Y value of that
intercept, i.e., the Fv is the one you use to calculate all the
losses/gains for all the other elements. Or read their log loss/gain
off the graph where their lines intersect the log Fv value (in Fig 2,
p. 163 it is 0.17)
In Grant's method, your step 3), for one of your samples there
should be only one Fv value for all elements derived from comparison
to one parent or the averge of several parents.
>5) The immobile element "lines" should cluster together in a
>sub-parallel array. Where they intersect loss/gain = 0, gives you a
>refined Fv value for the sample.
>
>6) Using Fv for a particular sample, one can calculate the actual
>change in mobile elements in gm/100 cc (which equation is used?).
>At this point you need S.G. measurements unless SG changes are
>assumed to be small (above ref p. 165).
You need SG measurements to determine gm/100cc, but if you use gm/100
gm (wt. %) and assume 100 gm of parent rock and no density change,
then you can immediately plug the Fv into Gresens's equation ( eqn
(1) in L & L) and calculate the changes in weight proportion of each
component. If you have SGs or can easily determine them, then by all
means do it, rather than asuming SB/SA=1.
>7) Check elemental fluxes against petrography.
>
>I have about 130 analyses, involving fresh lavas and about 5
>alteration types to run through the above so I want to get the
>method clear before I construct a spreadsheet. If you can advise on
>the above queries, or know of a clearly worked example that you can
>recommend , I would be most appreciative.
>
>Best wishes - Rob Willan
>
>
>
>----------------------------------------------
>Dr Robert CR Willan,
>Magmatic-Hydrothermal Processes
>Geological Sciences Division,
>British Antarctic Survey,
>Cambridge CB3 0ET, UK
>Tel: 01223 221420
>FAX: 01223 362616
>Email: [log in to unmask]
>-----------------------------------------
--
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