Atsushi KAMEYA, Yasutaka HAYASAKA and Teruyoshi IMAOKA GENMIX is a FORTRAN program composed by Le Maitre (1979, 1981). It has been widely used to asse

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1 Atsushi KAMEYA, Yasutaka HAYASAKA and Teruyoshi IMAOKA Reprinted from BULLETIN OF THE YAMAGUCHI MUSEUM No.27 (March 2001)

2 Atsushi KAMEYA, Yasutaka HAYASAKA and Teruyoshi IMAOKA GENMIX is a FORTRAN program composed by Le Maitre (1979, 1981). It has been widely used to assess the generalized petrological mixing model such as, biotite + sillimanite + quartz = garnet + K-feldspar + water, as well as simple mixing model such as, basalt = andesite + olivine + pyroxene + plagioclase. We rewrited this program to run on Power Macintosh and open as a free-wear through the internet ( ). GENMIX, mixing model, Macintosh GENMIX Le Maitre 1979 Generalized Mixing Model FORTRUN Le Maitre 1981 OS Le Maitre 1981 FORTRUN GENMIX BASIC Macintosh GENMIX GENMIX GENMIX

3 ...(1) GENMIX Le Maitre 1979 GENMIX GENMIX (1)...(2) (2) SiO 1 n X = a x + a x + + ax + + a x X = a x + a x + + a x + + a x i i1 p p i i2 p p2...(3) X j = a1x1 j+ a2x2 j+ + aixi j+ + apxpj Xn= a1x1n+ a2x2n+ + ax i in+ + apxpn (3) X = a1x1+ a2x2+ + aixi+ + apxp...(4) (3)

4 n S= ( Xj a1x1 j a2x2 j aixi j apx p j) j= (5) S = 2( x11)( X1 a1x11 a2x21 aixi1 apx p1) +... a1 + 2( x = 0 1 n)( Xn a x a x a x a x ) 1 1 n 2 2 n i in p pn S = 2( x i1)( X1 a1x11 a2x21 aixi1 apx p1) +... ai + 2( x in)( Xn a x a x ax a x ) = n 2 2 n i in p p n % 100% + + p = 1 (4) j = 1 X = a1x1+ arxr+ ( 1 a1... ar) x p...(6) r = p n 2 S = ( Xj a x j... arxr j ( 1 a... ar) x p j) j= 1 n = ( Z j a1x1 j... a r x r j ) j= (7) = = (7) (5) 100%

5 (2)...(8) (8) ax apxp = bw bqwq...(9) n 2 S = ( a1x1 j apxp j bw 1 1 j... bqwq j)...(10) j= = =... = = p q a j = 1 b j = 1 (10) j = 1 j = 1 n 2 S= ( Z j az 1 1 j arzr j bv 1 1 j... bv s s j)...(11) j= 1 r = p 1 s = q 1 =, =, = (11) (5) (2) (8) GENMIX generalized petrological mixing model programming general Le Maitre FORTRUN

6 (1) OS PowerMac G4/400(PCImodel) 10GbHD/192Mb MacOS9.04 REALbasic2.1.2J (2) OS Power Macintosh MacOS 17 (3) GENMIX (4) Le Maitre (1979) FORTRUN Le Maitre Le Maitre (1979) 100% Le Maitre (1981)

7 GENMIX Le Maitre

8 (1) (2) (3) SiO (4) P O P O P O P O RSS SQR (RSS) RSS residual sum of squares SQR (RSS) RSS

9 SQR (RSS)

10 (5) (6) (6-1) CSV SimpleText (6-2) GENMIX

11 (6-3) 100% 100% GENMIX Wood(1978) L11 = C64 + Ol + Pl + Aug + Mag GENMIX = RSS RSS

12 GENMIX Pre + Chl + Qz = Pum + Act + Wa EPMA GENMIX GENMIX EPMA = RSS

13 GENMIX EPMA Ti-Bt Phl Etn Ms Tlc GENMIX RSS RSS GENMIX (1) -32 -

14 GENMIX (2) EPMA (3) REE GENMIX

15 [X ] [a ] [W ] [b ] i n n j X i cps a i j cps/ppm W j ppm b i cps L 1 L 1 GENMIX REE GENMIX Macintosh GENMIX N88-BASIC GENMIX GENMIX Macintosh Roger W.Le Maitre Bryan, W.B., 1969, Materials balance in igneous rock suites. Carnegie Inst. Washington Yearb., Le Maitre, R.W., 1979, A new generalized petrological mixing model. Contrib. Mineral. Petrol.,, Le Maitre, R.W., 1981, GENMIX - A generalized petrological mixing model program. Comput. Geosci.,, , 1990, Ti - Ti -.,, Stormer, J.C. and Nicholls, J., 1978, XLFRAC: a program for the interactive testing of magmatic differentiation models. Comput. Geosci.,, Wood, D.A., 1978, Major and Trace element variation in the Tertiary lavas of eastern Iceland and their significance with respect to the Iceland geochemical anomaly. Jour. Petrology,,

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