Supporting Notes For Crustal Isotasy Indicates Anomalous Densities Beneath Iceland by William Menke ----------------------------- Note 1 -------------------------------- --------------------------------------------------------------------- Least Squares Fit of elevation(depth) data slope 35.54 +/- 6.4 (1 s) meters per kilometer intercept -585.48 +/- 178 (1s) counts 17 ----------------------------- Note 2 -------------------------------- --------------------------------------------------------------------- Apparent Moho delta-rho 1/0.03544 = 28.14 +/- 4.4 (1 s) kilometers of crust below msl for each km of crust above msl assummed upper crustal density 2500 kg/m3. This is an upper bound for the density in the upper kilometer, since it corresponds to the rather fast seismic velocity of 3.94 (using the standard formula, rho = 1.85 + 0.165 * Vp) 2500:1 = X:28.14 isostatic balance, X is delta-rho at Moho X = 89 +/- 12 kg/m3 ----------------------------- Note 3 -------------------------------- --------------------------------------------------------------------- Elevation if densoity contrast at Moho was 330 330 * (39-11) = 2500 X X = 3.7 km; round off to 4 for this silly calculation ----------------------------- Note 4 -------------------------------- --------------------------------------------------------------------- McKensie's melt calulation (Krafla model) 25% melt removal 1000 deg C, 35 km depth Crustal density 3.029 Mantle density 3.248 ----------------------------- Note 5 -------------------------------- --------------------------------------------------------------------- Stress Calculation, assuming crustal root is being held down by hoop stresses applied by elastic part of crust (assumed 6 km thick, as indicated by maximum depth of earthquakes in central Iceland). take volume density deficit as cylinder, 50 km radius, 30 km deep volume = pi * r**2 * h 3.14 * (50000)**2 * 20000 = 1.5 10*14 m**3 force = d-rho * g * v 330 kg/m3 * 9.8 m/s2 * 1.5 10**14 m3 = 5 10**17 kg m /s2 = 5 10**17 N take brittle layer to be 6 km thick, cyliner 50 km radius area = pi * r * h 3.14 * 50000 * 6000 = 9.4 10**8 m2 stress = force/area = 5 10**8 N/m2 1 N/m2 = 10**5 dynes / 10**4 cm2 = 10 dynes/cm2 1 bar = 10**6 dynes 5 10**8 N/m2 = 5 10**9 dynes/cm2 = 5000 bars which is at breaking ----------------------------- Note 6 -------------------------------- --------------------------------------------------------------------- To increase density of basalt by adding olivine rho-olivine 3330 rho-basalt 3050 rho-mixture 0.7 * 3050 + 0.3 * 3330 = 2130 + 1000 = 3130 but Vp-olivine = 8.2 Vp-basalt = 7.2 Vp mixture = 0.7 * 7.2 + 0.3 * 8.2 = 7.5 is rather too high for lower crust ----------------------------- Note 7 -------------------------------- --------------------------------------------------------------------- Density decrease due to depletion assume Iceland 25%, normal ridge 8% melt fraction, difference of 17%, or f=0.17 Oxburg and Parmentier (1977) give d-ro = 0.06 * rho * f = 34 ----------------------------- Note 8 -------------------------------- --------------------------------------------------------------------- Density decrease upon heating 250 deg C Oxburg and Parmentier (1977) give 20 ----------------------------- Note 9 -------------------------------- --------------------------------------------------------------------- The unpublished BB record section cited in the table can be viewed at http://doherty.ldeo.columbia.edu/user/menke/b96/bbeqrec.gif ----------------------------- Note 10 -------------------------------- --------------------------------------------------------------------- Ontong Java calculation Crustal Columns normal OJ water 5.6 3.2 crust 8.0 42.0 mantle 31.6 ____ ____ 45.2 45.2 bathymetric reflief of OJ: (5.6-3.2)=2.4 km root extends down 31.6 km balance mass excess of topography against mass deficit of root assume density of surficial rock is 2500, of sea water is 1030 (2.4)*(2500-1030) = 31.6 X X = 112 ----------------------------- Note 11 -------------------------------- --------------------------------------------------------------------- burying basalt to 10 kbar and 1000 C compression with beta = 1.1 10**-3 1/kb delta-rho = 3090 * 1.1 10**-3 * 10 = 30 heating with alpha = 20 x 10**-6 1/K delta-rho = - 3090 * 20**-6 * 1000 = -60 net decrease in density of 30; ie 3090 -> 3060 ----------------------------- Note 12 -------------------------------- --------------------------------------------------------------------- Could addition of an oxide phase like magnetite increase the density of the lower crust from 3050 to 3150? Magnetite rho=5200, Vp=7.38 3150 = (1-x) 3050 + x 5200 3150-3050 = (5200-3050)x 100 = 2150 x x = 0.0465 thus 4.65% (by volume) of the magnetite phase is needed. say basalt has velocity of 7.0, then 1/Vp = 0.0465/7.38 + 0.9535/7.0 = 0.006301 + 0.136214 = 0.142515 Vp = 7.02 so the velocity is raised only by a small amount, not enough to violate the seismic constraints. However, C. Langmuir (personal communication) argues that this much magnetite is not plausible.