Hawaii as a Site for the Moho Hole- — Woqllard 
275 
Pacific and Atlantic oceans for the same abyssal 
depths of water. Presumably, there will also be 
a difference in the magmas generated in the 
two areas and in the types of volcanic material 
erupted. The data bearing on this point are not 
too conclusive, as magmatic differentiation with 
gravity separation of early crystallized heavy 
mineral constituents such as olivine in the 
magma chamber can lead to differences in the 
lavas appearing at the surface. However, this 
subject will be deferred for the moment, and 
that of the relation between crustal thickness, 
surface elevation, the density contrast between 
the crust and mantle, and gravity relations will 
be considered. 
If the data for seismic determinations of 
crustal thickness in North America are selected 
on the basis of areas where the gravity data 
indicate regional isostatic equilibrium within 
±10 mgal, and the depth of the Moho is plot- 
ted as a function of surface elevation, the fol- 
lowing linear relation is found: 
He = — (317 + 6.0 h) ±6, where He 
is the depth of the Moho below sea level in 
kilometers, and h is the surface elevation above 
sea level in kilometers. This formula, however, 
will not apply -to oceanic areas unless the water 
column is reduced to equivalent crustal mate- 
rial of 2.86 gm/cc density to obtain a synthetic 
rock surface elevation. That the above formula 
will satisfy closely observed gravity data can 
be shown by example. 
Under isostatic equilibrium conditions, the 
free air anomaly in general increases with ele- 
vation in accordance with the formula F = —3 
-j- 7.5 h, where h is the regional surface eleva- 
tion in kilometers. This results from the in- 
crease in the depth of the compensating mass 
with elevation and crustal thickness and the in- 
tegration of the topographic effect from more 
rugged terrain which increases with elevation. 
The effect of distant topography and compen- 
sation likewise changes with elevation, in ac- 
cordance with the formula C = 13.7 h, where 
h is the surface elevation in kilometers. The 
local compensation (crustal root) for an area, 
therefore, is approximated by the equation: 
-BA - F + C 
AR = 
41.85 X Ao- 
where AR is the crustal root in kilometers 
greater than that at sea level; BA is the Bou- 
guer anomaly mass correction computed using 
a mean crustal density of 2.86 gm/cc for the 
crustal section above sea level; F, the free-air 
anomaly change with elevation; C, the effect of 
distant topography and compensation; and 
Ao- = 0.475 gm/cc to obtain agreement with 
the free board to root ratio of 1:6, as deter- 
mined empirically. 
For an assumed surface elevation of 2000 m, 
the Bouguer anomaly mass correction is (BA) 
= 2 X 41.85 X 2.86 = 239 mgal. The free- 
air effect (F) = -3 + 7.5 X 2 = 12 mgal. 
The distant compensation effect (C) = 13.7 
X 2 — 21 mgal. 
-239- 12 + 27 = -224 
41.85 X .475 19.87 
11.3 km 
On the basis of elevation alone, A R = 6.0 h, 
where h is the surface elevation in kilometers. 
For h = 2000 m,AR = 6.0X2= 12.0 km. 
The agreement is excellent, considering the 
approximate nature of the equations defining 
the free-air effect and that for distant topog- 
raphy and compensation/the uncertainty in de- 
fining the empirical relation between crustal 
thickness and elevation, and the unknown con- 
tribution of structure in the upper mantle. A 
crust having a density of 2.86 gm/cc with a 
mantle having a density of about 333 gm/cc, 
as derived from seismic velocity-density rela- 
tions, reasonably satisfies both isostasy and 
known gravity relations to elevation. It consti- 
tutes a major argument for the mantle’s having 
a composition comparable to that of dunite. 
Let us now turn our attention to the geologic 
evidence offered by volcanic eruptives. It has 
been known for some time that the basaltic 
lavas forming the Hawaiian Islands differ from 
those of most other oceanic islands in that they 
are predominantly tholeiitic with a very low per- 
centage of potassium. It has also been estab- 
lished that the alkalic basalts, trachytes, and 
andesites found in Hawaii are late stage erup- 
tives, and probably are differentiates of what 
was originally tholeiitic basaltic magma. The 
predominant alkalic basalts found in the Soci- 
ety Islands, Samoa, Fiji, and other islands pre- 
