Page 364 - Petroleum Geology

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(15.1)
indicates that the assumed mean weight density implies a mean porosity close
to 22%. Interbedded mudstones and sandstones may have such a mean den-
sity but, as we saw in the discussion of abnormal pressures, the porosity
and bulk density of abnormally-pressured mudstones correspond to nor-
mally compacted mudstone at a shallower depth. Dickinson (1953, p. 429)
appreciated the difficulties and showed that the error in taking the mudstone
compaction curve for estimating the overburden pressure is negligible (at least
in the Louisiana Gulf Coast).
However, we are concerned more with the relative densities of the sedi-
ments involved in mudstone diapirism, and the model chosen for this is a re-
gressive sequence of sedimentary rocks in which the permeable facies loads
the compactible.
Mudstone density depends on its state of compaction (with minor varia-
tion on account of the mineralogy). The formula 3.5a relating porosity, depth,
and pore-fluid pressure (through the parameter 6 ) is:

f= f, e--6z/b. (15.2)
Substituting this into eq. 15.1:

(15.3)

where the scale length b can be estimated from the sonic log. However, the
sonic transit time in mudstone is a linear function of porosity (p. 49), so we
may use the sonic log with a porosity scale:
Ybw = Ys-fO ( At - At,,
At, - At,, ) (7s - Yw) (15.4)
= 26.0 - 0.072 (At - 55) kPa/m.
Figure 15-7 shows a density inversion from about 23.3 kPa/m (pbw = 2380
kg m-3) at 1350 m to about 20.6 kPa/m (pbw = 2100 kg m-3) by 1800-
2000 my with the density increasing below this. (The very long transit times
on the diagram are probably due to hole caving and are spurious.) All the
ingredients for diapiric deformation exist - density inversion, reduced equi-
valent viscosity, unequal loading - and this is a mechanically unstable se-
quence. The mechanical boundary between the overburden and the potential
mother layer is not stratigraphic-lithologic, but rather the top of abnormal
pressures.
The vertical, buoyant forces acting on an incipient diapir by virtue of the
differing weight densities of the diapiric and overburden materials are of the
form:
(15.5)