Page 363 - Petroleum Geology

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OdC found that the rate of growth was significant for ratios with values of 1
to 5 (overburden/mother layer) and that the dominant wavelength was about
10 to 20 times the thickness of the mother layer. The relative density con-
trast affects the rate of development, but not the dominant wavelength.
Most physical models have to be started artificially; and mathematical
models must assume an initial deformation of the interface between the
mother layer and the overburden. But this need not detain us, because rock
units in a sedimentary sequence must not be regarded as a Dickensian geol-
ogical cake, and the interfaces between rock units are rarely, if ever, horizontal
planes. Furthermore, diapirism is a dynamic process taking place during the
evolution of a sedimentary basin, and the variation of all the parameters with
space and time cannot easily be incorporated into models. Nevertheless, both
physical and mathematical models lead to results that are consistent with
each other and with Nature.
Consider now a vessel in which a liquid is overlain and contained by two
identical, frictionless pistons (Fig. 15-6). The interface between the pistons
and the liquid is a plane because the vertical forces acting through each piston
are equal. If one piston is now loaded with a weight W and the other with a
weight 2W (merely a device to remind one that in nature the whole area may
be loaded, but unequally) the more heavily loaded piston will sink relative to
the less loaded piston, displacing a weight W of liquid to the volume under
the less loaded piston. If this is a valid, though simple, model of diapiric pro-
cess with a relatively rigid overburden, low equivalent viscosity and unequal
loading are the two essential factors in incipient diapirism. The density of
the liquid relative to that of the pist.ons is irrelevant.

Fig. 15-6. Simple model of diapirism as a result of loading.

However, the common materials with low equivalent viscosity - salt and,
under certain circumstances, mudstone - are also less dense than the average
overburden.
The mean mass density of the overburden has been assumed to be 2300 kg
m-3, for a weight density of 22.6 kPa/m (1 psi/ft), and this is a useful figure
for general purposes. However, bulk density is a linear function of porosity
and mean bulk grain density, and the relationship: