Universidade Fernando Pessoa
Porto, Portugal
Basic Principles in Foredeep & Foldbelt Basins
Flexural Subsidence
In the Colville foredeep basin, the geometry of the substratum of the foredeep basin (Lower Triassic, Scythian) can easily be explained by a simple theoretical geological model, i.e by overloading of the end of a thin and elastic lithospheric plate. The mathematical formulation of such a model was proposed by S. Cloetingh (1992). At a point x, the flexural response (w) of an elastic lithospheric plate to a horizontal force N and to a vertical loading q(x) is given by:
q(x) = D (d4w/dx4) - N (d2w/dx2) + (
m-
where,
w - is the displacement of the lithosphere.
D - is the flexural rigidity:
N - is the horizontzal force, which is equivalent to the product of the interplate stressN and the plate thickness T.
g - is the gravitational acceleration.
In this formula, the introduction of the horizontal force N, i.e. the temporal fluctuations of the stresses induced by the displacement of the lithospheric plates (“intraplate stresses”) has important geological consequences (see later). In fact, certain geologists correlate such stresses to local variations of the tectonic subsidence and consequently to the geometry of the basins.
On the other hand, the mathematical formulation of the flexure indicates that the tectonic subsidence of the foredeep basins is dependent on the vertical load q(x), but also of the flexural rigidity of the lithosphere (D), which controls the elastic thickness of the underlying lithosphere. Actually,
D=ET3/12(1-w2) withE - Young’s modulus,
T - plate thickness and w the Poisson’s ratio (15)(15) Poisson’s ratio is the ratio between the transverse and the longitudinal deformation of a rectangular body when lengthened by opposite forces acting parallel to its axis’ body
The theoretical models also suggest that the fold belt is created by a succession of thrusts faults. Each thrust fault is induced by a vertical load, i.e. for each thrust, the depression and the bulge migrate in the opposite direction of the fold belt. In other words, one can say that in all foredeep basins, at a time t, the tectonic subsidence changes all along of the fexural profile. A point near of the bulge, where the subsidence and the uplift are zero, the subsidence will be very small. On the other hand, a point near the fold belt, the subsidence will be very important. However, when a new vertical load takes place, the depression and the bulge will be displaced toward the margin, while the previous bulge is slightly tilted toward the fold belt. The calculation of the tectonic subsidence by “backstripping” indicates that it is quite important during the initial stages, but it progressively decreases significantly.
To end this appendix, we are going to sum up the calculation of the tectonic subsidence by “backstripping”:
- The tectonic subsidence is the total subsidence corrected for the influence of sediments and water depth. It corresponds to the burial of the substratum, without taking into account the sedimentary and water load. The “backstripping” is a technique allowing correction for these loads.
- T. Watts (1992) indicated that the tectonic subsidence can be calculate as:
m-s) / m-w)] + Wd-?sl [m / (m-w)]where,
ST - is the corrected subsidence or tectonic subsidence,
S - is the sedimentary thickness corrected for compaction,
Wd - is the water depth of deposition,
?sl - is the relative sea level change.
This formula clearly indicates that the calculation of tectonic subsidence depends mainly of the knowledge of the water depth of deposition and the compaction. The first is often difficult to determine, but it can be approached by a sequence stratigraphic analysis. Compaction, however is easily calculated knowing:
Es - the total thickness of the sedimentary column,
Eh - the depth of a point p,
fs - the porosity of the shallow sediments,
fd - the porosity of the deep sediments,
Es = Eh(1-fd) / (1-fs)
Calculations of tectonic subsidence by “backstripping” show local variations to the long term thermic subsidence profile. Geologists explain them according to their geological background and to their cosmological vision. In other words, geologists invoke their geological à priori ideas according to their philosophical “Leitbilder” (16) (K. Popper, 1968, 1982; C.E. Wegmann, 1950; C. Sengör, 1991).
(16) In hydrocarbon exploration, as well as in all other sciences, petroleum geologist follow two thinking schools, Democrite and Aristotle schools, i.e. the Atomist and the Peripathetic schools (D. Furley, 1987 and 1989), i.e. continuity versus discontinuity. “Leitbilder” means ideals.
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