Backstripping sediments progressively through geological time. The purpose of backstripping is to use the stratigraphic record to quantitatively estimate the depth that basement would be in the absence of sediment and water loading. This depth provides a measure of the unknown 'tectonic driving forces' that are responsible for basin formation and for this reason have been termed the tectonic subsidence or uplift of the basin. By comparing backstripped curves to theoretical curves for basin subsidence and uplift it has been possible to deduce information on the basin forming mechanisms. Fig. 1.1 Airy backstripping Consider the case shown in Fig.1.1 of two columns of the crust and upper mantle that before and after backstripping are in isostatic equilibrium. Balancing the pressure at the base of the two columns gives : ρ w gw di + ρ si gs i * + ρ c gt= Y i ρ w g + ρ c gt+ x ρ m g where Wdi, S* i, Yi are the water depth, de-compacted sediment thickness and, tectonic subsidence of the i th stratigraphic layer respectively, g is average gravity, T and ρ c are the mean crustal thickness and density respectively
(assumed to be constant during the unloading process), and ρ w and ρ si bar are the densities of the water and de-compacted sediment respectively. We can also write (Fig. 1.1) : x = W di + S i * + T (Y i + sli + T) where sli is the sea-level change. Y i = W di + S i * (ρ m ρ si ) sli ρ m (1.1) Equation (1.1) is known as the "backstripping equation". The equation allows Yi to be determined directly from the observed stratigraphic data. The first term in the equation is a water depth term, the second a sediment loading term, and the third a sea-level loading term. Since backstripping attempts to correct the stratigraphic record for the effects of loading in the past, it is not sufficient to use the sediment thickness and density of a stratigraphic unit as measured today. Both the thickness and density therefore needs to include the effects of post-depositional processes such as de-compaction. We will assume here a simple model in which de-compaction is a mechanical, non-reversible, process. Thus, there is no alteration of the grains due, for example, to diagenesis. Fig. 1.2 Vertical cylinder showing height of water and sediment grains. Consider the cylinder of sediment and water schematically illustrated in Fig. 1.2. The porosity of the sediment, φ, is given by the ratio of the volume of
water, v w, to the total volume, v t. Assuming the cylinder is of uniform crosssectional area, we can write that φ = h w /h t where h w and h t are the height of the water column and the total height of the column respectively. If h g is the height of the sediment grains then: h t = h w + h g (1.2) h g = h t (1-φ) We will assume that during de-compaction (and compaction) h g is constant and so as h t changes so will φ. Consider the i th stratigraphic unit at some depth in a well which due to compaction has a thickness Si and a porosity φi. The height of the grains is given by Equation (1.2) i.e. h g = S i (1 φ i ) (1.3) The height of the grains for the de-compacted unit is also h g and so is given by h g = S i * (1 φ i * ) (1.4) where Si * and φi* are the thickness and porosity of the de-compacted layer respectively (Fig. 1.4). Fig. 1.3 Schematic diagram showing the thickness and porosity of a sedimentary layer at the surface and at depth. Assuming that the equivalent height of the grains is the same before and after compaction then we get by equating (1.3) and (1.4): S i * = S i (1 φ i ) (1 φ i * ) (1.5)
Equation (1.5) shows that the thickness of the de-compacted layer depends on the present day (i.e. compacted) thickness and porosity and the porosity when the unit was near the surface, at the time of the formation. We can estimate this porosity by "sliding" a unit up an appropriate porosity vs. depth curve. The decrease of porosity with depth is illustrated for a number of different lithologies in Fig. 1.4. The figure shows that porosity decreases rapidly with depth. Fig. 1.4 Summary of porosity vs depth curves for different lithologies. Based on Bond & Kominz (1984) We can use the porosity vs. depth curves to decompact a sediment layer. Consider, for example, a 100 m thick shale horizon that is now at a depth of 3 km. The figure shows that the porosity of shales is ~ 0.12 at a depth of 3 km and ~0.70 at the surface. The de-compacted thickness from Equation 1.5 is therefore 100 (1-0.12)/(1-0.70) = 293 m, which is more than 2.5 times the original thickness of the layer. The backstripping technique involves the unloading of a de-compacted sedimentary layer and so requires its thickness as well as an estimate of its
density. This is most easily obtained by considering the volume and mass of the de-compacted i th layer. We have : or v t = v w + v g m t = m w + m g (1.6) (1.7) where m t, m w and m g are the total, water and grain mass respectively. It then follows that : ρ si v t = ρ w v w + ρ gi v g (1.8) where ρ si bar and ρ gi are the average density and grain density of the decompacted i th layer respectively. Substituting for v g from Equation (1.6) in (1.8) and dividing by v t we get : ρ si = ρ w φ i * + ρ gi (1 φ i * ) (1.9) Consider, for example, the shale layer that we discussed earlier. If ρ gi = 2650 kg m -3, then Equation (1.9) suggests that the density of the de-compacted shale layer is 1030 0.70 + 2650 (1-0.70) = 1516 kg m -3. This is significantly less than the density that the unit had at depth which is 1030 0.12 + 2650 (1-0.12) = 2456 kg m -3. We have so far only considered the backstripping of a single sediment layer (the i th layer). In practise, we need to be able to backstrip more than one layer. To backstrip multiple layers we need to "restore" all the stratigraphic units in a sequence for each time step - de-compacting the younger units and compacting the older ones. The procedure is illustrated in Fig. 1.5. The tectonic subsidence is calculated from the sediment thickness and the average density of the entire sedimentary sequence at a particular time.
Fig. 1.5 Schematic diagram illustrating how multiple sediment layers can be backstripped The total thickness, S*, is easily obtained by summing all the individual thicknesses. In the case of the density, the mass of the total thickness must sum the masses of all the individual stratigraphic units within it and so we have that ρ s S * n = Σ ρ w φ * i + ρ gi (1 φ * * i ) S i i =1 : where n is the total number of stratigraphic units in the sequence at a particular time. It follows then that : ρ s = n Σ i =1 ρ w φ i * + ρ gi (1 φ i * ) S i * S * (1.10) Finally, the total tectonic subsidence or uplift, Y, can then be obtained by substitution in the backstripping equation. Y = W d + S * (ρ m ρ s ) sl ρ m (1.11) where W d and sl are the water depth and sea-level height respectively at a particular time.