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Discussion |
1 3 Finedon Hall, Finedon NN9 5NL, UK
2 Department of Earth Sciences, University of Durham, South Road, Durham DH1 3LE, UK
D. M. D. James writes: the mechanics of formation of polygonal faults are widely acknowledged as not yet fully understood and it is welcome that Goulty & Swarbrick (2005) attempt a discriminatory test between rival hypotheses. It is however important that such a test bears some relation to physical reality.
The ‘test’ is based on the assumption that the ratio of horizontal to vertical effective stress as deduced from leak-off tests in two wells in the North Sea at depths of about 2 km yields the co-efficient of earth pressure at rest therein and hence the residual friction governing the post-nucleation development of polygonal faults, apparently globally and at any depth. It is not clear if the authors consider that the polygonal fault tiers at the well sites are currently active. Neither is it clear if they assume that the coefficient of residual friction along the fracture is a reasonable approximation to the coefficient of initial friction which governs the dip of the propagating fracture tip (and the fault surface as a whole) relative to the orientation of the vertical effective stress.
It is hardly surprising that the ratio of horizontal to vertical effective stress (k) is very high in the wells analysed; the leak-off tests are from highly overpressured horizons (ratios of pore fluid pressure to total vertical stress approximately 0.80 and 0.84) and the effect of pore fluid pressure coupling (Hillis 2003) will inevitably decrease the value of the horizontal effective stress to lesser extent than it does the vertical effective stress. It is certainly not yet demonstrated that polygonal faults require overpressures of this magnitude for their formation, by any mechanism. Leak-off tests tend to overestimate the horizontal effective stress if no correction is made for the excess mud pressure necessary to overcome the tensile strength of the formation. The calculated ratios of horizontal to vertical effective stress (k
0.83 and 0.77) are thus maxima and would be expected to be significantly less at the considerably shallower depths at which faulting is known to have taken place (Cartwright 1994) where both overpressure and any poro-elastic effects are likely to be reduced. This reduction is due to increase of porosity and permeability at shallower levels; a side effect of this is that k additionally reduces at shallow levels irrespective of overpressuring because framework density reduces and fluid density increases although this effect could be mitigated by any increase in the Poisson ratio. I thus find it difficult to accept either the precision or the relevance of the calculated k values.
The point that development of the fault system cannot be divorced from its nucleation was set out fully by Cartwright et al. (2003) and is not answered by the results of the ‘test’. Earth pressure ‘at rest’ (Ko) is generally applied to describe stress and residual frictional conditions (µr) during compaction, ie elasto-plastic deformation at very low strain rates across what may be thought of as micro-faults without cohesion. If the faults studied are currently inactive then k might now be equal to Ko, albeit not necessarily. However stress conditions at the former high strain rates of macroscopic faulting are generally considered to require description in terms of initial conditions of sediment cohesion and internal friction (µi) when k is less than Ko. Friction will be certainly be reduced across the fault behind the advancing tip whatever its mechanism of inception; the problem is to perturb regional stresses to permit fracture in the first place as the authors both admit and ignore. The syneresis hypothesis does at least address this difficulty. Moreover it favours faulting in regions of relatively low pore fluid pressure (favouring low k) between the centres of syneresis: within the centres pressures are higher, expelling fluid and allowing increased compaction at a rate buffered by this fluid loss. It also allows a degree of self-similarity to develop amongst these mutually interfering centres (after presumably random initial nucleation) and this may explain the common instances of a regular polygonal geometry in plan form.
Goulty & Swarbrick presumably choose to use the co-efficient of earth pressure at rest to assess frictional conditions on polygonal faults as they consider (p. 587) that these form in ‘sediment that has been compacted vertically, with zero lateral strain‘. In a regional sense it is of course true that there is no extension: in a local sense however this is not so as extension across the faults is compensated by shortening between them. The driving force for faulting is required to supply the energy for pore-fluid expulsion or at least redistribution such that rotation of strata can occur across the fault. This is a geometric requirement and is applicable whatever mechanism, syneresis or ‘gravitational loading‘, is involved. Geometries seen on seismic sections suggest that strain is accommodated internally and progressively by compaction/dilation around the growing fault tips and, once the lower fault tip enters a ductile substratum, by rigid body rotation above lateral ductile flow (Fig. 1). Ongoing strain over and above that of equilibrium compaction is endemic to this process and the entire concept of earth pressure at rest thus seems inapplicable. If so the ‘test’ cannot be used to argue for or against any mechanism.
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21 July 2005
N. R. Goulty & R. E. Swarbrick reply: We were surprised that James should criticize a test based on field data for not bearing some relation to physical reality, but infer that this comment relates to his later assertion that the polygonal fault systems concerned are inactive. This seems to be the key issue in his criticism and we address it below whilst dealing with his comments paragraph by paragraph.
Our test was indeed to estimate the ratio between the minimum horizontal effective stress, 
h, and the vertical effective stresses, v, in North Sea wells, but we did not equate this ratio with the coefficient of earth pressure at rest which we understand to be the effective stress ratio in sediments that have been compacted uniaxially. In the sequences cut by polygonal faults horizontal compaction has taken place to complement the heave on the normal faults. We did not suggest that the test estimated h/v globally: the estimates are local and apply at the depth of the measurements. We have assumed that the polygonal fault systems penetrated by the wells are active, but there is no assumption that the coefficient of residual friction along the fracture approximates the coefficient of initial friction that governs the initial (pre-compaction) dip of the faults, nor is such an assumption required by the hypothesis of low coefficients of residual friction (Goulty 2002).
James correctly notes that the leak-off tests are from overpressured formations, but we have never suggested that overpressures are required for the formation of polygonal faults. It is generally accepted that overpressure in the Tertiary clays of the Central North Sea has resulted from disequilibrium compaction only (e.g., Swarbrick et al. 2000, 2005), without any contribution from fluid expansion mechanisms, so the poroelastic coupling between pore pressure and horizontal stress discussed by Hillis (2003) is not relevant here. We are assuming that the present-day vertical effective stress is the maximum value that these sediments have experienced, which is consistent with disequilibrium compaction as the mechanism of overpressure generation. James cautions that leak-off tests need careful evaluation. We confirm that minimum horizontal stress was estimated as the leak-off pressure, and not as the formation breakdown pressure which includes the tensile strength of the formation (White et al. 2002). Thus we reject James’ criticisms that the values of present-day h/v are maximum estimates. He then asserts that faulting took place at considerably shallower depths, raising the question: are the polygonal fault systems active at the present-day?
We agree that initiation of polygonal fault systems takes place at relatively shallow depths of burial, but not that faulting also ceases at shallow depths. If James can provide convincing evidence, beyond mere assertion, that the faults are inactive then we will also agree the results of this test are unreliable, although at least we could claim to have developed a test methodology that may be applied elsewhere for a problem described by Cartwright et al. (2003) as untestable. However, there is plenty of circumstantial evidence to suggest that polygonal fault systems continue to be active at much greater depths of burial than James concedes. Firstly, we have observed on published seismic data a general correlation between the largest throws in polygonal fault systems and the maximum depth of burial experienced by the host sequences. In particular, some faults in polygonal fault systems of the Central North Sea have throws as great as 100 m (Cartwright & Lonergan 1996), and it seems unlikely that such large throws developed close to the sea floor. Secondly, water-escape features located vertically above the upper tips of faults in polygonal fault systems provide evidence of continued fluid expulsion at burial depths of 1 km on the mid-Norwegian margin (Berndt et al. 2003). Thirdly, the tests were made in undercompacted clay sequences with porosities of c.50%. Given that the overpressure is due to disequilibrium compaction, it is reasonable to suppose that the sediments are still compacting and expelling pore fluid at the present day, and that the faults are still active. We infer that James considers the polygonal fault systems to be inactive because he thinks that at least some of the overpressure has resulted from fluid expansion mechanisms, inducing a poroelastic response as the effective stresses are reduced. That opinion conflicts with the deduction that overpressure in the Tertiary sequences of the Central North Sea is due to disequilibrium compaction (Swarbrick et al. 2000, 2005). Another reason advanced in support of the contention that buried polygonal fault systems are inactive is that currently active faults would be expected to propagate up to the seafloor (J. Cartwright, pers. comm.). This argument would be valid for tectonic fault systems, but a key characteristic of polygonal fault systems is that they are layer-bound in lithological sequences having a clay fraction >70% (Cartwright & Dewhurst 1998; Dewhurst et al. 1999), and tectonic stresses are not required for their development. Thus we are not aware of any good reason to suppose that the faults are inactive.
We do not know which passage in Cartwright et al. (2003) is the one that James is referring to when he says that development of a polygonal fault system cannot be divorced from its nucleation, but we reject this assertion as absurd. He has himself referred to the distinction between the coefficient of friction governing initial rupture on a fault and the coefficient of residual friction that governs later slip on the fault. Unfortunately, the review article by Cartwright et al. (2003) must have gone to press before publication of the paper by Goulty (2002), which distinguished between fault initiation and the subsequent development of polygonal fault systems in the context of the hypothesis of low coefficients of residual friction as the governing parameter for the latter process. Consequently, the tendentious criticisms of this hypothesis by Cartwright et al. (2003), referred to by them as the gravitational loading model, were aimed at an earlier paper (Goulty 2001) in which the hypothesis had not been fully developed. James accuses us of ignoring the problem of perturbing regional stresses to permit fracture in the first place, but we referred to the suggestion by Goulty (2002) that nucleation might result from differential compaction around inhomogeneities. Propagation of the faults would then be facilitated by stress concentrations at the fault tips. Nucleation of faults takes place on a small scale, and we assume that initiation of each fault in a polygonal fault system took place independently. Fault growth involves expansion of the slip surface, as well as increase in the magnitude of slip, and Goulty (2002) subscribed to the interpretation by Lonergan et al. (1998) of the mechanism of fault linkage in polygonal networks.
In the same penultimate paragraph James says that the syneresis hypothesis favours faulting in regions of relatively low pore fluid pressure because low pore pressure favours low h/v. We think his reasoning is wrong. If it is accepted that one principal stress axis is (close to) vertical and that the horizontal stresses are (approximately) isotropic, the horizontal stress is (approximately) constant at a particular depth. Consequently h/v must be greater in regions of relatively low pore pressure, given that h<v.
In his final paragraph, James again misrepresents the basis of our test. As stated above, we distinguished between the present-day values of h/v, which we suggest are controlled by the coefficient of residual friction on fault surfaces, and the coefficient of earth pressure at rest. We take this opportunity to correct a misprint in equation (2): where normal faults have optimum orientation and dip for failure, Mohr–Coulomb theory for the case of zero cohesion relates the effective stress ratio to the coefficient of friction, µ, by
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Further discussion of the factors that control h/v in sedimentary basins may be found in Goulty (2003).
In conclusion, we consider that the most interesting point raised by James is whether the polygonal fault systems are active or inactive. We admit that we cannot prove the fault systems are active, but we think the available evidence strongly supports the assumption that they are.
30 August 2005
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References |
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