Paleo-depth of fault activity: an estimate from paleostress state calculations

Description

Paleostress state reconstructions using fault-slip data yield the orientation of principal stress axes (σ1 > σ2 > σ3) and the ratio of the difference between principal stress magnitudes, i.e. the reduced stress tensors. To reconstruct the complete stress tensor (defined by six independent variables), we need to determine the two remaining unknowns, using the rupture and friction laws (Angelier, 1989). With the complete stress tensor and some constraints on the pore pressure, we can infer a depth interval of fault activity. The method we propose is organized into different steps: 1. collect fault slip data; 2. calculate the reduced stress tensor through inversion of fault-slip data; we used the FSA software (Célérier, 1999); 3. calculate the complete stress tensor using: 3a) the friction law and 3b) the rupture law. 3a. The initial friction law is considered linear and intersecting the origin. All inherited faults, reactivated under the investigated stress field, correspond to points in the Mohr space that should lie on or above the initial friction line and below the failure envelope. As a consequence, defining the lower boundary of the cloud of points, we can identify the friction line. This operation fixes the abscissa origin of the Mohr diagram. 3b. We chose the rupture law of Hoek & Brown (1980) and calculated it with the software RocLab®: σ'1 = σ'3 + σci (m σ'3/σci + s) 0.5, where σ'1 and σ'3 are the major and minor effective principal stresses at failure; σci is the uniaxial compressive strength of the intact rock material and m and s are material constants. Moreover, in our fault population, we identified couples of conjugate faults, which are neoformed by definition. The angle between these faults (2Θ angle) fixes a point on the largest Mohr cicle, where the rupture law has to be tangent. This defines the scale of the axes, and therefore the values of the principal stresses; 4. Define paleodepth. Provided that one of the principal stresses is close to vertical, it will represent the vertical stress (sv) and therefore the lithostatic load. Assuming the average density of overlying rocks and the hydraulic conditions (i.e. the amount of pore pressure, Pf) we can then calculate paleo-depth, considering that: σv = ρgz, with ρ= density of the overburden, g = acceleration gravity (9,81 m/s2), z = depth, and σ'v = σv - Pf, where σ'v is the effective vertical stress. We report here our preliminary test in a well-constrained geological occurrence, and show that the calculated depth of fault activity fits well the depth derived from independent, stratigraphic investigations. Angelier, J. (1989): From orientation to magnitudes in paleostress determinations using fault slip data. J. Struct. Geol., 11, 37-50. Célérier, B. (1999): Fault Slip and Stress Analysis (FSA). Available at. Hoek, E. & Brown, E.T. (1980): Underground Excavations in Rock. London: Institution of Mining and Metallurgy 527 pp.

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