This work develops a method of stress inversion for a geometrically complex catalogue of microseismic events in a non-stationary stress field. We first use the k-means algorithm to split the data into suitably sized groups containing between Nmin < Ngroup < 2Nmin events. The centroids of these groups are then considered as the nodes of an unstructured grid, and we simultaneously solve for the stress state in each group using damped inversion. To account for the irregularity of the unstructured grid, we use the reciprocal square distance 1/r2 as weights between nodes, as opposed to the existing method where a weight of 1 is assigned between adjacent nodes on a regular grid. Focal planes are selected from the auxiliary plane using the fault instability criterion.
The method is applied to microseismic data from an unconventional shale play in the Vaca Muerta formation in Argentina, where results suggest the presence of a pre-existing strike-slip faulting stress regime. We also find that the unambiguous focal plane picks suggest the apparent dip-slip focal mechanisms are indeed dip-slip movement along sub-vertical natural fractures, which correlate well with image log data. We suggest that these dip-slip events are caused by shear stress induced by the opening of the hydraulic fractures.
The notion that observed fault planes are related to the local stress field dates back to Anderson (1905, 1951), who proposed that the stress-slip, normal, and reverse faulting regimes are dependent on the orientation of the three principal stresses. Wallace (1951) and Bott (1959) then proposed that the slip vector is parallel to the tangential shear traction on the fault. Following this, Michael (1984), Gephart and Forsyth (1984), and Angelier (2002) developed commonly used methods to solve for the stress tensor given a set of focal mechanisms. Specifically, these methods solve for the directions of the three principal stresses, and the stress ratio R = (σ1 – σ2)/(σ1 – σ3). In each case, only the direction of slip is considered, and so one can only solve for the deviatoric stress tensor, i.e. trace(σ) = 0. Modifications suggested by Lund and Slunga (1999), and Vavryčuk (2014) allow one to select the focal plane from the conjugate nodal plane pair by applying the Mohr-Coulomb failure criterion to each nodal plane, which returns the friction coefficient μ as an additional output.