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A Monte Carlo Approach to Calculate Stress Orientations and Differential Stress Ratios From Microseismicity Using Elastic Dislocation Modelling


Microseismicity is widely used to monitor hydraulic fracturing stimulations. A new iterative-statistical approach to calculate stress orientations and ratios from microseismic moment tensors, taking into account the fault-auxiliary plane uncertainty, is presented here. The approach uses triangular dislocation modelling to predict the strain and stress associated with microseismic events. The calculated local stress field is then used to resolve the shear and normal stress on focal planes in order to establish an instability criterion. The new technique uses an iterative Monte Carlo approach to randomly select one of the two nodal planes and corresponding slip vector at each focal mechanism. Using elastic dislocation modelling, locally induced stresses are calculated for each nodal plane according to the mechanical properties of the rock volume taking into account the mutual interaction between nodal planes. After each run, a fracture instability criterion is applied to identify unstable nodal planes that are used in a stress inversion. Thus, stress orientations and differential stress ratios can be statistically identified by investigating the result from hundreds of iterative stress inversions. The results are compared to an alternative stress inversion method that does not consider elastic deformation. In this approach, iterative Monte Carlo simulations are run to choose a random subset of microseismic events, of which one of the two nodal planes and the corresponding slip vector are randomly selected. Following a first approximation of the stress field using stress inversion, a fracture instability constraint is used to only select unstable fracture planes for a second, more refined stress inversion. Running a large number of stress inversions results in a range of possible stress orientations and differential stress ratios. These new techniques are tested on earthquake data to evaluate the approach before being applied to microseismic events from hydraulic fracturing of two wells in the Barnett shale in Texas. Comparison with existing stress inversion approaches shows that inversion techniques based on Monte Carlo fracture response modelling provides a more comprehensive assessment of the stress regime responsible for the microseismic events. This leads to a more restricted range of possible stress orientations and differential stress ratios, which can be used to evaluate fracture trends and model discrete fracture networks (DFN).