Microseismic data acquired in a single observation well parallel to the axis of rotational symmetry of surrounding rocks — typically, in a vertical well drilled through a horizontally layered isotropic or vertically transversely isotropic formation — cannot be uniquely inverted for six independent components comprising the full seismic moment tensor. To constrain the inversion for such a survey geometry and medium symmetry, one might assume certain physical properties of seismic sources, the properties relating otherwise independent moment components to each other, regularizing moment tensor inversion, and helping reduce its ambiguity. Our paper examines one possibility of this kind: the assumption of a tensile fracture, rupturing the focal region along a plane of its greatest weakness. Mathematical formulation of inversion of single-well microseismic records for the parameters of tensile fractures reveals that the true solution, always recoverable from properly acquired data, might be accompanied by two spurious solutions. The analysis of those solutions leads to a criterion that, although not perfect, makes it possible to select the correct solution for the majority of elastic models. After being tested on synthetic, our methodology is applied to a field data set recorded with multiple vertical downhole arrays, demonstrating that the results of dual-well moment tensor inversion can be replicated with single-well data.