The existing paradigm, widely accepted in the microseismic community, asserts the impossibility of unambiguous estimation of full seismic moment tensor from three-component data recorded in a single straight borehole. The statement of inversion nonuniqueness, related to the lack of illumination of the off-plane moment component in the zero solid-angle ray apertures, tacitly assumes the slowness vectors, normal to the relevant wave fronts, to be confined to the plane containing the ray trajectories. Although such arrangements of the rays and slownesses do take place for vertical wells drilled in horizontally layered isotropic and VTI (transversely isotropic with a vertical symmetry axis) formations, azimuthal anisotropy commonly expected for hydraulically fractured, hydrocarbon bearing shales makes the slowness vectors deviate from a plane, arrange themselves into nonzero solid-angle apertures, and yield theoretically unique inverse problems for seismic moment tensors. This paper examines those problems for the anisotropy parameters characterizing fractured shales and siltstones in the Bakken. Their strong azimuthal anisotropy entails not only formally unique but, importantly for practical applications, well-posed inverse problems, resulting in robust estimates of the complete moment tensors from single-borehole data.