Current paradigm asserts the impossibility of unambiguous estimation of full moment tensors from three-component microseismic 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 solidangle 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 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 singleborehole data.


Focal mechanisms of microseismic events triggered in the course of hydraulic stimulations of unconventional reservoirs contain information usefully complementing the event hypocenters and magnitudes. The value of this information lies in revealing important details of rock failure, such as the orientations of fractures along which the rock breaks, the directions of slips occurring at those fractures, and the relative portions of the double couple, the compensated linear vector dipole, and the isotropic source components..

Estimation of full seismic moment tensor, containing six independent elements (Aki and Richards, 1980; Shearer, 2009), relies on the measurements of vectorial amplitudes of the P- and often S-waves excited by a microseismic event or on certain attributes extracted from the amplitudes (e.g., Julian, 1986; Julian and Foulger, 1996). All six moment components cannot be constrained in a unique fashion in the farfield range from a source when rays and slowness vectors of waves used for the moment tensor inversion (MTI) are confined to a plane. This theoretical assertion, first discovered for isotropy (Nolen-Hoeksema and Ruff, 2001) and then extended to vertical monitor wells in horizontally stratified media composed of either isotropic or VTI layers (Vavry?cuk, 2007), has led to a commonly held belief that unambiguous MTI is impossible for ray apertures characterized by the zero solid angles (e.g., Baig and Urbancic, 2010; Leaney et al., 2011; Stan?ek and Eisner, 2013; Song et al., 2014) unless seismic data are recorded in the source near field (Song and Toks¨oz, 2011). Acting upon this perception, the industry currently employs two distinct data-acquisition geometries for carrying out full seismic MTI: wide-aperture surface arrays instrumented with vertical (Duncan and Eisner, 2010; Auger et al., 2013) or three-component (3C) geophones (Birkelo et al., 2012), or arrays of 3C receivers placed in multiple wells (Baig and Urbancic, 2010; Maxwell et al., 2010).

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