On the retrieval of moment tensors from borehole data

Abstract

A B S T R A C TThe complete moment tensors of seismic sources in homogeneous or vertically inhomogeneous isotropic structures cannot be retrieved using receivers deployed in one vertical borehole. The complete moment tensors can be retrieved from amplitudes of P-waves, provided that receivers are deployed in at least three boreholes. Using amplitudes of P-and S-waves, two boreholes are, in principle, sufficient. Similar rules also apply to transversely isotropic media with a vertical axis of symmetry.In the case of limited observations, the inversion can be stabilized by imposing the zero-trace constraint on the moment tensors. However, this constraint is valid only if applied to observations of shear faulting on planar faults in isotropic media, which produces double-couple mechanisms. For shear faulting on non-planar faults, for tensile faulting, and for shear faulting in anisotropic media, the zero-trace constraint is no longer valid and can distort the retrieved moment tensor and bias the fault-plane solution.Numerical modelling simulating the inversion of the double-couple mechanism from real data reveals that the errors in the double-couple and non-double-couple percentages of the moment tensors rapidly decrease with increase in the number of boreholes used. For noisy P-and S-wave amplitudes with noise of 15% of the top amplitude at each channel and for a velocity model biased by 10%, the errors in the double-couple percentage attain 25, 13 and 6% when inverting for the double-couple mechanism from one, two and three boreholes.

Challenges for microseismic monitoring

“…Vavrycuk (2007) shows that a single vertical monitoring array of receivers in vertically symmetric media (e.g., VTI layered structure) does not provide sufficient information for inversion of general source mechanism and some additional constraint needs to be added to complement the inversion. If both P-and S-wave amplitudes are used for the inversion, a sufficient additional constraint is the restriction of source mechanisms to being only shear.…”

Sensitivity Analysis of Seismic Velocity and Attenuation Variations for Longmaxi Shale during Hydraulic Fracturing Testing in Laboratory

“…The variation of P-and S-wave attenuation will have a significant impact on the quality of microseismic data, especially for the waveform of the S-wave [6]. Besides, most methods of microseismic data processing or inversion do not consider the dynamic variations of petrophysical parameters, i.e., the primary/secondary (P/S)-wave velocity, attenuation, and anisotropy [7,8]. Such factors may introduce additional errors to the location results and source mechanism inversion results of microseismic events, and thus should be sufficiently addressed [9].…”

Full-waveform based microseismic source mechanism studies in the Barnett Shale: Linking microseismicity to reservoir geomechanics

“…The complete moment tensor (MT) of the general source mechanism consists of six independent components (Aki and Richards, 2002). Previous studies have demonstrated that conventional methods using only far-field P-and S-amplitudes from one vertical well cannot retrieve the offplane MT component, and therefore we have to make additional assumptions, such as assuming a deviatoric source (Vavryčuk, 2007).…”

“…Knowledge of the complete MT, especially the non-DC components, is essential to understand the fracturing process especially the failure mechanisms (Šílený et al, 2009). Moreover, Vavryčuk (2007) has shown that, for shear faulting on nonplanar faults, or for tensile faulting, the deviatoric source assumption is no longer valid and neglecting it can severely distort the retrieved MT and bias the fault plane solution (FPS: strike, dip, and rake angles). Therefore, the complete MT inversion is crucial not only to the retrieval of the non-DC components but also to the correct estimation of the fracture plane orientation.…”