NaNDC: Full Moment Tensor Inversion and Uncertainty Analysis for Large-N Monitored Small Earthquakes

Abstract Although most earthquakes occur on near-linear planes and generate shear motions, the small-moderate events may contain explosive or nonlinear features, translating into the “non-double-couple” (NDC) components in the full moment tensors (FMTs). However, constraining such secondary components remains challenging and often involves full-waveform-based modeling, demanding high-resolution 3D velocity structures that are barely available at local scales. Alternatively, the recent boost of the dense nodal array provides an opportunity to resolve FMTs using polarities and amplitudes of body waves. In this study, we propose an FMT inversion algorithm that joints different far-field observations (i.e., P-wave polarities and amplitudes, S/P amplitude ratios) to constrain the NDC components for small earthquakes monitored by nodal arrays (nodal array non-double couple [NaNDC]). The optimal moment tensor and associated uncertainties are determined through a grid search over FMT space. Then uncertainties of the NDC components are projected onto the Lune plot for illustration. Synthetic tests demonstrate the robustness and high tolerance of NaNDC for station coverage, noise level, and perturbed velocity models, as well as the case-dependent benefit of incorporating S/P amplitude ratios in constraining FMTs. We then applied NaNDC to field observations near a hydraulic-fracturing well in Western Canada, where 167 M > 1 induced events were recorded by 69 three-component geophones. The resolved FMTs are predominantly strike-slip with subvertical or shallow dip nodal planes, with an average percentage of the double-couple component greater than 70%. Although our solutions are generally consistent with the previous results (90% of events displayed angular difference less than 20°), NaNDC reduced the amounts of NDC components for events located to the northeast. We provide NaNDC as an effective tool for FMT inversion of large-N-monitored small earthquakes. The uncertainty evaluation on the Lune plot also permits a more precise and quantitative interpretation of the NDC components observed from complex environments like volcanic or induced regions.