Uncertainties in Seismic Moment Tensors Inferred from Differences between Global Catalogs

Catalogs of moment tensors form the foundation for a wide variety of seismological studies. However, assessing uncertainties in the moment tensors and the quantities derived from them is difficult. To gain insight, we compare 5000 moment tensors in the U.S. Geological Survey (USGS) and the Global Centroid Moment Tensor (Global CMT) Project catalogs for November 2015–December 2020 and use the differences to illustrate the uncertainties. The differences are typically an order of magnitude larger than the reported errors, suggesting that the errors substantially underestimate the uncertainty. The catalogs are generally consistent, with intriguing differences. Global CMT generally reports larger scalar moments than USGS, with the difference decreasing with magnitude. This difference is larger than and of the opposite sign from what is expected due to the different definitions of the scalar moment. Instead, the differences are intrinsic to the tensors, presumably in part due to different phases used in the inversions. The differences in double-couple components of source mechanisms and the fault angles derived from them decrease with magnitude. Non-double-couple (NDC) components decrease somewhat with magnitude. These components are moderately correlated between catalogs, with correlations stronger for larger earthquakes. Hence, small earthquakes often show large NDC components, but many have large uncertainties and are likely to be artifacts of the inversion. Conversely, larger earthquakes are less likely to have large NDC components, but these components are typically robust between catalogs. If so, these can indicate either true deviation from a double couple or source complexity. The differences between catalogs in scalar moment, source geometry, or NDC fraction of individual earthquakes are essentially uncorrelated, suggesting that the differences reflect the inversion rather than the source process. Despite the differences in moment tensors, the location and depth of the centroids are consistent between catalogs. Our results apply to earthquakes after 2012, before which many moment tensors were common to both catalogs.

Analysis of Differences in Seismic Moment Tensors between Global Catalogs

<p>Catalogs of moment tensors form the foundation for a wide variety of studies in seismology. Despite their importance, assessing the uncertainties in the moment tensors and the quantities derived from them is difficult. To gain insight,<span>  </span>we compare 5000 moment tensors in catalogs of the USGS and the Global CMT Project for the period from September 2015 to December 2020. The GCMT Project generally reports larger scalar moments than the USGS, with the difference between the reported moments decreasing with magnitude. The effect of the different definitions of the scalar moment between catalogs, reflecting treatment of the non-double-couple component, is consistent with that expected. However, this effect is small and has a sign opposite to the differences in reported scalar moment. Hence the differences are intrinsic to the moment tensors in the two catalogs. The differences in the deviation from a double-couple source and in source geometry derived from the moment tensors also decrease with magnitude. The deviations from a double-couple source inferred from the two catalogs are moderately correlated, with the correlation stronger for larger deviations. However, we do not observe the expected correlation between the deviation from a double-couple source and the resulting differences in scalar moment due to the different definitions. There is essentially no correlation between the differences in source geometry, scalar moment, or fraction of the non-double-couple component, suggesting that the differences reflect aspects of the inversion rather than the source process. Despite the differences in moment tensors, the reported location and depth of the centroids are consistent between catalogs.</p>

Simulation of shape memory cycle of a polymeric beam undergoing large deflection using a simple incremental approach

Shape memory polymers are a group of polymers which can store a temporary shape at a relatively cold temperature and recover when heated above its glass transition temperature. Various constitutive models exist in literature to simulate the uniaxial shape memory cycle. One such popular model is based on the concept of multiple natural configurations. In the present work, the stress-strain-based model is adapted for bending application by converting it into a scalar moment-curvature-based relationship. The adapted model is used in a numerical framework for large deflection of beams to simulate the shape memory cycle. The employed numerical framework is based on linearising the non-linear governing differential equation and subsequently solving it in steps by numerical integration. The results are presented in suitable non-dimensional form for generality. Since coefficient of thermal expansion plays a minimal role in bending, it is found that the bending results are considerably different from their uniaxial counterpart. The approach may be claimed to be computationally economic as compared to finite element method because here large matrix inversion is avoided.

Variation of seismic scalar moment–corner frequency relationship during development of a hydraulic fracture system

We propose to utilize the corner frequency and seismic scalar moment relation as a new approach to monitor temporal changes of static stress drop as well as rupture velocity during development of a hydraulic fracture system. We introduce a single parameter M1 to describe a two-parameter relation (scalar moment and corner frequency relation) and analyze temporal variation of this two-parameter relation. Because M1 relates rupture velocity and static stress drop, we can infer temporal variation of rupture velocity and stress drop quantitatively. The parameter M1 is calculated in two case studies. We document that two types of fracturing processes exist: (1) stable rupture velocity and static stress drop during the development of rupture and (2) increase of rupture velocity and/or static stress drop while the fracture system develops. In the latter case, one possible scenario is increase of permeability at each fracture plane during development of the fracture system.

Multievent moment-tensor inversion for ill-conditioned geometries

Moment-tensor inversion under single monitoring well geometries becomes unstable due to the singularity of the inversion matrix. But microseismic events observed during hydraulic fracturing commonly show clusters of events with similar source mechanisms despite differences in the origin time and the magnitude. If the events with similar source mechanisms can be grouped and inverted for a single common moment tensor, the singularity can be eliminated. We have developed a normalized multievent moment-tensor inversion (NME-MTI) method, which does the MTI simultaneously for multiple events, to test the feasibility of this multievent approach. First, the scalar moment for each event was estimated using the far-field low-frequency level at each receiver. Then, the displacements measured at the receivers were normalized by the scalar moment and used to invert for the common moment tensor simultaneously for all the events in the group. We introduced a gradient search method to minimize the overall misfit by adjusting the scalar moment for each event to reduce the errors introduced by the scalar moment estimation. The algorithm was tested with a synthetic data set with four monitoring wells and a field data set with dual monitoring wells. It was proved that the NME-MTI method can retrieve the moment tensors of the event groups with data from a single monitoring well. The effects of uncertainties on the inversion were examined with data noise, scalar moment uncertainty, and event location uncertainty. The results showed that the ME-MTI result is much less sensitive to the data noise and the scalar moment uncertainty than the single-event approach. The results also determined that although the bias to the solutions increases when the event location uncertainty increases, the bias can be controlled by reducing the event location uncertainties using a more accurate location algorithm.

The matter of size: On the moment magnitude of microseismic events

We investigated the method of estimating seismic moment and moment magnitude for microseismic events. We determined that the [Formula: see text] defined by Bowers and Hudson is the proper scalar moment to be used in microseismic studies for characterizing the size of an event and calculating its moment magnitude. For non-double-couple sources, the proportional relationship between body-wave amplitude and seismic moment in the Brune model breaks down. So under such situations, the Brune model is not an appropriate way to estimate the seismic moment and magnitude. Moreover, the S-wave alone is not sufficient for determining the total seismic moment. Instead, the P-wave must be analyzed. An example Barnett Shale data set was studied, and the results concluded that the magnitudes estimated with the Brune model could be off by as much as 1.92, with an absolute average of 0.35. The moment magnitudes based on the scalar moment [Formula: see text] also gave a significantly different event size distribution and b-value estimation. Finally, attenuation also played a role in estimating the moment magnitude. With a typical average attenuation factor of [Formula: see text], the average magnitude correction for our field data set was on the order of 0.15. However, it could reach 0.3 for events far away from the monitoring well.