Publications

Abstract not provided.

Here, the determination of the geometrical properties of fractures plays a critical role in many engineering problems to assess the current hydrological and mechanical states of geological media and to predict their future states. However, numerical modeling of geoelectrical responses in realistic fractured media has been challenging due to the explosive computational cost imposed by the explicit discretizations of fractures at multiple length scales, which often brings about a tradeoff between computational efficiency and geologic realism. Here, we use the hierarchical finite element method to model electrostatic response of realistically complex 3D conductive fracture networks with minimal computational cost.

After the 23 August 2011 Mineral, Virginia, earthquake, a temporary dense array (Aftershock Imaging with Dense Arrays (AIDA)) consisting of ~200 stations was deployed at 200-400 m spacing near the epicenter for 12 days. Backprojection of the data was used to automatically detect and locate aftershocks. The co-deployment of a traditional aftershock network of 36 stations at ~2-10 km spacing enables a quantitative comparison. The AIDA backprojection aftershock catalog is complete to magnitude -1.0 and includes events as small as M-1.8. For comparison, the traditional network was complete to M-0.3 for the same time period. The AIDA backprojection catalog observes the same major patterns of seismicity in the epicentral region, but additional details are illuminated. The primary zone of seismicity is not a single fault but is a tabular zone of multiple small faults, this zone has a subtle concave shape along strike and with depth, and a broader zone of new events is observed at shallow depth. In addition, a new separate, shallow cluster was detected and located to the east of the main aftershock zone. The addition of smaller events to the catalog did not change the b-value or the temporal decay constant, but illuminated spatial and temporal patterns. Both the b-value and temporal decay constant are different for 12 days than for 4 months and are different at < 3km depth than at greater depth. Very low b-value, especially at greater depth, is consistent with observed very high stress drops. Conclusively, the results indicate the benefits of dense arrays and auto-detection by backprojection for aftershock studies. And finally, the reduced detection threshold and higher spatial resolution enabled the study of earthquake mechanisms and strain transfer at an unprecedented small scale.

Backprojection imaging has recently become a practical method for local earthquake detection and location due to the deployment of densely sampled, continuously recorded, local seismograph arrays. While backprojection sometimes utilizes the full seismic waveform, the waveforms are often pre-processed and simplified to overcome imaging challenges. Real data issues include aliased station spacing, inadequate array aperture, inaccurate velocity model, low signal-to-noise ratio, large noise bursts and varying waveform polarity. We compare the performance of backprojection with four previously used data pre-processing methods: raw waveform, envelope, short-termaveraging/long-termaveraging and kurtosis. Our primary goal is to detect and locate events smaller than noise by stacking prior to detection to improve the signal-to-noise ratio. The objective is to identify an optimized strategy for automated imaging that is robust in the presence of real-data issues, has the lowest signal-to-noise thresholds for detection and for location, has the best spatial resolution of the source images, preserves magnitude, and considers computational cost. Imaging method performance is assessed using a real aftershock data set recorded by the dense AIDA array following the 2011 Virginia earthquake. Our comparisons show that raw-waveform backprojection provides the best spatial resolution, preserves magnitude and boosts signal to detect events smaller than noise, but is most sensitive to velocity error, polarity error and noise bursts. On the other hand, the other methods avoid polarity error and reduce sensitivity to velocity error, but sacrifice spatial resolution and cannot effectively reduce noise by stacking. Of these, only kurtosis is insensitive to large noise bursts while being as efficient as the raw-waveformmethod to lower the detection threshold; however, it does not preserve the magnitude information. For automatic detection and location of events in a large data set, we therefore recommend backprojecting kurtosis waveforms, followed by a second pass on the detected events using noise-filtered raw waveforms to achieve the best of all criteria.

Methods for the efficient representation of fracture response in geoelectric models impact an impressively broad range of problems in applied geophysics. We adopt the recently-developed hierarchical material property representation in finite element analysis (Weiss, 2017) to model the electrostatic response of a discrete set of vertical fractures in the near surface and compare these results to those from anisotropic continuum models. We also examine the power law behavior of these results and compare to continuum theory. We find that in measurement profiles from a single point source in directions both parallel and perpendicular to the fracture set, the fracture signature persists over all distances. Furthermore, the homogenization limit (distance at which the individual fracture anomalies are too small to be either measured or of interest) is not strictly a function of the geometric distribution of the fractures, but also their conductivity relative to the background. Hence, we show that the definition of “representative elementary volume”, that distance over which the statistics of the underlying heterogeneities is stationary, is incomplete as it pertains to the applicability of an equivalent continuum model. We also show that detailed interrogation of such intrinsically heterogeneous models may reveal power law behavior that appears anomalous, thus suggesting a possible mechanism to reconcile emerging theories in fractional calculus with classical electromagnetic theory.