On the use of interferometric synthetic aperture radar for characterizing the response of reservoirs to fluid extraction and injection at wells
Keywords: Geophysics.

Interferometric synthetic aperture radar (InSAR) is a powerful tool used to measure displacements of the Earth's surface over expansive areas and with high temporal (6-24 days) and spatial (5-20 m) resolution. One important application is the management of natural resources and hazards related to the injection and production of fluids. Ground deformation begins within the reservoir as a response to changes in fluid pressure, and propagates to the surface as either subsidence (ground sinking) or uplift. This deformation can damage infrastructure, produce ground fissures, induce earthquakes, and affect fluid availability. InSAR can be used to identify these hazards and characterize the reservoir response to well activity, knowledge which can be used to develop tailored management practices. However, our analyses are only as good as the data we work with. We first identify and characterize an overlooked error source in InSAR and its derived time series: aliasing during 2D phase unwrapping. Phase unwrapping refers to the process of transforming the InSAR measurement -- the phase difference between two satellite passes, wrapped to a 2π ambiguity -- to the absolute phase relative to a reference point. We show that aliasing occurs when we do not adequately sample the true displacement field, resulting in a reconstructed (unwrapped) phase field that is different than the true signal. Our work demonstrates the condition that lead to aliasing, namely, when true phase gradients greater than π radians form a closed loop. Importantly, aliasing results in a biased magnitude-loss that is proportional to the number of high-gradient (> π) loops encircling the pixel. Given a displacement field, the occurrence of a high-gradient loop in an interferogram is influenced by the radar system wavelength, spatial resolution, imaging geometry, and the local noise level. Furthermore, spatial filtering may induce aliasing because it decreases the spatial resolution and, consequently, the physical gradient tolerance. We then extend our findings on aliasing to the effects of including aliased images in small-baseline subset (SBAS) time series generation. We find that aliasing has an intimate relationship with the time between image acquisitions forming a given interferogram (the temporal baseline). Often, aliasing errors increase with increasing temporal baseline, so we observe a systematic decreases in SBAS solution magnitudes and a spatiotemporal distortion of displacement patterns as we increase the maximum temporal baseline used in our calculations. However, Sentinel-1 observations in three study areas (Kilauea Volcano, HI, the Delaware Basin, TX, and California's Central Valley) highlight that some of the best time series solutions with respect to ground-truth include long-temporal baseline interferograms and others require their explicit exclusion. This indicates that the best set of phases to use in SBAS not only varies between study areas, but may even be unique to each pixel. Next we present a case study of reservoir characterization with InSAR in the Delaware Basin, TX, an expansive oil field in the Permian Basin. The motivation for our analysis is a marked increase in earthquake frequency since a revitalization of oil pumping in 2010 with horizontal wells. Our work shows widespread deformation related to oil and gas activity, some of which can be directly related to volume changes from pumping and injection through the correlation of InSAR time series with monthly well volumes. Deformation primarily due to volume change near wells is prevalent in the northern portion basin, where there is a notable absence of earthquake activity. However, the southeastern portion of the basin displays short-wavelength, curvilinear displacement features that do not correlate temporally or spatially with well locations or activity in any obvious way. Rather, these features are spatially correlated with trends in seismicity and the local stress conditions, which indicates that they may be the surface expression of slip on normal faults. We use analytic models of edge dislocations to test this hypothesis in a small study area. Our final three-fault, patched model reproduces the spatial patterns and magnitude of the main linear feature in both vertical and east-west horizontal displacement components. All three faults are high-angle (75◦) and span the Delaware Mountain group (1000-2000 m depth). Two of the faults dip toward one another in a graben structure. The areas of largest fault slip (up to 23 cm) are spatially correlated with nearby disposal wells, linking shallow wastewater injection to the reactivation of pre-existing faults. Though all fault planes contain the largest earthquakes in the study area, our analysis indicates that the fault slip is largely aseismic (stable), an important response to include in models of induced seismicity