Ground surface deformations detected with interferometric synthetic aperture radar provide valuable information for inferring subsurface reservoir processes that are difficult to observe directly. This study aims at building a reservoir model that honors the available geological, hydrological, and geomechanical data and also produces ground surface deformation consistent with interferometric synthetic aperture radar measurements at the Raft River Geothermal Field. In the thermo‐hydro‐mechanical coupled model developed, the reservoir deforms as a result of the rock's poroelastic response to changes in hydrologic pressure and thermal expansion/contraction. The results indicate that the observed deformation is the result of pressure decrease in the deep production reservoir and pressure increase in a shallower reservoir that accommodates the injected fluid (likely in the Salt Lake Formation). The combination of the uplift around injection wells with subsidence around the production wells, affected by the Bridge Fault as a flow barrier, creates a complex pattern of surface deformation in which the center of subtle subsidence significantly deviates from the location of the production wells. A parametric study suggests that (a) the Bridge Fault Zone is likely a flow barrier, (b) the surface deformation appears to be insensitive to the presence of the Narrows Structure, and (c) additional flow barriers likely exist to shape the flow system. This case study demonstrates the utility of a high‐fidelity forward model that honors available known information and thermo‐hydro‐mechanical coupled processes in understanding geothermal reservoir characteristics.

Graph theory is useful for analyzing time-dependent model parameters estimated from interferometric synthetic aperture radar (InSAR) data in the temporal domain. Plotting acquisition dates (epochs) as vertices and pair-wise interferometric combinations as edges defines an incidence graph. The edge-vertex incidence matrix and the normalized edge Laplacian matrix are factors in the covariance matrix for the pair-wise data. Using empirical measures of residual scatter in the pair-wise observations, we estimate the relative variance at each epoch by inverting the covariance of the pair-wise data. We evaluate the rank deficiency of the corresponding least-squares problem via the edge-vertex incidence matrix. We implement our method in a MATLAB software package called GraphTreeTA available on GitHub (https://github.com/feigl/gipht). We apply temporal adjustment to the data set described in Lu et al. (Geophys Res Solid Earth 110, 2005) at Okmok volcano, Alaska, which erupted most recently in 1997 and 2008. The data set contains 44 differential volumetric changes and uncertainties estimated from interferograms between 1997 and 2004. Estimates show that approximately half of the magma volume lost during the 1997 eruption was recovered by the summer of 2003. Between June 2002 and September 2003, the estimated rate of volumetric increase is \((6.2 \, \pm \, 0.6) \times 10^6~\mathrm{m}^3/\mathrm{year} \). Our preferred model provides a reasonable fit that is compatible with viscoelastic relaxation in the five years following the 1997 eruption. Although we demonstrate the approach using volumetric rates of change, our formulation in terms of incidence graphs applies to any quantity derived from pair-wise differences, such as range change, range gradient, or atmospheric delay.

We measure transient deformation at Coso geothermal field using interferometric synthetic aperture radar (InSAR) data acquired between 2004 and 2016 and relative positions estimated from global positioning system (GPS) to quantify relationships between deformation and pumping. We parameterize the reservoir as a cuboidal sink and solve for best-fitting reservoir dimensions and locations before and after 2010 in accordance with sustainability efforts implemented in late 2009 at the site. Time-series analysis is performed on volume changes estimated from pairs of synthetic aperture radar (SAR) and daily GPS data. We identify decreasing pore-fluid pressure as the dominant mechanism driving the subsidence observed at Coso geothermal field. We also find a significant positive correlation between deformation and production rate.

Detecting surface deformation associated with low-magnitude ($M_w\le 5$) seismicity using interferometric synthetic aperture radar (InSAR) is challenging due to the subtlety of the signal and the often challenging imaging environments. However, low-magnitude earthquakes are potential precursors to larger seismic events, and thus characterizing the crustal displacement associated with them is crucial for regional seismic hazard assessment. We combine InSAR time-series techniques with a Deep Learning (DL) autoencoder denoiser to detect the magnitude and extent of crustal deformation from the $M_w=3.4$ Gallina, New Mexico earthquake that occurred on 30 July 2020. Although InSAR alone cannot detect event-related deformation from such a low-magnitude seismic event, application of the DL method reveals maximum displacements as small as (±2.5 mm) in the vicinity of both the fault and earthquake epicenter without prior knowledge of the fault system. This finding improves small-scale displacement discernment with InSAR by an order of magnitude relative to previous studies. We additionally estimate best-fitting fault parameters associated with the observed deformation. The application of the DL technique unlocks the potential for low-magnitude earthquake studies, providing new insights into local fault geometries and potential risks from higher-magnitude earthquakes. This technique also permits low-magnitude event monitoring in areas where seismic networks are sparse, allowing for the possibility of global fault deformation monitoring.

Brady Hot Springs geothermal field has exhibited subsidence, as measured by interferometric synthetic aperture radar (InSAR). Previous studies have examined both the temporal evolution of the deformation from 2004 through 2016 and the spatial extent of the deformation, directly relating the observed subsidence to volumetric changes below the surface. We extend the modeling at Brady to analyze a data set of interferometric pairs spanning from the end of 2003 through 2018. We examine spatial and temporal trends in the observed deformation by time‐series analysis of each of the 1,656 cubic voxels in a parameterized elastic dislocation model to identify areas where the subsurface volume changes as a function of time. Joint time‐series analysis of Global Positioning System and InSAR pairs confirm significant changes in rates of volume change during time intervals when well operations were varied. The rate of subsidence increases with increased injection, consistent with the identification of thermal contraction of the rock matrix as the dominant driving mechanism. Conversely, the modeled volume increases when pumping ceases, suggesting thermal expansion of the rock matrix.