Graph theory is useful for estimating time-dependent model parameters via weighted least-squares using interferometric synthetic aperture radar (InSAR) data. 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 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. (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 +/- 0.6) x 10^6 m^3/yr. 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 wrapped phase or wrapped residuals. Date of final oral examination: 05/19/2016 This thesis is approved by the following members of the Final Oral Committee: Kurt L. Feigl, Professor, Geoscience Michael Cardiff, Assistant Professor, Geoscience Clifford H. Thurber, Vilas Distinguished Professor, Geoscience

Detailed geologic mapping, structural analysis, and well data have been integrated to elucidate the stratigraphic framework and structural setting of the Tuscarora geothermal area. Tuscarora is an amagmatic geothermal system that lies in the northern part of the Basin and Range province, ~15 km southeast of the Snake River Plain and ~90 km northwest of Elko, Nevada. The Tuscarora area is dominated by late Eocene to middle Miocene volcanic and sedimentary rocks, all overlying Paleozoic metasedimentary rocks. A geothermal power plant was constructed in 2011 and currently produces 18 MWe from an ~170 degrees C reservoir in metasedimentary rocks at a depth of ~1430 m. Analysis of drill core reveals that the subsurface geology is dominated to depths of ~700-1000 m by intracaldera deposits of the Eocene Big Cottonwood Canyon caldera, including blocks of basement-derived megabreccia. Furthermore, the Tertiary-Paleozoic nonconformity within the geothermal field has been recognized as the margin of this Eocene caldera. Structural relations combined with geochronologic data from previous studies indicate that Tuscarora has undergone extension since the late Eocene, with significant extension in the late Miocene-Pliocene to early Pleistocene. Kinematic analysis of fault slip data reveal an east-west-trending least principal paleostress direction, which probably reflects an earlier episode of Miocene extension. Two distinct structural settings at different scales appear to control the geothermal field. The regional structural setting is a 10-km wide complexly faulted left step or relay ramp in the west-dipping range-bounding Independence-Bull Run Mountains normal fault system. Geothermal activity occurs within the step-over where sets of east- and west-dipping normal faults overlap in a northerly trending accommodation zone. The distribution of hot wells and hydrothermal surface features, including boiling springs, fumaroles, and siliceous sinter, indicate that the geothermal system is restricted to the narrow (< 1 km) axial part of the accommodation zone, where permeability is maintained at depth around complex fault intersections. Shallow up-flow appears to be focused along several closely spaced steeply west-dipping north-northeast-striking normal faults within the axial part of the accommodation zone. These faults are favorably oriented for extension and fluid flow under the present-day northwest-trending regional extension direction indicated by previous studies of GPS geodetic data, earthquake focal mechanisms, and kinematic data from late Quaternary faults. The recognition of the axial part of an accommodation zone as a favorable structural setting for geothermal activity may be a useful exploration tool for development of drilling targets in extensional terranes, as well as for developing geologic models of known geothermal fields. Preliminary analysis of broad step-overs similar to Tuscarora reveals that geothermal activity occurs in a variety of subsidiary structural settings within these regions. In addition, the presence of several high-temperature systems in northeastern Nevada demonstrates the viability of electrical-grade geothermal activity in this region despite low present-day strain rates as indicated by GPS geodetic data. Geothermal exploration potential in northeastern Nevada may therefore be higher than previously recognized.