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Abstract: The fast expansion of seismic arrays has improved our ability to understand the Earth's internal structure and dynamics at various spatial scales. This thesis applies both conventional and novel approaches to dense array recordings to address major questions in (1) earthquake location and source mechanisms, (2) upper-crustal seismic structure, (3) subduction zone dynamics, and (4) variations in the elastic properties of upper mantle transition zone discontinuities. We present the first example of a quick-response nodal experiment in western Canada to investigate the spatiotemporal characteristics of a hydraulic fracturing-induced earthquake swarm in central Alberta at a local scale. A high-precision earthquake catalog is constructed using a machine-learning phase picker and a sequential earthquake association and location method. The outcomes capture the geometry of the reactivated faults and highlight the significance of trailing seismicity in hazard assessment. In Chapter 3, a regional background survey of southwestern Canada based on ambient noise tomography reveals lateral variations in both velocity and anisotropy with spatial affinities to major geological domains. We observe strong radial anisotropy in the southern Canadian Cordillera due to crustal extension similar to that observed in the western United States, while the anisotropic anomaly in the Cordilleran foreland may have resulted from horizontal compression during the plate convergence at the western margin of the North American craton. In the third component of the thesis, a self-consistent model of subduction dynamics at transition zone depths beneath South America is presented, through a combined analysis of travel times and amplitudes of underside shear wave reflections. Our updated topography model of transition zone discontinuities suggests contrasting styles of slab-transition zone interaction. A joint analysis of seismic data and mineral physics modeling provides observational evidence for thermochemical anomalies within the mantle. Finally, we expand the underside reflection data set for global coverage, and a novel amplitude-versus-offset inversion is applied to map lateral variations in density jump across the 660-km discontinuity. Major subduction zones are generally featured by low density jumps; this implies a compositional difference with excess basalt relative to the global average.

Incoherent superposition of gravitational waves from a large number of unresolved sources gives rise to the stochastic gravitational-wave background. This background could be of cosmological origin, produced by early universe events such as inflation. It could also be of astrophysical origin, produced by a large number of astrophysical objects such as binary neutron stars and black holes. Detection of the stochastic gravitational wave background would therefore provide information both about the state of the universe at its earliest moments and about its evolution at later times. Long gravitational-wave transients are gravitational waves whose times scales range from minutes to weeks. Such long gravitational-wave transients are predicted by a variety of astrophysical models, including stellar core collapse and accretion onto newly formed proto-neutron stars and black holes. Detection of long transient gravitational waves would provide clues about various dynamical process occurring in these astrophysical objects. In this thesis, we describe methods to search for stochastic and long transient gravitational waves in interferometric gravitational-wave detector data and present results obtained by using the Laser Interferometer Gravitational-wave Observatory (LIGO) data acquired during its fifth science run.