*Electronic Supplement:*Tables of *V*_{S} profiles and metadata for profile database (PDB) and site database (SDB) locations.

*Electronic Supplement:*Figures of Interferometric Synthetic Aperture Radar (InSAR) data, model, and resolution.

Here, we analyze 1-Hz Global Positioning System (GPS) data from the 24 January 2016 *M*_{w} 7.1 Iniskin earthquake, which ruptured 125 km under Cook Inlet in Alaska, to motivate the inclusion of GNSS-derived *S*-wave measurements into the trigger algorithms of EEW systems in regions lacking dense early-warning instrumentation networks. We derive a relationship between earthquake depth and distance to help determine whether GNSS *S*-wave observations could expedite warnings to specific locations.

Because the Iniskin earthquake was deep, by the time the *S* wave reached the surface, the *P* wave had already been observed over a wide region, limiting the potential for unique contributions from GNSS data to this event. For the same earthquake occurring near the surface, however, *S* waves derived from GNSS data have the potential to increase the warning time. Regardless of the depth, the Iniskin earthquake is an excellent example of the utility of GNSS in rapidly assessing the magnitude, improving predictions of ground shaking, and estimating the area of impact for the earthquake.

*Electronic Supplement:*Description of seismic-velocity model and wave propagation code and interpretation of directivity effects, and figures of fault geometry, Z1 and Z2.5 depths, effects of rupture speed variations on directivity effects and amplifications.

*Electronic Supplement:*Figures of seismograms and multichannel deconvolution (MCD) apparent source time functions (ASTFs) from the Kamaishi earthquake sequence.

*Electronic Supplement:*Animations of the waveform envelope fits and predicted shaking intensity for both the 2014 *M*_{w} 6.0 Napa earthquake and the 1 July 2015 false alarm, along with the details of all reports from all earthquake early warning (EEW) algorithms for both events, as well as for the 2014 *M*_{w} 6.8 off Cape Mendocino earthquake.

*Electronic Supplement:*Earthquake catalogs.

Assuming temporal step-function pressures and ignoring near-field nonlinear elasticity, shock waves, and reverberations in the air-filled cavity, we express the displacement fields for either explosion or tectonic release, in terms of a multipole expansion of spherical eigenvectors. This is done for both axisymmetric ellipsoidal and right cylindrical cavities. As in Ben-Menahem and Mikhailov, at long wavelengths the dominant spherical harmonics are found to be, at most, second order. This is true even for extreme geometries such as the finite-length line source and the disk. For long-period surface waves, the first two terms suffice. At very long periods, the radiation field is the same as that due to the rapid formation of a spherical cavity in the presence of tensile stress, and differs by only a sign in case the initial stress is compressive instead. The two sources differ only in their respective second-order moment tensor time functions.

]]>*Electronic Supplement:*OxCal code and figures of topographic profiles across fault scarps reactivated during the 2002 Denali fault earthquake, OxCal models of published age constraints on tephra exposed at the Wetfan trench site, and map showing locations and data used to measure near-surface dips of Susanna Glacier fault in the vicinity of the Wetfan trench site.

We find that earthquakes of magnitude *M*_{w}>5.8 can be recorded by GPS in real time at 10 km distance, that is, their Fourier spectrum exceeds the noise of the instruments enough to be used in strong-motion seismology. Postprocessing of GPS time series lowers the noise and can improve the minimum observable magnitude by 0.1–0.2. As GPS receivers can record at higher rates (>10 Hz), we investigate which sampling rate is sufficient to optimally record earthquake signals and conclude that a minimum sampling rate of 5 Hz is recommended. This is driven by recording events at short distances (below 10 km for magnitude 6 events and below 30 km for magnitude 7 events).

Furthermore, the maximum ground velocity derived from GPS is compared with the actual PGV for synthetic signals from the stochastic simulations and the 2008 *M*_{w} 6.9 Iwate earthquake. The proposed model, confirmed by synthetic and empirical data, shows that a reliable estimate of PGV for events of about magnitude 7 and greater can be basically retrieved by GPS in real time and could be included, for instance, in ShakeMaps for aiding postevent disaster management.

*Electronic Supplement:*Forward modeling details, and model selection with Bayesian information criterion. Figures showing parameterization of the noise covariance matrix using autocorrelations of noise seismograms, algorithm flowchart, and sampled centroid locations in four inversions of The Geysers earthquake.