Abstract:
Wave gradiometry is an array processing technique using the shape of seismic wavefields captured by dense seismic arrays to estimate fundamental wave propagation characteristics [Langston, 2007a,b; Liang and Langston, 2009]. We first explore a compatibility relation that links the spatial gradients to displacements and velocity seismograms through two unknown coefficients: Aâƒ— and Bâƒ—. We show that the Aâƒ—-coefficient corresponds to the gradient of logarithmic amplitude and the Bâƒ— -coefficient corresponds approximately to the local wave slowness. These coefficients are solved through iterative, damped least- squares inversions to provide estimates of four gradiometry products: dynamic phase velocity, back-azimuth, radiation pattern and geometrical spreading. Furthermore, Liu and Holt [2015] have advanced the technique by estimating the spatial gradients in a continuous field and combining wave gradiometry with Helmholtz equation solutions to obtain structural phase velocity. Compared with the dynamic phase velocity obtained in traditional methods, the structural phase velocity is independent of specific geometry of wavefields or source properties and thus itâ€™s more appropriate for surface wave tomography studies [Wielandt, 1993; Friederich et al., 1995; Lin and Ritzwoller, 2011a; Jin and Gaherty, 2015; Liu and Holt, 2015]. The Aâƒ— and Bâƒ—-coefficients are then interpolated to explore a second compatibility relation through the Helmholtz equation solutions. For most wavefields passing through the eastern U.S., we show that the Aâƒ— vectors are generally orthogonal to the Bâƒ— vectors. Where they are not completely orthogonal, there is a strong positive correlation between âˆ‡ Â· Bâƒ— and changes in geometrical spreading, which can be further linked with areas of strong energy focusing and defocusing. We provide Rayleigh wave isotropic structural phase velocities for 15 period bands between 20 s and 150 s, by stacking and averaging results from 37 earthquakes. We observe a velocity change for 20 s - 30 s Rayleigh waves, along the approximate boundary of the early Paleozoic continental margin. The most prominent features in the eastern U.S. are two low velocity anomalies, one centered over the central Appalachians (referred to as the Central Appalachian Anomaly, CAA) where Eocene basaltic volcanism occurred [Schmandt and Lin, 2014; Pollitz and Mooney, 2016], and the other within the northeastern U.S. (referred to as the Northeast Anomaly, NEA), possibly associated with the Great Meteor Hotspot track [Eaton and Frederiksen, 2007; Villemaire et al., 2012]. We continue to apply wave gradiometry to six earthquakes centered in Gulf of Cal- ifornia with similar source locations, focal mechanisms, depths and magnitudes. These separate events occurred over a time frame such that their wavefields were captured by the entire USArray Transportable Array. This analysis gives us an opportunity to inves- tigate the characteristics of a wavefield, generated by a relatively consistent source, that propagates across the entire contiguous United States. We then apply wave gradiometry methods to synthetic waveforms obtained from two crust and upper mantle models of the U.S., a relatively smoothed model US00, and an updated U.S. model US22 based on adjoint tomography. Given the correlations of gradiometry parameters from real records and synthetic data, and the similarity of source mechanisms for these six events, we com- bine gradiometry parameters for all events. This combined solution shows the wavefield characteristics from a single source, which defines the patterns of Aâƒ— and Bâƒ— vector fields and their spatial derivatives throughout the contiguous U.S. We show that the Aâƒ— vectors generally point along the steepest amplitude gradient towards amplitude highs, and they are generally orthogonal to the Bâƒ— vectors. These fields demonstrate the links between energy focusing/defocusing and amplitude variations. We are able to show that gradiometry parameters are sensitive to the underlying structures along with subtle variations in source radiation patterns. We thus argue these parameters can be used for determining viable structural models in the future. Furthermore, gradiometry parameters embedded in the transport equation, obtained from the imaginary part of the Helmholtz equation solutions, yields estimates of local amplification factors, which can potentially provide new constraints on the variations of elastic velocities and densities. We finally combine wave gradiometry and Helmholtz equation solutions to process wavefields from 696 earthquakes between 2006 and 2014, with magnitudes larger than 5.0 and focal depths shallower than 50 km, recorded by 1,739 USArray TA stations. After stacking, averaging, and smoothing Rayleigh wave structural phase velocities from all events, we obtain isotropic velocities and variances across the contiguous U.S. for the period range of 20 s - 150 s. The structural phase velocities generally increase with period from 3.2 Â± 0.1 km/s (20 s) to 4.5 Â± 0.2 km/s (150 s) and are consistent with the theoretical dispersion curves [Dahlen and Tromp, 1998]. Furthermore, we have identified several regions with potentially new constraints. For instance, we observe a belt of lower velocities along the Great Plains and Superior Uplands (SU) for the longest periods of 120 s - 150 s. The strong anomalies within the Central Appalachian Anomaly (CAA) and Northeast Anomaly (NEA) persist for the periods of 40 s - 150 s [Schmandt and Lin, 2014; Porter et al., 2016]. We observe a semi-continuous band of lower phase velocities between South Georgia Rift (SGR) and NEA for the longest periods of 140 s - 150 s. These patterns may be signatures in the lower lithosphere left by the Central Atlantic Magmatic Province (CAMP) [Heffner et al., 2012; Pollitz and Mooney, 2016], or due to hotspot interaction with the thermal-chemical lithosphere [Chu et al., 2013]. The gradiometry parameters and products are archived for future studies to better constrain viable 3-D structural models. In order to better understand the tectonic evolution in the North American continent, Porter et al. [2016] utilized seismic data recorded by USArray TA stations to build three- dimensional shear velocity models for the continental United States. The Rayleigh wave structural phase velocities are estimated using ambient noise tomography at short periods (8 s - 40 s) and wave gradiometry at longer periods (20 s - 150 s), which allows for a sensitivity to a broader depth range within the crust and upper mantle (6 - 200 km). The high-resolution model provides us key information about orogenic and postorogenic events on the evolution of the lithosphere beneath those velocity anomaly regions [Porter et al., 2016]. The lower and higher velocity regions in the western, central and eastern U.S. are all consistent with major geological provinces. The most prominent feature is the contrast in crustal and upper mantle structure between the relatively slow western and relatively fast eastern U.S. for all depths we investigated, similar to our Rayleigh wave structural phase velocity plots [Liu and Holt, 2015].