We present a theory for the multiple scattering of light by obstacles situated over a rough surface. This problem is important for applications in biological and chemical sensors. To keep the formulation of this theory simple, we study scalar waves. This theory requires knowledge of the scattering operator (t-matrix) for each of the obstacles as well as the reflection operator for the rough surface. The scattering operator gives the field scattered by the obstacle due to an exciting field incident on the scatterer. The reflection operator gives the field reflected by the rough surface due to an exciting field incident on the rough surface. We apply this general theory for the special case of point scatterers and a slightly rough surface with homogeneous Dirichlet and Neumann boundary conditions. We show examples that demonstrate the utility of this theory.

The origins of ultralow velocity zones, small-scale structures with extremely low seismic velocities found near the core–mantle boundary, remain poorly understood. One hypothesis is that they are mobile features that actively participate in mantle convection, but mantle flow adjacent to ultralow velocity zones is poorly understood and difficult to infer. Although deep mantle anisotropy observations can be used to infer mantle flow patterns, ultralow velocity zone structures are often not examined jointly with these observations. Here we present evidence from seismic waves that sample the lowermost mantle beneath the Himalayas for both an ultralow velocity zone and an adjacent region of seismic anisotropy associated with mantle flow. By modelling realistic mineral physics scenarios using global wavefield simulations, we show that the identified seismic anisotropy is consistent with horizontal shearing orientated northeast–southwest. Based on tomographic data of the surrounding mantle structure, we suggest that this southwestward flow is potentially linked to the remnants of the subducted slab impinging on the core–mantle boundary. The detected ultralow velocity zone is located at the southwestern edge of this anisotropic region, and therefore potentially affected by strong mantle deformation in the surrounding area.

Abstract: The dynamics of Earth's D″ layer at the base of the mantle plays an essential role in Earth's thermal and chemical evolution. Mantle convection in D″ is thought to result in seismic anisotropy; therefore, observations of anisotropy may be used to infer lowermost mantle flow. However, the connections between mantle flow and seismic anisotropy in D″ remain ambiguous. Here, we calculate the present‐day mantle flow field in D″ using 3D global geodynamic models. We then compute strain, a measure of deformation, outside the two large‐low velocity provinces (LLVPs) and compare the distribution of strain with previous observations of anisotropy. We find that, on a global scale, D″ materials are advected toward the LLVPs. The strains of D″ materials generally increase with time along their paths toward the LLVPs and toward deeper depths, but regions far from LLVPs may develop relative high strain as well. Materials in D″ outside the LLVPs mostly undergo lateral stretching, with the stretching direction often aligning with mantle flow direction, especially in fast flow regions. In most models, the depth‐averaged strain in D″ is >0.5 outside the LLVPs, consistent with widespread observations of seismic anisotropy. Flow directions inferred from anisotropy observations often (but not always) align with predictions from geodynamic modeling calculations.

Abstract: Shear‐wave splitting measurements are commonly used to resolve seismic anisotropy in both the upper and lowermost mantle. Typically, such techniques are applied to SmKS phases that have reflected (m‐1) times off the underside of the core‐mantle boundary before being recorded. Practical constraints for shear‐wave splitting studies include the limited number of suitable phases as well as the large fraction of available data discarded because of poor signal‐to‐noise ratios (SNRs) or large measurement uncertainties. Array techniques such as beamforming are commonly used in observational seismology to enhance SNRs, but have not been applied before to improve SmKS signal strength and coherency for shear wave splitting studies. Here, we investigate how a beamforming methodology, based on slowness and backazimuth vespagrams to determine the most coherent incoming wave direction, can improve shear‐wave splitting measurement confidence intervals. Through the analysis of real and synthetic seismograms, we show that (a) the splitting measurements obtained from the beamformed seismograms (beams) reflect an average of the single‐station splitting parameters that contribute to the beam; (b) the beams have (on average) more than twice as large SNRs than the single‐station seismograms that contribute to the beam; (c) the increased SNRs allow the reliable measurement of shear wave splitting parameters from beams down to average single‐station SNRs of 1.3. Beamforming may thus be helpful to more reliably measure splitting due to upper mantle anisotropy. Moreover, we show that beamforming holds potential to greatly improve detection of lowermost mantle anisotropy by demonstrating differential SKS–SKKS splitting analysis using beamformed USArray data.

Abstract: Observations of seismic waves that have passed through the Earth's lowermost mantle provide insight into deep mantle structure and dynamics, often on relatively small spatial scales. Here we use SKS, S2KS, S3KS, and PKS signals recorded across a large region including the United States, Mexico, and Central America to study the deepest mantle beneath large swaths of North America and the northeastern Pacific Ocean. These phases are enhanced via beamforming and then used to investigate polarization‐ and propagation direction‐dependent shear wave speeds (seismic anisotropy). A differential splitting approach enables us to robustly identify contributions from anisotropy. Our results show strong seismic anisotropy in approximately half of our study region, indicating that anisotropy may be more prevalent than commonly thought. In some regions, the anisotropy may be induced by flow driven by sinking cold slabs, and in other, more compact regions, by upwelling flow. Measured splitting due to lowermost mantle anisotropy is sufficiently strong to be non‐negligible in interpretations of SKS splitting due to upper mantle anisotropy in certain regions, which may prompt future re‐evaluations of upper mantle anisotropy beneath North and Central America.

Abstract: Low‐velocity anomalies in the upper mantle beneath eastern North America, including the Northern Appalachian Anomaly (NAA), the Central Appalachian Anomaly (CAA), and the weaker Southern Coastal Anomaly (SCA), have been characterized by many continent‐scale and regional seismic studies. Different models have been proposed to explain their existence beneath the passive margin of eastern North America, variously invoking the past passage of hot spot tracks, modern upwelling due to edge‐driven convection, or other processes. Depending on the nature and origin of these anomalies, they may influence, and/or be influenced by, the mantle transition zone (MTZ) structure beneath them. Previous receiver function studies have identified an overall thinner MTZ beneath the eastern margin of the US than beneath the continental interior. In this study, we resolve the MTZ geometry beneath these low‐velocity anomalies in unprecedented detail using the scattered wavefield migration technique. We find substantially thinned MTZ beneath the NAA and the CAA, and a moderately thinned MTZ beneath the SCA. In all cases, the thinning is achieved via a minor depression of the 410‐km discontinuity and a major uplift of the 660‐km discontinuity, which suggests the presence of a series of MTZ‐penetrating deep upwellings beneath eastern North America. The upwellings beneath eastern North America and a similar style upwelling beneath Bermuda may initiate from ponded thermally buoyant materials below the MTZ fed by hot return flows from the descending Farallon slab in the deep mantle.

We present a simple, ultra-rapid and robust method to create sharp nanostructures-nanopetals-in a shape memory polymer substrate demonstrating unprecedented enhancements for surface enhanced sensing over large surface areas. These bimetallic nanostructures demonstrate extremely strong surface plasmon resonance effects due to the high density multifaceted petal structures that increase the probability of forming nanogaps. We demonstrate that our nanopetals exhibit extremely strong surface plasmons, confining the emission and enhancing the fluorescence intensity of the nearby high-quantum yield fluorescein by >4000×. The enhancements are confined to the extremely small volumes at the nanopetal borders. This enables us to achieve single molecule detection at relatively high and physiological concentrations. © 2010 American Institute of Physics.

(Figure Presented) Controllable biaxial and uniaxial nanowrinkles (see figure) are fabricated by a simple two-step approach - metal deposition and subsequent heating - based on shape memory polymer (prestressed polystyrene) sheets. The wavelengths of the wrinkles can be tuned by controlling the thickness of deposited metal. The ready integration of the nanowrinkles into microchannels and their effectiveness in surface enhanced sensing is demonstrated. © 2009 Wiley-VCH Verlag GmbH & Co. KGaA.