We present tomographic evidence for the existence of deep-mantle thermal convection plumes. P-wave velocity images show at least six well-resolved plumes that extend into the lowermost mantle: Ascension, Azores, Canary, Easter, Samoa, and Tahiti. Other less well-resolved plumes, including Hawaii, may also reach the lowermost mantle. We also see several plumes that are mostly confined to the upper mantle, suggesting that convection may be partially separated into two depth regimes. All of the observed plumes have diameters of several hundred kilometers, indicating that plumes convey a substantial fraction of the internal heat escaping from Earth.

Summary We use body wave ray theory in conjunction with the Born approximation tocompute 3‐D Fréchet kernels for finite‐frequency seismic traveltimes, measured by cross‐correlation of a broad‐band waveform with a spherical earth synthetic seismogram. Destructive interference among adjacent frequencies in the broad‐band pulse renders a cross‐correlation traveltime measurement sensitive only to the wave speed in a hollow banana‐shaped region surrounding the unperturbed geometrical ray. The Fréchet kernel expressing this sensitivity is expressed as a double sum over all forward‐propagating body waves from the source and backward‐propagating body waves from the receiver to every single scatterer in the vicinity of this central ray. The kernel for a differential traveltime, measured by cross‐correlation of two phases at the same receiver, is simply the difference of the respective single‐phase kernels. In the paraxial approximation, an absolute or differential traveltime kernel can be computed extremely economically by implementing a single kinematic and dynamic ray trace along each source‐to‐receiver ray.

Summary 3‐D Born–Fréchet traveltime kernel theory is recast in the context of scalar‐wave propagation in a smooth acoustic medium, for simplicity. The predictions of the theory are in excellent agreement with ‘ground truth’ traveltime shifts, measured by cross‐correlation of heterogeneous‐medium and homogeneous‐medium synthetic seismograms, computed using a parallelized pseudospectral code. Scattering, wave‐front healing and other finite‐frequency diffraction effects can give rise to cross‐correlation traveltime shifts that are in significant disagreement with geometrical ray theory, whenever the cross‐path width of wave‐speed heterogeneity is of the same order as the width of the banana–doughnut Fréchet kernel surrounding the ray. A concentrated off‐path slow or fast anomaly can give rise to a larger traveltime shift than one directly on the ray path, by virtue of the hollow‐banana character of the kernel. The often intricate 3‐D geometry of the sensitivity kernels of P, PP, PcP, PcP2, PcP3, ? and P+pP waves is explored, in a series of colourful cross‐sections. The geometries of an absolute PP kernel and a differential PP−P kernel are particularly complicated, because of the minimax nature of the surface‐reflected PP wave. The kernel for an overlapping P+pP wave from a shallow‐focus source has a banana–doughnut character, like that of an isolated P‐wave kernel, even when the teleseismic pulse shape is significantly distorted by the depth phase interference. A numerically economical representation of the 3‐D traveltime sensitivity, based upon the paraxial approximation, is in excellent agreement with the ‘exact’ ray‐theoretical Fréchet kernel.

[1] The Pacific Northwest has undergone complex plate reorganization and intense tectono-volcanic activity to the east during the Cenozoic (last 65 Ma). Here we show new high-resolution tomographic images obtained using shear and compressional data from the ongoing USArray deployment that demonstrate first that there is a continuous, wholemantle plume beneath the Yellowstone Snake River Plain (YSRP) and second, that the subducting Juan de Fuca (JdF) slab is fragmented and even absent beneath Oregon. The analysis of the geometry of our tomographic models suggests that the arrival and emplacement of the large Yellowstone plume had a substantial impact on the nearby Cascadia subduction zone, promoting the tearing and weakening of the JdF slab. This interpretation also explains several intriguing geophysical properties of the Cascadia trench that contrast with most other subduction zones, such as the absence of deep seismicity and the trench-normal fast direction of mantle anisotropy. The DNA velocity models are available for download and slicing at http://dna.berkeley. edu. Citation: Obrebski, M., R. M. Allen, M. Xue, and S.-H.

S U M M A R YThe relation between the complex geological history of the western margin of the North American plate and the processes in the mantle is still not fully documented and understood. Several pre-USArray local seismic studies showed how the characteristics of key geological features such as the Colorado Plateau and the Yellowstone Snake River Plains are linked to their deep mantle structure. Recent body-wave models based on the deployment of the high density, large aperture USArray have provided far more details on the mantle structure while surfacewave tomography (ballistic waves and noise correlations) informs us on the shallow structure.Here we combine constraints from these two data sets to image and study the link between the geology of the western United States, the shallow structure of the Earth and the convective processes in mantle. Our multiphase DNA10-S model provides new constraints on the extent of the Archean lithosphere imaged as a large, deeply rooted fast body that encompasses the stable Great Plains and a large portion of the Northern and Central Rocky Mountains. Widespread slow anomalies are found in the lower crust and upper mantle, suggesting that low-density rocks isostatically sustain part of the high topography of the western United States. The Yellowstone anomaly is imaged as a large slow body rising from the lower mantle, intruding the overlying lithosphere and controlling locally the seismicity and the topography. The large E-W extent of the USArray used in this study allows imaging the 'slab graveyard', a sequence of Farallon fragments aligned with the currently subducting Juan de Fuca Slab, north of the Mendocino Triple Junction. The lithospheric root of the Colorado Plateau has apparently been weakened and partly removed through dripping. The distribution of the slower regions around the Colorado Plateau and other rigid blocks follows closely the trend of Cenozoic volcanic fields and ancient lithospheric sutures, suggesting that the later exert a control on the locus of magmato-tectonic activity today. The DNA velocity models are available for download and slicing at http://dna.berkeley.edu.

S U M M A R YThis paper presents a comparison of ray-theoretical and finite-frequency traveltime tomography for compressional waves. Our data set consists of 86 405 long-period P and PP-P traveltimes measured by cross-correlation. The traveltime of a finite-frequency wave is sensitive to anomalies in a hollow banana-shaped region surrounding the unperturbed ray path, with the sensitivity being zero on the ray. Because of the minimax nature of the surface-reflected PP wave, its sensitivity is more complicated. We compute the 3-D traveltime sensitivity efficiently by using the paraxial approximation in conjunction with ray theory and the Born approximation. We compare tomographic models with the same χ 2 fit for both ray theory and finite-frequency analysis. Depending on the depth and size of the anomaly, the amplitudes of the velocity perturbations in the finite-frequency tomographic images are 30-50 per cent larger than in the corresponding ray-theoretical images, demonstrating that wave front healing cannot be neglected when interpreting long-period seismic waves. The images obtained provide clear evidence that a limited number of hotspots are fed by plumes originating in the lower mantle.

[1] Tomographic models based on hypothetically infinite frequency ray interpretation of teleseismic travel time shifts have revealed a region of relatively low P and S wave speeds extending from shallow mantle to 400 km depth beneath Iceland. In reality, seismic waves have finite frequency bandwidths and undergo diffractive wave front healing. The limitation in ray theory leaves large uncertainties in the determinations of the magnitude and shape of the velocity anomaly beneath Iceland and its geodynamic implications. We developed a tomographic method that utilizes the banana-shaped sensitivity of finite frequency relative travel times from the paraxial kernel theory. Using available seismic data from the ICEMELT and HOTSPOT experiments, we applied the new method to image subsurface velocity structure beneath Iceland. Taking advantage that the sensitivity volume of broadband waveforms varies with frequency, we measured relative delay times in three frequency ranges from 0.03 to 2 Hz for P and 0.02 to 0.5 Hz for S waves. Given similar fit to data, the kernel-based models yield the root-mean-square amplitudes of P and S wave speed perturbations about 2-2.8 times those from ray tomography in the depths of 150-400 km. The kernel-based images show that a columnar low-velocity region having a lateral dimension of $250-300 km extends to the base of the upper mantle beneath central Iceland, deeper than that resolved by the ray-based studies. The improved resolution in the upper mantle transition zone is attributed to the deeper crossing of broad off-path sensitivity of travel time kernels than in ray approximation and frequency-dependent wave front healing as an intrinsic measure of the distance from velocity heterogeneity to receivers.

SUMMARY Wavefront healing is a ubiquitous diffraction phenomenon that affects cross‐correlation traveltime measurements, whenever the scale of the 3‐D variations in wave speed is comparable to the characteristic wavelength of the waves. We conduct a theoretical and numerical analysis of this finite‐frequency phenomenon, using a 3‐D pseudospectral code to compute and measure synthetic pressure‐response waveforms and ‘ground truth’ cross‐correlation traveltimes at various distances behind a smooth, spherical anomaly in an otherwise homogeneous acoustic medium. Wavefront healing is ignored in traveltime tomographic inversions based upon linearized geometrical ray theory, in as much as it is strictly an infinite‐frequency approximation. In contrast, a 3‐D banana–doughnut Fréchet kernel does account for wavefront healing because it is cored by a tubular region of negligible traveltime sensitivity along the source–receiver geometrical ray. The cross‐path width of the 3‐D kernel varies as the square root of the wavelength λ times the source–receiver distance L, so that as a wave propagates, an anomaly at a fixed location finds itself increasingly able to ‘hide’ within the growing doughnut ‘hole’. The results of our numerical investigations indicate that banana–doughnut traveltime predictions are generally in excellent agreement with measured ground truth traveltimes over a wide range of propagation distances and anomaly dimensions and magnitudes. Linearized ray theory is, on the other hand, only valid for large 3‐D anomalies that are smooth on the kernel width scale √(λ L). In detail, there is an asymmetry in the wavefront healing behaviour behind a fast and slow anomaly that cannot be adequately modelled by any theory that posits a linear relationship between the measured traveltime shift and the wave‐speed perturbation.