Cross-correlation of 1 month of ambient seismic noise recorded at USArray stations in California yields hundreds of short-period surface-wave group-speed measurements on interstation paths. We used these measurements to construct tomographic images of the principal geological units of California, with low-speed anomalies corresponding to the main sedimentary basins and high-speed anomalies corresponding to the igneous cores of the major mountain ranges. This method can improve the resolution and fidelity of crustal images obtained from surface-wave analyses.

/pdf/high-resolution-surface-wave-tomography-from-ambient-seismic-2rxarxopq3.pdf

High-resolution surface-wave tomography from ambient seismic noise.

[1] We demonstrate that the coherent information about the Earth structure can be extracted from the ambient seismic noise We compute cross-correlations of vertical component records of several days of seismic noise at different pairs of stations separated by distances from about one hundred to more than two thousand kilometers Coherent broadband dispersive wavetrains clearly emerge with group velocities similar to those predicted from the global Rayleigh-wave tomographic maps that have been constrained using ballistic surface waves Those results show that coherent Rayleigh waves can be extracted from the ambient seismic noise and that their dispersion characteristics can be measured in a broad range of periods This provides a source for new types of surface-wave measurements that can be obtained for numerous paths that could not be sampled with the ballistic waves and, therefore, can significantly improve the resolution of seismic images

/pdf/emergence-of-broadband-rayleigh-waves-from-correlations-of-2lpry85w2t.pdf

Emergence of broadband Rayleigh waves from correlations of the ambient seismic noise.

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.

https://science.sciencemag.org/content/sci/303/5656/338.full.pdf

Finite-Frequency Tomography Reveals a Variety of Plumes in the Mantle

We have developed model S40RTS of shear-velocity variation in Earth's mantle using a new collection of Rayleigh wave phase velocity, teleseismic body-wave traveltime and normal-mode splitting function measurements. This data set is an order of magnitude larger than used for S20RTS and includes new data types. The data are related to shear-velocity perturbations from the (anisotropic) PREM model via kernel functions and ray paths that are computed using PREM. Contributions to phase delays and traveltimes from the heterogeneous crust are estimated using model CRUST2.0. We calculate crustal traveltimes from long-period synthetic waveforms rather than using ray theory. Shear-velocity perturbations are parametrized by spherical harmonics up to degree 40 and by 21 vertical spline functions for a total of 35 301 degrees of freedom. S40RTS is characterised by 8000 resolved unknowns. Since we compute the exact inverse, it is straightforward to determine models associated with fewer or more unknowns by adjusting the model damping. S40RTS shares many characteristics with S20RTS because it is based on the same data types and similar modelling procedures. However, S40RTS shows more clearly than S20RTS the abrupt change in the pattern of shear-velocity heterogeneity across the 660-km phase transition and it presents a more complex patern of shear-velocity heterogeneity in the lower mantle. Utilities to visualise S40RTS and software to analyse the resolution of S40RTS (or models for different damping parameters) are made available.

/pdf/s40rts-a-degree-40-shear-velocity-model-for-the-mantle-from-4i5sq7pv6c.pdf

S40RTS: A degree-40 shear-velocity model for the mantle from new Rayleigh wave dispersion, teleseismic traveltime and normal-mode splitting function measurements

SUMMARY

We draw connections between seismic tomography, adjoint methods popular in climate and ocean dynamics, time-reversal imaging and finite-frequency ‘banana-doughnut’ kernels. We demonstrate that Frechet derivatives for tomographic and (finite) source inversions may be obtained based upon just two numerical simulations for each earthquake: one calculation for the current model and a second, ‘adjoint’, calculation that uses time-reversed signals at the receivers as simultaneous, fictitious sources. For a given model, m, we consider objective functions χ(m) that minimize differences between waveforms, traveltimes or amplitudes. For tomographic inversions we show that the Frechet derivatives of such objective functions may be written in the generic form , where δ ln m=δm/m denotes the relative model perturbation. The volumetric kernel Km is defined throughout the model volume V and is determined by time-integrated products between spatial and temporal derivatives of the regular displacement field s and the adjoint displacement field s†; the latter is obtained by using time-reversed signals at the receivers as simultaneous sources. In waveform tomography the time-reversed signal consists of differences between the data and the synthetics, in traveltime tomography it is determined by synthetic velocities, and in amplitude tomography it is controlled by synthetic displacements. For each event, the construction of the kernel Km requires one forward calculation for the regular field s and one adjoint calculation involving the fields s and s†. In the case of traveltime tomography, the kernels Km are weighted combinations of banana-doughnut kernels. For multiple events the kernels are simply summed. The final summed kernel is controlled by the distribution of events and stations. Frechet derivatives of the objective function with respect to topographic variations δh on internal discontinuities may be expressed in terms of 2-D kernels Kh and Kh in the form , where Σ denotes a solid-solid or fluid-solid boundary and ΣFS a fluid–solid boundary, and ∇Σ denotes the surface gradient. We illustrate how amplitude anomalies may be inverted for lateral variations in elastic and anelastic structure. In the context of a finite-source inversion, the model vector consists of the time-dependent elements of the moment-density tensor m(x, t). We demonstrate that the Frechet derivatives of the objective function χ may in this case be written in the form , where e† denotes the adjoint strain tensor on the finite-fault plane Σ. In the case of a point source this result reduces further to the calculation of the time-dependent adjoint strain tensor e† at the location of the point source, an approach reminiscent of an acoustic time-reversal mirror. The theory is illustrated for both tomographic and source inversions using a 2-D spectral-element method.

Seismic tomography, adjoint methods, time reversal and banana-doughnut kernels

SUMMARY We calculate three dimensional (3-D) sensitivity kernels for fundamental-mode surface wave observables based on the single-scattering (Born) approximation. The sensitivity kernels for measured phases, amplitudes and arrival angles are formulated in the framework of surface wave mode summation. We derive kernels for cross-spectral multitaper measurements; as a special case, the results are applicable to single-taper measurements. Cross-branch modecoupling effects are fully accounted for in the kernels; however, these effects can probably be ignored at the present level of spatial resolution in global phase-delay tomography. The narrowly concentrated spectra of the windows and tapers commonly used in global surface wave studies enable the kernels to be computed extremely efficiently.

/pdf/three-dimensional-sensitivity-kernels-for-surface-wave-hmaitzrdxo.pdf

Three‐dimensional sensitivity kernels for surface wave observables

Using a simple Gaussian beam solution to the one-way scalar wave equation, we derive analytical expressions for the evolution of phase and group delay after a wave passes through a Gaussian-shaped heterogeneity of half width L. As a function of distance χ, there are two clearly separated regimes, depending upon the wavelength λ of the wave. In regime I, when χ/L ≪ πL/λ, the absolute magnitude of the phase delay decreases approximately linearly with χ, and the anomaly does not widen appreciably except by developing small sidelobes with delays of opposite sign. Tomographie inversions of such delays will be damped but are theoretically well posed. In regime II, when χ/L ≫ πL/λ, the absolute delay decreases toward zero as 1/χ, most markedly on the ray itself, and the cross-path shape of the wave front bears little resemblance to the original anomaly. Tomographic inversions of delay times in this regime are ill posed. Group delay times show a similar behavior in the two regimes. Although their rate of decrease with distance is slower in regime I, they develop more disturbing sidelobe behavior off the central ray. The effects of wave front healing for surface waves traveling in two dimensions are less severe than those for body waves in three dimensions; as a result, surface wave inversions will commonly be in regime I. Short-period body wave group delays are also in regime I; nevertheless, the damping of delays in this regime is likely to contribute significantly to the scatter of observed travel time anomalies. Tomographie inversions of long-period body waves, which fall at the limit of regime I, or even in regime II, face perceptible limitations in theoretical resolving power. Finally, we show that there is an asymmetry in the evolution of positive versus negative travel time anomalies.

https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1029/2000JB900161

Wave front healing and the evolution of seismic delay times

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

/pdf/wavefront-healing-a-banana-doughnut-perspective-48upwvxe65.pdf

Wavefront healing: a banana–doughnut perspective

[1] We report global shear-wave velocity structure and radial anisotropy in the upper mantle obtained using finite-frequency surface-wave tomography, based upon complete three-dimensional Born sensitivity kernels. Because wavefront healing effects are properly taken into account, finite-frequency surface-wave tomography improves the resolution of small-scale mantle heterogeneities, especially for deep anomalies that are constrained by the longest-period surface waves. In our finite-frequency model FFSW1, the globally averaged radial anisotropy shows a transition from positive (SH > SV) to negative anisotropy (SV > SH) at about 220 km, consistent with a change in the dominant mantle circulation pattern from predominantly horizontal flow at shallow depths to vertical flow at greater depths. The radial anisotropy beneath cratons and the old Pacific plate agrees well with previous studies. However, our model exhibits a strong negative radial anisotropy at depths greater than 120 km beneath mid-ocean ridges, a feature that is not present in previous upper-mantle models. More interestingly, the depth extent of the ridge anomalies is distinctly different beneath fast- and slow-spreading centers; anomalies beneath fast-spreading centers are stronger, but the strength decreases rapidly below 250 km. In contrast, beneath slow-spreading centers such as the northern Mid-Atlantic Ridge and the Red Sea, anomalies extend down at least to the top of the transition zone. The different depth extent of the ridge anomalies suggests that the primary driving force of slow-spreading seafloor may be different from that of fast-spreading seafloor and that active upwelling beneath slow-spreading ridges may play a major role in the opening of the seafloor.

F. A. Dahlen

Papers

Three‐dimensional sensitivity kernels for surface wave observables

Wave front healing and the evolution of seismic delay times

Wavefront healing: a banana–doughnut perspective

Global upper-mantle structure from finite-frequency surface-wave tomography

Global Upper Mantle Structure from Finite-Frequency Surface-Wave Tomography