ALBERT

Beschreibung: Azimuthal anisotropy is a powerful tool to reveal information about both the present structure and past evolution of the mantle. Anisotropic images of the upper mantle are usually obtained by analysing various types of seismic observables, such as surface wave dispersion curves or waveforms, SKS splitting data, or receiver functions. These different data types sample different volumes of the earth, they are sensitive to different length scales, and hence are associated with different levels of uncertainties. They are traditionally interpreted separately, and often result in incompatible models. We present a Bayesian inversion approach to jointly invert these different data types. Seismograms for SKS and P phases are directly inverted using a cross-convolution approach, thus avoiding intermediate processing steps, such as numerical deconvolution or computation of splitting parameters. Probabilistic 1-D profiles are obtained with a transdimensional Markov chain Monte Carlo scheme, in which the number of layers, as well as the presence or absence of anisotropy in each layer, are treated as unknown parameters. In this way, seismic anisotropy is only introduced if required by the data. The algorithm is used to resolve both isotropic and anisotropic layering down to a depth of 350 km beneath two seismic stations in North America in two different tectonic settings: the stable Canadian shield (station FFC) and the tectonically active southern Basin and Range Province (station TA-214A). In both cases, the lithosphere–asthenosphere boundary is clearly visible, and marked by a change in direction of the fast axis of anisotropy. Our study confirms that azimuthal anisotropy is a powerful tool for detecting layering in the upper mantle.

Beschreibung: We present a method to construct non-stationary and anisotropic second-order random model realizations that can be used for numerical wave propagation simulations in various geometries. Models are generated directly from a given covariance matrix using its eigenvector decomposition (principal component or Karhunen-Loève method). Because this decomposition is very expensive computationally in 3-D, we use model symmetries to reduce the size of the covariance matrix to its non-stationary components. Stationary components can then be described through their power spectrum, such that models with axisymmetric or spherically symmetric statistics can be generated from a 1-D covariance matrix. We focus in particular on models with spherically symmetric statistics that are important to study wave propagation in the Earth. We use this method to show the influence of hypothetical small-scale structure in the Earth's mantle on the elastic wavefield. To this end, we extend tomographic models beyond their spatial resolution limit with different distributions of small-scale scatterers that generate a coda and attenuate direct waves (scattering attenuation). We observe that scattering attenuation of fundamental mode Rayleigh waves is small (0.5–2 per cent of the total attenuation), if the elastic mantle structure does not become significantly stronger at smaller scales. At the examined heterogeneity strengths, scattering attenuation scales linearly with the model variance. The long-period fundamental mode Rayleigh wave coda is difficult to measure because it is weak and overlaps with other signals. However, it can be shown that its intensity also scales linearly with model power, and that it depends strongly on the spherical geometry of the Earth. It can therefore be used to distinguish between models with different small-scale power. We show qualitatively that the coda generated by the type of random models we consider can explain observed scattered energy at long periods (100 s).

Beschreibung: SS precursor observations are a powerful tool to study the topography and character of transition zone discontinuities, especially in regions such as ocean basins where few seismic stations exist, precluding other high resolution approaches. Still, the available coverage is limited by the distribution of sources and stations, but also by the level of noise and by the fact that, in some distance ranges, interfering seismic phases mask the weak signal from the SS precursors. We introduce an array data processing tool, the local slant-stack filter, to address these challenges and clean up the otherwise noisy SS precursor record sections. We show that these filters are a powerful tool for extracting the weak yet coherent SS precursor signals while removing interfering seismic phases as well as random noise, yielding robust precursor traveltime measurements with spatial resolution higher than what can be achieved by the conventional common midpoint stacking method. The effectiveness of the filters are demonstrated by application to synthetic and real data. We systematically apply this filtering method to an SS precursor data set recorded by the U.S. Transportable Array that samples a vast region of the Pacific Ocean and its northwest margin, and present maps of 410 and 660 discontinuity topography. We discuss correlations observed between our discontinuity images and several fine-scale heterogeneities revealed by mantle shear wave tomography in the vicinity of Hawaii and the Pacific Superswell.

Beschreibung: In order to study fine scale structure of the Earth's deep interior, it is necessary to extract generally weak body wave phases from seismograms that interact with various discontinuities and heterogeneities. The recent deployment of large-scale dense arrays providing high-quality data, in combination with efficient seismic data processing techniques, may provide important and accurate observations over large portions of the globe poorly sampled until now. Major challenges are low signal-to-noise ratios (SNR) and interference with unwanted neighbouring phases. We address these problems by introducing scale-dependent slowness filters that preserve time-space resolution. We combine complex wavelet and slant-stack transforms to obtain the slant-stacklet transform. This is a redundant high-resolution directional wavelet transform with a direction (here slowness) resolution that can be adapted to the signal requirements. To illustrate this approach, we use this expansion to design coherence-driven filters that allow us to obtain clean PcP observations (a weak phase often hidden in the coda of the P wave), for events with magnitude M w  〉 5.4 and distances up to 80°. In this context, we then minimize a linear misfit between P and PcP waveforms to improve the quality of PcP–P traveltime measurements as compared to a standard cross-correlation method. This significantly increases both the quantity and the quality of PcP–P differential traveltime measurements available for the modelling of structure near the core–mantle boundary. The accuracy of our measurements is limited mainly by the highest frequencies of the signals used and the level of noise. We apply this methodology to two examples of high-quality data from dense arrays located in north America. While focusing here on body-wave separation, the tools we propose are more general and may contribute to enhancing seismic signal observations in global seismology in situations of low SNR and high signal interference.

Beschreibung: Resolving the topography of the core–mantle boundary (CMB) and the structure and composition of the D '' region is key to improving our understanding of the interaction between the Earth's mantle and core. Observations of traveltimes and amplitudes of short-period teleseismic body waves sensitive to lowermost mantle provide essential constraints on the properties of this region. Major challenges are low signal-to-noise ratio of the target phases and interference with other mantle phases. In a previous paper (Part I), we introduced the slant-stacklet transform to enhance the signal of the core-reflected ( PcP ) phase and to isolate it from stronger signals in the coda of the P wave. Then we minimized a linear misfit between P and PcP waveforms to improve the quality of PcP–P traveltime difference measurements as compared to standard cross-correlation methods. This method significantly increases the quantity and the quality of PcP–P traveltime observations available for the modelling of structure near the CMB. Here we illustrate our approach in a series of regional studies of the CMB and D '' using PcP–P observations with unprecedented resolution from high-quality dense arrays located in North America and Japan for events with magnitude M w 〉5.4 and distances up to 80 $\deg$ . In this process, we carefully analyse various sources of errors and show that mantle heterogeneity is the most significant. We find and correct bias due to mantle heterogeneities that is as large as 1 s in traveltime, comparable to the largest lateral PcP–P traveltime variations observed. We illustrate the importance of accurate mantle corrections and the need for higher resolution mantle models for future studies. After optimal mantle corrections, the main signal left is relatively long wavelength in the regions sampled, except at the border of the Pacific large-low shear velocity province (LLSVP). We detect the northwest border of the Pacific LLSVP in the western Pacific from array observations in Japan, and observe higher than average P velocities, or depressed CMB, in Central America, and slightly lower than average P velocities under Alaska/western Canada.

Beschreibung: The radially anisotropic shear velocity structure of the Earth's mantle provides a critical window on the interior dynamics of the planet, with isotropic variations that are interpreted in terms of thermal and compositional heterogeneity and anisotropy in terms of flow. While significant progress has been made in the more than 30 yr since the advent of global seismic tomography, many open questions remain regarding the dual roles of temperature and composition in shaping mantle convection, as well as interactions between different dominant scales of convective phenomena. We believe that advanced seismic imaging techniques, such as waveform inversion using accurate numerical simulations of the seismic wavefield, represent a clear path forwards towards addressing these open questions through application to whole-mantle imaging. To this end, we employ a ‘hybrid’ waveform-inversion approach, which combines the accuracy and generality of the spectral finite element method (SEM) for forward modelling of the global wavefield, with non-linear asymptotic coupling theory for efficient inverse modelling. The resulting whole-mantle model (SEMUCB-WM1) builds on the earlier successful application of these techniques for global modelling at upper mantle and transition-zone depths (≤800 km) which delivered the models SEMum and SEMum2. Indeed, SEMUCB-WM1 is the first whole-mantle model derived from fully numerical SEM-based forward modelling. Here, we detail the technical aspects of the development of our whole-mantle model, as well as provide a broad discussion of isotropic and radially anisotropic model structure. We also include an extensive discussion of model uncertainties, specifically focused on assessing our results at transition-zone and lower-mantle depths.

Beschreibung: We analyse the lateral heterogeneity scales of recent upper mantle tomographic shear velocity ( Vs ) global and regional models. Our goal is to constrain the spherical harmonics power spectrum over the largest possible range of scales to get an estimate of the strength and statistical distribution of both long and small-scale structure. We use a spherical multitaper method to obtain high quality power spectral estimates from the regional models. After deconvolution of the employed taper functions, we combine global and regional spectral estimates from scales of 20 000 to around 200 km (degree 100). In contrast to previous studies that focus on linear power spectral densities, we interpret the logarithmic power per harmonic degree l as heterogeneity strength at a particular depth and horizontal scale. Throughout the mantle, we observe in recent global models, that their low degree spectrum is anisotropic with respect to Earth's rotation axis. We then constrain the uppermost mantle spectrum from global and regional models. Their power spectra transfer smoothly into each other in overlapping spectral bands, and model correlation is in general best in the uppermost 250 km (i.e. the ‘heterosphere’). In Europe, we see good correlation from the largest scales down to features of about 500 km. Detailed analysis and interpretation of spectral shape in this depth range shows that the heterosphere has several characteristic length scales and varying spectral decay rates. We interpret these as expressions of different physical processes. At larger depths, the correlation between different models drops, and the power spectrum exhibits strong small scale structure whose location and strength is not as well resolved at present. The spectrum also has bands with elevated power that likely correspond to length scales that are enhanced due to the inversion process.

Beschreibung: Studies of seismic tomography have been highly successful at imaging the deep structure of subduction zones. In a study complementary to these tomographic studies, we use array seismology and reflected waves to image a stagnant slab in the mantle transition zone. Using P and S (SH) waves we find a steeply dipping reflector centred at ca . 400 km depth and ca . 550 km west of the present Mariana subduction zone (at 20N, 140E). The discovery of this anomaly in tomography and independently in array seismology (this paper) helps in understanding the evolution of the Mariana margin. The reflector/stagnant slab may be the remains of the hypothetical North New Guinea Plate, which was theorized to have subducted ca . 50 Ma.

Beschreibung: The lowermost few hundreds of kilometres of the Earth's mantle are elastically anisotropic; seismic velocities vary with direction of propagation and polarization. Observations of strong seismic anisotropy correlate with regions where subducted slab material is expected. In this study, we evaluate the hypothesis that crystal preferred orientation (CPO) in a slab, as it impinges on the core–mantle boundary, is the cause of the observed anisotropy. Next, we determine if fast polarization directions seen by shear waves can be mapped to directions of geodynamic flow. This approach is similar to our previous study performed for a 2-D geodynamic model. In this study, we employ a 3-D geodynamic model with temperature-dependent viscosity and kinematic velocity boundary conditions defined at the surface of the Earth to create a broad downwelling slab. Tracers track the deformation that we assume to be accommodated by dislocation creep. We evaluate the models for the presence of perovskite or post-perovskite and for different main slip systems along which dislocation creep may occur in post-perovskite [(100),(010) and (001)]—resulting in four different mineralogical models of CPO. Combining the crystal pole orientations with single crystal elastic constants results in seismically distinguishable models of seismic anisotropy. The models are evaluated against published seismic observations by analysing different anisotropic components: the radial anisotropy, the splitting for (sub-)vertical phases (i.e. azimuthal anisotropy), and the splitting for subhorizontal phases. The patterns in radial anisotropy confirm our earlier results in 2-D. Observations of radial anisotropy and splitting in subhorizontal phases are mostly consistent with our models of post-perovskite with (010)-slip and (001)-slip. Our model of (001)-slip predicts stronger splitting than for (010)-slip for horizontally propagating phases in all directions. The strongest seismic anisotropy in this model occurs where the slab impinges on the core–mantle boundary. The azimuthal anisotropy pattern for (001)-slip shows fast axis directions at the edges of the slab (sub-)parallel to flow directions, suggesting horizontal flows may be mapped out in the lowermost mantle using seismic observations.

Beschreibung: We derive a fast discrete solution to the scattering problem. This solution allows us to compute accurate synthetic seismograms or waveforms for arbitrary locations of sources and receivers within a medium containing localized perturbations. The key to efficiency is that wave propagation modelling does not need to be carried out in the entire volume that encompasses the sources and the receivers but only within the subvolume containing the perturbations or scatterers. The proposed solution has important applications, for example, it permits the imaging of remote targets located in regions where no sources or receivers are present. Our solution relies on domain decomposition: within a small volume that contains the scatterers, wave propagation is modelled numerically, while in the surrounding volume, where the medium isn't perturbed, the response is obtained through wavefield extrapolation. The originality of this work is the derivation of discrete formulas for representation theorems and Kirchhof–Helmholtz integrals that naturally adapt to the numerical scheme employed for modelling wave propagation. Our solution applies, for example, to finite difference methods or finite/spectral elements methods. The synthetic seismograms obtained with our solution can be considered ‘exact’ as the total numerical error is comparable to that of the method employed for modelling wave propagation. We detail a basic implementation of our solution in the acoustic case using the finite difference method and present numerical examples that demonstrate the accuracy of the method. We show that ignoring some terms accounting for higher order scattering effects in our solution has a limited effect on the computed seismograms and significantly reduces the computational effort. Finally, we show that our solution can be used to compute localized sensitivity kernels and we discuss applications to target oriented imaging. Extension to the elastic case is straightforward and summarized in a dedicated section.