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We present a general concept for evolutionary, collaborative, multiscale inversion of geophysical data, specifically applied to the construction of a first-generation Collaborative Seismic Earth Model. This is intended to address the limited resources of individual researchers and the often limited use of previously accumulated knowledge. Model evolution rests on a Bayesian updating scheme, simplified into a deterministic method that honors today's computational restrictions. The scheme is able to harness distributed human and computing power. It furthermore handles conflicting updates, as well as variable parameterizations of different model refinements or different inversion techniques. The first-generation Collaborative Seismic Earth Model comprises 12 refinements from full seismic waveform inversion, ranging from regional crustal- to continental-scale models. A global full-waveform inversion ensures that regional refinements translate into whole-Earth structure. [ABSTRACT FROM AUTHOR]

We demonstrate how effects of induced stress may be incorporated in seismic modelling and inversion. Our approach is motivated by the accommodation of pre-stress in global seismology. Induced stress modifies both the equation of motion and the constitutive relationship. The theory predicts that induced pressure linearly affects the unstressed isotropic moduli with a slope determined by their adiabatic pressure derivatives. The induced deviatoric stress produces anisotropic compressional and shear wave speeds; the latter result in shear wave splitting. For forward modelling purposes, we determine the weak form of the equation of motion under induced stress. In the context of the inverse problem, we determine induced stress sensitivity kernels, which may be used for adjoint tomography. The theory is illustrated by considering 2-D propagation of SH waves and related Fréchet derivatives based on a spectral-element method. [ABSTRACT FROM AUTHOR]

The robust and automated determination of earthquake source parameters on a global and regional scale is important for many applications in seismology. We present a novel probabilistic method to invert a wide variety of (waveform) data for point-source parameters in real time using pattern recognition. Inferences are made in the form of marginal probability density functions for point-source parameters and incorporate realistic posterior uncertainty estimates. The neural-network-based method is calibrated using samples from the prior distribution, which are synthetic data vectors, and corresponding sources located in a predefined monitoring volume. Once a set of trained neural networks is available, inversions are fast with very moderate demands on computational resources: an inversion takes less than a second on a standard desktop computer. Uncertainties in the layered Earth model are taken into account in the Bayesian framework and increase the robustness of the results with respect to neglected 3D heterogeneities. Moreover, we find that the method is very robust with respect to perturbations such as observational noise and missing data and therefore is potentially well suited for automated and real-time tasks, such as earthquake monitoring and early warning. We demonstrate the method by means of synthetic tests and by inverting an observed high-rate Global Positioning System displacement dataset for the 2010 Mw 7.2 El Mayor-Cucapah event. Our results are compatible with published point-source estimates for this event within the respective uncertainty bounds. [ABSTRACT FROM AUTHOR]

The determination of earthquake source parameters is an important task in seismology. For many applications, it is also valuable to understand the uncertainties associated with these determinations, and this is particularly true in the context of earthquake early warning (EEW) and hazard mitigation. In this paper, we develop a framework for probabilistic moment tensor point source inversions in near real time. Our methodology allows us to find an approximation to p(m|d), the conditional probability of source models (m) given observations (d). This is obtained by smoothly interpolating a set of random prior samples, using Mixture Density Networks (MDNs)—a class of neural networks which output the parameters of a Gaussian mixture model. By combining multiple networks as ‘committees’, we are able to obtain a significant improvement in performance over that of a single MDN. Once a committee has been constructed, new observations can be inverted within milliseconds on a standard desktop computer. The method is therefore well suited for use in situations such as EEW, where inversions must be performed routinely and rapidly for a fixed station geometry. To demonstrate the method, we invert regional static GPS displacement data for the 2010 MW 7.2 El Mayor Cucapah earthquake in Baja California to obtain estimates of magnitude, centroid location and depth and focal mechanism. We investigate the extent to which we can constrain moment tensor point sources with static displacement observations under realistic conditions. Our inversion results agree well with published point source solutions for this event, once the uncertainty bounds of each are taken into account. [ABSTRACT FROM AUTHOR]

How do body-wave traveltimes constrain the Earth's radial (1-D) seismic structure? Existing 1-D seismological models underpin 3-D seismic tomography and earthquake location algorithms. It is therefore crucial to assess the quality of such 1-D models, yet quantifying uncertainties in seismological models is challenging and thus often ignored. Ideally, quality assessment should be an integral part of the inverse method. Our aim in this study is twofold: (i) we show how to solve a general Bayesian non-linear inverse problem and quantify model uncertainties, and (ii) we investigate the constraint on spherically symmetric P-wave velocity (VP) structure provided by body-wave traveltimes from the EHB bulletin (phases Pn, P, PP and PKP). Our approach is based on artificial neural networks, which are very common in pattern recognition problems and can be used to approximate an arbitrary function. We use a Mixture Density Network to obtain 1-D marginal posterior probability density functions (pdfs), which provide a quantitative description of our knowledge on the individual Earth parameters. No linearization or model damping is required, which allows us to infer a model which is constrained purely by the data.We present 1-D marginal posterior pdfs for the 22 VP parameters and seven discontinuity depths in our model. P-wave velocities in the inner core, outer core and lower mantle are resolved well, with standard deviations of ∼0.2 to 1 per cent with respect to the mean of the posterior pdfs. The maximum likelihoods of VP are in general similar to the corresponding ak135 values, which lie within one or two standard deviations from the posterior means, thus providing an independent validation of ak135 in this part of the radial model. Conversely, the data contain little or no information on P-wave velocity in the D′′ layer, the upper mantle and the homogeneous crustal layers. Further, the data do not constrain the depth of the discontinuities in our model. Using additional phases available in the ISC bulletin, such as PcP, PKKP and the converted phases SP and ScP, may enhance the resolvability of these parameters. Finally, we show how the method can be extended to obtain a posterior pdf for a multidimensional model space. This enables us to investigate correlations between model parameters. [ABSTRACT FROM AUTHOR]

SUMMARY We propose a new method for the quantitative resolution analysis in full seismic waveform inversion that overcomes the limitations of classical synthetic inversions while being computationally more efficient and applicable to any misfit measure. The method rests on (1) the local quadratic approximation of the misfit functional in the vicinity of an optimal earth model, (2) the parametrization of the Hessian in terms of a parent function and its successive derivatives and (3) the computation of the space-dependent parameters via Fourier transforms of the Hessian, calculated with the help of adjoint techniques. In the simplest case of a Gaussian approximation, we can infer rigorously defined 3-D distributions of direction-dependent resolution lengths and the image distortion introduced by the tomographic method. We illustrate these concepts with a realistic full waveform inversion for upper-mantle structure beneath Europe. As a corollary to the method for resolution analysis, we propose several improvements to full waveform inversion techniques. These include a pre-conditioner for optimization schemes of the conjugate-gradient type, a new family of Newton-like methods, an approach to adaptive parametrization independent from ray theory and a strategy for objective functional design that aims at maximizing resolution. The computational requirements of our approach are less than for a typical synthetic inversion, but yield a much more complete picture of resolution and trade-offs. While the examples presented in this paper are rather specific, the underlying idea is very general. It allows for problem-dependent variations of the theme and for adaptations to exploration scenarios and other wave-equation-based tomography techniques that employ, for instance, georadar or microwave data. [ABSTRACT FROM AUTHOR]

Wave front healing, in which diffractions interfere with directly travelling waves causing a reduction in recorded traveltime delays, has been postulated to cause a bias towards faster estimated earth models. This paper reviews the theory from the mathematical physics community that explains the properties of diffractions and applies it to a suite of increasingly complicated numerical examples. We focus in particular on the elastic case and on the differences between P and S healing. We find that rather than introducing a systemic fast bias, wave front healing gives a more complicated bias in the results of traveltime tomography, with fast anomalies even manifesting themselves as slow anomalies in some situations. Of particular interest, we find that a negative correlation between the bulk and shear or compressional velocities may result to a large extend from healing. [ABSTRACT FROM AUTHOR]

Splitting of SKS waves caused by anisotropy may be analyzed by measuring the splitting intensity, i.e., the amplitude of the transverse signal relative to the radial signal in the SKS time window. This quantity is simply related to structural parameters. Extending the widely used cross-correlation method for measuring travel-time anomalies to anisotropic problems, we propose to measure the SKS-splitting intensity by a robust cross-correlation method that can be automated to build large high-quality datasets. For weak anisotropy, the SKS-splitting intensity is retrieved by cross-correlating the radial signal with the sum of the radial and transverse signals. The cross-correlation method is validated based upon a set of Californian seismograms. We investigate the sensitivity of the SKS-splitting intensity to general anisotropy in the mantle based upon a numerical technique (the adjoint spectral-element method) considering the full physics of wave propagation. The computations reveal a sensitivity remarkably focused on a small number of elastic parameters and on a small region of the upper mantle. These fundamental properties and the practical advantages of the measurement make the cross-correlation SKS-splitting intensity particularly well adapted for finite-frequency imaging of upper-mantle anisotropy. [ABSTRACT FROM AUTHOR]

We investigate the sensitivity of finite-frequency body-wave observables to mantle anisotropy based upon kernels calculated by combining adjoint methods and spectral-element modelling of seismic wave propagation. Anisotropy is described by 21 density-normalized elastic parameters naturally involved in asymptotic wave propagation in weakly anisotropic media. In a 1-D reference model, body-wave sensitivity to anisotropy is characterized by ‘banana–doughnut’ kernels which exhibit large, path-dependent variations and even sign changes. P-wave traveltimes appear much more sensitive to certain azimuthally anisotropic parameters than to the usual isotropic parameters, suggesting that isotropic P-wave tomography could be significantly biased by coherent anisotropic structures, such as slabs. Because of shear-wave splitting, the common cross-correlation traveltime anomaly is not an appropriate observable for S waves propagating in anisotropic media. We propose two new observables for shear waves. The first observable is a generalized cross-correlation traveltime anomaly, and the second a generalized ‘splitting intensity’. Like P waves, S waves analysed based upon these observables are generally sensitive to a large number of the 21 anisotropic parameters and show significant path-dependent variations. The specific path-geometry of SKS waves results in favourable properties for imaging based upon the splitting intensity, because it is sensitive to a smaller number of anisotropic parameters, and the region which is sampled is mainly limited to the upper mantle beneath the receiver. [ABSTRACT FROM AUTHOR]

This article describes a new method to estimate (1) the self-noise as a function of frequency of three-channel, linear systems and (2) the relative transfer functions between the channels, based on correlation analysis of recordings from a common, coherent input signal. We give expressions for a three-channel model in terms of power spectral densities. The method is robust, compared with the conventional two-channel approach, as both the self-noise and the relative transfer functions are extracted from the measurements only and do not require a priori information about the transfer function of each channel. We use this technique to measure and model the self noise of digitizers and to identify the frequency range in which the digitizer can be used without precaution. As a consequence the method also reveals under which conditions the interpretation of data may be biased by the recording system. We apply the technique to a Quanterra Q4120 datalogger and to a Network of Autonomously Recording Seismographs (NARS) datalogger. At a sampling rate of 20 samples/sec, the noise of the Q4120 digitizer is modeled by superposition of a flat, 23.6-bit spectrum and a 24.7-bit spectrum with 1/f1.55 noise. For the NARS datalogger the noise level is modeled by superposition of a 20.8-bit flat spectrum and a 23.0-bit spectrum with 1/f1.0 noise. The measured gain ratios between the digitizers in the Q4120 datalogger, smoothed over a tenth of a decade between 0.01 Hz and 8 Hz for data sampled with 20 samples/sec, are within 1.6% (or 0.14 dB) of the values given by the manufacturer. Finally, we show an example of seismic background noise observations at station HGN as recorded by both an STS-1 and a STS-2 sensor. Between 0.01 and 0.001 Hz the vertical STS-2 noise levels are 10-15 dB above the STS-1 observations. The Quanterra Q4120 digitizer noise model enables us to exclude the contribution of the digitizer noise to be responsible for this difference. [ABSTRACT FROM AUTHOR]

We applied Sambridge's Neighbourhood Algorithm (NA) to degree-8 fundamental mode Love and Rayleigh wave phase velocity maps between 40 and 150 s to find models of radial anisotropy in the upper 220 km of the mantle. The NA is a powerful tool to explore a multidimensional model space and retrieve an ensemble of models from which statistical inferences (posterior probability density functions (PPDFs) and trade-offs) can be made. We sought solutions for density anomalies and perturbations in the five elastic coefficients that describe transverse isotropy and obtained independent probability density functions for S-wave anisotropy, P-wave anisotropy, intermediate parameter η, Vp, Vs and density anomalies. We find robust departures from PREM in S-wave anisotropy (ξ) under cratons and oceans alike, with a clear change of sign in the anomalies with respect to the reference model at approximately 100 km depth. No significant difference is observed between cratons and oceans, both in the amplitude and depth variation of ξ. The signal within continents is clearly age related, with platforms and tectonically active regions characterized by a rapid decrease in ξ with depth, while cratons display a more constant signal. A similar age dependence in S-wave anisotropy is also observed beneath oceans: a strong and rapidly decreasing anisotropy for young oceans and a more constant anisotropy for older oceans. Perturbations in P-wave anisotropy (φ) are small and limited to the shallowest part of the continents. A small age-dependent signal for φ is observed beneath oceans. Anomalies in intermediate parameter η are similar to those in φ (but not globally correlated), but the deviation from PREM is stronger for η than for φ. Cratons appear to be devoid of any η anisotropy in the top 100 km. There is no obvious global correlation between deviations in φ and deviations in ξ, and the ratio between dη and dξ is clearly regionally variable, which cautions against the use of commonly used proportionality factors between these variables in inversions. In all regions, we found a good correlation between the equivalent isotropic P- and S-wave velocity anomalies, with a ratio d  ln  Vs/ d  ln  Vp close to 1. Density anomalies were not sufficiently well resolved with fundamental mode data alone, but do not influence the results for anisotropy. [ABSTRACT FROM AUTHOR]

Examines the seismic modeling of long-wavelength mantle structure using a neighborhood algorithm. Production of model space maps for the long-wavelength model parametrizations; Reliable mantle density error bars; Seismic constraints on density heterogeneity.

Although water has a major influence on tectonic and other geodynamic processes, little is known about its quantity and distribution within the deep Earth. In the last few decades, laboratory experiments on nominally anhydrous minerals (NAMs) of the transition zone have shown that these minerals can contain significant amounts of water, up to 3.3 wt%. In this study, we investigate if it is possible to use seismic observations to distinguish between a hydrous and anhydrous transition zone. We perform an extensive literature search of mineral experimental data, to generate a compilation of the water storage capacities, elastic parameters and phase boundary data for potentially hydrous minerals in the transition zone, and use thermodynamic modelling to compute synthetic seismic profiles of density, V P and V S at transition zone temperatures and pressures. We find that large uncertainties on the mineral phase equilibria (ca. 2 GPa) and elastic properties produce a wide range of seismic profiles. In particular, there is a lack of data at temperatures corresponding to those along a 1300 °C adiabat or hotter, which may be expected at transition zone pressures. Comparing our hydrous transition zone models with equivalent profiles at anhydrous conditions, we see that the depths of the 410 and 660 discontinuities cannot at present be used to map the water content of the transition zone due to these uncertainties. Further, while average velocities and densities inside the transition zone clearly decrease with increasing water content, there is a near-perfect trade-off with increases in temperature. It is therefore difficult to distinguish thermal from water effects, and the conventional view of a slow and thick transition zone for water and slow and thin transition zone for high temperature should be regarded with caution. A better diagnostic for water may be given by the average velocity gradients of the transition zone, which increase with increasing water content (but decrease for increasing temperature). However the significance of this effect depends on the degree of water saturation and partitioning between the NAMs. Since seismology is better able to constrain the thickness of the transition zone than velocity gradients, our study indicates that the most useful input from future mineral physics experiments would be to better constrain the phase relations between hydrous olivine and its high-pressure polymorphs, especially at high temperatures. Additionally, the uncertainties on the mineral seismic properties could be reduced significantly if the experimentally-observable correlations between bulk and shear moduli and their corresponding pressure derivatives would be published. [ABSTRACT FROM AUTHOR]

Abstract: We present a high-resolution S-velocity model of the North Atlantic region, revealing structural features in unprecedented detail down to a depth of 1300km. The model is derived using full-waveform tomography. More specifically, we minimise the instantaneous phase misfit between synthetic and observed body- as well as surface-waveforms iteratively in a full three-dimensional, adjoint inversion. Highlights of the model in the upper mantle include a well-resolved Mid-Atlantic Ridge and two distinguishable strong low-velocity regions beneath Iceland and beneath the Kolbeinsey Ridge west of Jan Mayen. A sub-lithospheric low-velocity layer is imaged beneath much of the oceanic lithosphere, consistent with the long-wavelength bathymetric high of the North Atlantic. The low-velocity layer extends locally beneath the continental lithosphere of the southern Scandinavian Mountains, the Danish Basin, part of the British Isles and eastern Greenland. All these regions experienced post-rift uplift in Neogene times, for which the underlying mechanism is not well understood. The spatial correlation between the low-velocity layer and uplifted regions suggests dynamic support by low-density asthenosphere originating from the Iceland and Jan Mayen hotspots. Our model further suggests a lower-mantle source for the Iceland and Jan Mayen hotspots. Two distinguishable low-velocity conduits are imaged, connecting the upper-mantle anomalies beneath Iceland and Jan Mayen into the lower mantle. Both conduits are tilted to the South-East, reflecting the westward motion of the Mid-Atlantic Ridge. The location of the imaged Iceland conduit is in agreement with the observation of a locally thinned transition zone south of Iceland from receiver function studies. [Copyright &y& Elsevier]

Abstract: Recent experimental studies indicate that perovskite, the dominant lower mantle mineral, undergoes a phase change to post-perovskite at high pressures. However, it has been unclear whether this transition occurs within the Earth’s mantle, due to uncertainties in both the thermochemical state of the lowermost mantle and the pressure–temperature conditions of the phase boundary. In this study we compare the relative fit to global seismic data of mantle models which do and do not contain post-perovskite, following a statistical approach. Our data comprise more than 10,000 P diff and S diff travel-times, global in coverage, from which we extract the global distributions of dln VS and dln VP near the core–mantle boundary (CMB). These distributions are sensitive to the underlying lateral variations in mineralogy and temperature even after seismic uncertainties are taken into account, and are ideally suited for investigating the likelihood of the presence of post-perovskite. A post-perovskite-bearing CMB region provides a significantly closer fit to the seismic data than a post-perovskite-free CMB region on both a global and regional scale. These results complement previous local seismic reflection studies, which have shown a consistency between seismic observations and the physical properties of post-perovskite inside the deep Earth. [Copyright &y& Elsevier]

Abstract: Depth distributions of seismic velocities and their directional dependence (anisotropy) in the crust and mantle beneath cratons yield essential constraints on processes of their formation and evolution. Despite recent progress in mapping the lateral extent of cratonic roots around the globe, profiles of seismic velocities within them remain uncertain. In this study we employ a novel combination of waveform-analysis techniques and measure inter-station Rayleigh- and Love-wave phase velocities in broad period ranges that enable resolution from the upper crust to deep upper mantle. Sampling a selection of 10 Archean and Proterozoic locations, we derive new constraints on the isotropic and radially anisotropic seismic structure of Precambrian lithosphere. Shear-wave speed V S is consistently higher in the lithosphere of cratons than in the lithosphere of Proterozoic foldbelts. Because known effects of compositional variations in the lithosphere on V S are too small to account for the difference, this implies that temperature in cratonic lithosphere is consistently lower, in spite of sub-lithospheric mantle beneath continents being thermally heterogeneous, with some cratons underlain, as we observe, by a substantially hotter asthenosphere compared to others. Lithospheric geotherms being nearly conductive, this confirms that the stable, buoyant lithosphere beneath cratons must be substantially thicker than beneath younger continental blocks. An increase in V S between the Moho and a 100-150 km depth is consistently preferred by the data in this study and is present in seismic models of continents published previously. We argue that this is largely due to the transition from spinel peridotite to garnet peridotite, proposed previously to give rise to the “Hales discontinuity” within this depth interval. The depth and the width of the phase transformation depend on mantle composition; it is likely to occur deeper and over a broader depth interval beneath cratons than elsewhere because of the high Cr content in the depleted cratonic lithosphere, as evidenced by a number of xenolith studies. Seismic data available at present would be consistent with both a sharp and a gradual increase in V S in the upper lithosphere (a Hales discontinuity or a “Hales gradient”). The V S profile in the upper mantle lithosphere is not shaped by the temperature distribution only; this needs to be considered when relating seismic velocities to lithospheric temperatures. Radial anisotropy in the upper crust is observed repeatedly and indicates vertically oriented anisotropic fabric (V SH < V SV); this may yield a clue on how cratons grew, lending support to the view that distributed crustal shortening with sub-vertical flow patterns occurred over large scales in hot ancient orogens. In the lower crust and upper lithospheric mantle, radial anisotropy consistently reveals horizontal fabric (V SH > V SV); the fabric can be interpreted as a record of (sub-)horizontal ductile flow in the lower crust and lithospheric mantle at the time of the formation and stabilisation of the cratons. We also find indications for radial anisotropy below 200 km depth, corroborating recent evidence for anisotropy in the asthenosphere beneath cratons due to current and recent asthenospheric flow. [Copyright &y& Elsevier]