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SUMMARY We measured inner core normal mode pair 10S2–11S2, which cross-couples strongly for 1-D structure and is sensitive to shear wave velocity, and find that our measurements agree with a strongly attenuating inner core. In the past, this mode pair has been used to try to resolve the debate on whether the inner core is strongly or weakly attenuating. Its large spectral amplitude in observed data, possible through the apparent low attenuation of 10S2, has been explained as evidence of a weakly attenuating inner core. However, this contradicted body waves and other normal modes studies, which resulted in this pair of modes being excluded from inner core modelling. Modes 10S2 and 11S2 are difficult to measure and interpret because they depend strongly on the underlying 1-D model used. This strong dependence makes these modes change both their oscillation characteristics and attenuation values under a small 1-D perturbation to the inner core model. Here, we include this effect by allowing the pair of modes to cross-couple or resonate through 1-D structure and treat them as one hybrid mode. We find that, unlike previously thought, the source of 10S2 visibility is its strong cross-coupling to 11S2 for both 1-D elastic and anelastic structure. We also observe that the required 1-D perturbation is much smaller than the 2 per cent vs perturbation previously suggested, because we simultaneously measure 3-D structure in addition to 1-D structure. Only a 0.5 per cent increase in inner core vs or a 0.5 per cent decrease in inner core radius is required to explain 10S2–11S2 observations and a weakly attenuating inner core is not needed. In addition, the 3-D structure measurements of mode 10S2 and its cross-coupling to 11S2 show the typical strong zonal splitting pattern attributed to inner core cylindrical anisotropy, allowing us to add further constrains to deeper regions of the inner core.

We present a novel approach for imaging global mantle discontinuities based on full-waveform inversion (FWI). Over the past decades, extensive research has been done on imaging mantle discontinuities at approximately 400 km and 670 km depth. Accurate knowledge of their topography can put strong constraints on thermal and compositional variations and hence geodynamic modelling. So far, however, there is little consensus on their topography. We present an approach based on adjoint tomography, which has the advantage that Fréchet derivatives for discontinuities and measurements, to be inverted for, are fully consistent. Rather than working with real data, we focus on synthetic tests, where the answer is known in order to be able to evaluate the performance of the developed method. All calculations are based on the community code SPECFEM3D_GLOBE. We generate data in fixed 1-D or 3-D elastic background models of mantle velocity. Our ‘data’ to be inverted contain topography along the 400 km and 670 km mantle discontinuities. To investigate the approach, we perform several tests: (i) In a situation where we know the elastic background model 1-D or 3-D, we recover the target topography fast and accurately, (ii) The exact misfit is not of great importance here, except in terms of convergence speed, similar to a different inverse algorithm, (iii) In a situation where the background model is not known, the convergence is markedly slower, but there is reasonable convergence towards the correct target model of discontinuity topography. It has to be noted that our synthetic test is idealised and in a real data situation, the convergence to and uncertainty of the inferred model is bound to be larger. However, the use of data consistent with Fréchet kernels seems to pay off and might improve our consensus on the nature of mantle discontinuities. Our workflow could be incorporated in future FWI mantle models to adequately infer boundary interface topography., Geophysical Journal International, 226 (3), ISSN:0956-540X, ISSN:1365-246X

The Groningen gas field in the Netherlands is an ideal test bed for in-situ reservoir monitoring techniques because of the availability of both active and passive in-reservoir seismic data. In this study, we use deconvolution interferometry to estimate the reflection and transmission response using active and passive borehole data within the reservoir at ∼3-km depth and separate up- and downgoing P- and S-wave fields by f-k filtering. We validate the results using synthetic data of a 1D elastic model built from sonic logs recorded in the well. The estimated full-waveform reflection response for a virtual source at the top geophone is consistent with the synthetic response. For the virtual source at the bottom geophone, the reflection response appears to be phase delayed, though its arrivals are consistent with the local subsurface geology. Similarly, the first-order estimated local transmission response successfully approximates that of the P-wave velocity in the reservoir. The study shows that reliable subsurface information can be obtained from borehole interferometry without detailed knowledge of the medium parameters. In addition, the method could be used for passive reservoir monitoring to detect velocity, attenuation, and/or interface time-lapse variations.

To establish a consistent framework for seismic wave propagation that accommodates the effects of stress changes, it is critical to take into account the different definitions of stress and their corresponding effects on seismic quantities (e.g., wave speeds) as dictated by continuum mechanics. Revisiting this fundamental theoretical foundation, we first emphasize the role of stress within various forms of the wave equation resulting from different choices of stress definitions. Subsequently, using this basis, we investigate connections among existing theories that describe the variation of elastic moduli as a function of changes in stress. We find that there is a direct connection between predicting stress-induced elastic changes with the well-known third-order elasticity tensor and the recently proposed adiabatic pressure derivatives of elastic moduli. However, each of these approaches has different merits and drawbacks in terms of experimental validation as well as in their use. In addition, we investigate the connection with another general approach that relies on micromechanical structures (e.g., cracks and pores). Although this can be done algebraically, it remains unclear as to which definition of stress and which corresponding constitutive relationship should be considered in practical scenarios. We support our analysis with validations using previously published benchmark experimental data.

Previous studies examining the relationship between the groundwater table and seismic velocities have been guided by empirical relationships only. Here, we develop a physics-based model relating fluctuations in groundwater table and pore pressure with seismic velocity variations through changes in effective stress. This model justifies the use of seismic velocity variations for monitoring of the pore pressure. Using a subset of the Groningen seismic network, near-surface velocity changes are estimated over a four-year period, using passive image interferometry. The same velocity changes are predicted by applying the newly derived theory to pressure-head recordings. It is demonstrated that the theory provides a close match of the observed seismic velocity changes.

We present a 3D shear-wave velocity model of the southern African upper mantle developed using 30–200 s period Rayleigh waves recorded on regional seismic networks spanning the subcontinent. The model shows high velocities (∼4.7–4.8 km/s) at depths of 50–250 km beneath the Archean nucleus and several surrounding Paleoproterozoic and Mesoproterozoic terranes, placing the margin of the greater Kalahari Craton along the southern boundary of the Damara Belt and the eastern boundaries of the Gariep and Namaqua-Natal belts. At depths ≥250 km, there is little difference in velocities beneath the craton and off-craton regions, suggesting that the cratonic lithosphere extends to depths of about 200–250 km. Upper mantle velocities beneath uplifted areas of southern Africa are higher than the global average and significantly higher than beneath eastern Africa, indicating there that is little thermal modification of the upper mantle present today beneath the Southern African Plateau.

International audience; A new submarine volcano has been discovered offshore Mayotte, a part of the Comoros volcanic archipelago located between Africa and Madagascar. The edifice arose from the sea-floor following a seismo-volcanic crisis that started in May 2018. This seismo-volcanic activity highlights very deep magma reservoirs and dykes in the East Mayotte volcanic system. Since the crisis, the region has experienced >2000 earthquakes with magnitude ≥3.5 and activity continues today (August 17, 2021). The earthquakes are unusually deep and distributed into two swarms: one 5–15 km east of Petite-Terre at 25–55 km depth and a second 25 km away at 30–50 km depth. Significant subsidence of Mayotte to the East has been assigned to the drainage of a deep magma chamber, inferred to be located 30 km from the coast. However, at present, the earthquake locations and geodetic observations have not been sufficient to image entirely the structure of the volcanic plumbing system. In this study, we construct Vp, Vs, dVp, dVs and Vp/Vs 3D velocity models to assess the deeper structure of the young volcano plumbing system, offshore and East of Mayotte. Using >3000 earthquakes from an ongoing monitoring effort, and a 1D velocity model determined onboard, we jointly inverted for velocity structures, earthquake locations, origin times, and station corrections using LOTOS software. The calculated 3D velocity models highlight a complex volcanic system down to 40 km depth. Specifically, we image 3 interpreted reservoirs, more or less consolidated/old. The main reservoir is located at about 30 km depth and deeper, making it one of the deepest magmatic chamber imaged. The reservoirs are connected by several old crystallized conduits, whose existence could have been influenced by the presence of an old fracture zone, globally oriented N130°, due to a regional strike-slip motion of the lithosphere. Moreover, gas-saturated rock may be present below the currently degassing Horse Shoe structure. We were unable to image connections between the new volcanic edifice and reservoirs or conduits due to a lack of resolution in that part of the study area.

We report new P and S wave velocity models of the upper mantle beneath southern Africa using data recorded on seismic stations spanning the entire subcontinent. Beneath most of the Damara Belt, including the Okavango Rift, our models show lower than average velocities (−0.8% Vp; −1.2% Vs) with an abrupt increase in velocities along the terrane's southern margin. We attribute the lower than average velocities to thinner lithosphere (~130 km thick) compared to thicker lithosphere (~200 km thick) immediately to the south under the Kalahari Craton. Beneath the Etendeka Flood Basalt Province, higher than average velocities (0.25% Vp; 0.75% Vs) indicate thicker and/or compositionally distinct lithosphere compared to other parts of the Damara Belt. In the Rehoboth Province, higher than average velocities (0.3% Vp; 0.5% Vs) suggest the presence of a microcraton, as do higher than average velocities (1.0% Vp; 1.5% Vs) under the Southern Irumide Belt. Lower than average velocities (−0.4% Vp; −0.7% Vs) beneath the Bushveld Complex and parts of the Mgondi and Okwa terranes are consistent with previous studies, which attributed them to compositionally modified lithosphere resulting from Precambrian magmatic events. There is little evidence for thermally modified upper mantle beneath any of these terranes which could provide a source of uplift for the Southern African Plateau. In contrast, beneath parts of the Irumide Belt in southern and central Zambia and the Mozambique Belt in central Mozambique, deep‐seated low velocity anomalies (−0.7% Vp; −0.8% Vs) can be attributed to upper mantle extensions of the African superplume structure.

Recent developments in the densification of the seismic network covering the Groningen gas field allow a more detailed study of the connection between induced seismicity and reactivated faults around the gas reservoir at 3 km depth. With the reduction of the average station distance from 20 km to 4–5 km, a probabilistic full-waveform moment tensor inversion procedure could be applied, resulting in both improved hypocenter location accuracy and full moment tensor solutions for events of M≥2.0 recorded in the period 2016–2019. Hypocenter locations as output from the moment tensor inversion are compared to locations from the application of other methods and are found similar within 250 m distance. Moment tensor results show that the double-couple (DC) solutions are in accordance with the known structure, namely normal faulting along 50°–70° dipping faults. Comparison with reprocessed 3D seismic sections, extended to a depth of 6–7 km, demonstrate that (a) most events occur along faults with a small throw and (b) reactivated faults in the reservoir often continue downward in the Carboniferous underburden. From non-DC contributions, the isotropic (ISO) component is dominant and shows consistent negative values, which is expected in a compacting medium. There is some indication that events connected to faults with a large throw (>70 m) exhibit the largest ISO component (40%–50%).

Summary Induced seismicity in the Groningen gas field in the Netherlands has been related to reservoir compaction caused by gas pressure depletion. In situ measurement of compaction is therefore relevant for seismic hazard assessment. In this study, we investigated the potential of passively recorded deep borehole noise data to detect temporal variations in the Groningen reservoir. Train signals recorded by an array of 10 geophones at reservoir depth were selected from the continuous noise data for two 5-month deployments in 2015. Interferometry by deconvolution was applied to the high-frequency train signals that acted as stable, repetitive noise sources. Direct intergeophone P and S wave traveltimes were then used to construct the P- and S-wave velocity structure along the geophone array. The resulting models agree with independently obtained velocity profiles and have very small errors. Most intergeophone P wave traveltimes showed decreasing traveltimes per deployment period, suggestive of compaction. However, the retrieved traveltime changes are very small, up to tens of microseconds per deployment period, with uncertainties that are of similar size, about 10 microseconds. An unambiguous interpretation in terms of compaction is therefore not warranted, although the 10 μs error per 5-month period is probably smaller than can be achieved from active time-lapse seismic surveys that are commonly used to measure reservoir compaction. The direct P-wave amplitudes of the train-signal deconvolutions were investigated for additional imprints of compaction. Whereas the P-wave amplitudes consistently increased during the second deployment, suggestive of compaction, no such trend was observed for the first deployment, rendering the interpretation of compaction inconclusive. Our results therefore present hints, but no obvious effects of compaction in the Groningen reservoir. Yet, this study demonstrates that the approach of deconvolution interferometry applied to deep borehole data allows monitoring of small temporal changes in the subsurface for stable repetitive noise sources such as trains.

SUMMARY The method of ScS reverberation migration is based on a ‘common reflection point’ analysis of multiple ScS reflections in the mantle transition zone (MTZ). We examine whether ray-theoretical traveltimes, slownesses and reflection points are sufficiently accurate for estimating the thickness H of the MTZ, defined by the distance between the 410- and 660-km phase transitions. First, we analyse ScS reverberations generated by 35 earthquakes and recorded at hundreds of seismic stations from the combined Arrays in China, Hi-NET in Japan and the Global Seismic Network. This analysis suggests that H varies by about 30 km and therefore that dynamic processes have modified the large-scale structure of the MTZ in eastern Asia and the western Pacific region. Second, we apply the same procedure to spectral-element synthetics for PREM and two 3-D models. One 3-D model incorporates degree-20 topography on the 410 and 660 discontinuities, otherwise preserving the PREM velocity model. The other model incorporates the degree-20 velocity heterogeneity of S20RTS and leaves the 410 and 660 flat. To optimize reflection point coverage, our synthetics were computed assuming a homogeneous grid of stations using 16 events, four of which are fictional. The resolved image using PREM synthetics resembles the PREM structure and indicates that the migration approach is correct. However, ScS reverberations are not as strongly sensitive to H as predicted ray-theoretically because the migration of synthetics for a model with degree-20 topography on the 410 and 660: H varies by less than 5 km in the resolved image but 10 km in the original model. In addition, the relatively strong influence of whole-mantle shear-velocity heterogeneity is evident from the migration of synthetics for the S20RTS velocity model and the broad sensitivity kernels of ScS reverberations at a period of 15 s. A ray-theoretical approach to modelling long-period ScS traveltimes appears inaccurate, at least for continental-scale regions with relatively sparse earthquake coverage. Additional modelling and comparisons with SS precursor and receiver function results should rely on 3-D waveform simulations for a variety of structures and ultimately the implementation of full wave theory.

Parameter estimation from reflection moveout analysis represents one of the most fundamental problems in subsurface model building. We have developed an efficient moveout inversion method based on the process of automatic flattening of common-midpoint (CMP) gathers using local slopes. We find that as a by-product of this flattening process, we can also estimate reflection traveltimes corresponding to the flattened CMP gathers. This traveltime information allows us to construct a highly overdetermined system and subsequently invert for moveout parameters including normal-moveout velocities and quartic coefficients related to anisotropy. We use the 3D generalized moveout approximation (GMA), which can accurately capture the effects of complex anisotropy on reflection traveltimes as the basis for our moveout inversion. Due to the cheap forward traveltime computations by GMA, we use a Monte Carlo inversion scheme for improved handling of the nonlinearity between the reflection traveltimes and moveout parameters. This choice also allows us to set up a probabilistic inversion workflow within a Bayesian framework, in which we can obtain the posterior probability distributions that contain valuable statistical information on estimated parameters such as uncertainty and correlations. We use synthetic and real data examples including the data from the SEAM Phase II unconventional reservoir model to demonstrate the performance of our method and discuss insights into the problem of moveout inversion gained from analyzing the posterior probability distributions. Our results suggest that the solutions to the problem of traveltime-only moveout inversion from 2D CMP gathers are relatively well constrained by the data. However, parameter estimation from 3D CMP gathers associated with more moveout parameters and complex anisotropic models are generally nonunique, and there are trade-offs among inverted parameters, especially the quartic coefficients.

Previous locations of earthquakes induced by depletion of the Groningen gas field were not accurate enough to infer which faults in the reservoir are reactivated. A multiplet analysis is performed to identify clusters of earthquakes that have similar waveforms, representing repeating rupture on the same or nearby faults. The multiplet analysis is based on the cross-correlation of seismograms to assess the degree of similarity. Using data of a single station, six earthquake clusters within the limits of the Groningen field were identified for the period 2010 to mid-2014. Four of these clusters were suitable for a relocation method that is based on the difference in travel time between the P- and the S-wave. Events within a cluster can be relocated relative to a master event with improved accuracy by cross-correlating first arrivals. By choosing master events located with a new dense seismic network, the relocated events likely not only have better relative, but also improved absolute locations. For a few clusters with sufficient signal-to-noise detections, we show that the relocation method is successful in assigning clusters to specific faults at the reservoir level. Overall, about 90% of the events did not show clustering, despite choosing low correlation thresholds of 0.5 and 0.6. This suggests that different faults and/or fault segments with likely varying source mechanisms are active in reservoir sub-regions of a few square kilometres.

SUMMARY Earth’s normal modes, or whole Earth oscillations, provide important constraints on Earth’s large-scale 3-D structure. In addition to constraining shear and compressional wave velocities, they are the only seismic data sensitive to density perturbations. Density is particularly difficult to determine, and previous studies have found contradicting results, hence the method chosen to invert normal mode data for 3-D structure becomes important. In the problem of inverting the measured frequency spectra for an earth model, we can take two approaches: (i) a one-step full-spectrum inversion, where normal mode spectra are directly inverted for a mantle model and (ii) a two-step splitting function inversion, where first the spectra are inverted for splitting functions, which are then inverted for a mantle model. Here we compare the methodology and results of both approaches, continuing the work done by Li et al. and Durek & Romanowicz, and extending it to higher spherical harmonic degrees. Using exactly the same normal mode data set, we use both inversion approaches to make 3-D shear wave velocity mantle models. Both approaches give models consistent with previous tomographic studies, although spectral misfits are consistently lower for the one-step full-spectrum inversion. We also show that we cannot draw any conclusions on odd-degree structure in the lower mantle with the currently available normal mode data sets.

Many processes affect sea level near the coast. In this paper, we discuss the major uncertainties in coastal sea-level projections from a process-based perspective, at different spatial and temporal scales, and provide an outlook on how these uncertainties may be reduced. Uncertainty in centennial global sea-level rise is dominated by the ice sheet contributions. Geographical variations in projected sea-level change arise mainly from dynamical patterns in the ocean response and other geophysical processes. Finally, the uncertainties in the short-duration extreme sea-level events are controlled by near coastal processes, storms and tides.

SUMMARY Mantle plumes may play a major role in the transport of heat and mass through the Earth, but establishing their existence and structure using seismology has proven challenging and controversial. Previous studies have mainly focused on imaging plumes using waveform modelling and inversion (i.e. tomography). In this study we investigate the potential visibility of mantle plumes using array methods, and in particular whether we can detect seismic scattering from the plumes. By combining geodynamic modelling with mineral physics data we compute ‘seismic’ plumes whose shape and structure correspond to dynamically plausible thermochemical plumes. We use these seismic models to perform a full-waveform simulation, sending seismic waves through the plumes, in order to generate synthetic seismograms. Using velocity spectral analysis and slowness-backazimuth plots, we are unable to detect scattering. However at longer dominant periods (25 s) we see several arrivals from outside the plane of the great circle path, that are consistent with an apparent bending of the wave front around the plume conduit. At shorter periods (15 s), these arrivals are less obvious and less strong, consistent with the expected changes in the waves' behaviour at higher frequencies. We also detect reflections off the iron-rich chemical pile which serves as the plume source in the D″ region, indicating that D″ reflections may not always be due to a phase transformation. We suggest that slowness-backazimuth analysis may be a useful tool to locate mantle plumes in real array data sets. However, it is important to analyse the data at different dominant periods since, depending on the width of the plume, there is probably an optimum frequency band at which the plume is most visible. Our results also show the importance of studying the incoming energy in all directions, so that any apparently out-of-plane arrivals can be correctly interpreted.

SUMMARYThe mantle transition zone is the region between the globally observed major seismic velocity discontinuities around depths of 410 and 660 km and is important for determining the style of convection and mixing between the upper and the lower mantle. In this study, P-to-S converted waves, or receiver functions, are used to study these discontinuities beneath the Alaskan subduction zone, where the Pacific Plate subducts underneath the North American Plate. Previous tomographic models do not agree on the depth extent of the subducting slab, therefore improved imaging of the Earth structure underneath Alaska is required. We use 27 800 high quality radial receiver functions to make common conversion point stacks. Upper mantle velocity anomalies are accounted for by two recently published regional tomographic S-wave velocity models. Using these two tomographic models, we show that the discontinuity depths within our CCP stacks are highly dependent on the choice of velocity model, between which velocity anomaly magnitudes vary greatly. We design a quantitative test to show whether the anomalies in the velocity models are too strong or too weak, leading to over- or undercorrected discontinuity depths. We also show how this test can be used to rescale the 3-D velocity corrections in order to improve the discontinuity topography maps.After applying the appropriate corrections, we find a localized thicker mantle transition zone and an uplifted 410 discontinuity, which show that the slab has clearly penetrated into the mantle transition zone. Little topography is seen on the 660 discontinuity, indicating that the slab has probably not reached the lower mantle. In the southwest, P410s arrivals have very small amplitudes or no significant arrival at all. This could be caused by water or basalt in the subducting slab, reducing the strength at the 410, or by topography on the 410 discontinuity, preventing coherent stacking. In the southeast of Alaska, a thinner mantle transition zone is observed. This area corresponds to the location of a slab window, and thinning of the mantle transition zone may be caused by hot mantle upwellings.

Although the Planchon-Peteroa Volcanic Complex (PPVC) has undergone many hazardous eruptions, only a small number of geological, geochemical, and geophysical studies have been performed to describe this active volcanic system. In order to characterize the subsurface structures present at the PPVC, we applied seismic interferometry to fracture seismicity originating in this volcanic complex and along active geologic faults located nearby. We utilized seismic data recorded by two arrays of stations deployed in Argentina and Chile. Nine of these stations (three in Chile and six in Argentina) recorded data simultaneously and were used for this application. Only seismic events with energy arriving (sub) vertically to the stations were chosen for processing. According to the magnitude and the location of the selected seismic events, relocated seismic sources were used for the Chilean stations while, for the Argentine stations, only seismic sources located near that array were used. We obtained seismic evidence of the location of the subsurface reflectors underneath each station using zero-offset reflection responses retrieved from seismic interferometry by autocorrelation of (time windows extracted from) the selected seismic events. Then, applying a comparative analysis between the seismic results and the available geological information, we imaged the shallow subsurface of the area enclosed by the Chilean stations, and also by the Argentine stations. The results are consistent with the available geological information, provide accurate depth values for several subsurface discontinuities, indicate areas of higher heterogeneity, and support the emplacement of a magma body at ∼4 km depth from the surface. This work shows the first application of a novel variation of seismic interferometry based on autocorrelations to local-earthquake data recorded in a volcanic area., Facultad de Ciencias Astronómicas y Geofísicas

SUMMARYThe correct implementation of the continuity conditions between different media is fundamental for the accuracy of any wave equation solver used in applications from seismic exploration to global seismology. Ideally, we would like to benchmark a code against an analytical Green’s function. The latter, however, is rarely available for more complex media. Here, we provide a general framework through which wave equation solvers can be benchmarked by comparing plane wave simulations to transmission/reflection (R/T) coefficients from plane-wave analysis with exact boundary conditions (BCs). We show that this works well for a large range of incidence angles, but requires a lot of computational resources to simulate the plane waves. We further show that the accuracy of a numerical Green’s function resulting from a point-source spherical-wave simulation can also be used for benchmarking. The data processing in that case is more involved than for the plane wave simulations and appears to be sufficiently accurate only below critical angles. Our approach applies to any wave equation solver, but we chose the poroelastic wave equation for illustration, mainly due to the difficulty of benchmarking poroelastic solvers, but also due to the growing interest in imaging in poroelastic media. Although we only use 2-D examples, our exact R/T approach can be extended to 3-D and various cases with different interface configurations in arbitrarily complex media, incorporating, for example, anisotropy, viscoelasticity, double porosities, partial saturation, two-phase fluids, the Biot/squirt flow and so on.

We propose a new approach for generating synthetic earthquakes based on the physics of soft glasses. The continuum approach produces yield-stress materials based on Lattice-Boltzmann simulations. We show that if the material is stimulated below yield stress, plastic events occur, which have strong similarities to seismic events. Based on a suitable definition of displacement in the continuum, we showthat the plastic events obey a Gutenberg-Richter lawwith exponents similar to those for real earthquakes. We also find that the average acceleration, energy release, stress drop and interoccurrence times scale with the same exponent. Furthermore, choosing a suitable definition for aftershocks, we show that they follow Omori's law. Finally, the far field power spectra of elastic waves generated by these plastic events decay as ω-2 similar to those observed for seismic waves. Our approach is fully self-consistent and all quantities can be calculated at all scales without the need of ad hoc friction or statistical assumptions. We herefore suggest that our approach may lead to new insights into the physics connecting the micro- and macroscales of earthquakes.

SummarySeismological models of the outer core’s radial velocity structure show that the outermost core is slower than PREM. For models derived from body-wave data these low velocities are confined to the top of the outer core, while normal-mode data prefer a velocity gradient that deviates from PREM throughout the entire outer core. These different models have led to conflicting interpretations regarding the presence of stratification at the top of the outer core. While body-wave based models have been shown to require a compositionally stratified outermost core, the velocity and density profiles obtained from normal-mode data correspond to a homogeneous outer core. In addition, the observed low velocities in the outermost core are difficult to reconcile with compositional models of stratification, as the required enrichment in light elements would generally increase seismic velocities. Here, we investigate how well-suited both seismic body-wave and normal-mode data are to constrain the velocity and density structure of the outer core. To this end, we model and compare the effects of outer-core structure and D″ structure on the differential traveltimes of body-wave phases SmKS and on the centre frequencies of normal modes. We find that a trade-off between outer-core structure and D″ structure exists for both data types, but neither data can be readily explained by reasonable D″ velocities and densities. Low outermost-core velocities are therefore still required by seismological data. Using additional information from the centre frequencies of Stoneley modes—normal modes that are particularly sensitive to variations in velocity and density at the top of the outer core—we confirm that normal-mode data indeed require low velocities with respect to PREM in the outermost core, similar to a recent normal-mode model, and an overall higher outer-core density. The presence of buoyant stratification in the outermost core is therefore not immediately supported by the centre frequencies of Stoneley modes. Stratification with high seismic velocity, as one would expect from most straightforward stratification-forming processes, is directly contradicted by our results.

SUMMARY We measure the seismic anisotropy of the inner core using PKPbc-PKPdf and PKPab-PKPdf differential traveltimes, as a function of the angle ζ between the Earth’s rotation axis and the ray path in the inner core. Previous research relied heavily on body waves originating in the South Sandwich Islands (SSI) and travelling to seismic stations in Alaska to sample inner core velocities with low ζ (polar paths). These SSI polar paths are problematic because they have anomalous travel time anomalies, there are no ultra-polar SSI paths with ζ < 20° and they only cover a small part of the inner core. Here we improve constraints on inner core anisotropy using recently installed seismic stations at high latitudes, especially in the Antarctic, allowing us to measure ultra-polar paths with ζ ranging from 20°–5°. Our new data show that the SSI’s polar events are fast but still within the range of velocities measured from ray paths originating elsewhere. We further investigate the effect of mantle structure on our data set finding that the SSI data are particularly affected by fast velocities underneath the SSI originating from the subducted South Georgia slab, which is currently located just above the core mantle boundary. This fast velocity region results in mantle structure being misinterpreted as inner core structure and we correct for this using a P-wave tomographic model. We also analyse the effect of velocity changes on the ray paths within the inner core and find that faster velocities significantly change the ray path resulting in the ray travelling deeper into the inner core and spending more time in the inner core. To remove this effect, we propose a simple but effective method to correct each event-station pair for the velocity-dependent ray path changes in the inner core, producing a more reliable fractional traveltime measurement. Combining the new ultra-polar data with mantle and ray path corrections results in a more reliable inner core anisotropy measurement and an overall measured anisotropy of 1.9–2.3 per cent for the whole inner core. This is lower than previous body wave studies (3 per cent anisotropy) and in better agreement with the value of inner core anisotropy measured by normal modes (2 per cent anisotropy). We also identify regional variation of anisotropic structure in the top 500 km of the inner core, which appears to be more complex than simple hemispherical variations. These regional variations are independent of the SSI data and are still present when these data are excluded. We also find a potential innermost inner core with a radius of 690 km and stronger anisotropy.

We present an accelerated full-waveform inversion based on dynamic mini-batch optimization, which naturally exploits redundancies in observed data from different sources. The method rests on the selection of quasi-random subsets (mini-batches) of sources, used to approximate the misfit and the gradient of the complete data set. The size of the mini-batch is dynamically controlled by the desired quality of the gradient approximation. Within each mini-batch, redundancy is minimized by selecting sources with the largest angular differences between their respective gradients, and spatial coverage is maximized by selecting candidate events with Mitchell’s best-candidate algorithm. Information from sources not included in a specific mini-batch is incorporated into each gradient calculation through a quasi-Newton approximation of the Hessian, and a consistent misfit measure is achieved through the inclusion of a control group of sources. By design, the dynamic mini-batch approach has several main advantages: (1) The use of mini-batches with adaptive size ensures that an optimally small number of sources is used in each iteration, thus potentially leading to significant computational savings; (2) curvature information is accumulated and exploited during the inversion, using a randomized quasi-Newton method; (3) new data can be incorporated without the need to re-invert the complete data set, thereby enabling an evolutionary mode of full-waveform inversion. We illustrate our method using synthetic and real-data inversions for upper-mantle structure beneath the African Plate. In these specific examples, the dynamic mini-batch approach requires around 20 per cent of the computational resources in order to achieve data and model misfits that are comparable to those achieved by a standard full-waveform inversion where all sources are used in each iteration., Geophysical Journal International, 221 (2), ISSN:0956-540X, ISSN:1365-246X

Lower mantle tomography models consistently feature an increase in the ratio of shear-wave velocity ( V S ) to compressional-wave velocity ( V P ) variations and a negative correlation between shear-wave and bulk-sound velocity ( V C ) variations. These seismic characteristics, also observed in the recent SP12RTS model, have been interpreted to be indicative of large-scale chemical variations. Other explanations, such as the lower mantle post-perovskite (pPv) phase, which would not require chemical heterogeneity, have been explored less. Constraining the origin of these seismic features is important, as geodynamic simulations predict a fundamentally different style of mantle convection under both scenarios. Here, we investigate to what extent the presence of pPv explains the observed high V S / V P ratios and negative V S – V C correlation globally. We compare the statistical properties of SP12RTS with the statistics of synthetic tomography models, derived from both thermal and thermochemical models of 3-D global mantle convection. We convert the temperature fields of these models into seismic velocity structures using mineral physics lookup tables with and without pPv. We account for the limited tomographic resolution of SP12RTS using its resolution operator for both V S and V P structures. This allows for direct comparisons of the resulting velocity ratios and correlations. Although the tomographic filtering significantly affects the synthetic tomography images, we demonstrate that the effect of pPv remains evident in the ratios and correlations of seismic velocities. We find that lateral variations in the presence of pPv have a dominant influence on the V S / V P ratio and V S – V C correlation, which are thus unsuitable measures to constrain the presence of large-scale chemical variations in the lowermost mantle. To explain the decrease in the V S / V P ratio of SP12RTS close to the CMB, our results favour a pPv-bearing CMB region, which has implications for the stability field of pPv in the Earth's mantle.

Time-domain processing has a long history in seismic imaging and has always been a powerful workhorse that is routinely used. It generally leads to an expeditious construction of the subsurface velocity model in time, which can later be expressed in the Cartesian depth coordinates via a subsequent time-to-depth conversion. The conventional practice of such a conversion is done using Dix inversion, which is exact in the case of laterally homogeneous media. For other media with lateral heterogeneity, the time-to-depth conversion involves solving a more complex system of partial differential equations (PDEs). We have developed an efficient alternative for time-to-depth conversion and interval velocity estimation based on the assumption of weak lateral velocity variations. By considering only first-order perturbative effects from lateral variations, the exact system of PDEs required to accomplish the exact conversion reduces to a simpler system that can be solved efficiently in a layer-stripping (downward-stepping) fashion. Numerical synthetic and field data examples show that our method can achieve reasonable accuracy and is significantly more efficient than previously proposed methods with a speedup by an order of magnitude.

In seismic tomography we map the wave speed structure inside the Earth, but we ultimately seek to interpret those images in terms of physical parameters. This is challenging because many parameters can trade‐off with each other to produce a given wave speed. The problem is compounded by the convention of mapping seismic structures as perturbations relative to a 1‐D reference model, rather than absolute wave speeds. Using a full waveform tomography model of Europe as a case study, we quantify the extent to which thermochemical and dynamic properties can be constrained using only S wave speed, expressed in absolute values. The wave speed distributions of this tomography model are compared with 4 million thermochemical models, whose seismic properties are computed via thermodynamic modeling. These models sample the full range of realistic mantle compositions, including variable water and melt contents, and mineral intrinsic anelasticity is taken into account. Intrinsic anelasticity causes waves to travel more slowly at higher temperatures, leading to seismic attenuation, but the sensitivity of the wave speed reduction to temperature is, in turn, controlled by the wave frequency. Global studies of surface waves indicate an anticorrelation between S wave speed and attenuation. We therefore only retain thermochemical models satisfying this anticorrelation. Our study indicates that the frequency dependence of anelasticity, α, depends on temperature or rheology, with α ≈ 0.1 being most appropriate in cold or lithospheric mantle and α ≈ 0.3 in warmer regions (i.e., the asthenosphere). Additionally, the slowest regions require specific compositions and/or a velocity‐weakening mechanism, such as partial melting, elastically accommodated grain boundary sliding, or water., Key Points Knowing the S wave speed precisely with a loose constraint on mantle attenuation places strong constraints on the temperatureThe frequency dependence of anelasticity α is variable: ~0.1 in cold/lithospheric mantle and ~0.3 in warm/asthenospheric mantleEither partial melting or elastically accommodated grain boundary sliding is required to explain the slowest wave speeds at 130 km

Spectra of whole Earth oscillations or normal modes provide important constraints on Earth’s large scale structure. The most convenient way to include normal mode constraints in global tomographic models is by using splitting functions or structure coefficients, which describe how the frequency of a specific mode varies regionally. Splitting functions constrain 3D variations in velocity, density structure and boundary topography. They may also constrain anisotropy, especially when combining information from spheroidal modes, which are mainly sensitive to P-SV structure, with toroidal modes, mainly sensitive to SH structure. Spheroidal modes have been measured extensively, but toroidal modes have proven to be much more difficult and as a result only a limited number of toroidal modes have been measured so far. Here we expand the splitting function studies by Resovsky and Ritzwoller (1998) and Deuss et al. (2013), by focusing specifically on toroidal mode overtone observations. We present splitting function measurements for 19 self-coupled toroidal modes of which 13 modes have not been measured before. They are derived from radial and transverse horizontal component normal mode spectra up to 5 mHz for 91 events with MW ≥ 7.4 from the years 1983-2018. Our data include the Tohoku event of 2011 (9.1MW), the Okhotsk event of 2013 (8.3MW) and the Fiji Island event from 2018 (8.2MW). Our measurements provide new constraints on upper and lower mantle shear wave velocity structure and in combination with existing spheroidal mode measurements can be used in future inversions for anisotropic mantle structure. Our new splitting function coefficient data set will be available online.

Advances in our understanding of Earth's thermal evolution and the style of mantle convection rely on robust seismological constraints on lateral variations of density. The large-low-shear-wave velocity provinces (LLSVPs) atop the core–mantle boundary beneath Africa and the Pacific are the largest structures in the lower mantle, and hence severely affect the convective flow. Here, we show that anomalous splitting of Stoneley modes, a unique class of free oscillations that are perturbed primarily by velocity and density variations at the core–mantle boundary, is explained best when the overall density of the LLSVPs is lower than the surrounding mantle. The resolved density variations can be explained by the presence of post-perovskite, chemical heterogeneity or a combination of the two. Although we cannot rule out the presence of a ∼100-km-thick denser-than-average basal structure, our results support the hypothesis that LLSVPs signify large-scale mantle upwelling in two antipodal regions of the mantle., Large-low-shear-wave velocity provinces (LLSVPs) are present at the core–mantle boundary. Here, the authors show that splitting of Stoneley modes is probably due to a lower density of LLSVPs than the surrounding mantle because of the presence of post-perovskite, chemical heterogeneity or both.

Density variations drive mass transport in the Earth from plate tectonics to convection in the mantle and core. Nevertheless, density remains poorly known because most geophysical measurements used to probe the Earth's interior either have little sensitivity to density, suffer from trade-offs or from non-uniqueness. With the ongoing expansion of computational power, it has become possible to accurately model complete seismic wavefields in a 3-D heterogeneous Earth, and to develop waveform inversion techniques that account for complicated wavefield effects. This may help to improve resolution of density. Here, we present a pilot study where we explore the extent to which waveform inversion may be used to better recover density as a separate, independent parameter. We perform numerical simulations in 2-D to investigate under which conditions, and to what extent density anomalies may be recovered in the Earth's mantle. We conclude that density can indeed be constrained by seismic waveforms, mainly as a result of scattering effects at density contrasts. As a consequence, the low-frequency part of the wavefield is the most important for constraining the actual extent of anomalies. While the impact of density heterogeneities on the wavefield is small compared to the effects of velocity variations, it is likely to be detectable in modern regional- to global-scale measurements. We also conclude that the use of gravity data as additional information does not help to further improve the recovery of density anomalies unless strong a priori constraints on the geometry of density variations are applied. This is a result of the inherent physical non-uniqueness of potential-field inverse problems. Finally, in the limited numerical setup that we employ, we find that the initially supplied anomalies in S- and P-velocity models are of minor importance., Geophysical Journal International, 209 (2), ISSN:0956-540X, ISSN:1365-246X

An areal distribution of sensors can be used for estimating the direction of incoming waves through beamforming. Beamforming may be implemented as a phase-shifting and stacking of data recorded on the different sensors (i.e., conventional beamforming). Alternatively, beamforming can be applied to cross-correlations between the waveforms on the different sensors. We derive a kernel for beamforming cross-correlated data and call it cross-correlation beamforming (CCBF). We point out that CCBF has slightly better resolution and aliasing characteristics than conventional beamforming. When auto-correlations are added to CCBF, the array response functions are the same as for conventional beamforming. We show numerically that CCBF is more resilient to non-coherent noise. Furthermore, we illustrate that with CCBF individual receiver-pairs can be removed to improve mapping to the slowness domain. An additional flexibility of CCBF is that cross-correlations can be time-windowed prior to beamforming, e.g., to remove the directionality of a scattered wavefield. The observations on synthetic data are confirmed with field data from the SPITS array (Svalbard). Both when beamforming an earthquake arrival and when beamforming ambient noise, CCBF focuses more of the energy to a central beam. Overall, the main advantage of CCBF is noise suppression and its flexibility to remove station pairs that deteriorate the signal-related beampower. ELECTRONIC SUPPLEMENTARY MATERIAL: The online version of this article (doi:10.1007/s10950-016-9612-6) contains supplementary material, which is available to authorized users.

Using spectral-element simulations of wave propagation, we investigated the sensitivity of seismic waveforms, recorded on transverse components, to upper-mantle discontinuities in 1-D and 3-D background models. These sensitivity kernels, or Fréchet derivatives, illustrate the spatial sensitivity to model parameters, of which those for shear wave speed and the surface topography of internal boundaries are discussed in this paper. We focus on the boundaries at 400 and 670 km depth of the mantle transition zone. SS precursors have frequently been used to infer the topography of upper-mantle discontinuities. These seismic phases are underside reflections off these boundaries and are usually analysed in the distance range of 110°–160°. This distance range is chosen to minimize the interference from other waves. We show sensitivity kernels for consecutive time windows at three characteristic epicentral distances within the 110°–160° range. The sensitivity kernels are computed with the adjoint method using synthetic data. From our simulations we can draw three main conclusions: (i) The exact Fréchet derivatives show that in all time windows, and also in those centred on the SS precursors, there is interference from other waves. This explains the difficulty reported in the literature to correct for 3-D shear wave speed perturbations, even if the 3-D structure is perfectly known. (ii) All studies attempting to map the topography of the 400 and 670 km discontinuities to date assume that the traveltimes of SS precursors can be linearly decomposed into a 3-D elastic structure and a topography part. We recently showed that such a linear decomposition is not possible for SS precursors, and the sensitivity kernels presented in this paper explain why. (iii) In agreement with previous work, we show that other parts of the seismograms have greater sensitivity to upper-mantle discontinuities than SS precursors, especially multiply bouncing S waves exploiting the S-wave triplications due to the mantle transition zone. These phases can potentially improve the inference of global topographic variations of the upper-mantle discontinuities in the context of full waveform inversion in a joint inversion for (an)elastic parameters and topography., Geophysical Journal International, 210 (3), ISSN:0956-540X, ISSN:1365-246X

In a coordinate system fixed with respect to the rotating Earth, the Coriolis force deflects an object sideways relative to its direction of motion. A beautiful demonstration of that effect is the Foucault pendulum, illustrated in figure 1a. As the long pendulum rocks back and forth, the Coriolis force deflects it the same way on both the forward and reverse swings—to the right in the Northern Hemisphere and to the left in the Southern Hemisphere. The net result is that the pendulum’s plane of oscillation rotates clockwise in the Northern Hemisphere, a change evidenced in figure 1a by the little cylinders that the pendulum has knocked down. The time rate of change of the oscillation direction is given by ϕ̇=−Ωcosθϕ̇=−Ωcosθ, where, as illustrated in figure 1b, Ω is the rotation rate of Earth and θθ is the colatitude—that is, the angle between the local vertical and Earth’s rotation axis. The minus sign arises because the pendulum maintains its oscillation direction as Earth rotates under it. As a consequence, the pendulum’s direction of oscillation rotates in the sense opposite that of Earth’s rotation, a result most readily visualized by imagining the pendulum to be at the North Pole.

We investigate the velocity and density structure of the mantle beneath the Northern Atlantic at a depth of 410 km where the olivine to wadsleyite phase transformation occurs. Measuring polarities of precursor arrivals to PP seismic waves that reflect at this transition we analyze over 1700 teleseismic seismograms from 13 different source-receiver combinations using the advantages of high-resolution array seismology methods and crossing ray paths. The final dataset consists of 45 events with Mw ≥ 5.8 with a good coverage of reflection points beneath the investigation area. We find several events where the polarity of the precursor signal is opposite to that of the PP wave, however, events with same polarity of precursor and PP wave are also observed. We test several causes for changing polarity of reflections at the 410 km discontinuity and find out that there is a dependence of the polarity on epicentral distance. We computed the reflection coefficients of the precursor wave using the Zoeppritz equations with the initial values of density, VP and VS of a pyrolite model for the olivine-wadsleyite phase transition and varied the values by ±10% above and below 410 km depth. More than 729 million combinations of density, compressional and shear wave velocities for olivine and wadsleyite layers were tested to find the combinations that can explain our polarity-distance observations. While the best-fitting models have a smaller positive contrast than pyrolite in density, a small negative contrast for P and S wave velocities is needed. Possibilities to explain these values include combination of a hydrous wadsleyite layer beneath, and anhydrous or Fe-enriched olivine above the boundary.

Using the spectral-element method, we explored the effect of topography of upper-mantle discontinuities on the traveltimes of SS precursors recorded on transverse component seismograms. The latter are routinely used to infer the topography of mantle transition zone discontinuities. The step from precursory traveltimes to topographic changes is mainly done using linearised ray theory, or sometimes using finite-frequency kernels. We simulated exact seismograms in 1-D and 3-D elastic models of the mantle. In a second simulation, we added topography to the discontinuities. We compared the waveforms obtained with and without topography by cross correlation of the SS precursors. Since we did not add noise, the precursors are visible in individual seismograms without the need of stacking. The resulting time anomalies were then converted into topographic variations and compared to the original topographic models. Based on the correlation between initial and inferred models, and provided that ray coverage is good, we found that linearised ray theory gives a relatively good idea on the location of the uplifts and depressions of the discontinuities. It seriously underestimates the amplitude of the topographic variations by a factor ranging between 2 and 7. Real data depend on the 3-D elastic structure and the topography. All studies to date correct for the 3-D elastic effects assuming that the traveltimes can be linearly decomposed into a structure and a discontinuity part. We found a strong non-linearity in this decomposition which cannot be modelled without a fully non-linear inversion for elastic structure and discontinuities simultaneously.

We present the first nationwide crustal thickness and Vp/Vs maps for Botswana based on the analysis of new P wave receiver functions of NARS‐Botswana network integrated with previous receiver function results in Botswana. Using H‐K analysis, we found crustal thickness values ranging from 34 km for the Okavango Rift Zone to 49 km at the border between the Magondi Belt and the Zimbabwe Craton. For stations with significant sediment cover, a sediment correction was applied based on sequential H‐K stacking. We observed distinct differences for the Kaapvaal craton. The eastern part has a high Vp/Vs ratio typical of a predominantly mafic composition, suggesting lateral extension of the Bushveld mafic complex. On the other hand, the western part with a Vp/Vs ratio of 1.67 is felsic, probably as a result of delamination caused by Proterozoic rifting processes. Further to the west of the Kaapvaal Craton, we found a crustal thickness of 42 km and a Vp/Vs ratio of 1.76 for the Nosop Basin. These values are similar to other cratonic regions in Botswana, suggesting the presence of a buried craton as proposed by previous studies. We confirm a relatively thin crust (∼34–39 km), compared to the rest of Botswana, and high Vp/Vs ratio (∼1.84) underneath the Okavango Rift Zone found by previous receiver function studies. Notably, we also found a relatively thin crust (37 km) and high Vp/Vs ratio (1.84) in central Botswana underneath the Passarge Basin.

An analysis of seismic data reveals the location and quantity of melted rock, known as melt, in Earth’s upper mantle. The results show how these factors are correlated with the movement of the planet’s tectonic plates. A possible explanation for the low-velocity zone in the mantle.

We present seismic observations of the uppermost layer of the inner core. This was formed most recently, thus its seismic features are related to current solidification processes. Previous studies have only constrained the east-west hemispherical seismic velocity structure in the Earth’s inner core at depths greater than 15 km below the inner core boundary. The properties of shallower structure have not yet been determined, because the seismic waves PKIKP and PKiKP used for differential travel time analysis arrive close together and start to interfere. Here, we present a method to make differential travel time measurements for waves that turn in the top 15 km of the inner core, and measure the corresponding seismic velocity anomalies. We achieve this by generating synthetic seismograms to model the overlapping signals of the inner core phase PKIKP and the inner core boundary phase PKiKP. We then use a waveform comparison to attribute different parts of the signal to each phase. By measuring the same parts of the signal in both observed and synthetic data, we are able to calculate differential travel time residuals. We apply our method to data with ray paths which traverse the Pacific hemisphere boundary. We generate a velocity model for this region, finding lower velocity for deeper, more easterly ray paths. Forward modelling suggests that this region contains either a high velocity upper layer, or variation in the location of the hemisphere boundary with depth and/or latitude. Our study presents the first direct seismic observation of the uppermost 15 km of the inner core, opening new possibilities for further investigating the inner core boundary region.

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 M w 7.2 El Mayor–Cucapah event. Our results are compatible with published point‐source estimates for this event within the respective uncertainty bounds. Online Material: Additional information on the neural network methodology and implementation details, tables on neural network parameters, crustal model and reference double‐couple solution, and figures showing prediction error, crustal models, normalized displacements, and histograms of weighted parameters.

Density heterogeneities are the source of mass transport in the Earth. However, the 3-D density structure remains poorly constrained because travel times of seismic waves are only weakly sensitive to density. Inspired by recent developments in seismic waveform tomography, we investigate whether the visibility of 3-D density heterogeneities may be improved by inverting not only travel times of specific seismic phases but complete seismograms. As a first step in this direction, we perform numerical experiments to estimate the effect of 3-D crustal density heterogeneities on regional seismic wave propagation. While a finite number of numerical experiments may not capture the full range of possible scenarios, our results still indicate that realistic crustal density variations may lead to travel-time shifts of up to ∼ 1s and amplitude variations of several tens of percent over propagation distances of ∼ 1000km. Both amplitude and travel-time variations increase with increasing epicentral distance and increasing medium complexity, i.e. decreasing correlation length of the heterogeneities. They are practically negligible when the correlation length of the heterogeneities is much larger than the wavelength. However, when the correlation length approaches the wavelength, density-induced waveform perturbations become prominent. Recent regional-scale full-waveform inversions that resolve structure at the scale of a wavelength already reach this regime. Our numerical experiments suggest that waveform perturbations induced by realistic crustal density variations can be observed in high-quality regional seismic data. While density-induced travel-time differences will often be small, amplitude variations exceeding ±10% are comparable to those induced by 3-D velocity structure and attenuation. While these results certainly encourage more research on the development of 3-D density tomography, they also suggest that current full-waveform inversions that use amplitude information may be biased due to the neglect of 3-D variations in density. ISSN:1869-9510 ISSN:1869-9529

The formation of the Gulf of California has been related to the cessation of subduction of the Guadalupe and Magdalena microplates. Various studies have identified features that point to the presence of a slab remnant beneath the Baja California peninsula, but its depth range and lateral extent remained unclear. In this study we used surface wave phase velocity and receiver function data of NARS-Baja stations around the Gulf of California to better constrain the location of the slab. For stations in central and southern Baja California the shear velocity models show an upper mantle high-velocity layer with its top in the depth range from 115 to 135km and a thickness varying between roughly 40 and 60km. These high-velocity anomalies are interpreted as subducted slab remnants. In contrast, the models for the northern peninsula show no slab signature. This change directly correlates with the variation in relative motion between the Baja California peninsula and the Pacific plate as measured by GPS data. It is inferred that the stalled slab fragments beneath the peninsula produce strong coupling between Baja California and the Pacific plate. The shear velocity models for stations on the Mexican mainland show a layer of higher velocities above a low-velocity upper mantle. In the North, the low-velocity mantle, starting at a depth of 40km, is associated with upwelling as suggested by previous studies. Further south, the transition from higher to lower mantle velocities occurs around 80km depth, which is a typical value for the lithosphere-asthenosphere boundary. Furthermore, the models show strong crustal thinning towards the gulf, both from the peninsula as well as from the Mexican mainland.

The results of mantle convection simulations are fully determined by the input parameters and boundary conditions used. These input parameters can be for initialisation, such as initial mantle temperature, or can be constant values, such as viscosity exponents. However, knowledge of Earth-like values for many input parameters are very poorly constrained, introducing large uncertainties into the simulation of mantle flow. Convection is highly non-linear, therefore linearised inversion methods cannot be used to recover past configurations over more than very short periods of time, which makes finding both initial and constant simulation input parameters very difficult. In this paper, we demonstrate a new method for making inferences about simulation input parameters from observations of the mantle temperature field after billions of years of convection. The method is fully probabilistic. We use prior sampling to construct probability density functions for convection simulation input parameters, which are represented using neural networks. Assuming smoothness, we need relatively few samples to make inferences, making this approach much more computationally tractable than other probabilistic inversion methods. As a proof of concept, we show that our method can invert the amplitude spectra of temperature fields from 2D convection simulations, to constrain yield stress, surface reference viscosity and the initial thickness of primordial material at the CMB, for our synthetic test cases. The best constrained parameter is yield stress. The reference viscosity and initial thickness of primordial material can also be inferred reasonably well after several billion years of convection., Physics of the Earth and Planetary Interiors, 257, ISSN:0031-9201, ISSN:1872-7395

We present the new model SP12RTS of isotropic shear-wave (Vs) and compressional-wave (Vp) velocity variations in the Earth’s mantle. SP12RTS is derived using the same methods as employed in the construction of the shear-wave velocity models S20RTS and S40RTS, and the same data types. SP12RTS includes additional traveltime measurements of P-waves and new splitting measurements: 33 normal modes with sensitivity to the compressional-wave velocity and 9 Stoneley modes with sensitivity primarily to the lowermost mantle. Contrary to S20RTS and S40RTS, variations in Vs and Vp are determined without invoking scaling relationships. Lateral velocity variations in SP12RTS are parametrised using spherical harmonics up to degree 12, to focus on long-wavelength features of Vs and Vp and their ratio R. Largelow-velocity provinces (LLVPs) are observed for both Vs and Vp. SP12RTS also features an increase of R up to 2500 km depth, followed by a decrease towards the core-mantle boundary. A negative correlation between the shear-wave and bulk-sound velocity variations is observed for both the LLVPs and the surrounding mantle. These characteristics can be explained by the presence of post-perovskite or large-scale chemical heterogeneity in the lower mantle.

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 Frechet derivatives based on a spectral-element method.

The increase in number and strength of shallow induced seismicity connected to the Groningen gas field since 2003 and the occurrence of aML3.6 event in 2012 started the development of a full probabilistic seismic hazard assessment (PSHA) for Groningen, required by the regulator. Densification of the monitoring network resulted in a decrease of the location threshold and magnitude of completeness down to ~ML=0.5. Combined with a detailed local velocity model, epicentre accuracy could be reduced from 0.5–1km to 0.1–0.3km and a vertical resolution ~0.3km. Time-dependent seismic activity is observed and taken into account into PSHA calculations. Development of the Ground Motion Model for Groningen resulted in a significant reduction of the hazard. Comparison of different implementations of the PSHA, using different source models, based on either a compaction model and production scenarios or on extrapolation of past seismicity, and methods of calculation, shows similar results.

Despite the ever increasing availability of computational power, real-time source inversions based on physical modeling of wave propagation in realistic media remain challenging. We investigate how a nonlinear Bayesian approach based on pattern recognition and synthetic 3-D Green's functions can be used to rapidly invert strong-motion data for point source parameters by means of a case study for a fault system in the Los Angeles Basin. The probabilistic inverse mapping is represented in compact form by a neural network which yields probability distributions over source parameters. It can therefore be evaluated rapidly and with very moderate CPU and memory requirements. We present a simulated real-time inversion of data for the 2008 Mw 5.4 Chino Hills event. Initial estimates of epicentral location and magnitude are available ∼14 s after origin time. The estimate can be refined as more data arrive: by ∼40 s, fault strike and source depth can also be determined with relatively high certainty.

The Tyrrhenian Sea in the Mediterranean formed as the result of roll-back of the Adriatic and Ionian subducting plates. It is mostly underlain by strongly thinned continental lithosphere, but contains two small oceanic basins in the southern Tyrrhenian, the youngest one located just behind the active magmatic arc. Its regional setting with dense station coverage provides a unique opportunity to derive a high-resolution, 3-D shear-velocity model of this back-arc basin and surrounding onshore areas using interstation Rayleigh-wave dispersion measurements. Our tomographic model, extending to a depth of approximately 160 km, displays a pronounced, nearly ring-shaped low shear-velocity zone between 70 and 110 km depth which surrounds the older oceanic Vavilov Basin. The sharp velocity decrease at 70 km depth can be explained by the transition from a relatively dry lithospheric mantle to more hydrous asthenospheric mantle material. The tectonic evolution of the region and the correlation of the low-velocity anomaly with subduction-related volcanism indicate that the low-velocity anomaly reflects hydrous mantle material in (present or former) mantle wedge regions. We suggest that the absence of the low-velocity zone beneath the Vavilov Basin is due to mantle dehydration caused by the creation of MORB crust. Whereas temperature effects may dominate the asthenospheric shear-velocity differences between various back-arc basins, we find that the variations in shear-velocity structure within the Tyrrhenian area are best explained by variations in mantle water content.

Seismic free oscillations, or normal modes, provide a convenient tool to calculate low-frequency seismograms in heterogeneous Earth models. A procedure called ‘full mode coupling’ allows the seismic response of the Earth to be computed. However, in order to be theoretically exact, such calculations must involve an infinite set of modes. In practice, only a finite subset of modes can be used, introducing an error into the seismograms. By systematically increasing the number of modes beyond the highest frequency of interest in the seismograms, we investigate the convergence of full-coupling calculations. As a rule-of-thumb, it is necessary to couple modes 1–2 mHz above the highest frequency of interest, although results depend upon the details of the Earth model. This is significantly higher than has previously been assumed. Observations of free oscillations also provide important constraints on the heterogeneous structure of the Earth. Historically, this inference problem has been addressed by the measurement and interpretation of splitting functions. These can be seen as secondary data extracted from low frequency seismograms. The measurement step necessitates the calculation of synthetic seismograms, but current implementations rely on approximations referred to as self- or group-coupling and do not use fully accurate seismograms. We therefore also investigate whether a systematic error might be present in currently published splitting functions. We find no evidence for any systematic bias, but published uncertainties must be doubled to properly account for the errors due to theoretical omissions and regularization in the measurement process. Correspondingly, uncertainties in results derived from splitting functions must also be increased. As is well known, density has only a weak signal in low-frequency seismograms. Our results suggest this signal is of similar scale to the true uncertainties associated with currently published splitting functions. Thus, it seems that great care must be taken in any attempt to robustly infer details of Earth's density structure using current splitting functions.

When oceanic basins close after a long period of convergence and subduction, continental collision and mountain building is a common consequence. Slab segmentation is expected to have been relatively common just prior to closure of other oceans in the geological past, and may explain some of the complexity that geologists have documented in the Tibetan plateau also. We focus on the eastern Mediterranean basin, which is the last remainder of a once hemispherical neo-Tethys ocean that has nearly disappeared due to convergence of the India and Africa/Arabia plates with the Eurasia plate. We present new results of full-waveform tomography that allow us to image both the crust and upper mantle in great detail. We show that a major discontinuity exists between western Anatolia lithosphere and the region to the east of it. Also, the correlation of geological features and the crustal velocities is substantially stronger in the west than in the east. We interpret these observations as the imprint in the overriding plate of fragmentation of the neo-Tethys slab below it. This north-dipping slab may have fragmented following the Eocene (about 35 million years ago) arrival of a continental promontory (Central Anatolian Core Complex) at the subduction contact. From the Eocene through the Miocene, slab roll-back ensued in the Aegean and west Anatolia, while the Cyprus–Bitlis slab subducted horizontally beneath central and east Anatolia. Following collision of Arabia (about 16 million years ago), the Cyprus–Bitlis slab steepened, exposing the crust of central and east Anatolia to high temperature, and resulting in the velocity structure that we image today. Slab fragmentation thus was a major driver of the evolution of the overriding plate as collision unfolded.

This work presents the first comprehensive 3-D model of the crust beneath The Netherlands. To obtain this model, we designed the NARS-Netherlands project, a dense deployment of broadband stations in the area. Rayleigh and Love wave group velocity dispersion was measured from ambient noise cross-correlations. Azimuthally anisotropic group velocity maps were then constructed and the isotropic part was used to determine a shear wave speed model that includes the effects of radial anisotropy. Employing the Neighbourhood Algorithm for the depth inversion, we obtained probabilistic estimates of the radially anisotropic model parameters. We found that the variations in the thickness of the top layer largely match the transition from sediments of Permian age to those of Carboniferous age. Regions of high faulting density such as the West Netherlands Basin and Roer Valley Graben are recognized in our model by their negative radial anisotropy (V SH − V SV < 0). The model has a mid-crustal discontinuity at a depth of around 13 km and the average Moho depth is 33 km, with most of its depth variations within 2 km. Specifically, a localized Moho uplift to a depth of 29 km is found within Roer Valley Graben, in the Campine region in Belgium. Furthermore, our Rayleigh and Love wave group velocity data at periods of around 20 s show evidence for azimuthal anisotropy with a NW-SE fast direction. This anisotropy is likely related to NW-SE rock fabric in the lower crust thought to originate from the Caledonian deformation.

Whenever a geophysical image is to be constructed, a variety of choices must be made. Some, such as those governing data selection and processing, or model parametrization, are somewhat arbitrary: there may be little reason to prefer one choice over another. Others, such as defining the theoretical framework within which the data are to be explained, may be more straightforward: typically, an ‘exact’ theory exists, but various approximations may need to be adopted in order to make the imaging problem computationally tractable. Differences between any two images of the same system can be explained in terms of differences between these choices. Understanding the impact of each particular decision is essential if images are to be interpreted properly—but little progress has been made towards a quantitative treatment of this effect. In this paper, we consider a general linearized inverse problem, applicable to a wide range of imaging situations. We write down an expression for the difference between two images produced using similar inversion strategies, but where different choices have been made. This provides a framework within which inversion algorithms may be analysed, and allows us to consider how image effects may arise. In this paper, we take a general view, and do not specialize our discussion to any specific imaging problem or setup (beyond the restrictions implied by the use of linearized inversion techniques). In particular, we look at the concept of ‘hybrid inversion’, in which highly accurate synthetic data (typically the result of an expensive numerical simulation) is combined with an inverse operator constructed based on theoretical approximations. It is generally supposed that this offers the benefits of using the more complete theory, without the full computational costs. We argue that the inverse operator is as important as the forward calculation in determining the accuracy of results. We illustrate this using a simple example, based on imaging the density structure of a vibrating string.