Surface wave tomography for azimuthal anisotropy in a strongly reduced parameter space

Large scale seismic anisotropy in the Earth's mantle is likely dynamically supported by the mantle's deformation; therefore, tomographic imaging of 3-D anisotropic mantle seismic velocity structure is an important tool to understand the dynamics of the mantle. While many previous studies have focused on special cases of symmetry of the elastic properties, it would be desirable for evaluation of dynamic models to allow more general axis orientation. In this study, we derive 3-D finite-frequency surface wave sensitivity kernels based on the Born approximation using a general expression for a hexagonal medium with an arbitrarily oriented symmetry axis. This results in kernels for two isotropic elastic coefficients, three coefficients that define the strength of anisotropy, and two angles that define the symmetry axis. The particular parametrization is chosen to allow for a physically meaningful method for reducing the number of parameters considered in an inversion, while allowing for straightforward integration with existing approaches for modelling body wave splitting intensity measurements. Example kernels calculated with this method reveal physical interpretations of how surface waveforms are affected by 3-D velocity perturbations, while also demonstrating the non-linearity of the problem as a function of symmetry axis orientation. The expressions are numerically validated using the spectral element method. While challenges remain in determining the best inversion scheme to appropriately handle the non-linearity, the approach derived here has great promise in allowing large scale models with resolution of both the strength and orientation of anisotropy.     

Finite-frequency sensitivity of body waves to anisotropy based upon adjoint methods

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.     

Finite-frequency vectorial tomography: a new method for high-resolution imaging of upper mantle anisotropy

Amplitude measurements of the transverse component of SKS waves, the so-called splitting intensity, can be used to formulate a non-linear inverse problem to image the 3-D variations of upper mantle anisotropy. Assuming transverse isotropy (or hexagonal symmetry), one can parametrize anisotropy by two anisotropic parameters and two angles describing the orientation of the symmetry axis. These can also be written as two collinear pseudo-vectors. The tomographic process consists of retrieving the spatial distribution of these pseudo-vectors, and thus resembles surface wave vectorial tomography. Spatial resolution results from the sensitivity of low-frequency SKS waves to seismic anisotropy off the ray path. The expressions for the 3-D sensitivity kernels for splitting intensity are derived, including the near-field contributions, and validated by comparison with a full wave equation solution based upon the finite element method. These sensitivity kernels are valid for any orientation of the symmetry axis, and thus generalize previous results that were only valid for a horizontal symmetry axis. It is shown that both lateral and vertical subwavelength variations of anisotropy can be retrieved with a dense array of broad-band stations, even in the case of vertically propagating SKS waves.     

On crustal corrections in surface wave tomography

Mantle models from surface waves rely on good crustal corrections. We investigated how far ray theoretical and finite frequency approximations can predict crustal corrections for fundamental mode surface waves. Using a spectral element method, we calculated synthetic seismograms in transversely isotropic PREM and in the 3-D crustal model Crust2.0 on top of PREM, and measured the corresponding time-shifts as a function of period. We then applied phase corrections to the PREM seismograms using ray theory and finite frequency theory with exact local phase velocity perturbations from Crust2.0 and looked at the residual time-shifts. After crustal corrections, residuals fall within the uncertainty of measured phase velocities for periods longer than 60 and 80 s for Rayleigh and Love waves, respectively. Rayleigh and Love waves are affected in a highly non-linear way by the crustal type. Oceanic crust affects Love waves stronger, while Rayleigh waves change most in continental crust. As a consequence, we find that the imperfect crustal corrections could have a large impact on our inferences of radial anisotropy. If we want to map anisotropy correctly, we should invert simultaneously for mantle and crust. The latter can only be achieved by using perturbation theory from a good 3-D starting model, or implementing full non-linearity from a 1-D starting model.     

Crustal and upper-mantle structure in the Eastern Mediterranean from the analysis of surface wave dispersion curves

The dispersive properties of surface waves are used to infer earth structure in the Eastern Mediterranean region. Using group velocity maps for Rayleigh and Love waves from 7 to 100 s, we invert for the best 1-D crust and upper-mantle structure at a regular series of points. Assembling the results produces a 3-D lithospheric model, along with corresponding maps of sediment and crustal thickness. A comparison of our results to other studies finds the uncertainties of the Moho estimates to be about 5 km. We find thick sediments beneath most of the Eastern Mediterranean basin, in the Hellenic subduction zone and the Cyprus arc. The Ionian Sea is more characteristic of oceanic crust than the rest of the Eastern Mediterranean region as demonstrated, in particular, by the crustal thickness. We also find significant crustal thinning in the Aegean Sea portion of the backarc, particularly towards the south. Notably slower S -wave velocities are found in the upper mantle, especially in the northern Red Sea and Dead Sea Rift, central Turkey, and along the subduction zone. The low velocities in the upper mantle that span from North Africa to Crete, in the Libyan Sea, might be an indication of serpentinized mantle from the subducting African lithosphere. We also find evidence of a strong reverse correlation between sediment and crustal thickness which, while previously demonstrated for extensional regions, also seems applicable for this convergence zone.     

Finite-frequency sensitivity kernels for head waves

Head waves are extremely important in determining the structure of the predominantly layered Earth. While several recent studies have shown the diffractive nature and the 3-D Fréchet kernels of finite-frequency turning waves, analogues of head waves in a continuous velocity structure, the finite-frequency effects and sensitivity kernels of head waves are yet to be carefully examined. We present the results of a numerical study focusing on the finite-frequency effects of head waves. Our model has a low-velocity layer over a high-velocity half-space and a cylindrical-shaped velocity perturbation placed beneath the interface at different locations. A 3-D finite-difference method is used to calculate synthetic waveforms. Traveltime and amplitude anomalies are measured by the cross-correlation of synthetic seismograms from models with and without the velocity perturbation and are compared to the 3-D sensitivity kernels constructed from full waveform simulations. The results show that the head wave arrival-time and amplitude are influenced by the velocity structure surrounding the ray path in a pattern that is consistent with the Fresnel zones. Unlike the 'banana–doughnut' traveltime sensitivity kernels of turning waves, the traveltime sensitivity of the head wave along the ray path below the interface is weak, but non-zero. Below the ray path, the traveltime sensitivity reaches the maximum (absolute value) at a depth that depends on the wavelength and propagation distance. The sensitivity kernels vary with the vertical velocity gradient in the lower layer, but the variation is relatively small at short propagation distances when the vertical velocity gradient is within the range of the commonly accepted values. Finally, the depression or shoaling of the interface results in increased or decreased sensitivities, respectively, beneath the interface topography.     

Three-dimensional seismic structure beneath the Australasian region from refracted wave observations

The earthquakes in the seismicity belt extending through Indonesia, New Guinea, Vanuatu and Fiji to the Tonga–Kermadec subduction zone recorded at the 65 portable broad-band stations deployed during the Skippy experiment from 1993–1996 provide good coverage of the lithosphere and mantle under the Australian continent, Coral Sea and Tasman Sea.
The variation in structure in the upper part of the mantle is characterized by deter-mining a suite of 1-D structures from stacked record sections utilizing clear P and S arrivals, prepared for all propagation paths lying within a 10° azimuth band. The azimuth of these bands is rotated by 20° steps with four parallel corridors for each azimuth. This gives 26 separate azimuthal corridors for which 15 independent 1-D seismic velocity structures have been derived, which show significant variation in P and S structure.
The set of 1-D structures is combined to produce a 3-D representation by projecting the velocity values along the ray path using a turning point approximation and stacking into 3-D cells (5° by 50 km in depth). Even though this procedure will tend to underestimate wave-speed perturbations, S -velocity deviations from the ak135 reference model exceed 6 per cent in the lithosphere.
In the uppermost mantle the results display complex features and very high S -wave speeds beneath the Precambrian shields with a significant low-velocity zone beneath. High velocities are also found towards the base of the transition zone, with high S -wave speeds beneath the continent and high P -wave speeds beneath the ocean. The wave-speed patterns agree well with independent surface wave studies and delay time tomography studies in the zones of common coverage.     

Structural effects of the crust on the geoid modelled using deep seismic sounding interpretations

According to the theory of isostasy, the Earth has a tendency to deform its surface in order to reach an equilibrium state. The land-uplift phenomenon in the area of the Fennoscandian Shield is thought to be a process of this kind. The geoid, as an equipotential surface of the Earth's gravity field, contains information on how much the Earth's surface departs from the equilibrium state. In order to study the isostatic process through geoidal undulations, the structural effects of the crust on the geoid have to be investigated.
  The structure of the crust of the Fennoscandian Shield has been extensively explored by means of deep seismic sounding (DSS). The data obtained from DSS are used to construct a 3-D seismic-velocity structure model of the area's crust. The velocity model is converted to a 3-D density model using the empirical relationship that holds between seismic velocities and crustal mass densities. Structural effects are then estimated from the 3-D density model.
  The structural effects computed from the crustal model show that the mass deficiency of the crust in Fennoscandia has caused a geoidal depression twice as deep as that observed from the gravimetric geoid. It proves again that the crust has been isostatically compensated by the upper mantle. In other words, an anomalously high-density upper mantle must exist beneath Fennoscandia.     

Surface wave tomography of the Barents Sea and surrounding regions

The goal of this study is to refine knowledge of the structure and tectonic history of the European Arctic using the combination of all available seismological surface wave data, including historical data that were not used before for this purpose. We demonstrate how the improved data coverage leads to better depth and spatial resolution of the seismological model and discovery of intriguing features of upper-mantle structure. To improve the surface wave data set in the European Arctic, we extensively searched for broad-band data from stations in the area from the beginning of the 1970s until 2005. We were able to retrieve surface wave observations from regional data archives in Norway, Finland, Denmark and Russia in addition to data from the data centres of IRIS and GEOFON. Rayleigh and Love wave group velocity measurements between 10 and 150 s period were combined with existing data provided by the University of Colorado at Boulder. This new data set was inverted for maps showing the 2-D group-velocity distribution of Love and Rayleigh waves for specific periods. Using Monte Carlo inversion, we constructed a new 3-D shear velocity model of the crust and upper mantle beneath the European Arctic which provides higher resolution and accuracy than previous models. A new crustal model of the Barents Sea and surrounding areas, published recently by a collaboration between the University of Oslo, NORSAR and the USGS, constrains the 3-D inversion of the surface wave data in the shallow lithosphere. The new 3-D model, BARMOD, reveals substantial variations in shear wave speeds in the upper mantle across the region with a nominal resolution of 1°× 1°. Of particular note are clarified images of the mantle expression of the continent-ocean transition in the Norwegian Sea and a deep, high wave speed lithospheric root beneath the Eastern Barents Sea, which presumably is the remnant of several Palaeozoic collisions.     

Full three-dimensional tomography: a comparison between the scattering-integral and adjoint-wavefield methods

This paper analyses the computational issues of full 3-D tomography, in which the starting model as well as the model perturbation is 3-D and the sensitivity (Fréchet) kernels are calculated using the full physics of 3-D wave propagation. We compare two formulations of the structural inverse problem: the adjoint-wavefield (AW) method, which back-propagates the data from the receivers to image structure, and the scattering-integral (SI) method, which sets up the inverse problem by calculating and storing the Fréchet kernels for each data functional. The two inverse methods are closely related, but which one is more efficient depends on the overall problem geometry, particularly on the ratio of sources to receivers, as well as trade-offs in computational resources, such as the relative costs of compute cycles to data storage. We find that the SI method is computationally more efficient than the AW method in regional waveform tomography using large sets of natural sources, although it requires more storage.     

Analysis of the crustal velocity structure of the British Isles using teleseismic receiver functions

The onshore crustal and upper mantle velocity structure of the British Isles has been investigated by teleseismic receiver function analysis. The results of the study augment the dense offshore and sparse onshore models of the velocity structure beneath the area. In total almost 1500 receiver functions have been analysed, which have been calculated using teleseismic data from 34 broadband and short-period, three-component seismic recording instruments. The crustal structure has primarily been investigated using 1-D grid search and forward modelling techniques, returning crustal thicknesses, bulk crustal V_p / V_s ratio and velocity-depth models. H −κ stacking reveals crustal thicknesses between 25 and 36 km and V_p / V_s ratios between 1.6 and 1.9. The crustal thicknesses correlate with the results of previous seismic reflection and refraction profiles to within ±2 km. The significant exceptions are the stations close to the Iapetus Suture where the receiver function crustal thicknesses are up to 5 km less than the seismic refraction Moho. This mismatch could be linked to the presence of underplated magmatic material at the base of the crust. 1-D forward modelling has revealed subcrustal structures in northern Scotland. These correlate with results from other UK receiver function studies, and correspond with the Flannan and W-reflectors. The structures are truncated or pinch out before they reach the Midland Valley of Scotland. The isolated subcrustal structure at station GIM on the Isle of Man may be related to the closure of the Iapetus Ocean.     

Global anisotropic phase velocity maps for higher mode Love and Rayleigh waves

It is well established that the Earth's uppermost mantle is anisotropic, but there are no clear observations of anisotropy in the deeper parts of the mantle. Surface waves are well suited to observe anisotropy since they carry information about both radial and azimuthal anisotropy. Fundamental mode surface waves, for commonly used periods up to 200 s, are sensitive to structure in the first few hundred kilometres, and therefore, do not provide information on anisotropy below. Higher mode surface waves have sensitivities that extend to and beyond the transition zone, and should thus give insight about azimuthal anisotropy at greater depths. We have measured higher mode Love and Rayleigh phase velocities using a model space search approach, which provides us with consistent relative uncertainties from measurement to measurement and from mode to mode. From these phase velocity measurements, we constructed global anisotropic phase velocity maps. Prior to inversion, we determine the optimum relative weighting for anisotropy. We present global azimuthal phase velocity maps for higher mode Rayleigh waves (up to the sixth higher mode) and Love waves (up to the fifth higher mode) with corresponding average model uncertainties. The anisotropy we derive is robust within the uncertainties for all modes. Given the ray theoretical sensitivity kernels of Rayleigh and Love wave modes, the source of anisotropy is complex, but mainly located in the asthenosphere and deeper. Our models show a good correspondence with other studies for the fundamental mode, but we have been able to achieve higher resolution.     

The Backus–Gilbert approach to the 3-D structure in the upper mantle – II. SH and SV velocity

Summary. Phase velocity variations obtained in the previous paper are inverted by the Backus–Gilbert method for the velocity structure of the upper mantle. Spheroidal modes and toroidal modes in the period range of 125–260 s are used in the inversion. The data cannot constrain all six parameters in a transversely isotropic medium and we chose to perturb only two parameters, SH and SV velocities. SV velocities are resolved between the depths of about 200 and 400 km and SH velocities between 0 and 200 km. Resolution kernels have half-peak widths of about 200–300 km in depth, becoming broader for deeper target depths. SV velocity kernels show secondary peaks near the surface of the Earth, with widths varying from 50 to 100 km. The deeper the target depths, the wider the secondary peaks near the surface. SH velocity kernels do not possess such secondary peaks. The trade-off between SV and SH velocities is small. SV velocity is essentially determined by spheroidal modes and SH velocity by toroidal modes. Because of the broad width of the resolution kernels, the structure in the resolved region is difficult to detect from our data set; for example the differences in SV velocity structure between 250 and 350 km or the differences in SH velocity between 100 and 200 km are difficult to distinguish. Considering the horizontal resolution of about 2000 km, obtained in the previous paper, averaging kernels for 3-D structure are quite elongated in the horizontal dimension.     

Two efficient algorithms for iterative linearized inversion of seismic waveform data

We present two equivalent algorithms for iterative linearized waveform inversion for 3-D Earth structure with respect to an arbitrary 3-D starting model; one is a matrix formulation, and the second is a wavefield formulation. Both algorithms require the computation of accurate synthetic seismograms, but neither requires that any particular method be used to compute the synthetics. The matrix formulation is equivalent to our previously published algorithm (Hara, Tsuboi & Geller 1991), but requires less than 10 per cent of the CPU time of the previous algorithm. The wavefield algorithm is equivalent to that of Tarantola (1986) and Mora (1987), but appears to be substantially more efficient.     

Deep resistivity structure of the Trans-European Suture Zone in Central Poland

The deep resistivity structure was estimated along a 400-km profile in central Poland crossing the Malopolska Massif (MM), the Lysogory Unit (LU), the Trans-European Suture Zone (TESZ) and ending at the East European Craton (EEC). Magnetotelluric transfer functions, corresponding to 20 sites, were supplemented by magnetovariational responses obtained at the geomagnetic observatories situated at the same tectonic units. Such a combination made it possible to extend the initial period range, which is from fractions of a second to several hours, up to months in order to reliably cover crustal and upper-mantle depths. The geoelectrical structures, revealed using 2-D inversions, do not contradict the known features of the lithosphere structure determined using seismic and gravity data along the profile.
The subsurface conductance, varying from approximately 10 Siemens at the inner part of the EEC to about 600 Siemens in the TESZ, is produced by sediments, the deep part of which contains conductive, highly mineralized water. The existence of two crustal conductive faults at the southwest and northeast of the TESZ were established mainly by the use of induction arrows. It was also revealed that rather high mantle conductivity beneath the MM, LU and TESZ at depths of about 150–200 km contrasts with the resistive upper mantle of the EEC. This can be interpreted as the decrease of asthenosphere conductance and/or as its submersion beneath the EEC. Generally, the results confirm the idea that the TESZ forms not only specific seismic boundaries but also causes peculiar conductivity anomalies in the crust and upper mantle.     

Surface wave tomography: global membrane waves and adjoint methods

We implement the wave equation on a spherical membrane, with a finite-difference algorithm that accounts for finite-frequency effects in the smooth-Earth approximation, and use the resulting 'membrane waves' as an analogue for surface wave propagation in the Earth. In this formulation, we derive fully numerical 2-D sensitivity kernels for phase anomaly measurements, and employ them in a preliminary tomographic application. To speed up the computation of kernels, so that it is practical to formulate the inverse problem also with respect to a laterally heterogeneous starting model, we calculate them via the adjoint method, based on backpropagation, and parallelize our software on a Linux cluster. Our method is a step forward from ray theory, as it surpasses the inherent infinite-frequency approximation. It differs from analytical Born theory in that it does not involve a far-field approximation, and accounts, in principle, for non-linear effects like multiple scattering and wave front healing. It is much cheaper than the more accurate, fully 3-D numerical solution of the Earth's equations of motion, which has not yet been applied to large-scale tomography. Our tomographic results and trade-off analysis are compatible with those found in the ray- and analytical-Born-theory approaches.     

Regional tomographic inversion of the amplitude and phase of Rayleigh waves with 2-D sensitivity kernels

In this study, we test the adequacy of 2-D sensitivity kernels for fundamental-mode Rayleigh waves based on the single-scattering (Born) approximation to account for the effects of heterogeneous structure on the wavefield in a regional surface wave study. The calculated phase and amplitude data using the 2-D sensitivity kernels are compared to phase and amplitude data obtained from seismic waveforms synthesized by the pseudo-spectral method for plane Rayleigh waves propagating through heterogeneous structure. We find that the kernels can accurately predict the perturbation of the wavefield even when the size of anomaly is larger than one wavelength. The only exception is a systematic bias in the amplitude within the anomaly itself due to a site response.
An inversion method of surface wave tomography based on the sensitivity kernels is developed and applied to synthesized data obtained from a numerical simulation modelling Rayleigh wave propagation over checkerboard structure. By comparing recovered images to input structure, we illustrate that the method can almost completely recover anomalies within an array of stations when the size of the anomalies is larger than or close to one wavelength of the surface waves. Surface wave amplitude contains important information about Earth structure and should be inverted together with phase data in surface wave tomography.     

The Mid-Atlantic Ridge: structure at 45° N

Summary. A structural model of the Mid-Atlantic Ridge at 45° N is proposed on the basis of travel-time data, amplitudes and synthetic seismograms. The crustal structure seems to be similar to that in the FAMOUS area (Fowler). At the ridge axis there is an absorptive zone in the upper mantle, the depth below the seabed to the top of this zone being about 6 km. Away from the ridge axis there is a positive velocity gradient of about 0.04 to 0.05 km/(skm) in the top 5 to 8 km of the upper mantle. Shear waves propagate across the ridge axis, suggesting that there is no sizeable crustal magma chamber. The shear-wave velocity of the uppermost mantle is 4.35 km/s.     

Upper mantle anisotropy: evidence from free oscillations

Summary Isotropic earth models are unable to provide uniform fits to the gross Earth normal mode data set or, in many cases, to regional Love-and Rayleigh-wave data. Anisotropic inversion provides a good fit to the data and indicates that the upper 200km of the mantle is anisotropic. The nature and magnitude of the required anisotropy, moreover, is similar to that found in body wave studies and in studies of ultramafic samples from the upper mantle. Pronounced upper mantle low-velocity zones are characteristic of models resulting from isotropic inversion of global or regional data sets. Anisotropic models have more nearly constant velocities in the upper mantle.
Normal mode partial (Frediét) derivatives are calculated for a transversely isotropic earth model with a radial axis of symmetry. For this type of anisotropy there are five elastic constant. The two shear-type moduli can be determined from the toroidal modes. Spheroidal and Rayleigh modes are sensitive to all five elastic constants but are mainly controlled by the two compressional-type moduli, one of the shear-type moduli and the remaining, mixed-mode, modulus. The lack of sensitivity of Rayleigh waves to compressional wave velocities is a characteristic only of the isotropic case. The partial derivatives of the horizontal and vertical components of the compressional velocity are nearly equal and opposite in the region of the mantle where the shear velocity sensitivity is the greatest. The net compressional wave partial derivative, at depth, is therefore very small for isotropic perturbations. Compressional wave anisotropy, however, has a significant effect on Rayleigh-wave dispersion. Once it has been established that transverse anisotropy is important it is necessary to invert for all five elastic constants. If the azimuthal effect has not been averaged out a more general anisotropy may have to be allowed for.     

A Teleseismic Delay Time Study Across the Central African Shear Zone In the Adamawa Region of Cameroon, West Africa

Summary. P -wave relative teleseismic residuals were measured for a network of seismological stations along a 300 km profile across the Adamawa Plateau and the Central African Shear Zone of central Cameroon, to determine the variation in crust and upper mantle velocity associated with these structures. A plot of the mean relative residuals for the stations shows a long wavelength (> 300 km) variation of amplitude 0.45 s. the slowest arrivals are located over and just to the north, of the faulted northern margin of the Adamawa Plateau. the residuals do not correlate with topography, surface geology or the previously determined crustal structure, in any simple way.
The Aki inversion technique has been used to invert the relative residuals into a 3-D model of velocity perturbations from a mean earth model. the results show the region is divided roughly into three blocks by two subvertical boundaries, striking ENE and traversing both the crust and upper mantle down to depths greater than 190km. the central block, which is 2 per cent slower than the adjacent blocks, roughly corresponds to the Central African Shear Zone. the Adamawa Plateau, as an individual uplifted area, is explained by the interaction of a regional anomalous upper mantle associated with the West African Rift System, and the Central African Shear Zone, which provided a conduit for heat flow to the surface.