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In this thesis, we investigate the feasability of using higher modes in seismic interferometry. This is done by a theoretical and computation analysis of the approximations involved, development of a method of stacking noise traces, and analysis of a small array in the northern part of the Netherlands. Higher modes are unambiguously present in ambient noise, and can thus be used to improve vertical resolution in the subsequent inversion procedure. The practical issue in their use, remains the problem of distinguishing them from spurious events/noise, and even distinghuising higher modes from the fundamental mode, since at high frequencies they can be in close proximity in a time-frequency diagram. Higher modes can furthermore be lost in the data due to: -their small amplitude compared to the fundamental mode. -intermodal cross-terms that occur with imperfect distributions, but occur even in the case of a perfectly surrounding integration surface. However, if noise is generated in a large band-like distribution (or very far away) the cross-terms should pose no problem. - source-source correlation terms. The signal to noise ratio is much smaller for higher modes. The exact instantaneous phase takes much longer to converge to the true solution than the envelope, implying larger uncertainty for phase velocity measurements. -incoherent noise not associated to wave propagation, or local effects. Directional noise shows much faster convergence for higher modes, again at least for station paths inline in this direction. Also in our data, the noise is strongly directional. It can be argued that the higher mode information would not be retrieved if this were not the case. The higher mode has a different origin from the dominant secondary microseism.The TF-phase weighted stack is a powerful tool to denoise the retrieved seismograms. It is possible to measure the group velocity from the phase stack directly. To retrieve higher modes, the phase stack provides an easy to use, additional tool. Most information remains in relative few TF-stacks from long displacement traces. Verification with additional information was essential for a robust estimate of the 1D S-velocity structure beneath Annerveen, The Netherlands. As an average for the region, the higher mode information gives additional constraint on the deeper sedimentary layers. The tomographic images seem to correlate with the main geological features, but for the higher modes the amount of interstation paths that can be reliably measured is not large enough. This is due to interference with the fundamental mode in the group velocity images and the limited directionality. The choice of a substantial spread in interstation distances led to a broad frequency range of analysis, but also limited the number of measurements per frequency. A recommendation for future studies is to use a strict 1-D configuration along the prevalent noise direction. The advantages are the large possible frequency bandwidth, and the possibility to use and invert the higher modes.

Over the last three decades a vast number of tomographic images has been produced, but the quantitative assessment of their accuracy and uniqueness has only just started. A relatively recent technique in this direction has been made by (Trampert et al., 2004) using probabilistic tomography. It is based on a full model space search, the Neighbourhood Algorithm (NA), with which to solve the inverse problem. This provides a representation of seismic constraints as probability density functions (pdfs) from which one can easily calculate the most likely model and its associated uncertainty. Since a full model space search quickly limits the dimension of the explorable parameter space, an essential condition to apply the NA is to have a small number of unknowns. Probabilistic tomography has been applied to invert surface waves and normal-modes. The aim of this thesis was to incorporate body wave data to increase the depth resolution in the lowermost mantle. The first step, therefore, was to establish a formalism which allows us to treat body waves as surface waves and free oscillations and, thus, separate the inverse problem into its lateral and radial components. In a spherically layered Earth using the path-average approximation, body wave delay times can be inverted in two steps. The first step is the construction of vertical travel-time residual maps as a function of ray parameter. The second step is their depth inversion, less well constrained than the first step but characterized by a small number of parameters and, hence, suitable to be solved by the NA. Such a procedure, called path-average approach, works well for long wavelength structure for the forward and inverse problem. Combing a body wave dataset characterized by a good resolution between 2441 and 2891 km and the advantages of the path-average approach, we provided a new insight into the lowermost mantle based on lateral variations of P-, S-seismic velocities and the corresponding seismologically observed ratio without an explicit depth inversion for seismic wave velocities variation. Following a robust statistical approach, we are able to link these seismic heterogeneities to mineral physics and provide evidence for the existence of post-perovskite near the core-mantle boundary. In the framework of probabilistic tomography, applying the path-average approach we inverted body wave vertical travel-time residual maps, normal-mode splitting functions and surface wave phase velocity maps locally for depth using the NA. We constructed a shear wave, compressional wave, bulk sound speeds and density perturbation model with associated uncertainty. The estimation of the correlation between parameters and the RMS amplitude of seismic variations clearly indicates a thermal and chemical nature of heterogeneity in the lower mantle. Furthermore, our models fully confirm the conclusions achieved by the model of Resovsky & Trampert (2003), produced without body waves. One strength of probabilistic tomography is the possibility to convert easily the pdfs of seismic velocities and density perturbations into pdfs of thermal and compositional anomalies. We constructed a model of temperature, iron and perovskite variations combining mineral physics data with the shear, bulk sound wave-speeds and density variation models described above.

We have reached a stage in seismic tomography where further refinements with classical techniques become very difficult. Advances in numerical methods and computational facilities are providing new opportunities in seismic tomography to enhance the resolution of tomographic mantle images. 3-D numerical simulations of seismic wavefields also allow us to check the reliability of the current mantle images and the classical techniques. In this thesis, using 3-D wave simulations by a spectral element method, we present three specific studies which underline some shortcomings in global mantle tomography. We first investigated crustal corrections for fundamental mode surface waves. We compared the crustal corrections estimated by first order approximations such as great circle approximation, exact ray theory and finite-frequency theory, to those obtained from 3-D wave simulations. We observed that crustal corrections can produce errors larger than those in phase measurements at periods longer than 60 and 80 s for Rayleigh and Love waves, respectively. Rayleigh and Love waves are differently influenced by the crust. Therefore imperfect crustal corrections have potential to produce radial anisotropy which may bias our interpretation of anisotropy in the upper-mantle. Extensions to the great circle approximation do not improve the results because of the highly non-linear behaviour of the crust. Thus either the mantle has to be inverted together with the crust or 3-D background models have to be used for the measurements. We then compared real data with synthetic seismograms computed in various 3-D mantle models. We particularly investigated the effect of damping on global mantle models. In addition, we tried to examine the elastic and anelastic contribution of the models by comparing seismograms computed in 1-D and 3-D crustal and mantle models. Our results show that different 3-D mantle models give statistically similar results although they are different from each other. We observed that a large part of the seismograms remained unexplained, particularly the amplitudes. 3-D velocity models are not enough to explain amplitude information alone. Attenuation may have an important contribution to surface-wave amplitudes whereas body waves are more affected by scattering effects. Lastly, we proposed new misfit functions based on instantaneous phase and cross-correlation measurements for full waveform inversion. In addition, we qualitatively compared them to classical ones such as waveform and travel-time misfits by computing the finite-frequency sensitivity kernels using adjoint methods based upon a spectral element method. We observed that instantaneous phase measurements provide complementary information to the other misfit functions and are promising to exploit more information from a single seismogram.

This thesis is a study on upper mantle shear velocity structure beneath the Gulf of California. Surface wave interstation dispersion data were measured in the Gulf of California area and vicinity to obtain a 3-D shear velocity structure of the upper mantle. This work has particular significance for understanding the tectonic evolution history in this region and the potential processes that control lithospheric rupture and the initiation of seafloor spreading in the Gulf of California. The NARS-Baja project is designed as a passive seismic experiment to explore the mantle beneath the Gulf of California region. This thesis presents the results on the upper mantle structure beneath the Gulf of California from surface wave dispersion analysis. The study contains three aspects: the Rayleigh wave phase velocity structure with azimuthal anisotropy in the Gulf of California region; a shear velocity model of Gulf of California and its vicinity inferred from Rayleigh wave dispersion data; the radially anisotropic shear wave velocity model inferred from Love and Rayleigh wave dispersion . The seismic models of the upper mantle beneath the Gulf of California and surrounding regions show some interesting features. The average shear-velocity structure has a strong low-velocity zone beneath a thin lid. The average phase velocity data are even suggestive of lower velocities than the global average down into the transition zone. The low velocities at asthenospheric depths are indicative of fluids and/or melt. A striking feature of our seismic models is a relatively high shear-velocity anomaly beneath the central-southern gulf extending from a depth of roughly 120 to 160 km. This anomaly is interpreted as a remnant of a subducted Farallon microplate fragment . There is no evidence for such a slab remnant beneath the northern part of the gulf, in agreement with the tectonic interpretation of the region. We therefore interpret this region as having a slab window, similar to the area at the mouth of the gulf. Additional evidence on the upper mantle structure is obtained from anisotropy. An along-rift-axis variation is observed in the azimuthally anisotropic phase velocity maps of the fundamental mode Rayleigh waves, as well as in the radially anisotropic structure . The obtained upper mantle structure sheds light onto the interior of this dynamic plate boundary developing area. Our new tectonic interpretation of evolution the Gulf of California is based upon tectonic reconstructions, volcanic evidence, and our seismic interpretation of a stalled slab remnant. In our model, the development of the slab window beneath the North American lithosphere and pre-existing fracture zones in the subducting plate are essential in the tectonic evolution. The details of the subduction dynamics and the plate boundary relocation can therefore be largely be attributed to pre-existing weak features in the plates. Ridges and fracture zones of the subducted plate can determine tearing and fracturing of the slab, whereas faults and extended back-arc basins in the overriding plate can be essential to the plate boundary relocation.

We present a neural network approach to invert surface wave data for discontinuities and velocity structure in the upper mantle. We show how such a neural network can be trained on a set of random samples to give a continuous approximation to the inverse relation in a compact and computationally efficient form. The trained networks are applied to a real data set consisting of surface wave dispersion measurements. For each inversion, performed on a global grid, we obtain the a posteriori probability density function (pdf) of crustal thickness and independently of vertically averaged crustal shear wave velocity. From this pdfs, any desired statistic such as mean and variance can be computed. The obtained results are compared with current knowledge of crustal structure. Generally our results are in good agreement with other crustal models. However in certain regions such as central Africa and the back arc of the Rocky Mountains we observe a thinner crust than the other models. We also see evidence for thickening of oceanic crust with increasing age. We show that the resulting model allows to compute global crustal corrections for surface wave tomography for periods T>50 s for phase velocities and T>60 s for group velocities. In a second application we invert surface wave overtone measurements for posterior pdfs of the 400- and 660-km discontinuities as well as the transition zone thickness. We find that posterior uncertainties are almost as large as the observed variations of the mean 400- and 660-km depth as well as the mean transition zone thickness. Nevertheless, the model of the mean 660-km topography agrees reasonably well with other global models constrained by SS precursors, giving further evidence for a well defined and sharp 660-km discontinuity. The situation for the 400-km discontinuity however is more complicated. Agreement between four different 400-km topography models is very poor and we find a global average discontinuity depth of 394 km which is significantly lower than 409 and 418 km reported previously. Surface wave overtones and SS precursors should give similar results for a sharp 400-km discontinuity. If the 400-km discontinuity however is broad, it might be that surface wave overtones map an average depth that differs from the bottom of the discontinuity as mapped by SS precursors. Experimental studies suggest that if water concentrations are sufficiently high the 400-km discontinuity might be as broad as 20 km. The observed difference in the mean depth of the 400-km discontinuity between surface wave overtone measurements and SS precursor studies might therefore be indicative of high water concentrations near 400-km depth on a global scale.

In this thesis we present all three stages of the inversion approach proposed by Kennett and Yoshizawa (2002). The three stage inversion approach consists of obtaining fundamental and higher mode Love and Rayleigh wave phase velocity measurements through waveform fitting in the first stage, combining them into multimode phase velocity models using the path average assumption in the second stage and an inversion for local shear wave speed properties to obtain a three-dimensional shear wave velocity model in the third stage. We first present a fully automated Monte Carlo modelspace search approach to measure fundamental and higher mode Love and Rayleigh wave phase velocities. The advantage of this approach is that we do not only obtain the best fitting model but the whole ensemble of models with their corresponding fit. This allows us to obtain mutually consistent uncertainties for the fundamental and higher mode phase velocity measurements. Our phase velocity measurements agree remarkably well with previous studies, but we have been able to enlarge the available dataset dramatically (>350,000 measurements). Surface waves are well suited to observe anisotropy since they carry information about both radial and azimuthal anisotropy. The presence of anisotropy is well established in the Earth's uppermost mantle, but it is more ambiguous in the deeper mantle. Since we use higher mode phase velocities which have a larger sensitivity to deeper structure compared to the fundamental mode, we improve our understanding of anisotropy into the deeper mantle. In the second stage, we thus invert the phase velocity measurements to obtain isotropic and azimuthally anisotropic phase velocity maps. Prior to inversion, we determine the optimum relative weighting for the isotropic and azimuthally anisotropic terms. We found that all fundamental and higher mode measurements require anisotropy. Special care was taken to obtain the posterior model uncertainties, needed to obtain the radial anisotropic shear wave velocity model. The azimuthal anisotropic phase velocity maps give indications of anisotropy at larger depths but a more detailed depth inversion using finite frequency kernels will provide more information on the depth extend of azimuthal anisotropy. Finally, we inverted the local azimuthally averaged phase velocity maps for radial shear wave anisotropy taking the full non-linearity into account using a Monte Carlo modelspace search approach. For the anisotropic model, we decided to compute the total probability of radial anisotropy and likewise that the amplitude of radial anisotropy is above 1% or 2%. We find a lithosphere dominated by fast horizontally polarized shear wave anisotropy (horizontal flow), an asthenosphere dominated by fast vertically polarized shear wave anisotropy (vertical flow) and a transition zone also dominated by fast vertically polarized shear wave anisotropy (vertical flow). The amplitude of anisotropy is likely large (>2%) in the lithosphere and asthenosphere and smaller in the transition zone (1%-2%). The lower mantle is most likely isotropic (or anisotropic with a very small amplitude