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S U M M A R YWe calculate finite-frequency anisotropic traveltime sensitivity kernels for Rayleigh and Love waves using the recently developed combination of the adjoint method with spectral-element modelling of seismic wave propagation. We describe anisotropy following the 'natural' 13 elastic parameters for surface waves (A, C). Along the ray path, the adjoint spectralelement computations agree well with asymptotic theory, but also expose the limitations of the asymptotic description. The adjoint spectral-element method is an efficient and flexible numerical tool, but it does not allow one to identify the various wave propagation phenomena contributing to the observed sensitivity. To decipher the numerical results, we apply Born scattering theory together with a surface-wave mode-coupling formulation. We identify a strong effect due to mode coupling. The sensitivity of Rayleigh waves for some of the anisotropic parameters is affected by Love-Rayleigh coupling, while Love-wave sensitivity is affected by cross-branch coupling. In addition, and very specific to anisotropy, the directional dependence of the sensitivity to azimuthal anisotropy may strongly distort the kernels, rendering them highly path-dependent. Because of these combined effects, the anisotropic sensitivity kernels can deviate substantially from the simple elliptical kernels used in recent isotropic finitefrequency tomography.

[1] We present a series of synthetic tests showing that regional surface wave tomographies with a dense path coverage of the target region can be safely conducted under ray theory because the shortcomings of ray theory in considering finite-frequency effects can be counterbalanced by a physically-based regularization of the inversion. In particular, we show that with ray theory applied under the above conditions, it is possible to detect heterogeneities with length scales smaller than the wavelength of the data set.

S U M M A R YWe 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.

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

International audienceWe use a principal component analysis to characterize the finite-frequency sensitivity of seismic observables to anisotropy. A general anisotropic medium may be described in terms of 21 independent elastic parameters, each of which has an associated 'primary' sensitivity kernel. Our principal component analysis ranks linear combinations of the primary kernels to ascertain the dominant anisotropic parameters associated with a particular seismic observable. The principal parameters are those to which a given data set is the most sensitive. We demonstrate the efficiency of the method for a single arrival associated with a particular source–receiver combination, and apply it to a small synthetic Love-wave data set with a simple source–receiver geometry. For direct body wave arrivals, such as P, S and SKS, and direct Love and Rayleigh surface waves, our principal component analysis finds the same small combinations of dominant anisotropic parameters previously identified based upon asymptotic methods. The analysis further confirms the importance of mode coupling in finite-frequency surface wave sensitivity kernels. Our approach can be directly incorporated into a tomographic inversion to automatically select the general anisotropic parameters which are best constraint, for example, without prescribing the model to be transversely isotropic with a particular symmetry axis. The computational overhead associated with the calculation of the 21 primary kernels and the subsequent principal component analysis is minimal relative to an isotropic calculation