Most existing implementations of full-waveform inversion (FWI) are limited to acoustic approximations. In this paper, we present an algorithm for time-domain elastic FWI in laterally heterogeneous VTI (transversely isotropic with a vertical symmetry axis) media. The adjoint-state method is employed to derive the gradients of the objective function with respect to the stiffness coefficients and then to a chosen set of VTI parameters. To test the algorithm, we introduce Gaussian anomalies in the Thomsen parameters of a homogeneous VTI medium and perform 2D FWI of multicomponent transmission data for two different model parameterizations. To analyze the sensitivity of the objective function to the model parameters, the Fréchet kernel of FWI is obtained by linearizing the elastic wave equation using the Born approximation and employing the asymptotic Green’s function. The amplitude of the kernel (“radiation pattern”) yields the angle-dependent energy scattered by a perturbation in a certain model parameter. Then we convert the general expressions into simple approximations for the radiation patterns of P- and SV-waves in VTI media. These analytic developments provide valuable insight into the potential of multicomponent elastic FWI and help explain the numerical results for models with Gaussian anomalies in the VTI parameters.

S U M M A R YWe study the excitation of low-frequency (0.001-10 Hz) electromagnetic and density fluctuations in the ionosphere during the passage of seismic triggered acoustic waves (AWs). The study involves the generation of ionospheric currents by AWs and subsequent perturbations of the electromagnetic fields and ion and electron density. In this study, the non-local analysis of the fluctuations is carried out in the framework of hydromagnetic theory. Our objective is to examine the spatial and frequency distributions of these fluctuations and to compare them qualitatively with the available observations. The dynamics of both electrojet and F region of ionosphere are included. Also included are the effects of the dip-angle variations of the Earth's magnetic field. Significant anisotropy and inhomogeneities are noted in the fluctuations. The amplitudes of current and magnetic field fluctuations are found to be maximum in the F region where ion inertia is large enough to support the plasma waves and where electron number density and acoustic wave amplitudes are also large. The density fluctuations also follow similar trends. Both electromagnetic and density fluctuations are large in the latitude region where the acoustic wave vibration parallel to the Earth's magnetic field is large. The fluctuations have the tendency to be maximum in the 0.1-1 Hz frequency range. In this range, AWs driven currents and electromagnetic fluctuations may become of order of μAm −2 , nV m −1 and nT, respectively in the F region.

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Full waveform inversion (FWI) applications on 3D ocean bottom cable (OBC) data fromthe Valhall oil field in the North Sea have demonstrated the importance of appropriately ac-counting for attenuation. The Valhall field contains unconsolidated shallow sediments anda low velocity anomaly in its center - indicative of gas clouds - which have a significantattenuation imprint on the data. The challenge in which we are interested is to performtime-domain visco-acoustic 3D FWI, which requires more sophisticated tools than in thefrequency domain wherein attenuation can be incorporated in a straightforward manner.The benefit of employing a visco-acoustic, instead of a purely acoustic, modeling engineis illustrated. We show that, in the frequency band employed (2.5 - 7.0 Hz), it is betterto reconstruct velocity only keeping attenuation fixed, because simultaneous inversion ofvelocity and quality factor Q does not provide reliable Q-updates. We design an efficienttime-domain workflow combining a random source decimation algorithm, modeling usingstandard linear solid mechanisms, and wavefield preconditioning. Our results are similarto those obtained from state-of-the-art frequency-domain algorithms, at a lower computa-tional cost compared to conventional checkpointing techniques. We clearly illustrate theimprovement in terms of imaging and data fit achieved when accounting for attenuation.