Frechet derivatives of coupled seismograms with respect to an anelastic rotating earth

International audienceA theory, based on higher-order perturbations, is given and used to express the partial derivatives of the seismic waveform with respect t o perturbations of density, anelasticity and anisotropy. Frechet derivatives are expressed with respect to a general aspherical model by using modulation functions, which are already used for the computation of aspherical seismograms. A direct solution method (DSM) that optimizes other previously proposed DSMs is proposed for the computation of the modulation functions. Numerical tests point out significant differences between the general FrCchet derivatives and those used for more classical approaches (great-circle average or frozen-path approximation), as well as important focusing/defocusing effects. This theory will enable future imaging inversions of the small-scale heterogeneities of the Earth

Diffraction of long period Rayleigh waves effects of mode coupling by a slab: effects of mode coupling

International audienceWe compute seismograms of the fundamental Rayleigh waves propagating through a slab structure , with either a lateral variation in seismic velocities , or in attenuation. At periods of 100 sec, we show that the phase delay is strongly reduced by the surface waves Fresnel zone, and that coupling must be considered far along the dispersion branch, up to at least oe-• 25. Limiting the coupling to fewer modes produces a signal associated to a ghost structure at the antipode of the slab. We also show that the amplitude perturbations produced by the diffraction and the attenuation of the slab are comparable in size. Future waveform studies, especially those associated to global waveform inversions, must then carefully consider these effects

Computation of seismograms and atmospheric oscillations by normal-mode summation for a spherical earth model with realistic atmosphere

We describe a theory to compute seismograms and atmospheric disturbances such as ionospheric oscillations or pressure variations in a realistic spherical earth model with atmosphere. This theory is valid for a source located either in the solid earth or in the atmosphere. Solid earth and atmospheric normal modes are computed for a radiation boundary condition that models the dissipation of acoustic signals in the high atmosphere of the Earth. We show that the coupling between ground and atmosphere occurs at a set of frequencies related to fundamentals and harmonics of atmospheric modes. Spheroidal modes near these frequencies have up to 0.04 per cent of their energy in the atmosphere, and thus may be strongly excited by atmospheric sources. This theory can be used for more accurate modelling of the seismic data from meteoritic events or volcanic eruptions as well as for the analysis of barograms or ionograms recorded after large earthquakes

Normal modes and long period seismograms in a 3D anelastic elliptical rotating Earth

International audienceWe present results of a direct method to compute realistic long period (>200 s in this example) synthetic seismograms using higher order perturbation theory (up to the 3rd order). Normal modes are computed for the Earth, taking into account rotation, ellipticity, 3D elastic lateral heterogeneities (SAW12D) for the whole mantle, and anelastic lateral variations in the upper mantle (QR19). Coupling between different modes and branches is included in the computation. We study the sensitivity of the waveform to 3D anelasticity and the biases between 3D elastic and 3D anelastic variations. The resulting seismograms can be computed to higher frequency and may then be used to perform whole mantle joint inversions for elastic and anelastic structure

Time-reversal imaging of seismic sources and application to the great Sumatra earthquake

International audienceThe increasing power of computers and numerical methods (like spectral element methods) allows continuously improving modelization of the propagation of seismic waves in heterogeneous media and the development of new applications in particular time reversal in the three-dimensional Earth. The concept of time-reversal (hereafter referred to as TR) was previously successfully applied for acoustic waves in many fields like medical imaging, underwater acoustics and non destructive testing. We present here the first application at the global scale of TR with associated reverse movies of seismic waves propagation by sending back long period time-reversed seismograms. We show that seismic wave energy is refocused at the right location and the right time of the earthquake. When TR is applied to the Sumatra-Andaman earthquake (26 Dec. 2004), the migration of the rupture from the south towards the north is retrieved. Therefore, TR is potentially interesting for constraining the spatio-temporal history of complex earthquakes

10 Normal modes of the earth and planets

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Observation of split modes from the 26th December 2004 Sumatra-Andaman mega-event

International audienceThe high quality of the records obtained after the huge Sumatra-Andaman earthquake of December 2004 from the broad-band seismological stations of all FDSN networks offers unique opportunity for studying the free oscillations of the Earth and consequently the behavior of some particular modes. The observation and clear identification of singlets of the gravest seismic normal modes (frequencies lower than 1 mHz) and of some particular anomalously split modes should offer strong constraints on Earth structure. We carefully analyzed 23 different modes and report the detailed results of 17 of them, showing an enhancement on the eigenfrequencies determination thanks to the high SNR (Signal to Noise Ratio) of the recordings. We analyzed vertical component recordings but also additional horizontal components. We present modal frequency measurements of some spheroïdal fundamental gravest modes, of some particular higher modes such as inner core modes exhibiting normal or anomalous splitting. The results are compared with the theoretical eigenfrequencies computed for the PREM model, taking into account both rotation and ellipticity effects of the Earth and lateral heterogeneities of the SAW12D model ( Li and Romanowicz, 1996). The misfit between measured and theoretical eigenfrequencies point out that some physical parameters are not well constrained. The new catalogue of modal eigenfrequencies provided from the Sumatra-Andaman 2004 event analysis offers a plethora of perspectives; it is an important step towards the resolution of deep Earth parameters

New determinations of Q quality factors and eigenfrequencies for the whole set of singlets of the Earth's normal modes 0S0, 0S2, 0S3 and 2S1 using superconducting gravimeter data from the GGP network

International audienceWe present new modal Q measurements of the 0S0 and 0S2 modes, and first modal frequencies and Q measurements of 2S1 and 0S3 modes. The high quality of the GGP (Global Geodynamics Project) superconducting gravimeters (SGs) contributes to the clear observation of seismic normal modes at frequencies lower than 1 mHz and offers a good opportunity for studying the behaviour of these modes. The interest of scientists in the gravest normal modes is due to the fact that they do contribute to a better knowledge of the density profile in the Earth, helping to constrain Earth's models. These modes have been clearly identified after some large recent events recorded with superconducting gravimeters, particularly well-suited for low-frequency investigations. The Ms = 8.1 (Mw = 8.4) Peruvian earthquake of June 2001 and the Ms = 9.0 (Mw = 9.3) Sumatra-Andaman earthquake of December 2004 provide us with individual spectra which exhibit a clear splitting of the spheroidal modes 0S2, 0S3 and 2S1, and a clear identification of each of the individual singlets, with a resolution never obtained from broad-band seismometers records. The Q quality factors have been determined from the apparent decrease of the amplitude of each singlet with time, according to a well-suited technique [Roult, G., Clévédé, E., 2000. New refinements in attenuation measurements from free-oscillation and surface-wave observations. Phys. Earth Planet. Inter. 121, 1 37]. The results are compared to the theoretical frequencies and Q quality factors computed for the PREM and 1066A models, taking into account both rotation and ellipticity effects of the Earth. The two observed datasets (frequencies and Q quality factors) exhibit a splitting on the observed values different from the predicted one. That seems to point out that some parameters as density or attenuation values used in the theoretical models do not explain the observations. A new dataset of frequencies and Q quality factors of the whole set of singlets of the gravest spheroidal modes is thus under construction. That dataset includes the five individual singlets of the 0S2 mode clearly identified on the SG records, the three singlets of the 2S1 mode recently observed for the first time by [Rosat, S., Hinderer, J., Rivera, L., 2003b. First observation of 2S1 and study of the splitting of the football mode 0S2 after the June 2001 Peru earthquake of magnitude 8.4. Geophys. Res. Lett. 30, 21211, doi:10-1029/2003L018304], the 0S0 radial mode, and the seven individual singlets of the 0S3 mode

The COSY Project: Verification of Global Seismic Modeling Algorithms

Progress in understanding the details in the global 3-D seismic velocity structure rests on the assumption that we can accurately model seismic wave propagation (e.g. travel times, waveforms, etc.) through heterogeneous 3-D Earth models. While for spherically symmetric models (quasi-)analytical solutions are available for the verification of numerical algorithms this is not the case for general heterogeneous models. It is therefore desirable to establish global 3-D test models and verified reference seismograms, which allow us to access the accuracy of these algorithms in a quantitative way. Prior to a workshop held on this issue at the 1997 IASPEI Meeting, a 3-D test model was handed out to various groups and synthetic seismograms returned. This workshop was the initiation of the COSY Project (COmparison of global SYnthetic seismogram techniques) which aims at establishing a a WWW page (http://www.itg.cam.ac.uk/COSY) where the test models and seismograms as well as some of the used al..