Yann Capdeville

Full seismic waveform modelling and inversion

Introduction.- Numerical Solution of the Elastic Wave Equation.- Computing Sensitivity Kernels.- Seismological Data Functionals and their Associated Adjoint Sources.- Iterative Optimisation.- Full Waveform Tomography for Upper-mantle Structure in Australasian Region.- A Comparative Study of Local-scale full Waveform Tomographies.- Source Staking and Data Reduction in Global full Waveform Tomography.

Spectral Element Analysis in Seismology

We present a review of the application of the spectral-element method to regional and global seismology. This technique is a high-order variational method that allows one to compute accurate synthetic seismograms in three-dimensional heterogeneous Earth models with deformed geometry. We first recall the strong and weak forms of the seismic wave equation with a particular emphasis set on fluid regions. We then discuss in detail how the conditions that hold on the boundaries, including coupling boundaries, are honored. We briefly outline the spectral-element discretization procedure and present the time-marching algorithm that makes use of the diagonal structure of the mass matrix. We show examples that illustrate the capabilities of the method and its interest in the context of the computation of three-dimensional synthetic seismograms.

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

The 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.

Numerical modeling of the Mount Steller landslide flow history and of the generated long period seismic waves

The rock-ice avalanche that occurred in 2005 on Mount Steller, Alaska and the resulting long period seismic waves have been simulated for different avalanche scenarios (i.e., flow histories), with and without erosion processes taken into account. This 40-60 Mm3 avalanche traveled about 10 km down the slope, mainly on top of a glacier, eroding a significant amount of ice. It was recorded by 7 broadband seismic stations. The simulations were compared with the recorded long period seismic signal and with the inverted flow history. The results show that, when erosion processes are taken into account, the simulations reproduce the observed signal at all the stations over a wide range of azimuths and source-station distances (37-623 km). This comparison makes it possible to constrain the rheological parameters involved which should help constrain the volume of eroded material. Because landslides are continuously recorded by seismic networks, this method could significantly broaden quantitative insights into natural flow dynamics.

Oceanic lithosphere‐asthenosphere boundary from surface wave dispersion data

Abstract According to different types of observations, the nature of lithosphere-asthenosphere boundary (LAB) is controversial. Using a massive data set of surface wave dispersions in a broad period range (15–300 s), we have developed a three-dimensional upper mantle tomographic model (first-order perturbation theory) at the global scale. This is used to derive maps of the LAB from the resolved elastic parameters. The key effects of shallow layers and anisotropy are taken into account in the inversion process. We investigate LAB distribution primarily below the oceans, according to different kinds of proxies that correspond to the base of the lithosphere from the shear velocity variation at depth, the amplitude radial anisotropy, and the changes in azimuthal anisotropy G orientation. The estimations of the LAB depth based on the shear velocity increase from a thin lithosphere (∼20 km) in the ridges, to a thick old-ocean lithosphere (∼120–130 km). The radial anisotropy proxy shows a very fast increase in the LAB depth from the ridges, from ∼50 km to the older ocean where it reaches a remarkable monotonic subhorizontal profile (∼70–80 km). The LAB depths inferred from the azimuthal anisotropy proxy show deeper values for the increasing oceanic lithosphere (∼130–135 km). The difference between the evolution of the LAB depth with the age of the oceanic lithosphere computed from the shear velocity and azimuthal anisotropy proxies and from the radial anisotropy proxy raises questions about the nature of the LAB in the oceanic regions and of the formation of the oceanic plates

On the shaping factors of the secondary microseismic wavefield

Seismic noise in the period band 3-10 s is known as secondary microseism and it is generated at the ocean surface by the interaction of ocean gravity waves coming from nearly opposite directions. In this paper, we investigate the seismic content of the wavefield generated by a source at the ocean surface and three of the major wavefield shaping factors using the 2D spectral-element method: the ocean-continent boundary, the source site effect and the thickness of seafloor sediments. The seismic wavefield recorded on the vertical component seismograms below the seafloor is mainly composed of the fundamental mode and the first overtone of Rayleigh waves. A mode conversion from the first overtone to the fundamental mode of Rayleigh waves occurs at the ocean-continent boundary. The presence of a continental shelf at the ocean-continent boundary produces a negligible effect on land-recorded seismograms, whereas the source site effect, i.e. the source location with respect to the local ocean depth and sediment thickness, plays the major role. A source in shallow water mostly enhances the fundamental mode of Rayleigh waves, whereas a source in deep water mainly enhances the first overtone of Rayleigh waves. Land-recorded long period signals (T > 6 s) are mostly due to deep water sources, whereas land-recorded short period signals (T > 6 s) are due to sources in relatively shallow water, located close to the shelf break. Seafloor sediments around the source region trap seismic waves reducing the amplitude of land-recorded signals, especially at long periods (T > 6 s).

Numerical modeling of the Mount Meager landslide constrained by its force history derived from seismic data

We focus on the 6 August 2010 Mount Meager landslide that occurred in Southwest British Columbia, Canada. This 48.5 Mm3 rockslide that rapidly changed into a debris flow was recorded by over 25 broadband seismic stations. We showed that the waveform inversion of the seismic signal making it possible to calculate the time history of the force applied by the landslide to the ground is very robust and stable, even when using only data from a single station. By comparing this force with the force calculated through numerical modeling of the landslide, we are able to support the interpretation of seismic data made using a simple block model. However, our study gives different values of the friction coefficients involved and more details about the volumes and orientation of the subevents and the flow trajectory and velocity. Our sensitivity analysis shows that the characteristics of the released mass and the friction coefficients all contribute to the amplitude and the phase of the force. Despite this complexity, our study makes it possible to discriminate the best values of all these parameters. Our results suggest that comparing simulated and inverted forces helps to identify appropriate rheological laws for natural flows. We also show that except for the initial collapse, peaks in the low-frequency force related to bends and runup over topography changes are associated with high-frequency generation, possibly due to an increased agitation of the granular material involved

Effect of a plume on long period surface waves computed with normal modes coupling

Abstract The physical characterization and depth origin of mantle plumes are not well constrained. In order to address these issues, we look for observable effects of plumes on long period surface wave seismograms. The effect of a weak but sharp heterogeneity on long period surface waves is computed by a first order normal mode theory using a generalization of the spherical harmonic summation theorem to reduce the number of operations. It turns out that it is necessary to couple very far along a given dispersion branch ( l ±40 up to ±80) to remove spurious phases in seismograms. The coupling between different overtone branches (different overtone numbers) of the same kind (spheroidal or toroidal) and of different kinds are computed as well. By taking into account a large number of overtones, we are able to compute the effect of the heterogeneity on all seismogram phases from surface waves to body waves, including P–SH and SV–SH coupling. This technique is applied to different plausible models of mantle plume: a small vertical conduit down to 660 km depth, down to the core–mantle-boundary (CMB) and with or without head. We show that for a finite size plume the radiation pattern is essentially forward, which is not the case when the heterogeneity is considered as punctual. The scattered amplitude displays large variations for the different cases according to the temperature contrast, but an effect up to 10% of the incident amplitude can be expected, and should be observable on good quality seismic data.

Synthetic dataset to benchmark global tomographic methods

A new set of global synthetic seismograms calculated in a three-dimensional (3-D), heterogeneous, anisotropic, anelastic model of the Earth using the spectral element method has been released by the European network SPICE (Seismic Wave Propagation and Imaging in Complex Media: a European Network). The set consists of 7424 three-component records with a minimum period of 32 seconds, a sampling rate of one second, and a duration of 10,500 seconds.The aim of this synthetic data set is to conduct a blind test of existing global tomographic methods based on long-period data, in order to test how current imaging techniques are limited by approximations in theory and by the inadequacy of data quality and coverage. The correlation between modern global tomographic models is generally correct at long wavelengths, but these tomographic models are less similar at shorter wavelengths [Becker and Boschi, 2002].In order to interpret the fine details of tomographic models, it is a fundamental prerequisite to understand quantitatively the resolving properties of specific imaging algorithms. Without knowledge of the true model, it is difficult to properly evaluate the tomographic methods.

Homogenized moment tensor and the effect of near‐field heterogeneities on nonisotropic radiation in nuclear explosion

We investigate the effect of small-scale heterogeneities close to a seismic explosive source, at intermediate periods (20-50 s), with an emphasis on the resulting nonisotropic far-field radiation. First, using a direct numerical approach, we show that small-scale elastic heterogeneities located in the near-field of an explosive source, generate unexpected phases (i.e., long period S waves). We then demonstrate that the nonperiodic homogenization theory applied to 2-D and 3-D elastic models, with various pattern of small-scale heterogeneities near the source, leads to accurate waveforms at a reduced computational cost compared to direct modeling. Further, it gives an interpretation of how nearby small-scale features interact with the source at low frequencies, through an explicit correction to the seismic moment tensor. In 2-D simulations, we find a deviatoric contribution to the moment tensor, as high as 21% for near-source heterogeneities showing a 25% contrast of elastic values (relative to a homogeneous background medium). In 3-D this nonisotropic contribution reaches 27%. Second, we analyze intermediate-periods regional seismic waveforms associated with some underground nuclear explosions conducted at the Nevada National Security Site and invert for the full moment tensor, in order to quantify the relative contribution of the isotropic and deviatoric components of the tensor. The average value of the deviatoric part is about 35%. We conclude that the interactions between an explosive source and small-scale local heterogeneities of moderate amplitude may lead to a deviatoric contribution to the seismic moment, close to what is observed using regional data from nuclear test explosions.