Accurate and fast magnitude determination for large, shallow earthquakes is of key importance for post-seismic response and tsumami alert purposes. When no local real-time data are available, which is today the case for most subduction earthquakes, the first information comes from teleseismic body waves. Standard body-wave methods give accurate magnitudes for earthquakes up to Mw= 7–7.5. For larger earthquakes, the analysis is more complex, because of the non-validity of the point-source approximation and of the interaction between direct and surface-reflected phases. The latter effect acts as a strong high-pass filter, which complicates the magnitude determination. We here propose an automated deconvolutive approach, which does not impose any simplifying assumptions about the rupture process, thus being well adapted to large earthquakes. We first determine the source duration based on the length of the high frequency (1–3 Hz) signal content. The deconvolution of synthetic double-couple point source signals—depending on the four earthquake parameters strike, dip, rake and depth—from the windowed real data body-wave signals (including P, PcP, PP, SH and ScS waves) gives the apparent source time function (STF). We search the optimal combination of these four parameters that respects the physical features of any STF: causality, positivity and stability of the seismic moment at all stations. Once this combination is retrieved, the integration of the STFs gives directly the moment magnitude. We apply this new approach, referred as the SCARDEC method, to most of the major subduction earthquakes in the period 1990–2010. Magnitude differences between the Global Centroid Moment Tensor (CMT) and the SCARDEC method may reach 0.2, but values are found consistent if we take into account that the Global CMT solutions for large, shallow earthquakes suffer from a known trade-off between dip and seismic moment. We show by modelling long-period surface waves of these events that the source parameters retrieved using the SCARDEC method explain the observed surface waves as well as the Global CMT parameters, thus confirming the existing trade-off. For some well-instrumented earthquakes, our results are also supported by independent studies based on local geodetic or strong motion data. This study is mainly focused on moment determination. However, the SCARDEC method also informs us about the focal mechanism and source depth, and can be a starting point to study systematically the complexity of the STF

International audienceWe propose a class of spherical wavelet bases for the analysis of geophysical models and for the tomographic inversion of global seismic data. Its multiresolution character allows for modelling with an effective spatial resolution that varies with position within the Earth. Our procedure is numerically efficient and can be implemented with parallel computing. We discuss two possible types of discrete wavelet transforms in the angular dimension of the cubed sphere. We describe benefits and drawbacks of these constructions and apply them to analyse the information in two published seismic wave speed models of the mantle, using the statistics of wavelet coefficients across scales. The localization and sparsity properties of wavelet bases allow finding a sparse solution to inverse problems by iterative minimization of a combination of the ℓ2 norm of the data residuals and the ℓ1 norm of the model wavelet coefficients. By validation with realistic synthetic experiments we illustrate the likely gains from our new approach in future inversions of finite-frequency seismic dat

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[1] We present a realistic application of an inversion scheme for global seismic tomography that uses as prior information the sparsity of a solution, defined as having few nonzero coefficients under the action of a linear transformation. In this paper, the sparsifying transform is a wavelet transform. We use an accelerated iterative soft-thresholding algorithm for a regularization strategy, which produces sparse models in the wavelet domain. The approach and scheme we present may be of use for preserving sharp edges in a tomographic reconstruction and minimizing the number of features in the solution warranted by the data. The method is tested on a data set of time delays for finite-frequency tomography using the USArray network, the first application in global seismic tomography to real data. The approach presented should also be suitable for other imaging problems. From a comparison with a more traditional inversion using damping and smoothing constraints, we show that (1) we generally retrieve similar features, (2) fewer nonzero coefficients under a properly chosen representation (such as wavelets) are needed to explain the data at the same level of root-mean-square misfit, (3) the model is sparse or compressible in the wavelet domain, and (4) we do not need to construct a heterogeneous mesh to capture the available resolution.