[1] We present a novel method for joint inversion of receiver functions and surface wave dispersion data, using a transdimensional Bayesian formulation. This class of algorithm treats the number of model parameters (e.g. number of layers) as an unknown in the problem. The dimension of the model space is variable and a Markov chain Monte Carlo (McMC) scheme is used to provide a parsimonious solution that fully quantifies the degree of knowledge one has about seismic structure (i.e constraints on the model, resolution, and trade-offs). The level of data noise (i.e. the covariance matrix of data errors) effectively controls the information recoverable from the data and here it naturally determines the complexity of the model (i.e. the number of model parameters). However, it is often difficult to quantify the data noise appropriately, particularly in the case of seismic waveform inversion where data errors are correlated. Here we address the issue of noise estimation using an extended Hierarchical Bayesian formulation, which allows both the variance and covariance of data noise to be treated as unknowns in the inversion. In this way it is possible to let the data infer the appropriate level of data fit. In the context of joint inversions, assessment of uncertainty for different data types becomes crucial in the evaluation of the misfit function. We show that the Hierarchical Bayes procedure is a powerful tool in this situation, because it is able to evaluate the level of information brought by different data types in the misfit, thus removing the arbitrary choice of weighting factors. After illustrating the method with synthetic tests, a real data application is shown where teleseismic receiver functions and ambient noise surface wave dispersion measurements from the WOMBAT array (South-East Australia) are jointly inverted to provide a probabilistic 1D model of shear-wave velocity beneath a given station.Citation: Bodin, T., M. Sambridge, H. Tkalčić, P. Arroucau, K. Gallagher, and N. Rawlinson (2012), Transdimensional inversion of receiver functions and surface wave dispersion,

SUMMARY A meaningful interpretation of seismic measurements requires a rigorous quantification of the uncertainty. In an inverse problem, the data noise determines how accurately observations should be fit, and ultimately the level of detail contained in the recovered model. A common problem in seismic tomography is the difficulty in quantifying data uncertainties, and thus the required level of data fit. Traditionally, the complexity of the solution model (defined by both the number of basis functions and the regularization) is defined arbitrarily by the user prior to inversion with only limited use of data errors. In the context of multiscale problems, dealing with multiple data sets that are characterized by different noise variances and that span the Earth at different scales is a major challenge. Practitioners are usually required to arbitrarily weigh the contribution of each data type into the final solution. Furthermore, the basis functions are usually spatially uniform across the velocity field and regularization procedures are global, which prevents the solution model from accounting for the uneven spatial distribution of information. In this work we propose to address these issues with a Hierarchical Bayesian inversion. The new algorithm represents an extension of the transdimensional tomography to account for uncertainties in data noise. This approach has the advantage of treating the level of noise in each data set, as well as the number of model parameters, as unknowns in the inversion. It provides a parsimonious solution that fully represents the degree of knowledge one has about seismic structure (i.e. constraints, resolution and trade‐offs). Rather than being forced to make decisions on parametrization, level of data fit and weights between data types in advance, as is often the case in an optimization framework, these choices are relaxed and instead constrained by the data themselves. The new methodology is presented in a synthetic example where both the data density and the underlying structure contain multiple length scales. Three ambient noise data sets that span the Australian continent at different scales are then simultaneously inverted to infer a multiscale tomographic image of Rayleigh wave group velocity for the Australian continent. The procedure turns out to be particularly useful when dealing with multiple data types with different unknown levels of noise as the algorithm is able to naturally adjust the fit to the different data sets and provide a velocity map with a spatial resolution adapted to the spatially variable information present in the data.

International audienceThe aim of the SI-Hex project (acronym for « Sismicité Instrumentale de l’Hexagone ») is to provide a catalogue of seismicity for metropolitan France and the French marine economic zone for the period 1962–2009 by taking into account the contributions of the various seismological networks and observatories from France and its neighbouring countries. The project has been launched jointly by the Bureau Central Sismologique Français (CNRS-University/BCSF) and the Laboratoire de Détection et de Géophysique (CEA-DAM/LDG). One of the main motivations of the project is to provide the end user with the best possible information on location and magnitude of each earthquake. So far, due to the various procedures in use in the observatories, the different locations and magnitudes of earthquakes located in the SI-Hex zone were presenting large discrepancies. In the 2014 version of the catalogue, 1D localizations of hypocentres performed with a unique computational scheme and covering the whole 1962–2009 period constitute the backbone of the catalogue (SI-Hex solutions). When available, they are replaced by more precise localizations made at LDG or, for recent times, by the regional observatories within: 1) the French Alps, 2) the southernmost Alps and the Mediterranean domain including Corsica, 3) the Pyrenees, and 4) the Armorican massif. Moment magnitudes Mw are systematically reported in the SI-Hex catalogue. They are computed from coda-wave analysis of the LDG records for most Mw>3.4 events, and are converted from local magnitudes ML for smaller magnitude events. Finally, special attention is paid to the question of discrimination between natural and artificial seismic events in order to produce a catalogue for direct use in seismic hazard analysis and seismotectonic investigations. The SI-Hex catalogue is accessible on the web site www.franceseisme.fr and contains 38,027 earthquake hypocentres, together with their seismic moment magnitudes Mw

Detailed images of Rayleigh wave group velocity are derived from ambient seismic noise recorded by WOMBAT, a large rolling seismic array project in southeast Australia. Group velocity maps sensitive to crustal structure exhibit low velocity anomalies in the presence of sedimentary basins and recent hot‐spot volcanism, and high velocities in regions of out‐cropping metamorphic and igneous rocks. Distinct and well‐constrained patches of low velocity within the Murray Basin provide new insight into the spatial extent and possible composition of pre‐Tertiary infra‐basins. In a broader tectonic context, our results show little evidence for the Palaeozoic building blocks of the southeast Australian continent that have been inferred from geological mapping and potential field data. This may mean that apparent changes in basement terrane near the surface are not associated with major changes in composition at depth.