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  • 1
    Electronic Resource
    Electronic Resource
    Oxford, UK : Blackwell Publishing Ltd
    Geophysical journal international 119 (1994), S. 0 
    ISSN: 1365-246X
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Geosciences
    Notes: We present a practical algorithm for determining the Bayesian solution of non-linear inverse problems with a limited number of parameters. This approach allows the use of very general conditional probability density functions (pdfs of the data given the model parameters) and a priori pdfs (prior beliefs upon the parameters). The results consist in the a posteriori marginal pdfs of the model parameters. The marginal pdfs describe the additional information (if any) brought by the data to the prior knowledge about the model parameters.We have paid a special attention to the numerical calculation of the a posteriori pdfs and we propose a solution which enables the simultaneous determination of the numerical estimates of the a posteriori pdfs and their uncertainties.With the help of a practical example (the 1-D magnetotelluric inverse problem) with synthetic and real data, we show that in most cases, the a posteriori marginal pdfs are complicated functions and cannot be predicted from the data pdf or the a priori pdfs. Consequently, the standard analyses applied to the same data sets such as the maximum likelihood techniques or the asymptotic estimation technique would lead to severely biased estimates of the parameters. This remark is likely to be true for any non-linear inverse problem.
    Type of Medium: Electronic Resource
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  • 2
    Publication Date: 2014-05-15
    Description: Grímsvötn Volcano is the most active volcano in Iceland, and its last three eruptions were in 1998, 2004 and 2011. Here we analyze the displacement around Grímsvötn during these last three eruptive cycles using 10 GPS stations. The observed displacements in this region generally contain a linear component of tectonic and glacio-isostatic origin, in agreement with the previously estimated values of plate motions and vertical rebound. Larger amplitude deformation observed close to Grímsvötn at the GFUM continuous GPS station clearly reflects a major volcanic contribution superimposed on a tectonic component. We estimate and substract the tectonic trend at this station using regional observed displacement. The direction and pattern of the residual volcanic displacement (for co-eruptive and inter-eruptive periods) are consistent for all three of these eruptive cycles. The post-eruptive inflation is characterized by an exponential trend, followed by a linear trend. In this study, we explain this temporal behavior using a new analytic model that has two connected magma chambers surrounded by an elastic medium and fed by a constant basal magma inflow. During the early post-eruptive phase, pressure re-adjustment occurs between the two reservoirs, with replenishment of the shallow chamber from the deep chamber. Afterwards, due to the constant inflow of magma into the deep reservoir, the pressurization of the system produces linear uplift. A large deep reservoir favors magma storage rather than surface emission. Based on displacement measured at GFUM station, we estimate an upper limit for the radius of the deep reservoir of ~10 km.
    Print ISSN: 0148-0227
    Topics: Geosciences , Physics
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