Quantifying uncertainties on the solution model of seismic tomography

Abstract : Reflection tomography allows the determination of a velocity model that fits the traveltime data associated with reflections of seismic waves in the subsurface. A least-square formulation is used to compare the observed traveltimes and the traveltimes computed by the forward operator based on a ray tracing. This non linear optimization problem is solved classicaly by a Gauss-Newton method based on successive linearizations of the forward operator. The obtained solution is only one among many possible models. Indeed, the uncertainties on the observed traveltimes (resulting from an interpretative event picking on seismic records) and more generally the underdetermination of the inverse problem lead to uncertainties on the solution. An a posteriori uncertainty analysis is then crucial to delimit the range of possible solutions that fit, with the expected accuracy, the data and the a priori information. A linearized a posteriori analysis is possible by an analysis of the a posteriori covariance matrix, inverse of the Gauss-Newton approximation of the matrix. The computation of this matrix is generally expensive (the matrix is huge for 3D problems) and the physical interpretation of the results is difficult. Then we propose a formalism which allows to compute uncertainties on relevant geological quantities for a reduced computational time. Nevertheless, this approach is only valid in the vicinity of the solution model (linearized framework) and complex cases may require a non linear approach. An application on a 2D real data set illustrates the linearized approach to quantify uncertainties on the solution of seismic tomography and the limitations of this approach are discussed.
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Carole Duffet, Delphine Sinoquet. Quantifying uncertainties on the solution model of seismic tomography. European Congress on Computational Methods in Applied Sciences and Engineering, Jul 2004, Jyvaskyla, Finland. pp.24 - 28. ⟨hal-02284262⟩

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