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Formulation de la tomographie des temps de première arrivée à partir d'une méthode de gradient : un pas vers une tomographie interactive

Abstract : First arrival traveltime tomography aims at inferring a seismic wave propagation velocity model from first arrival traveltimes picked on seismograms. The velocity model inferred can be used directly to perform a structural interpretation of the subsurface or as an initial model for another seismic imaging method. This technique can be applied at different scales from geotechnical studies to seismology through oil exploration. The geophysicist know-how plays an important role in the difficult resolution of the nonlinear and ill-posed tomographic problem. Numerous studies have tried to ease and improve this resolution considering a physical or mathematical approach. Within the scope of this work, we wish to develop a pragmatic approach, i.e. we consider that the tomographic problem should be solved using an interactive algorithm whose tuning parameters are clearly identified. The interactive aspect of the algorithm facilitates the acquisition of the tomographic know-how because it allows performing, within a reasonable time, many simulations for different kinds of parameterization. The goal pursued in this work is the definition of a first arrival traveltime tomography algorithm that fulfills these specifications at best. Conventional first arrival traveltime tomography algorithms do not match our criteria of a pragmatic approach. Indeed, their implementation hardly takes benefit of the parallel architecture of current supercomputers in order to reduce the computation times. Moreover, their practical application implies a complex parameterization due to the resolution of the linear tomographic system. All these practical limitations issue from the original formulation of the algorithm based on a Gauss-Newton minimization method. The idea developed in this work is to formulate the resolution of the tomographic problem using a steepest descent method to overcome all these limitations. The key step of this formulation is the computation of the gradient of the misfit function with respect to the model parameters. We use the adjoint state method and a method based on an a posteriori ray tracing to compute this gradient. These two methods differ from their formulation, respectively nonlinear and linearized, and their implementation. Then, we clearly define the parameterization of the new algorithm and validate on a supercomputer its practical properties that are: a direct and efficient parallelization, a memory requirement independent of the amount of input data and a straightforward implementation. Finally, in order to validate the tomographic behaviour of this new algorithm, in terms of obtained results and stability, we present tomography results for 2-D and 3-D, synthetics and real, marine and land, seismic refraction acquisitions. A great number of simulations have been carried out thanks to the fast execution time of the algorithm, typically few minutes for 2-D simulations.
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Submitted on : Wednesday, March 4, 2009 - 8:00:00 AM
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  • HAL Id : pastel-00004850, version 1


Cédric Taillandier. Formulation de la tomographie des temps de première arrivée à partir d'une méthode de gradient : un pas vers une tomographie interactive. Planète et Univers [physics]. École Nationale Supérieure des Mines de Paris, 2008. Français. ⟨NNT : 2008ENMP1588⟩. ⟨pastel-00004850⟩



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