Modeling a Priori Information on the Velocity Field in Reflection Tomography

International audienceReflection tomography consists in determining a velocity field and reflector geometries from traveltimes picked on multioffset seismic section. The solution of the tomographic inverse problem being underdetermined, we need to integrate a priori information on the model. A regularization by means of model curvature has in general no physical justification and leads to geologically incorrect models. This paper presents a formulation that integrates in a realistic way a priori geological information associated with the regularity of the model and with the relation between the velocity distribution and the interface geometries. Such an integration seems particularly critical when dealing with smooth velocity models in which velocity and interfaces are defined independently from each other. We validate the interest of our formulation on a real data example

B44 Adapted Nonlinear Optimization Method for Production Data and 4D Seismic Inversion

International audienceIntegrated inversion of production history data and 4D seismic data for reservoir model characterization leads to a nonlinear inverse problem that is usually cumbersome to solve : the associated forward problem based, on one hand, on fluid flow simulation in the reservoir for production data modeling, and on the other hand, on a petro-elastic model for 4D time lapse seismic data modeling, is usually computationally time consuming, the number of measurements to be inverted is large (up to 500 000), the number of model parameters to be determined is up to 100. Moreover, all the derivatives of the modeled data with respect to those parameters are usually not available. We propose an optimization method based on a Sequential Quadratic Programming algorithm which uses gradient approximation coupled with a BFGS approximation of the Hessian. In addition, the proposed method allows to handle equality and inequality nonlinear constraints. Some realistic applications are presented to illustrate the efficiency of the method

Constrained optimization in seismic reflection tomography: a Gauss-Newton augmented Lagrangian approach

International audienceS U M M A R Y Seismic reflection tomography is a method for determining a subsurface velocity model from the traveltimes of seismic waves reflecting on geological interfaces. From an optimization viewpoint , the problem consists in minimizing a non-linear least-squares function measuring the mismatch between observed traveltimes and those calculated by ray tracing in this model. The introduction of a priori information on the model is crucial to reduce the under-determination. The contribution of this paper is to introduce a technique able to take into account geological a priori information in the reflection tomography problem expressed as inequality constraints in the optimization problem. This technique is based on a Gauss-Newton (GN) sequential quadratic programming approach. At each GN step, a solution to a convex quadratic optimization problem subject to linear constraints is computed thanks to an augmented Lagrangian algorithm. Our choice for this optimization method is motivated and its original aspects are described. First applications on real data sets are presented to illustrate the potential of the approach in practical use of reflection tomography

Uncertainty and Sensitivity Analysis in Turbulent Pipe Flow Simulation

In this study, we would like to evaluate and improve the performance of Wall-Modeled LargeEddy Simulation (WMLES) on the modeling of a pipe flow for which Direct Numerical Simulation (DNS) data is available [1] and considered as a reference for further comparisons. Models used in WMLES may raise problems of accuracy which come from the uncertain values of model parameters and model simplifications. In this study, we focus firstly on the impact of the model parameter uncertainties on the simulation results, and then on the reduction of these uncertainties via data calibration. These studies using sampling-based approaches can be unaffordable when coupled with a high-fidelity simulation that requires several CPU hours for a single execution. To reduce the computational cost while maintaining a target accuracy, we propose to build surrogate models based on Gaussian Processes for simulations outputs, and replace the simulator for evaluating the large size sampled sets. For this study, a CFD-UQ methodology is developed which couples our internal UQ tool and a CFD solver. It has been applied on a turbulent pipe flow case that allows us to validate its implementation

Does shade improve light interception efficiency? A comparison among seedlings from shade-tolerant and -intolerant temperate deciduous tree species

• Here, we tested two hypotheses: shading increases light interception efficiency (LIE) of broadleaved tree seedlings, and shade-tolerant species exhibit larger LIEs than do shade-intolerant ones. The impact of seedling size was taken into account to detect potential size-independent effects on LIE. LIE was defined as the ratio of mean light intercepted by leaves to light intercepted by a horizontal surface of equal area. • Seedlings from five species differing in shade tolerance (Acer saccharum, Betula alleghaniensis, A. pseudoplatanus, B. pendula, Fagus sylvatica) were grown under neutral shading nets providing 36, 16 and 4% of external irradiance. Seedlings (1- and 2-year-old) were three-dimensionally digitized, allowing calculation of LIE. • Shading induced dramatic reduction in total leaf area, which was lowest in shade-tolerant species in all irradiance regimes. Irradiance reduced LIE through increasing leaf overlap with increasing leaf area. There was very little evidence of significant size-independent plasticity of LIE. • No relationship was found between the known shade tolerance of species and LIE at equivalent size and irradiance

Competition for light and nitrogen in a canavalia-sorghum intercrop

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Uncertainty Analysis for Seismic Inverse Problems: Two Practical Examples

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