Seismic imaging of transmission overhead line structure foundations

The goal of the presented work is to determine the shape of transmission overhead line structure foundations. A seismic imaging technique is used. It is formulated as an inverse scattering problem where two-dimensional maps of the pressure-and shear-wave velocities are estimated. The inversion amounts to a large-scale, nonlinear programming problem. It is rendered all the more difficult by the large dimensions of the scattering object and the high velocity contrasts. In this context, our goal is to propose an inversion scheme that produces precise images with an acceptable computational effort. This goal is met by combining the following elements: (i) minimization of a penalized least-square criterion with a quasi-Newton algorithm, (ii) frequency domain formulation in order to introduce the measured data progressively and (iii) introduction of a logarithmic change of variables for the quantities to be estimated. The latter point is our main contribution. Its role is to counterbalance the lack of sensitivity of the criterion and its introduction results in a significant acceleration of the inversion process.