CAVITY IDENTIFICATION USING 3-D ELASTODYNAMIC BEM, SHAPE SENSITIVITY AND TOPOLOGICAL DERIVATIVE

摘要

The problem of mapping underground cavities from surface, i.e.. using non-intrusive seismic measurements, is investigated via a regularized boundary integral equation method With the ground modeled as a three-dimensional uniform, isotropic elastic half-space, the inverse analysis of seismic waves scattered by a three-dimensional void is formulated as a task of minimizing a cost function involving the misfit between experimental observations and theoretical (i e forward) predictions This conventional choice of setting is dictated by the very high computational cost of solving the forward elastodynamic scattering problem, which makes e.g. global search strategies infeasible. For an accurate treatment of the gradient search technique employed to solve the inverse problem, derivatives of the predictive boundary element model with respect to the cavity parameters are evaluated using an adjoint problem approach Here as in most situations where conventional descent methods (here the quasi-Newton algorithm with BFGS formula) are used, results depend on the choice of initial guess and occasional lack of convergence occurs This has prompted the authors to investigate the use of topological derivative as a tool for preliminary probing. The topological derivative field is computed via a relatively inexpensive procedure, and appears to yield useful indications as to the topology and approximate location of the cavity system. Numerical examples are included to illustrate the effectiveness of the various steps developed so far.