The problem of mapping underground cavities from surface seismic measurements is investigated within the framework of a regularized boundary integral equation (BIE) method. With the ground modeled as a uniform elastic half-space, the inverse analysis of elastic waves scattered by a three-dimensional void is formulated as a task of minimizing the misfit between experimental observations and theoretical predictions for an assumed void geometry. For an accurate treatment of the gradient search technique employed to solve the inverse problem, sensitivities of the predictive BIE model with respect to cavity parameters are evaluated semi-analytically using an adjoint problem approach and a continuum kinematics description. Several key features of the formulation, including the rigorous treatment of the radiation condition for semi-infinite solids, modeling of an illuminating seismic wave field, and treatment of the prior information, are highlighted. A set of numerical examples with spherical and ellipsoidal cavity geometries is included to illustrate the performance of the method. It is shown that the featured adjoint problem approach reduces the computational requirements by an order of magnitude relative to conventional finite-difference estimates, thus rendering the three-dimensional elastic-wave imaging of solids tractable for engineering applications.
Bibliographical noteFunding Information:
The support provided by the National Science Foundation through CAREER Award No. CMS-9875495 to B. Guzina and the University of Minnesota Supercomputing Institute during the course of this investigation is gratefully acknowledged. Special thanks are due to MTS Systems Corporation for providing the opportunity for M. Bonnet to visit the University of Minnesota through the MTS Visiting Professorship of Geomechanics.
- Boundary integral equation methods
- Elastic waves
- Inverse scattering
- Radiation condition