Bojan Guzina, Associate Fellow

Three-Dimensional Subterranean Imaging via Elastic Waves

Vertical ground motion (termed incident field) generated by an axial force vibrating at a frequency of 70 Hz. The scatterer is represented by an ellipsoidal cavity, located two meters beneath the ground surface.

The focus of this investigation is the development of a theoretical and computational framework for expeditive three-dimensional mapping of underground objects using elastic (i.e. seismic) waves. In contrast to existing computational treatments that require partitioning of an unknown object and its surroundings for simulation purposes, the imaging problem is formulated so that only the outline of an unknown structure is rendered. This approach, which offers formidable computational savings, has its origins in radar and sonar technologies, but has been largely unexplored in the context of seismic imaging. Building on this foundation, this research aims to develop the first three-dimensional, elasticwave imaging technology that is tractable in the context of a personal computer. Further applications of the methodology may find use in non-destructive material testing and medical diagnosis.

In the first phase of this study, the problem of mapping underground cavities from surface seismic measurements was 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 were formulated as a task of minimizing the mis-fit 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 were evaluated semi-analytically using an adjoint problem approach and a continuum kinematics description. Key features of the formulation include the rigorous treatment of the radiation condition for semi-infinite solids and assimilation of the prior information. Numerical results indicate 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.

When the incident wave reaches the cavity, part of the energy will be reflected back to the surface. This figure details the latter component of the ground motion (so-called scattered field), which is key information for the imaging problem.

On the forefront of material characterization, this group developed a comprehensive analytical and computational framework for the nondestructive, wave-based testing of lossy (i.e. dissipative) media. By enhancing the treatment of an inverse problem through a fully-coupled viscoelastic analysis of the observed waveforms, the method was designed to provide independent estimates of the in situ material stiffness, damping, and density which are not available from conventional seismic interpretations. The presence of noise in experimental observations is accounted for via the use of the maximum likelihood inverse theory. The consistent viscoelastic analysis of waveforms in media with intrinsic dissipation improves the well-posedness of the inverse problem by introducing the internal constraints on the solution which are otherwise absent in traditional (i.e. elastodynamic) seismic analyses. To deal with the significant number of material constants arising in viscoelastic wave interpretation, these researchers also developed a hybrid technique that uncouples the inverse problem via the systematic use of horizontally- and verticallypolarized wave fields.

In parallel with the foregoing developments, this group investigated near-field effects of dynamic interaction between the ground and an impacting annular plate, used worldwide as a seismic source for nondestructive testing of highways. To this end, they developed a mathematical interaction model that demonstrates that the customary uniform-pressure assumption for the contact load between the loading plate and the ground may lead to significant errors in the diagnosis of subsurface pavement conditions.

Research Group

Sylvain Nintcheu Fata, Graduate Student Researcher
Andrew Madyarov, Graduate Student Researcher