In recent years, there have been several important innovations that have increased the accuracy and reliability of surface wave methods used in geotechnical and earthquake engineering. However, one aspect of surface wave testing that has changed little in 30 years is the subsurface forward model underlying the inverse problem. The most widely used one is a horizontally layered model with soil properties that vary only in the vertical direction. Further advancement of surface wave methods in geotechnical engineering is thus limited by the lack of robust and efficient computational models that enable more realistic representations of two- or three-dimensional soil media. This research will formulate a new class of geometric numerical inverse models for surface wave measurements that will lead to more realistic modeling of subsurface soil properties than the current state of the art and consequently more accurate subsurface characterization. Using a multidisciplinary approach, a powerful new class of innovative computational models, referred to as "BEM Adjoint-based Active Surfaces," will be derived to solve the geometric inverse problem of the identification of the spatially varying soil properties in heterogeneous elastic media directly from raw data via the Boundary Element Method (BEM).
The derived inverse model will represent a major change in extracting unseen geometric structures from digital surface measurements, where the standard procedure is to transform the raw sensor data into more intuitive volumetric data (e.g., cross-sectional images), from which geometric features (such as layer boundaries) can then be extracted afterward via signal and image processing methods. This new inverse model paradigm will offer a new computational method to pass directly from raw tomographic measurements to potentially complex geometric shapes (such as geometry of thickness varying layer interfaces, soil occlusions or cavity identification). The new inverse methods will also be applicable to a broader set of non-invasive wave propagation characterization techniques for civil infrastructure. The investigators will incorporate the research into graduate courses on solid mechanics, image processing, in-situ seismic testing, and geometric inverse problems.
