Tomographic DST Algorithm for Stone Column Site Imaging and Characterization-Paper

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The paper presents the Forward Modeling Downhill Simplex Method for Stone Columns (FMDSMSC), an algorithm for estimating in-situ shear-wave velocities from Downhole Seismic Testing (DST) at sites improved with stone columns. These sites are difficult to characterize because seismic waves may travel through the faster stone columns, refract into surrounding soil, and produce complex arrival times that cannot be reliably interpreted using a straight-ray assumption.<br /><br />FMDSMSC adapts the authors’ earlier NMO-SCTT tomographic method. It models wave refraction through two-dimensional velocity profiles, using vertical as well as horizontal boundaries to represent stone columns and soil layers. A multidimensional Newton–Raphson method traces ray paths according to Fermat’s principle, while Monte Carlo searches help identify optimal velocity estimates despite multiple local minima. The method also applies site-specific prior constraints: stone-column velocities vary little, the densified soil is substantially slower than the columns, and waves enter the columns at small angles.<br /><br />A simulated test-bed example showed that FMDSMSC recovered soil interval velocities close to the assumed values and estimated the stone-column velocity at about 829 m/s, compared with the assumed 800 m/s. In contrast, straight-ray estimates produced unrealistic results. The authors conclude that the method enables DST-based characterization of stone-column sites, while noting that validation with actual field data remains future work.

Keywords

Forward Modeling Downhill Simplex Method

FMDSMSC

stone columns

downhole seismic testing

shear-wave velocity

wave refraction

Fermat's principle

Monte Carlo search

velocity profiling

straight-ray assumption