A Mathematical Model for the Acoustic and Seismic Properties of the Landmine Detection Problem

Acoustic landmine detection is accomplished by using a loud speaker to generate airborne source low-frequency waves that are transmitted to the soil above a buried landmine target. At a specific frequency, the landmine will vibrate at resonance, imparting an enhanced velocity on the soil particles above it at the surface that is detected by a scanning Laser Doppler Vibrometer system. If the soil surface velocity profiles measured from these experiments could be predicted mathematically under a variety of conditions, the physical system would be able to accurately detect landmines in more challenging environments. The mathematical modeling of the buried landmine detection problem involved wave propagation in a layered waveguide in the presence and absence of a buried circular target. In this study, emphasis was placed on acoustic to seismic coupling of an airborne continuous wave point source into the soil. Soil resonances were calculated with a model that represents the soil as a finite, fluid-filled rigid porous layer below a finite atmospheric layer. This two-layer waveguide incorporated density and sound speed in both the soil and atmosphere, which was adjusted based on soil type, compactness, and moisture content in both the air and soil. An analytic solution of the two-layer waveguide problem involved solving the Helmholtz equation in cylindrical coordinates in both layers along with using a delta function point source to simulate a compact loudspeaker in the upper layer. Boundary conditions along with conditions of orthogonality were used to obtain complicated analytical expressions for the eigenvalues and eigenfunctions of the problem. A MATLAB(Trademark) program was used to numerically solve for the eigenvalues and plot solutions of pressure and particle velocity vs. frequency and spatial variables. The original document contains color images.