Ultrasonic imaging of spherical solids embedded in ice

The transmission of compressional ultrasonic waves into a rigid and dense solid with a doubly-curved surface is impeded when the solid is placed in a liquid medium and its surface is irradiated with waves traveling through the liquid. Measurable power transmission is only possible when the incident ultrasonic beam is close to normal to the surface. This condition is difficult to realize when the waves are excited and detected by a linear array of transducers and limits the possibility of forming cross-sectional images of the solid from the array data. Here, it is shown that the interior of the solid can be imaged with enhanced fidelity if the water is frozen. The high speed of compressional waves in polycrystalline ice (approximately 4000 ms^-1) along with its rigid behavior ensure that ultrasonic waves can be transmitted through the surface over a broad range of angles of incidence. However, due to the double curvature, the rays that form the ultrasonic beam can be deflected outside the array azimuthal plane after entering the solid. Therefore, the two-dimensional images obtained from the linear array data may not be consistent with the fully three-dimensional structure of the ray paths. The analysis of this phenomenon for the special case of solid spheres reveals that the image, to a good approximation, corresponds to a section of the sphere that is parallel to the azimuthal plane and at a standoff distance from it. The distance increases with the angle that the normal to the surface forms relative to the azimuthal plane while it decreases as the velocity contrast between ice and the material of the sphere decreases. While this property is not expected to hold for more complex surfaces, the ray-based framework used in this study is applicable to more general surface configurations and can be used to correlate the images to the structure of the solid. These findings are relevant to the inspection of metallic components with complex geometry which represents a long-standing challenge in the field of nondestructive testing.