We describe a new technique for detecting and characterizing ellipsoidal shapes automatically from any type of image. This technique is a single pass algorithm which can extract any group of ellipse parameters or characteristics which can be computed from those parameters without having to detect all five parameters for each ellipsoidal shape. Moreover, the method can explicitly incorporate any a priori knowledge the user may have concerning ellipse parameters. The method is based on techniques from projective geometry and on the Hough transform. This technique can significantly reduce interpretation and computation time by automatically extracting only those features or geometric parameters of interest from images and making exact use of a priori information.

The up/down convolutional velocity filter is commonly used in vertical seismic profiling to separate an upgoing from a downgoing wave field. In the neighborhood of a velocity discontinuity one expects to see transient effects. For a simple medium containing a single velocity discontinuity it is possible to derive an explicit formula for these transients. This analysis predicts that the transients decay at a rate inversely proportional to the distance from the velocity discontinuity. Despite the slow decay rate, these transients are found to be quite insignificant.>

The dynamics of a rigid 2-dimensional body in contact with walls is systematically considered. The body is seen to exhibit four different kinds of motion when it is contact with one wall and nine different kinds of motion when it is in contact with two walls. Each kind of motion is discussed and the region in the (F,T) space where the motion is exhibited is delineated. In addition it is seen that in some situations two or more of these regions can overlap leading to ambiguities.