We demonstrate a specific power series expansion technique to solve the three-dimensional homogeneous and inhomogeneous wave equations. As solving functions, so-called wave polynomials are used. The presented method is useful for a finite body of certain shape. Recurrent formulas to improve efficiency are obtained for the wave polynomials and their derivatives in a Cartesian, spherical, and cyl...

Wave-equation migration using one-way wavefield extrapolation operators is commonly used in industry to generate images of complex geologic structure from 3D seismic data. By design, most conventional wave-equation approaches restrict propagation to downward continuation, where wavefields are recursively extrapolated to depth on Cartesian meshes. In practice, this approach is limited in high-an...

The isotope effects appear as the deviation and unsymmetrization of the potential profile along the IRC in the mass-weighted Cartesian coordinate system, whereas in the ordinary nonmass-weighted Cartesian coordinate system they appear as the differences of the effective mass. The analysis of tunneling probability has shown that the difference in the effective mass which is greatest in the vicin...

Linear Kirchhoff beams, also known as curved Euler-Bernoulli are reformulated using tangential differential calculus (TDC). The model is formulated in a two dimensional Cartesian coordinate system. Isogeometric analysis (IGA) employed, hence, NURBS used for the geometry definition and generation of sufficiently smooth shape functions. Dirichlet boundary conditions enforced weakly Lagrange multi...

We construct a nonlinear mapping from a high-dimensional sample space to a low-dimensional vector space, effectively recovering a Cartesian coordinate system for the manifold from which the data is sampled. The mapping preserves local geometric relations in the manifold and is pseudo-invertible. We show how to estimate the intrinsic dimensionality of the manifold from samples, decompose the sam...

We present an algorithm for efficiently computing ray intersections with multi-resolution global terrain which is partitioned by spheroidal height-augmented quadtrees. While previous methods support terrain defined on a Cartesian coordinate system, our methods support terrain defined on a two-parameter ellipsoidal coordinate system. This curvilinear system is necessary for an accurate model of ...

Riemannian wavefield extrapolation is a technique for one-way extrapolation of acoustic waves. Riemannian wavefield extrapolation generalizes wavefield extrapolation by downward continuation by considering coordinate systems different from conventional Cartesian ones. Coordinate systems can conform with the extrapolated wavefield, with the velocity model or with the acquisition geometry. When c...

We present an algorithm for eeciently computing ray intersections with multi-resolution global terrain partitioned by spheroidal height-augmented quadtrees. While previous methods support terrain deened on a Cartesian coordinate system, our methods support terrain deened on a two-parameter ellipsoidal coordinate system. This curvilin-ear system is necessary for an accurate model of global terra...

Image translation, size scaling and rotation can be analyzed from a unified standpoint. Let for and denote a discrete destination image that is created by geometrical modification of a discrete source image for and . In this derivation, the source and destination images may be different in size. Geometrical image transformations are usually based on a Cartesian coordinate system representation ...