In data continuation, the information present in the collected data is used to estimate data at new positions. We investigate two examples of data continuation: data healing and dip moveout. By composing a modeling operator with an imaging operator we can construct an operator to perform each of the tasks. We review the theory and present an algorithm for data continuation specifically directed...

A linear dispersive mechanism leading to a burst in the L∞ norm of the error in numerical simulation of polychromatic solutions is identified. This local error pile-up corresponds to the existence of spurious caustics, which are allowed by the dispersive nature of the numerical error. From the mathematical point of view, spurious caustics are related to extrema of the numerical group velocity a...

Migration of seismic reflection data to common image-point gathers is an integral part of both migration velocity analysis (MVA) and amplitude (AVA) analysis. Its applicability in complex geology depends on whether these gathers will be artifact free, and is related to the formation of caustics and turning ‘rays’ due to the heterogeneity of the velocity model used. Here, we discuss an angle tra...

The dynamics of small, yet heavy, identical particles in turbulence exhibits singularities, called caustics, that lead to large fluctuations the spatial particle-number density, and collision velocities. For particle, inertia fluid velocity at particle position is essentially a white-noise signal caustic formation analogous Kramers escape. Here we show small different. Caustics tend form vicini...

An e,;perimental technique for the investigation of the behaviour of acoustic wave propagation through a turbulent medium is discussed. The present study utilizes the ultrasonic travel-time technique to di­ agnose a grid-generated turbulence. Travel-time variance is studied versus mean Dow velocity. travel distance and outer turbulence scale. The effect of therma.l fluctuations. which result in...

A fundamental hypothesis for the interpretation of the measured large-scale line-of-sight peculiar velocities of galaxies is that the large-scale cosmic flows are irrotational. In order to assess the validity of this assumption, we estimate, within the frame of the gravitational instability scenario, the amount of vorticity generated after the first shell crossings in large-scale caustics. In t...

We present a new algorithm to render caustics. The algorithm discretizes the specular surfaces into sample points. Each of the sample points is treated as a pinhole camera that projects an image of the incoming light onto the diffuse receiver surfaces. Anti-aliasing is performed by considering the local surface curvature at the sample points to filter the projected images. The algorithm can be ...

– Networks of caustics can occur in the distribution of particles suspended in a randomly moving gas. These can facilitate coagulation of particles by bringing them into close proximity, even in cases where the trajectories do not coalesce. The long-time morphology of these caustic patterns depends upon the Lyapunov exponents λ1, λ2 of the suspended particles, as well as the rate J at which par...

We propose the frozen Gaussian approximation for computation of high frequency wave propagation. This method approximates the solution to the wave equation by an integral representation. It provides a highly efficient computational tool based on the asymptotic analysis on phase plane. Compared to geometric optics, it provides a valid solution around caustics. Compared to the Gaussian beam metho...

A linear dispersive mechanism leading to a burst in the L∞ norm of the error in numerical simulation of polychromatic solutions is identified. This local error pile-up corresponds to the existence of spurious caustics, which are allowed by the dispersive nature of the numerical error. From the mathematical point of view, spurious caustics are related to extrema of the numerical group velocity a...