Using common-offset migration in a constant background medium as an example, we show that using curvelets as building blocks of seismic data, the Kirchhoff diffractionstack can, to leading-order in angular frequency, horizontal wavenumber, and migrated location, be rewritten as a transformation of coordinates of the curvelets in the data, combined with amplitude scaling. This transformation is ...

Currently used one-way wave equations in depth fail at horizontal propagation. One-way wave equations in time do not have that shortcoming; they are omni-directional in space. In these equations, spatial derivatives appear in a pseudo-differential operator—the square root of the Laplacian. With an appropriate definition of this operator, we have proved via ray theory that the solutions of one-w...

Purpose The purpose of this study was to investigate the feasibility of regenerative therapy with a collagenated bone graft and resorbable membrane in intrabony defects, and to evaluate the effects of the novel extracellular matrix (ECM)-based membrane clinically and radiologically. Methods Periodontal tissue regeneration procedure was performed using an ECM-based resorbable membrane in combi...

We introduce and analyze several algorithms for optimal illumination in array imaging. We consider time reversal and Kirchhoff migration imaging in homogeneous media, in regimes where the signal-to-noise ratio is high (infinite). Extensions to coherent interferometric imaging in clutter are described briefly. We show with numerical simulations that the optimal illumination algorithms image sele...

INTRODUCTION New fast and efficient multi-channel ultrasonic echo measurement systems are currently introduced for practical applications in NDT-CE [ 1, 2]. The acquired multi-offset data are currently processed and imaged by the synthetic aperture focussing technique (SAFT, see e.g. [ 3, 4]). The application of SAFT, which is closely related to the seismic Kirchhoff migration method, is succes...

Let G be a connected graph of order n with Laplacian eigenvalues μ1 ≥ μ2 ≥ . . .≥ μn−1 > μn = 0. The Kirchhoff index of G is defined as Kf = Kf(G) = n∑n−1 k=1 1/μk. In this paper. we give lower and upper bounds on Kf of graphs in terms on n, number of edges, maximum degree, and number of spanning trees. Moreover, we present lower and upper bounds on the Nordhaus–Gaddum-type result for the Kirch...

The aim of this article is to describe asymptotic profiles for the Kirchhoff equation, and to establish time decay properties and dispersive estimates for Kirchhoff equations. For this purpose, the method of asymptotic integration is developed for the corresponding linear equations and representation formulae for their solutions are obtained. These formulae are analysed further to obtain the ti...

Ground Penetrating Radar (GPR) is a promising sensor for landmine detection, however there are two major problems to overcome. One is the rough ground surface. The other problem is the distance between the antennas of GPR. It remains irremovable clutters on a sub-surface image output from GPR by first problem. Geography adaptive scanning is useful to image objects beneath rough ground surface. ...

It is well known that Kirchhoff equations admit infinitely many simple modes, i. e. time periodic solutions with only one Fourier component in the space variables. We prove that, for some choices of the nonlinearity, these simple modes are unstable provided that their energy is large enough. This result, stated in an abstract Hilbert space setting, and proved by reducing to a system of two seco...

Real-time location of earthquakes can be achieved by using direct imaging of the recorded wave field based on a Kirchhoff reconstruction method similar to that used in the migration of seismic reflection data. The standard method of event location requires the wave arrival at each sensor to be picked and associated with an event. By using direct imaging, the event is identified once in the imag...