Current algorithms for imaging seismic reflection data can be subdivided into two classes: Kirchhoff (generalized Radon transform) and wave-equation (double-square-root and reverse-time) migration. Kirchhoff type methods rely on asymptotic and ray-geometrical considerations. Wave-equation imaging algorithms (one-way or twoway) appear to be more robust in the case of complicated velocity models ...

In this paper, a comparison of two ground penetrating radar (GPR) systems is presented, the classical bi-static one and the Multiple Input Multiple Output (MIMO) system both using N Vivaldi antennas. For both configurations a Linear Sampling Metthod (LSM) imaging algorithm and Kirchhoff migration technique are used for target detection and localization. The performance of both systems are compa...

This paper is the second in a series of two in which we care about the asymptotics of the three-dimensional displacement field in thin elastic plates as the thickness tends to zero. In Part I we have investigated four types of lateral boundary conditions when the transverse component is clamped. In this Part II we study four other types of lateral conditions when the transverse component is fre...

Wave-equation migration is an accurate and robust alternative to Kirchhoff migration when multipathing and other complex wave phenomena occur, such as in subsalt exploration. In these situations, images obtained by wave-equation migration are often superior to images obtained by Kirchhoff methods. However, 3-D wave-equation prestack imaging is an immature technology compared with Kirchhoff imag...

The resistance distance between any two vertices of G is defined as the network effective resistance between them if each edge of G is replaced by a unit resistor. The Kirchhoff index Kf(G) is the sum of resistance distances between all the pairs of vertices in G. We firstly provided an exact formula for the Kirchhoff index of the hypercubes networks Q n by utilizing spectral graph theory. More...

The Kirchhoff analogy for elastic rods establishes the equivalence between the solutions of the classical spinning top and the stationary solutions of the Kirchhoff model for thin elastic rods with circular cross-sections. In this paper the Kirchhoff analogy is further generalized to show that the classical Kovalevskaya solution for the rigid body problem is formally equivalent to the solution ...

Pre-stack Kirchhoff time migration (PKTM) is one of the most widely used migration algorithms in seismic imaging area. However, PKTM takes considerable time due to its high computational cost, which greatly affects the working efficiency of oil industry. Due to its high fault tolerance and scalability, Hadoop has become the most popular platform for big data processing. To overcome the shortcom...

Firstand second-order reflection coefficients are presented for the small slope approximation. The first-order reflection coefficient is identical to the Kirchhoff, or physical optics, result, and the secondorder reflection coefficient reduces to those of perturbation theory and the Kirchhoff approximation in the appropriate limits. Numerical results are obtained for acoustic or TE-polarized el...

In this paper, we studied the long-time properties of solutions generalized Kirchhoff-type equation with strongly damped terms. Firstly, appropriate assumptions are made for nonlinear source term g (u) and Kirchhoff stress term M (s) in equation, existence uniqueness solution proved by using uniform prior estimates time Galerkin’s finite element method. Then, abounded absorption set B0k is obta...