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...

Currently, the amount of recorded data in a seismic survey is order hundreds Terabytes. The processing such implies significant computational challenges. One them I/O bottleneck between main memory and node memory. This results from fact that disk access speed thousands-fold slower than co-processors (eg. GPUs). We propose special Kirchhoff migration develops process over compressed data. by us...

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...

In this article we state a relation between the Kirchhoff and Wiener indices of a simple connected graph G and the Kirchhoff and Wiener indices of those subgraphs of G which are induced by its blocks. Then as an application, we define a composition of a rooted tree T and a graph G and calculate its Kirchhoff index in terms of parameters of T and G. Finally, we present an algorithm for computing...

Free-surface multiples can be considered to be signal and migrated by the crosscorrelogram migration method (Schuster and Rickett, 2000; Sheng, 2000). By merging the Kirchhoff and crosscorrelogram migration images, the true reflectors can be reinforced and the artifacts can be attenuated. For simple flat layered models direct multiplication of the Kirchhoff and crosscorrelogram migration images...

Least squares migration (LSM) is applied to synthetic data with the purpose of removing the ”acquisition footprint” noise from migrated sections. Results for simple point scatterer and meandering stream channel models suggest that LSM can significantly attenuate the acquisition footprint noise. For comparison, the corresponding Kirchhoff migrated sections show noticeable artifacts due to a coar...

Let G be a connected graph with vertex set V.G/. The degree Kirchhoff index of G is defined as S .G/D P fu;vg V.G/ d.u/d.v/R.u;v/, where d.u/ is the degree of vertex u, and R.u;v/ denotes the resistance distance between vertices u and v. In this paper we obtain some upper and lower bounds for the degree Kirchhoff index of graphs. We also obtain some bounds for the Nordhaus-Gaddum-type result fo...