Common-image gathers are an important output of prestack depth migration. They provide information needed for velocity model building and amplitude and phase information for subsurface attribute interpretation. Conventionally, common-image gathers are computed using Kirchhoff migration on commonoffset/azimuth data volumes. When geologic structures are complex and strong contrasts exist in the v...

The k-th semi-total point graph R(G) of a graph G, is a graph obtained from G by adding k vertices corresponding to each edge and connecting them to the endpoints of the edge considered. In this paper, we obtain formulas for the resistance distance and Kirchhoff index of R(G).

The Kirchhoff-Love plate model is a widely used in the analysis of thin elastic plates. It is well known that Kirchhoff-Love solutions can be viewed as certain limits of displacements and stresses for elastic plates where the thickness tends to zero. In this paper, we consider the problem from a different point of view and derive computable upper bounds of the difference between the exact three...

Prestack migration is necessary before AVO analysis. Most of the present migration algorithms not only try to focus the reflections on the subsurface but also strive to preserve the amplitude for subsequent amplitude studies. A migration/inversion method developed by Lumley (1993) estimates the angle dependent reflectivity at each subsurface point by using least-squares Kirchhoff migration foll...

A simplex of a graph G is a subgraph of G which is a complete graph. The simplex graph Simp(G) of G is the graph whose vertex set is the set of all simplices of G and in which two vertices are adjacent if and only if they have a non-empty intersection. The simplex graph operator is the operator which to every graph G assigns its simplex graph Simp(G). The paper studies graphs which are fixed in...

A theoretical model is developed to describe the interferometric coherency between pairs of SAR images of rough soil surfaces. The model is derived using a dyadic form for surface reflectivity in the Kirchhoff approximation. This permits the combination of Kirchhoff theory and spotlight synthetic aperture radar (SAR) image formation theory. The resulting model is used to describe the interferom...

ly, we may think of a differential operator ~ on M as a mapping on the smooth functions on M. That is, let C~(M) denote the space of smooth real-valued functions on M. Then 3' : C~(M) ~ C~(M). Bifurcations on Hemispheres 215 In our extension theory we consider only those operators that respect the symmetries on M and N. We define these operators as follows. There is a natural action of ISO(M) o...

Motivated by the approach to Laplacian on undirected weighted graphs, we provide a setting for general point of view Kirchhoff type divergence and Laplace operator built trivial gradient $f(y)-f(x)$ order zero. We consider some par