IMPROVED METHOD OF INTERACTIVE DESIGN AND ADJUSTMENTS OF THE RATIONAL SCHEME OF PATTERING FLAT GEOMETRIC OBJECTS

This allowed to highlight the disadvantages of these methods and develop an improved method of interactive design and correction of rational schemes for the decomposition of flat geometric objects with different configurations of the external contour in a rectangular area of the given size. In this method, it is possible to distinguish three main stages: the preliminary check of the intersection of rectangles, which are described around an active flat geometric object and a flat geometric object that has already been placed; If these rectangles intersect, check the intersection of these flat geometric objects by the ray tracing method; If these flat geometric objects do not intersect by the ray tracing method, then an additional check of their intersection by the ray method. The proposed method for designing dense layout schemes was implemented in a software product for interactive design and correction of rational schemes for the decomposition of dense combinations of flat geometric objects with different configurations of external contours in a rectangular area of a given size. An analysis of the existing methods of interactive design and correction of rational schemes for cutting flat geometric objects has been carried out.

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The paraxial ray method

Geophysics ◽

10.1190/1.1442281 ◽

1987 ◽

Vol 52 (12) ◽

pp. 1639-1653 ◽

Cited By ~ 38

Author(s):

Wafik B. Beydoun ◽

Timothy H. Keho

Keyword(s):

Wave Field ◽

Ray Tracing ◽

Heterogeneous Media ◽

Computation Time ◽

Ray Method ◽

Ray Tracing Method ◽

Paraxial Ray ◽

The Cost ◽

Seismic Wave Field ◽

Tracing Method

The paraxial ray method is an economical way of computing approximate Green’s functions in heterogeneous media. The method uses information from the standard dynamic ray‐tracing method to extrapolate the seismic wave field at receivers in the neighborhood of a ray so that two‐point ray tracing is not required. Applicability conditions are explicit: they define where asymptotic (high‐frequency) methods are valid, and how far away from the ray the extrapolation remains accurate. Increasing the density of the ray fan improves accuracy but increases computation time. However, since reasonable accuracy is obtained with relatively few rays, the method yields results similar to the two‐point ray‐tracing method, but at a fraction of the cost. Examples of wave‐field extrapolation from a ray to neighboring receivers show that traveltime extrapolation is more accurate than amplitude extrapolation. Accuracy, robustness, and efficiency tests, comparing paraxial ray synthetic seismograms with acoustic finite‐difference and elastic discrete‐wavenumber synthetics, are judged very satisfactory.

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Band-limited beam propagator and its application to seismic migration

Geophysics ◽

10.1190/geo2017-0094.1 ◽

2018 ◽

Vol 83 (4) ◽

pp. S311-S319 ◽

Cited By ~ 5

Author(s):

Shaoyong Liu ◽

Hanming Gu ◽

Bingkai Han ◽

Zhe Yan ◽

Dingjin Liu ◽

...

Keyword(s):

Wave Propagation ◽

Ray Tracing ◽

Seismic Wave ◽

Fresnel Zone ◽

Seismic Wave Propagation ◽

Ray Method ◽

Ray Tracing Method ◽

Band Limited ◽

And Migration ◽

Tracing Method

The ray-tracing technique under the high-frequency assumption has been widely used in seismic wave propagation and migration. However, the practical use of conventional ray tracing is limited in complicated media especially when seismic data are band limited. Besides, the ray-tracing method also suffers from shadow zones in complex media. To alleviate these problems, we have developed a band-limited beam propagator and we apply it in seismic wave propagation and migration, which is flexible to implement and can be friendly to extract angle gathers. To derive the band-limited beam propagator, the band-limited ray-tracing method is adopted to compute the central ray of the beam. These rays in the first Fresnel zone are weighted to obtain the band-limited ray based on the assumption of a local plane wave. Then, the band-limited ray is extended to the band-limited beam propagator using the paraxial approximation. Because the beam propagator has a certain beam width perpendicular to the central ray, it has better illumination than the conventional ray-tracing method, and it could partially alleviate the problem of shadow zones. Finally, we use the band-limited beam propagator to develop a band-limited beam migration and analyze the angle gathers in complicated areas. Numerical examples on synthetic models indicate that the proposed band-limited beam propagator outperforms the conventional ray method in terms of illumination. Its applications in migration determine that it could enhance the imaging quality and produce better angle gathers in a complex area.

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