SPG 4th Conference & Exposition on Petroleum Geophysics — Mumbai, India, 7 - 9 January 2002 Summary This paper describes an approach for selection of aperture width in Kirchhoff time migration and discusses parallel implementation of the algorithm for 2D and 3D data sets. Selection of aperture width in Kirchhoff migration is a crucial factor in obtaining a high-resolution image of the subsurface geological structures. The spatial extent of the diffraction hyperbola used for summation is determined using a combination of the geological complexities and characteristics of the diffraction amplitudes. In this study we propose a new methodology for aperture width selection in Kirchhoff time migration based upon the decay of diffraction amplitude and compare it with two other methods. The parallel algorithms are developed on PARAM10000, a distributed memory parallel computer, using MPI (Message Passing Interface) and MPI I/O parallel programming environment. The effectiveness of this technique is demonstrated by applying it to a data set from SEG/EAGE overthrust model. Introduction Seismic migration is an integral part of the data processing sequence that maps the dipping events to their true geological locations and collapses the diffractions at the discontinuities of physical parameters. It is widely used as an indispensable tool for geological interpretation of seismic sections. Kirchhoff migration based upon the diffraction summation approach is one of the most popular techniques in seismic processing industry. In Kirchhoff migration, the amplitudes are summed along the diffraction hyperbola and the result is placed at its apex (Schneider 1976). The aperture width used for the amplitude summation is an important parameter that affects the quality and performance of the Kirchhoff migration. In this paper we have proposed a new criterion for aperture width selection in Kirchhoff migration. It is compared with two other selection techniques. The first part of the paper discusses different aperture width selection methods. The second part of the paper focuses on the parallel implementation of Kirchhoff time migration algorithm. Highly efficient and scalable algorithm is developed for PARAM 10000 by proper restructuring of the code. Like other migration techniques, Kirchhoff migration algorithm is also computationally very expensive. To migrate large volumes of 2D and 3D, post-stack or pre-stack data, high performance computers with fast CPUs, large memory, storage and I/O are necessary. Centre for Development of Advanced Computing (C-DAC) located at Pune, developed the OpenFrame architecture for scalable parallel computing applications. Kirchhoff time migration algorithms for both 2D and 3D data volumes are developed and implemented on a 100 GF distributed memory parallel computer, popularly known as PARAM 10000. Aperture Width Selection in Kirchhoff Migration In this section of the paper we shall discuss the aperture width selection criterion in Kirchhoff migration. Theoretically the diffraction hyperbolas, along which the amplitude summation is carried out in Kirchhoff migration, extend to infinite time and distance. In practice, we have to deal with truncated hyperbolic summation paths. The spatial extent of the actual summation path, called aperture width, is measured in terms of the number of traces the hyperbolic path spans (Yilmaz, 1987). The curvature of the diffraction hyperbola is governed by the velocity and time. A low velocity hyperbola has narrower aperture when compared to the high velocity hyperbolas. When the medium velocity varies with depth, diffraction hyperbolas have different curvatures at different times. Therefore we need different aperture widths at different times. In the first part of this section, we will discuss the effects of migrating a seismic data set with a constant aperture width method. Then we will look at the migration results with the aperture width based upon the horizontal displacement method. Next we propose a method for calculation of the aperture width based upon the decay of diffraction amplitude. Finally, we compare the proposed method with the other methods and show its effectiveness. Constant Aperture Width Method In this technique the aperture width is measured in terms of number of traces, the hyperbolic path spans (Yilmez, 1987). This span remains the same for all time levels. There is no fixed rule for deciding a constant aperture width. Any number of traces can be taken as aperture width or we can decide it according to the maximum horizontal displacement that takes place in migration. A small aperture width causes smearing in the deeper part of the section, which destroys the dipping events and produces spurious horizontally dominant events. A larger aperture width degrades the migration quality in shallower regions. The main reason for this type of behavior of migration with constant aperture with time is that as the time increases the RMS velocity also increases. Therefore, the hyperbolic paths become flattened in time and extended in spatial dimension. The summation using smaller aperture includes only the traces near the apex portion of the diffraction hyperbola, where the dip is nearly flat. Hence, the smaller aperture passes only the flat or nearly flat events and the high velocity dipping events at the later times are destroyed. Large aperture width for shallower events causes summation of amplitudes from the flanks of the hyperbolic paths beyond the recognizable diffraction amplitudes. This degrades the migration quality in the shallower part of the section. The problem is overcome to a great extent by choosing an aperture width as a function of time. Optimal aperture width selection and parallel implementation of Kirchhoff migration algorithm R. RASTOGI and S. PHADKE Centre for Development of Advanced Computing, Pune University Campus, Pune 411007, India