K3D: 3-D Kirchhoff Prestack Depth Migration Fusion's 3-D Kirchhoff prestack depth migration (K3D) package is based on a state-of-the-art implementation of the algorithm designed to achieve maximum efficiency on parallel-vector and cache-based supercomputers. The algorithm includes several choices of anti-aliasing and an amplitude equalization operator to preserve the amplitude information in the final image even when the spatial sampling of the input data is irregular. Through scaling of the input and output data K3D can be run on workstations as well as supercomputers, though the best efficiency is obtained on larger computing platforms.

Geophysical Aspects
Kirchhoff migration is recognized as the most flexible method of imaging prestack 3-D seismic data. 3-D prestack migration of surface seismic data is the ultimate tool for imaging the Earth's subsurface in areas of complicated geological structure and velocity. Kirchhoff migration is particularly appropriate for 3-D prestack data, because of its flexibility in imaging irregularly sampled data and because of its relative computational efficiency. Kirchhoff migration images seismic data by approximately solving the wave equation with a boundary integral method. The acoustic reflectivity at every point of the Earth's interior is computed by summing the recorded data on multidimensional surfaces; the shape of the summation surfaces and the summation weights are computed from the Green's functions of the single scattering wave propagation experiment.

Green's function computation One of the main elements of 3-D prestack Kirchhoff depth migration is the traveltime tables used to parameterize the asymptotic Green's functions. Fusion's GETT3D software module offers a very fast and stable solution for generating the 5-D traveltime tables needed for 3-D Kirchhoff migration. GETT3D is a 3-D traveltime computation module based on an extremely fast proprietary finite-difference algorithm (patent pending). The algorithm is unconditionally stable in complex velocity media and correct to the order of accuracy of the finite-difference solution. Green's function tables can be compressed before storage. K3D offers both the option of using uncompressed or compressed traveltime tables.

K3D: an advanced migration algorithm At the core of the K3D package is the data summation engine, designed to execute efficiently on parallel-vector and cache-based supercomputers. The K3D inner kernel uses very long vectors to take advantage of vector architectures while the output image is divided into processing blocks that are distributed over parallel processors. The problem of load balancing the computation across processors is solved by exploiting the locality of the Kirchhoff migration operator; that is, a seismic data record collected in a certain area of the survey will mostly contribute to the part of the seismic image that is directly below the recording location. Locality is exploited by designing an optimal partitioning scheme for both the input and the output data.

The user can choose from several anti-aliasing methods that enhance the imaging and resolution of steep faults and salt-sediment interfaces.

Scalable software implementation 3-D prestack data processing requires very powerful computers for efficiently handling the large number of computations necessary to accurately image the data. While more efficient on large platforms, Fusion's K3D software can be run on a variety of computer sizes and architectures. Through scaling of the input and output data, the design of the K3D ensures that the same problem can be solved on workstations or supercomputers.

Easy Integration The K3D package is modular in design and can be customized and integrated into a client's specific environment. K3D is available on Unix workstations, parallel-vector and cache-based supercomputers, and other architectures. If desired, Fusion can integrate the package into a client's processing environment or add it as a Promax, Focus or Views module. Of course it is fully integrated into Fusion's GeoPRO™ platform.

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