Kirchhoff-type Migration Research Articles

Kirchhoff migration using eikonal-based computation of traveltime source derivatives

The computational efficiency of Kirchhoff-type migration can be enhanced by using accurate traveltime interpolation algorithms. We addressed the problem of interpolating between a sparse source sampling by using the derivative of traveltime with respect to the source location. We adopted a first-order partial differential equation that originates from differentiating the eikonal equation to compute the traveltime source derivatives efficiently and conveniently. Unlike methods that rely on finite-difference estimations, the accuracy of the eikonal-based derivative did not depend on input source sampling. For smooth velocity models, the first-order traveltime source derivatives enabled a cubic Hermite traveltime interpolation that took into consideration the curvatures of local wavefronts and can be straightforwardly incorporated into Kirchhoff antialiasing schemes. We provided an implementation of the proposed method to first-arrival traveltimes by modifying the fast-marching eikonal solver. Several simple synthetic models and a semirecursive Kirchhoff migration of the Marmousi model demonstrated the applicability of the proposed method.

Adaptive focusing window for seismic angle migration

Kirchhoff migration is based on a continuous integral ranging from minus infinity to plus infinity. The necessary discretization and truncation of this integral introduces noise in the migrated image. The attenuation of this noise has been studied by many authors who propose different strategies. The main idea is to limit the migration operator around the specular point. This means that the specular point must be known before migration and that a criterion exists to determine the size of the migration operator. We propose an original approach to estimate the size of the focusing window, knowing the geologic dip. The approach benefits from the use of prestack depth migration in angle domain, which is recognized as the most artifact-free Kirchhoff-type migration. The main advantages of the method are ease of implementation in an existing angle-migration code (two or three dimensions), user friendliness, ability to take into account multiorientation of the local geology as in faulted regions, and flexibility with respect to the quality of the estimated geologic dip field. Common-image gathers resulting from the method are free from migration noise and can be postprocessed in an easier way. We validate the approach and its possibilities on synthetic data examples with different levels of complexity.

Prestack depth imaging via model-independent stacking

Most seismic reflection imaging methods are confronted with the difficulty of accurately knowing input velocity information. To eliminate this, we develop a special prestack depth migration technique which avoids the necessity of constructing a macro-velocity model. It is based upon the weighted Kirchhoff-type migration formula expressed in terms of model-independent stacking velocity and arrival angle. This formula is applied to synthetic sub-basaltic data. Numerical results show that the method can be used to successfully image beneath basalts.

3-D Prestack Kirchhoff Migration of the ISO89-3D Data Set

— This paper presents an overview of the results obtained from a 3-D prestack depth migration of the ISO89-3D data set. The algorithm is implemented as a Kirchhoff-type migration, in which the migrated image is generated by weighted summation along diffraction surfaces through the shot record section. The diffraction surfaces are computed by a 3-D finite difference solution of the eikonal equation. A 3-D macro-velocity model derived mainly from wide-angle tomographic inversion served as input for the travel-time calculations. The results of the migration are presented as slices through a volume covering an area of 21 km × 21 km in the horizontal and 15 km in the vertical direction, centered around the KTB drill hole. In these slices the continuation of the Franconian Lineament or SE1 reflector, respectively, can be identified over most of the survey area as a northeast dipping reflector plane. Its signature appears partly curved and discontinuous and with different strength of reflection down to a maximum depth of 9 km. About 5 km to the south-southeast of the KTB drill hole the uppermost top reflection of the Erbendorf body (EB) can be recognized at approximately the same depth. The slices clearly show its complicated internal structure consisting of several apparently separated reflective parts. Moreover, the geometry and the shape of a few other subsurface structures are described.