Method for enhancing the determination of a seismic horizon

摘要

The invention pertains to a method for enhancing the determination, from a seismic image of at least a portion of a seismic horizon in a three-dimensional domain. The method comprises: receiving the seismic image; receiving a plurality of related control points; defining pseudo-rectangles; for each pseudo-rectangle applying a diffeomorphic transformation F: defining a new domain; transforming points of the seismic image; transforming said pseudo-rectangle into a corresponding rectangle; applying a horizon reconstruction algorithm to the transformed points, to determine a part of a transformed horizon, the reconstruction comprising solving a Poisson equation; and computing a part of the horizon, said computing comprising applying an inverse diffeomorphic transformation F−1 to the determined part of a transformed horizon.

主权项

1. A method for enhancing the determination, from a seismic image, of at least a portion of a seismic horizon in a three-dimensional domain comprising axes {right arrow over (X)}, {right arrow over (Y)}, {right arrow over (Z)}, said seismic horizon being a function of coordinates along axes {right arrow over (X)}, {right arrow over (Y)} in said three-dimensional domain,
wherein said method comprises:
receiving the seismic image, the seismic image having points associated with coordinates along axes {right arrow over (X)}, {right arrow over (Y)}, {right arrow over (Z)};receiving a plurality of related control points associated with coordinates on axes {right arrow over (X)}, {right arrow over (Y)}, {right arrow over (Z)};in a reference plane defined by axes {right arrow over (X)} and {right arrow over (Y)}, defining, for at least one related control point among the plurality of related control points, an associated reference point with coordinates along axes {right arrow over (X)}, {right arrow over (Y)}, among a plurality of reference points, the reference point having coordinates on axes {right arrow over (X)} and {right arrow over (Y)} identical to coordinates on axes {right arrow over (X)} and {right arrow over (Y)} of the related control point,defining pseudo-rectangles in said reference plane, each pseudo-rectangle comprising a reference point among a plurality of reference points;for each current pseudo-rectangle among the defined pseudo-rectangles:
applying a diffeomorphic transformation F, said diffeomorphic transformation F:
being a function of coordinates along {right arrow over (X)}, {right arrow over (Y)} and defining a new domain comprising axes {right arrow over (X′)}, {right arrow over (Y′)}, {right arrow over (Z)};transforming points of the seismic image having coordinates along axes {right arrow over (X)}, {right arrow over (Y)} identical to coordinates along axes {right arrow over (X)}, {right arrow over (Y)} of points in said current pseudo-rectangle, said points of the seismic image including the related control point associated with the current pseudo-rectangle;transforming said current pseudo-rectangle into a corresponding rectangle;applying a horizon reconstruction algorithm to the transformed points, to determine a part of a transformed horizon, said part of a transformed horizon comprising the transformed related control point, the reconstruction of the seismic horizon comprising solving the Poisson equation Δ(δτ)=−div(r), where δτ is an unknown function of coordinates along axes {right arrow over (X′)}, {right arrow over (Y′)}, Δ denotes the Laplace operator in the new domain, div denotes the divergence vector operator in the new domain and r is a fixed function of coordinates along axes {right arrow over (X′)}, {right arrow over (Y′)};computing a part of the horizon, said computing of a part of the horizon comprising applying an inverse diffeomorphic transformation F−1 to the determined part of a transformed horizon.