Fracture Surface Extraction from Image Volumes Computed from Passive Seismic Traces
The invention comprises a method of imaging a volume of the earth's subsurface. A selected volume of the earth's subsurface is divided into a three-dimensional grid of voxels. Seismic signals representing seismic energy emanating from the earth's subsurface and detected by sensors deployed in proximity to said selected subsurface volume and conducted to a recorder for recording. The recorded signals are transformed into a grid of discrete voxel signals representing energy emanating from voxels included in said three-dimensional grid of voxels in the earth's subsurface. A smooth analytic function is defined in three dimensional space based on the grid of discrete voxel signals; and fracture surfaces are derived from the smooth analytic function.
1 . A method of imaging a volume of the earth's subsurface, comprising:
dividing a selected volume of the earth's subsurface into a three-dimensional grid of voxels;
conducting seismic signals representing seismic energy emanating from the earth's subsurface and detected by sensors deployed in proximity to said selected subsurface volume to a recorder for recording:
transforming the recorded signals into a grid of discrete voxel signals representing energy emanating from voxels included in said three-dimensional grid of voxels in the earth's subsurface;
defining a smooth analytic function in three dimensional space based on the grid of discrete voxel signals; and
deriving fracture surfaces from the smooth analytic function.
2 . The method of claim 1 wherein fracture surfaces in two spatial dimensions are derived from the smooth analytic function
3 . The method of claim 1 wherein fracture surfaces in three spatial dimensions are derived from the smooth analytic function.
4 . The method of claim 2 wherein fracture surfaces are approximated by ridges of the smooth analytic function, said ridges being curves such that each point in the curve is a local maximum of the defined analytic function in the direction normal to a curve.
5 . The method of claim 3 wherein fracture surfaces are approximated by ridges of the smooth analytic function, said ridges being surfaces such that each point in the surface is a local maximum of the defined analytic function in the direction normal to the surface.
6 . The method of claim 4 wherein said grid of discrete voxel signals is semblance data and a smooth semblance function is constructed from the semblance data and the smooth semblance function is used to define a semblance surface in which the fractures are one-dimensional curves in the x-y plane, each fracture curve being a ridge on the surface, such that every point on the curve is a local maximum in the direction normal to the curve.
7 . The method of claim 6 wherein computing the ridges comprises an iterative scheme that first finds a suitable starting ridge point on a surface ridge and then incrementally extends this first ridge point to a discrete set of points that approximates the ridge.
8 . The method of claim 5 wherein said grid of discrete voxel signals is semblance data and a smooth semblance function is constructed from the semblance data and a semblance surface is constructed in which the ridges are surfaces which can be approximated by triangular surfaces consisting of the discrete ridge points.
9 . The method of claim 8 further comprising: finding suitable starting points on each of the semblance ridges by finding local minima of the minimum curvature function c min (x, y, z); then for each starting point, computing the eigenvector corresponding to the minimum eigenvalue of the Hessian matrix H, said eigenvector being normal to the ridge surface and defining a tangent plane to the ridge surface; finding an orthonormal basis for the tangent plane, for each of the two tangent plane basis vectors, the span of the basis vector and the eigenvector being a plane perpendicular to the tangent plane; for each of the two perpendicular planes defining a circle of small radius about a boundary point (x 0 , y 0 , z 0 ) and find the two local minima of the minimum curvature function c min (x, y, z); thereby yielding four more points on the ridge surface, together with (x 0 , y 0 , z 0 ) which can be triangulated by four triangles to initiate the triangulated surface.
10 . The method of claim 9 further comprising incrementally extending the discrete set of triangles approximating the ridge surface from each boundary edge (having only one neighboring triangle), by finding a local minimum of the minimum curvature function c min (x, y, z,); on a circle of small radius about the boundary point (x 0 , y 0 , z 0 ) in the plane orthogonal to the boundary edge, defining a new triangle consisting of the boundary edge and the new point and triangulate any holes or gaps remaining where point density is sufficient.