Research

Image processing, computer graphics, subsurface modeling, seismic imaging, fluid flow, ...

A method for estimating apparent displacement vectors from time-lapse seismic images

Reliable estimates of vertical, inline and crossline components of apparent displacements in time-lapse seismic images are difficult to obtain for two reasons. First, features in 3-D seismic images tend to be locally planar, and components of displacement within the planes of such features are poorly resolved. Second, searching directly for peaks in 3-D cross-correlations is less robust, more complicated, and computationally more costly than searching for peaks of 1-D cross-correlations. We estimate all three components of displacement with a process designed to mitigate these two problems. We address the first problem by computing for each image sample a local phase-correlation instead of a local cross-correlation. We address the second problem with a cyclic sequence of searches for peaks of correlations computed for lags constrained to one of the three axes of our images.
Hale, D., 2007, CWP Report 566.
[Report]

Local dip filtering with directional Laplacians

Local dip filters attenuate or enhance features with a specified dip that may vary for each image sample. Because these multi-dimensional filters change with each sample, they should have a small number of coefficients that can be computed efficiently from local dips. They should handle features that are vertical as well as horizontal. They should have efficient and stable inverses that facilitate the design and application of more discriminate notch filters. Local dip filters constructed from approximations to directional Laplacians have these properties and are easily implemented in any number of dimensions.
Hale, D., 2007, CWP Report 567.
[Report]

An efficient method for computing local cross-correlations of multi-dimensional signals

Consider two multi-dimensional digital signals, each with S samples. For some number of lags L (L much less than S), the cost of computing a single cross-correlation of these two signals is proportional to S×L. By exploiting several properties of Gaussian windows, we can compute S local cross-correlations, again with computational cost proportional to S×L. Here, local means the cross-correlation of signals after applying a Gaussian window centered on a single sample. Computational cost is independent of the size of the window.
Hale, D., 2006, CWP Report 544.
[Report]

Seamless local prediction filtering

An efficient method for computing local auto-correlations leads to a new method for local adaptive prediction or prediction error filtering of multi-dimensional images. Using a conjugate-gradient method for least-squares optimization, we compute a different prediction filter for each sample in an image. These adaptive prediction filters preserve locally coherent signals, while attenuating random noise.
Hale, D., 2006, CWP Report 545.
[Report]

Recursive Gaussian filters

Gaussian or Gaussian derivative filtering is in several ways optimal for applications requiring low-pass filters or running averages. For short filters with lengths of a dozen samples or so, direct convolution with a finite-length approximation to a Gaussian is the best implementation. However, for longer filters such as those used in computing running averages, recursive implementations may be much more efficient. Based on the filter length, we select one of two popular methods for designing and implementing recursive Gaussian filters.
Hale, D., 2006, CWP Report 546.
[Report]

Meshing for velocity modeling and ray tracing in complex velocity fields

We automatically generate meshes of subsurface velocity structures from finely-sampled uniform velocity grids without providing external additional constraints such as horizons and faults. Unlike uniform grids, these new meshes provide a topological framework that enables rapid editing of velocity models, while facilitating numerical tasks such as seismic modeling and inversion.
Rüger, A., & Hale, D., 2004, 74th Annual International Meeting, Society of Exploration Geophysicists.
[Expanded Abstract]

Seismic interpretation with fluid flow simulation

We construct simple reservoir models with a small number of flow units, such as geologic layers and fault blocks. We call these units tanks and connect them with tubes. For such simple models, we may interactively adjust reservoir properties, such as porosities of tanks and transmissibilities of tubes, and then simulate fluid flow during seismic interpretation. Numerical experiments suggest that parameters we estimate for coarse tanks & tubes models are meaningful; specifically, they may be used to constrain more detailed models.
Hale, D., Killough, J., & Emanuel, J., 2004, 74th Annual International Meeting, Society of Exploration Geophysicists.
[Expanded Abstract]

Seismic interpretation using global image segmentation

A first step in seismic interpretation is seismic image segmentation. For most seismic images, with incompletely or poorly imaged faults and horizons, global methods for segmentation are more robust than local event tracking or region growing methods often used today. The disadvantage of global image segmentation methods has been their relatively high computational cost. We reduce this cost by applying these methods to a space-filling mesh aligned automatically with features in seismic images. The mesh makes global segmentation of 3-D seismic images feasible.
Hale, D., & Emanuel, J., 2003, 73th Annual International Meeting, Society of Exploration Geophysicists.
[Expanded Abstract]

Atomic meshing of seismic images

Today's work cycle from seismic imaging to reservoir simulation requires a variety of data structures - simple arrays, triangulated surfaces, non-manifold frameworks, corner-point grids, etc. - to represent the earth's subsurface. Conversions among these different representations are both time consuming and error prone. Using simple image processing techniques, we automatically align a lattice of points (atoms) with horizons and faults in a seismic image. Connecting these points yields an unstructured space-filling polyhedral (atomic) mesh. This single data structure can integrate multiple tasks, such as seismic interpretation, reservoir characterization, and flow simulation, thereby reducing work cycle times and errors.
Hale, D., & Emanuel, J., 2002, 72th Annual International Meeting, Society of Exploration Geophysicists.
[Expanded Abstract]

Atomic meshes — from seismic imaging to reservoir simulation

Seismically imaged horizons and faults often correspond to discontinuities in subsurface properties, such as permeability. We automatically align a lattice of points (atoms) either on or alongside such features. 3-D Delaunay triangulation of atoms aligned on image features yields a tetrahedral mesh, with triangular faces of tetrahedra coincident with subsurface discontinuities. Alternatively, the same triangulation of atoms aligned alongside image features yields a dual Voronoi polyhedral mesh in which polygonal faces coincide with subsurface discontinuities. Either mesh is suitable for fluid flow simulation.
Hale, D., 2002, Proceedings of the 8th European Conference on the Mathematics of Oil Recovery.
[Paper]

Atomic images — a method for meshing digital images

By combining a digital image with a lattice of points called atoms, in which atom coordinates are computed to minimize a potential energy function of the combination, we obtain a mesh suitable for further computations. Each atom in the lattice contributes a potential function to an atomic potential field. The image represents another potential field. Total potential energy of the lattice is a weighted sum of the atomic and image potential fields, evaluated at atom coordinates. Beginning with a pseudo-regular lattice, a generic optimization algorithm moves atoms to minimize this total potential energy. After optimization, we connect the atoms to form a mesh that tends to be aligned with image features.
Hale, D., 2001, Proceedings of the 10th International Meshing Roundtable, p. 85-196.
[Paper]