3D Grid-based Tomography
Update subsurface velocity and anisotropic material parameters along a predefined coarse grid.
Paradigm® GeoDepth® Tomography supports both grid-based and model-based methods that can be used according to the problem to be solved. For example, Gulf of Mexico sediments affected by long period compaction are normally parameterized by a Cartesian grid.
Velocity volume updates
3D grid tomography updates velocity volumes and (optionally) volumes of the anisotropic parameters ε and δ. The updates are calculated on a spatial grid which is generally coarser than the velocity volume. After calculations are completed, the updates are interpolated to the size of velocity and anisotropic parameter grids. The interpolated updates are added to the current volumes to produce new volumes of velocities and anisotropic parameters.
3D grid tomography can use well markers in the form of mistie maps as an additional constraint on the updated subsurface model.
Direct 3D grid-based tomography
For large-scale models and especially those with high-resolution update grids, where the size of the tomography matrix can be too large (quadratic with the number of model parameters) to be handled even by the largest super-computers, a new approach is required. GeoDepth 3D direct grid-based tomography has have been shown to overcome these inherent limitations by reducing the memory and disk space required through more intense computation.
While the resulting updated subsurface velocities are identical to those of conventional 3D grid tomography, the difference is in the implementation. In 3D direct tomography, the tomography matrix is never generated explicitly, dramatically reducing the memory and disk space required by the application, where the inversion process (including ray tracing and the construction of the tomography equations) is performed in a single stage using an iterative process.
Direct tomography implementation advantage:
Can handle large 3D updated grids (either due to the size of the survey or due to the requirements for high resolution) that could not be used before.
Is very efficient when using clusters with massive amounts of nodes.
The runtime of direct tomography is mainly related to CPU power in globally running the ray tracing many times (for each iteration), whereas conventional 3D grid-based tomography suffers mainly from being I/O bounded, where most of the time is spent reading and manipulating the tomography matrix (many terabytes of data).