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Computational issues

The separation of wave-modes for heterogeneous TI models requires non-stationary spatial filtering with large operators (operators of $ 50$ samples in each dimension are used in this chapter), which is computationally expensive. The cost is directly proportional to the size of the model and to the size of each operator. Furthermore, in a simple implementation, the storage for the separation operators of the entire model is proportional to the size of the model and to the size of each operator. Suppose that a 3D elastic TTI model is characterized by the model parameters $ V_{P0}$ , $ V_{S0}$ , Thomsen parameters $ \epsilon$ and $ \delta$ , and symmetry axis tilt angle $ \nu$ and azimuth angle $ \alpha$ . For a 3D model of $ 300 \times
300 \times 300$  grid points, if one assumes that all operators have a size of $ 50 \times 50 \times
50$  samples, the storage for the operators is $ 300^3$  grid points $ \times 50^3$  samples/independent operator$ \times 3$ independent operators/grid point$ \times 4$  Bytes/sample $ =40.5$  TB. This is not feasible in ordinary processing. However, since there are relatively few medium parameters, i.e.,the $ V_{P0}/ V_{S0}$ ratio, $ \epsilon$ , $ \delta$ , and angles $ \nu$ and $ \alpha$ , which determine the properties of the operators, one can construct a look-up table of operators as a function of these parameters, and search the appropriate operators at every location in the model when doing wave-mode separation. For example, suppose one knows that $ V_{P0}/V_{S0}\in\left [1.5, 2.0\right]$ , $ \epsilon\in\left [0,
0.3\right]$ , $ \delta\in\left [0, 0.1\right]$ , and the symmetry axis tilt angle $ \nu\in\left [-90^{\circ},90^{\circ}\right]$ and azimuth angle $ \alpha\in\left [-180^{\circ},180^{\circ}\right]$ , one can sample the $ V_{P0}/ V_{S0}$ ratio at every $ 0.1$ , $ \epsilon$ and $ \delta$ at every $ 0.03$ , and the angles at every $ 15^{\circ}$ . In this case, one only needs a storage of $ 6 \times 10 \times 3 \times 12 \times 24$ combinations of medium parameters $ \times 50^3$  sample/independent operator$ \times 3$  independent operators/combination of medium parameters$ \times$ $ 4$  Bytes/sample $ =77$  GB; this is more manageable, although it is still a large volume to store.


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Next: S wave-mode amplitudes Up: Discussion Previous: Discussion

2013-08-29