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Malcolm White
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# Welcome to the *pykonal* repository! | ||
This code implements a mixed- (first- and second-) order finite-difference solver for the 2D Eikonal equation in Cartesian coordinates using the Fast-Marching Method of Sethian et al. (1996). | ||
This code implements a mixed- (first- and second-) order finite-difference solver for the 3D Eikonal equation in Cartesian coordinates using the Fast-Marching Method of Sethian et al. (1996). | ||
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## Planned development | ||
1. Extend to 3D | ||
2. Implement in spherical coordinates | ||
1. Implement in spherical coordinates | ||
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## Example results | ||
### Compute synthetic arrival times in 3 dimensions: | ||
![Figure 1](figures/figure_1.png) | ||
### For multiple sources: | ||
![Figure 2](figures/figure_2.png) | ||
### And trace raypaths through heterogeneous velocity fields: | ||
#### Velocity model | ||
![Figure 3](figures/figure_3.png) | ||
#### Travel time field | ||
![Figure 4](figures/figure_4.png) | ||
![Figure 5](figures/figure_5.png) | ||
![Figure 6](figures/figure_6.png) | ||
![Figure 7](figures/figure_7.png) | ||
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## References | ||
Sethian, J. A. (1996). A fast marching level set method for monotonically advancing fronts. Proceedings of the National Academy of Sciences, 93(4), 1591–1595. https://doi.org/10.1073/pnas.93.4.1591 |
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