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UPDATE:: Update README.md
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Malcolm White committed Jun 11, 2019
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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).

## Planned development
1. Extend to 3D
2. Implement in spherical coordinates
1. Implement in spherical coordinates

## 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)

## 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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