scratch
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Eikonal Equation [WIP ]
created 2023-05-19 · last edited 2023-09-22
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1D
§
nD
Since everything is determined by 1D parametrization (curves)
∣
∇
ϕ
(
r
)
∣
=
1
/
v
(
r
)
|\nabla \phi(r)| = 1/v(r)
∣
∇
ϕ
(
r
)
∣
=
1
/
v
(
r
)
r
r
r
is position in space.
v
(
r
)
v(r)
v
(
r
)
is the speed of light at position
r
r
r
.
ϕ
(
r
)
\phi(r)
ϕ
(
r
)
represents the travel time of a wavefront to reach
r
r
r
.
So, the gradient of the travel time is
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References
Video on eikonal equation
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