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minor: improved documentation of PhaseShift
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mrava87 committed Feb 6, 2025
1 parent 2d12a61 commit 4fc8979
Showing 1 changed file with 10 additions and 5 deletions.
15 changes: 10 additions & 5 deletions pylops/waveeqprocessing/oneway.py
Original file line number Diff line number Diff line change
Expand Up @@ -103,10 +103,10 @@ def PhaseShift(
freq : :obj:`numpy.ndarray`
Positive frequency axis
kx : :obj:`int`, optional
Horizontal wavenumber axis (centered around 0) of size
Horizontal spectroscopic wavenumber axis (centered around 0) of size
:math:`[n_x \times 1]`.
ky : :obj:`int`, optional
Second horizontal wavenumber axis for 3d phase shift
Second horizontal spectroscopic wavenumber axis for 3d phase shift
(centered around 0) of size :math:`[n_y \times 1]`.
dtype : :obj:`str`, optional
Type of elements in input array
Expand All @@ -130,9 +130,14 @@ def PhaseShift(
d(f, k_x, k_y) = m(f, k_x, k_y)
e^{-j \Delta z \sqrt{\omega^2/v^2 - k_x^2 - k_y^2}}
where :math:`v` is the constant propagation velocity and
:math:`\Delta z` is the propagation depth. In adjoint mode, the data is
propagated backward using the following transformation:
where :math:`v` is the constant propagation velocity,
:math:`\Delta z` is the propagation depth, :math:`\omega=2\pi f` is the
angular frequency axis (where :math:`f` is represented by ``freq``),
:math:`k_x=2\pi \tilde{k}_x` is the horizontal wavenumber (where
:math:`\tilde{k}_x` is represented by ``kx``), and :math:`k_y=2\pi \tilde{k}_y`
is the second horizontal wavenumber (where :math:`\tilde{k}_y`
is represented by ``ky``). In adjoint mode, the data is propagated backward
using the following transformation:
.. math::
m(f, k_x, k_y) = d(f, k_x, k_y)
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