diff --git a/pylops/waveeqprocessing/oneway.py b/pylops/waveeqprocessing/oneway.py index 14e5f7f1..ae7aa3c9 100644 --- a/pylops/waveeqprocessing/oneway.py +++ b/pylops/waveeqprocessing/oneway.py @@ -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 @@ -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)