def _obliquity3D(
nt,
nr,
dt,
dr,
rho,
vel,
nffts,
critical=100.0,
ntaper=10,
composition=True,
backend="numpy",
dtype="complex128",
):
r"""3D Obliquity operator and FFT operator
Parameters
----------
nt : :obj:`int`
Number of samples along the time axis
nr : :obj:`tuple`
Number of samples along the receiver axes
dt : :obj:`float`
Sampling along the time axis
dr : :obj:`tuple`
Samplings along the receiver array
rho : :obj:`float`
Density along the receiver array (must be constant)
vel : :obj:`float`
Velocity along the receiver array (must be constant)
nffts : :obj:`tuple`, optional
Number of samples along the wavenumber and frequency axes
critical : :obj:`float`, optional
Percentage of angles to retain in obliquity factor. For example, if
``critical=100`` only angles below the critical angle
:math:`\sqrt{k_y^2 + k_x^2} < \frac{\omega}{vel}` will be retained
ntaper : :obj:`float`, optional
Number of samples of taper applied to obliquity factor around critical
angle
composition : :obj:`bool`, optional
Create obliquity factor for composition (``True``) or
decomposition (``False``)
backend : :obj:`str`, optional
Backend used for creation of obliquity factor operator
(``numpy`` or ``cupy``)
dtype : :obj:`str`, optional
Type of elements in input array.
Returns
-------
FFTop : :obj:`pylops.LinearOperator`
FFT operator
OBLop : :obj:`pylops.LinearOperator`
Obliquity factor operator
"""
# create Fourier operator
FFTop = FFTND(dims=[nr[0], nr[1], nt],
nffts=nffts,
sampling=[dr[0], dr[1], dt],
dtype=dtype)
# create obliquity operator
[Ky, Kx, F] = np.meshgrid(FFTop.fs[0],
FFTop.fs[1],
FFTop.fs[2],
indexing="ij")
k = F / vel
Kz = np.sqrt((k**2 - Ky**2 - Kx**2).astype(dtype))
Kz[np.isnan(Kz)] = 0
if composition:
OBL = Kz / (rho * np.abs(F))
OBL[F == 0] = 0
else:
OBL = rho * (np.abs(F) / Kz)
OBL[Kz == 0] = 0
# cut off and taper
OBL = _filter_obliquity(OBL, F, Kx, vel, critical, ntaper, Ky=Ky)
OBL = get_module(backend).asarray(OBL)
OBLop = Diagonal(OBL.ravel(), dtype=dtype)
return FFTop, OBLop