import logging
import numpy as np
from pylops import LinearOperator
from ._ChirpRadon2D import _chirp_radon_2d
logging.basicConfig(format='%(levelname)s: %(message)s', level=logging.WARNING)
[docs]class ChirpRadon2D(LinearOperator):
r"""2D Chirp Radon transform
Apply Radon forward (and adjoint) transform using Fast
Fourier Transform and Chirp functions to a 2-dimensional array of size
:math:`[n_x \times n_t]` (and :math:`[n_{x} \times n_t]`).
Note that forward and adjoint are swapped compared to the time-space
implementation in :class:`pylops.signalprocessing.Radon2D` and a direct
`inverse` method is also available for this implementation.
Parameters
----------
taxis : :obj:`np.ndarray`
Time axis
haxis : :obj:`np.ndarray`
Spatial axis
pmax : :obj:`np.ndarray`
Maximum slope defined as :math:`\tan` of maximum stacking angle in
:math:`x` direction :math:`p_{max} = \tan(\alpha_{x, max})`.
If one operates in terms of minimum velocity :math:`c_0`, set
:math:`p_{x, max}=c_0 dy/dt`.
dtype : :obj:`str`, optional
Type of elements in input array.
Attributes
----------
shape : :obj:`tuple`
Operator shape
explicit : :obj:`bool`
Operator contains a matrix that can be solved explicitly (``True``) or
not (``False``)
Notes
-----
Refer to [1]_ for the theoretical and implementation details.
.. [1] Andersson, F and Robertsson J. "Fast :math:`\tau-p` transforms by
chirp modulation", Geophysics, vol 84, NO.1, pp. A13-A17, 2019.
"""
def __init__(self, taxis, haxis, pmax, dtype='float64'):
self.dt = taxis[1] - taxis[0]
self.dh = haxis[1] - haxis[0]
self.nt, self.nh = taxis.size, haxis.size
self.pmax = pmax
self.shape = (self.nt * self.nh,
self.nt * self.nh)
self.dtype = np.dtype(dtype)
self.explicit = False
def _matvec(self, x):
x = x.reshape(self.nh, self.nt)
y = _chirp_radon_2d(x, self.dt, self.dh, self.pmax, mode='f')
return y.ravel()
def _rmatvec(self, x):
x = x.reshape(self.nh, self.nt)
y = _chirp_radon_2d(x, self.dt, self.dh, self.pmax, mode='a')
return y.ravel()
def inverse(self, x):
x = x.reshape(self.nh, self.nt)
y = _chirp_radon_2d(x, self.dt, self.dh, self.pmax, mode='i')
return y.ravel()