class pylops.signalprocessing.ChirpRadon3D(taxis, hyaxis, hxaxis, pmax, engine='numpy', dtype='float64', **kwargs_fftw)[source]

3D Chirp Radon transform

Apply Radon forward (and adjoint) transform using Fast Fourier Transform and Chirp functions to a 3-dimensional array of size \([n_y \times n_x \times n_t]\) (both in forward and adjoint mode).

Note that forward and adjoint are swapped compared to the time-space implementation in pylops.signalprocessing.Radon3D and a direct inverse method is also available for this implementation.

taxis : np.ndarray

Time axis

hxaxis : np.ndarray

Fast patial axis

hyaxis : np.ndarray

Slow spatial axis

pmax : np.ndarray

Two element array \((p_{y,\text{max}}, p_{x,\text{max}})\) of \(\tan\) of maximum stacking angles in \(y\) and \(x\) directions \((\tan(\alpha_{y,\text{max}}), \tan(\alpha_{x,\text{max}}))\). If one operates in terms of minimum velocity \(c_0\), then \(p_{y,\text{max}}=c_0\,\mathrm{d}y/\mathrm{d}t\) and \(p_{x,\text{max}}=c_0\,\mathrm{d}x/\mathrm{d}t\)

engine : str, optional

Engine used for fft computation (numpy or fftw)

dtype : str, optional

Type of elements in input array.


Arbitrary keyword arguments for pyfftw.FTTW (reccomended: flags=('FFTW_ESTIMATE', ), threads=NTHREADS)


Refer to [1] for the theoretical and implementation details.

[1]Andersson, F and Robertsson J. “Fast \(\tau-p\) transforms by chirp modulation”, Geophysics, vol 84, NO.1, pp. A13-A17, 2019.
shape : tuple

Operator shape

explicit : bool

Operator contains a matrix that can be solved explicitly (True) or not (False)


__init__(taxis, hyaxis, hxaxis, pmax[, …]) Initialize this LinearOperator.
adjoint() Hermitian adjoint.
apply_columns(cols) Apply subset of columns of operator
cond([uselobpcg]) Condition number of linear operator.
conj() Complex conjugate operator
div(y[, niter, densesolver]) Solve the linear problem \(\mathbf{y}=\mathbf{A}\mathbf{x}\).
dot(x) Matrix-matrix or matrix-vector multiplication.
eigs([neigs, symmetric, niter, uselobpcg]) Most significant eigenvalues of linear operator.
matmat(X) Matrix-matrix multiplication.
matvec(x) Matrix-vector multiplication.
rmatmat(X) Matrix-matrix multiplication.
rmatvec(x) Adjoint matrix-vector multiplication.
todense([backend]) Return dense matrix.
toimag([forw, adj]) Imag operator
toreal([forw, adj]) Real operator
tosparse() Return sparse matrix.
trace([neval, method, backend]) Trace of linear operator.
transpose() Transpose this linear operator.

Examples using pylops.signalprocessing.ChirpRadon3D