pylops.signalprocessing.ChirpRadon3D

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

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.

Parameters:

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.

**kwargs_fftw

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

Notes

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.

Attributes:

shape : tuple

Operator shape

explicit : bool

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

Methods

__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.
inverse(x)
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

Chirp Radon Transform