pylops.waveeqprocessing.Deghosting(p, nt, nr, dt, dr, vel, zrec, pd=None, win=None, npad=(11, 11), ntaper=(11, 11), restriction=None, sptransf=None, solver=<function lsqr>, dottest=False, dtype='complex128', **kwargs_solver)[source]

Wavefield deghosting.

Apply seismic wavefield decomposition from single-component (pressure) data. This process is also generally referred to as model-based deghosting.

p : np.ndarray

Pressure data of of size \(\lbrack n_{r_x}\,(\times n_{r_y}) \times n_t \rbrack\) (or \(\lbrack n_{r_{x,\text{sub}}}\, (\times n_{r_{y,\text{sub}}}) \times n_t \rbrack\) in case a restriction operator is provided. Note that \(n_{r_{x,\text{sub}}}\) (and \(n_{r_{y,\text{sub}}}\)) must agree with the size of the output of this operator)

nt : int

Number of samples along the time axis

nr : int or tuple

Number of samples along the receiver axis (or axes)

dt : float

Sampling along the time axis

dr : float or tuple

Sampling along the receiver array of the separated pressure consituents

vel : float

Velocity along the receiver array (must be constant)

zrec : float

Depth of receiver array

pd : np.ndarray, optional

Direct arrival to be subtracted from p

win : np.ndarray, optional

Time window to be applied to p to remove the direct arrival (if pd=None)

ntaper : float or tuple, optional

Number of samples of taper applied to propagator to avoid edge effects

npad : float or tuple, optional

Number of samples of padding applied to propagator to avoid edge effects

restriction : pylops.LinearOperator, optional

Restriction operator

sptransf : pylops.LinearOperator, optional

Sparsifying operator

solver : float, optional

Function handle of solver to be used if kind='inverse'

dottest : bool, optional

Apply dot-test

dtype : str, optional

Type of elements in input array. If None, directly inferred from p


Arbitrary keyword arguments for chosen solver

pup : np.ndarray

Up-going wavefield

pdown : np.ndarray

Down-going wavefield


Up- and down-going components of seismic data \(p^-(x, t)\) and \(p^+(x, t)\) can be estimated from single-component data \(p(x, t)\) using a ghost model.

The basic idea [1] is that of using a one-way propagator in the f-k domain (also referred to as ghost model) to predict the down-going field from the up-going one (excluded the direct arrival and its source ghost referred here to as \(p_d(x, t)\)):

\[p^+ - p_d = e^{-j k_z 2 z_\text{rec}} p^-\]

where \(k_z\) is the vertical wavenumber and \(z_\text{rec}\) is the depth of the array of receivers

In a matrix form we can thus write the total wavefield as:

\[\mathbf{p} - \mathbf{p_d} = (\mathbf{I} + \Phi) \mathbf{p}^-\]

where \(\Phi\) is one-way propagator implemented via the pylops.waveeqprocessing.PhaseShift operator.

[1]Amundsen, L., 1993, Wavenumber-based filtering of marine point-source data: GEOPHYSICS, 58, 1335–1348.

Examples using pylops.waveeqprocessing.Deghosting