pylops.avo.poststack.PoststackLinearModelling

pylops.avo.poststack.PoststackLinearModelling(wav, nt0, spatdims=None, explicit=False, sparse=False, kind='centered', name=None)[source]

Post-stack linearized seismic modelling operator.

Create operator to be applied to an elastic parameter trace (or stack of traces) for generation of band-limited seismic post-stack data. The input model and data have shape \([n_{t_0} \,(\times n_x \times n_y)]\).

Parameters:
wav : np.ndarray

Wavelet in time domain (must have odd number of elements and centered to zero). If 1d, assume stationary wavelet for the entire time axis. If 2d, use as non-stationary wavelet (user must provide one wavelet per time sample in an array of size \([n_{t_0} \times n_\text{wav}]\) where \(n_\text{wav}\) is the length of each wavelet). Note that the dtype of this variable will define that of the operator

nt0 : int

Number of samples along time axis

spatdims : int or tuple, optional

Number of samples along spatial axis (or axes) (None if only one dimension is available)

explicit : bool, optional

Create a chained linear operator (False, preferred for large data) or a MatrixMult linear operator with dense matrix (True, preferred for small data)

sparse : bool, optional

Create a sparse matrix (True) or dense (False) when explicit=True

kind : str, optional

Derivative kind (forward or centered).

name : str, optional

New in version 2.0.0.

Name of operator (to be used by pylops.utils.describe.describe)

Returns:
Pop : LinearOperator

post-stack modelling operator.

Raises:
ValueError

If wav is two dimensional but does not contain nt0 wavelets

Notes

Post-stack seismic modelling is the process of constructing seismic post-stack data from a profile of an elastic parameter of choice in time (or depth) domain. This can be easily achieved using the following forward model:

\[d(t, \theta=0) = w(t) * \frac{\mathrm{d}\ln m(t)}{\mathrm{d}t}\]

where \(m(t)\) is the elastic parameter profile and \(w(t)\) is the time domain seismic wavelet. In compact form:

\[\mathbf{d}= \mathbf{W} \mathbf{D} \mathbf{m}\]

In the special case of acoustic impedance (\(m(t)=AI(t)\)), the modelling operator can be used to create zero-offset data:

\[d(t, \theta=0) = \frac{1}{2} w(t) * \frac{\mathrm{d}\ln m(t)}{\mathrm{d}t}\]

where the scaling factor \(\frac{1}{2}\) can be easily included in the wavelet.