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

Post-stack linearized seismic modelling operator.

Create operator to be applied to an acoustic impedance trace (or stack of traces) for generation of band-limited seismic post-stack data. The input model and data have shape \([n_{t0} (\times n_x \times n_y)]\).

wav : np.ndarray

Wavelet in time domain (must had odd number of elements and centered to zero)

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

Pop : LinearOperator

post-stack modelling operator.


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

\[d(t, \theta=0) = w(t) * \frac{dln(AI(t))}{dt}\]

where \(AI(t)\) is the acoustic impedance profile and \(w(t)\) is the time domain seismic wavelet. In compact form:

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

On the other hand, post-stack inversion aims at recovering the impedance profile from the band-limited seismic stack data.

Examples using pylops.avo.poststack.PoststackLinearModelling