pylops.avo.poststack.PoststackLinearModelling¶
-
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 elastic parameter trace (or stack of traces) for generation of band-limited seismic post-stack data. The input model and data have shape \([n_{t0} (\times n_x \times n_y)]\).
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 \([n_{t0} \times n_{wav}]\) where \(n_{wav}\) is the lenght of each wavelet)
- nt0 :
int
Number of samples along time axis
- spatdims :
int
ortuple
, 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 aMatrixMult
linear operator with dense matrix (True
, preferred for small data)- sparse :
bool
, optional Create a sparse matrix (
True
) or dense (False
) whenexplicit=True
Returns: - Pop :
LinearOperator
post-stack modelling operator.
Raises: - ValueError
If
wav
is 2dimensional but does not containnt0
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:
\[d(t, \theta) = w(t) * \frac{dln(m(t))}{dt}\]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:
\[d(t, \theta=0) = \frac{1}{2} w(t) * \frac{dln(m(t))}{dt}\]where the scaling factor \(\frac{1}{2}\) can be easily included in the wavelet.
- wav :