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
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
- kind
str
, optional Derivative kind (
forward
orcentered
).- name
str
, optional New in version 2.0.0.
Name of operator (to be used by
pylops.utils.describe.describe
)
- wav
- Returns
- Pop
LinearOperator
post-stack modelling operator.
- Pop
- Raises
- ValueError
If
wav
is two dimensional 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:
\[d(t, \theta=0) = w(t) * \frac{\mathrm{d}\ln m(t)}{\mathrm{d}t}\]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.