pylops.avo.prestack.PrestackLinearModelling¶
-
pylops.avo.prestack.
PrestackLinearModelling
(wav, theta, vsvp=0.5, nt0=1, spatdims=None, linearization='akirich', explicit=False, kind='centered')[source]¶ Pre-stack linearized seismic modelling operator.
Create operator to be applied to elastic property profiles for generation of band-limited seismic angle gathers from a linearized version of the Zoeppritz equation. The input model must be arranged in a vector of size \(n_m \times n_{t_0}\,(\times n_x \times n_y)\) for
explicit=True
and \(n_{t_0} \times n_m \,(\times n_x \times n_y)\) forexplicit=False
. Similarly the output data is arranged in a vector of size \(n_{\theta} \times n_{t_0} \,(\times n_x \times n_y)\) forexplicit=True
and \(n_{t_0} \times n_{\theta} \,(\times n_x \times n_y)\) forexplicit=False
.Parameters: - wav :
np.ndarray
Wavelet in time domain (must had odd number of elements and centered to zero). Note that the
dtype
of this variable will define that of the operator- theta :
np.ndarray
Incident angles in degrees. Must have same
dtype
ofwav
(or it will be automatically casted to it)- vsvp :
float
ornp.ndarray
\(V_S/V_P\) ratio (constant or time/depth variant)
- nt0 :
int
, optional number of samples (if
vsvp
is a scalar)- spatdims :
int
ortuple
, optional Number of samples along spatial axis (or axes) (
None
if only one dimension is available)- linearization : {“akirich”, “fatti”, “PS”} or
callable
, optional - “akirich”: Aki-Richards. See
pylops.avo.avo.akirichards
. - “fatti”: Fatti. See
pylops.avo.avo.fatti
. - “PS”: PS. See
pylops.avo.avo.ps
. - Function with the same signature as
pylops.avo.avo.akirichards
- “akirich”: Aki-Richards. See
- 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)- kind :
str
, optional Derivative kind (
forward
orcentered
).
Returns: - Preop :
LinearOperator
pre-stack modelling operator.
Raises: - NotImplementedError
If
linearization
is not an implemented linearization- NotImplementedError
If
kind
is notforward
norcentered
Notes
Pre-stack seismic modelling is the process of constructing seismic pre-stack data from three (or two) profiles of elastic parameters in time (or depth) domain. This can be easily achieved using the following forward model:
\[d(t, \theta) = w(t) * \sum_{i=1}^{n_m} G_i(t, \theta) m_i(t)\]where \(w(t)\) is the time domain seismic wavelet. In compact form:
\[\mathbf{d}= \mathbf{G} \mathbf{m}\]On the other hand, pre-stack inversion aims at recovering the different profiles of elastic properties from the band-limited seismic pre-stack data.
- wav :