pylops.avo.prestack.PrestackInversion¶
-
pylops.avo.prestack.
PrestackInversion
(data, theta, wav, m0=None, linearization='akirich', explicit=False, simultaneous=False, epsI=None, epsR=None, dottest=False, returnres=False, epsRL1=None, kind='centered', vsvp=0.5, **kwargs_solver)[source]¶ Pre-stack linearized seismic inversion.
Invert pre-stack seismic operator to retrieve a set of elastic property profiles from band-limited seismic pre-stack data (i.e., angle gathers). Depending on the choice of input parameters, inversion can be trace-by-trace with explicit operator or global with either explicit or linear operator.
Parameters: - data :
np.ndarray
Band-limited seismic post-stack data of size \([(n_\text{lins} \times) \, n_{t_0} \times n_{\theta} \, (\times n_x \times n_y)]\)
- theta :
np.ndarray
Incident angles in degrees
- wav :
np.ndarray
Wavelet in time domain (must had odd number of elements and centered to zero)
- m0 :
np.ndarray
, optional Background model of size \([n_{t_0} \times n_{m} \,(\times n_x \times n_y)]\)
- linearization : {“akirich”, “fatti”, “PS”} or
list
, optional - “akirich”: Aki-Richards. See
pylops.avo.avo.akirichards
. - “fatti”: Fatti. See
pylops.avo.avo.fatti
. - “PS”: PS. See
pylops.avo.avo.ps
. - List which is a combination of previous options (required only when
m0 is None
).
- “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)- simultaneous :
bool
, optional Simultaneously invert entire data (
True
) or invert trace-by-trace (False
) when usingexplicit
operator (note that the entire data is always inverted when working with linear operator)- epsI :
float
orlist
, optional Damping factor(s) for Tikhonov regularization term. If a list of \(n_{m}\) elements is provided, the regularization term will have different strenght for each elastic property
- epsR :
float
, optional Damping factor for additional Laplacian regularization term
- dottest :
bool
, optional Apply dot-test
- returnres :
bool
, optional Return residuals
- epsRL1 :
float
, optional Damping factor for additional blockiness regularization term
- kind :
str
, optional Derivative kind (
forward
orcentered
).- vsvp :
float
ornp.ndarray
\(V_S/V_P\) ratio (constant or time/depth variant)
- **kwargs_solver
Arbitrary keyword arguments for
scipy.linalg.lstsq
solver (ifexplicit=True
andepsR=None
) orscipy.sparse.linalg.lsqr
solver (ifexplicit=False
and/orepsR
is notNone
))
Returns: - minv :
np.ndarray
Inverted model of size \([n_{t_0} \times n_{m} \,(\times n_x \times n_y)]\)
- datar :
np.ndarray
Residual data (i.e., data - background data) of size \([n_{t_0} \times n_{\theta} \,(\times n_x \times n_y)]\)
Notes
The different choices of cost functions and solvers used in the seismic pre-stack inversion module follow the same convention of the seismic post-stack inversion module.
Refer to
pylops.avo.poststack.PoststackInversion
for more details.- data :