pylops.waveeqprocessing.LSM¶

class
pylops.waveeqprocessing.
LSM
(z, x, t, srcs, recs, vel, wav, wavcenter, y=None, mode='eikonal', dottest=False)[source]¶ Leastsquares Migration (LSM).
Solve seismic migration as inverse problem given smooth velocity model
vel
and an acquisition setup identified by sources (src
) and receivers (recs
)Parameters:  z :
numpy.ndarray
Depth axis
 x :
numpy.ndarray
Spatial axis
 t :
numpy.ndarray
Time axis for data
 srcs :
numpy.ndarray
Sources in array of size \(\lbrack 2(3) \times n_s \rbrack\)
 recs :
numpy.ndarray
Receivers in array of size \(\lbrack 2(3) \times n_r \rbrack\)
 vel :
numpy.ndarray
orfloat
Velocity model of size \(\lbrack (n_y \times)\, n_x \times n_z \rbrack\) (or constant)
 wav :
numpy.ndarray
Wavelet
 wavcenter :
int
Index of wavelet center
 y :
numpy.ndarray
Additional spatial axis (for 3dimensional problems)
 mode :
numpy.ndarray
, optional Computation mode (
eikonal
,analytic
 only for constant velocity) dottest :
bool
, optional Apply dottest
See also
pylops.waveeqprocessing.Demigration
 Demigration operator
Notes
Inverting a demigration operator is generally referred in the literature as leastsquares migration (LSM) as historically a leastsquares cost function has been used for this purpose. In practice any other cost function could be used, for examples if
solver='pylops.optimization.sparsity.FISTA'
a sparse representation of reflectivity is produced as result of the inversion.Finally, it is worth noting that in the first iteration of an iterative scheme aimed at inverting the demigration operator, a projection of the recorded data in the model domain is performed and an approximate (bandlimited) image of the subsurface is created. This process is referred to in the literature as migration.
Attributes:  Demop :
pylops.LinearOperator
Demigration operator
Methods
__init__
(z, x, t, srcs, recs, vel, wav, …)Initialize self. solve
(d[, solver])Solve leastsquares migration equations with chosen solver

solve
(d, solver=<function lsqr>, **kwargs_solver)[source]¶ Solve leastsquares migration equations with chosen
solver
Parameters:  d :
numpy.ndarray
Input data of size \(\lbrack n_s \times n_r \times n_t \rbrack\)
 solver :
func
, optional Solver to be used for inversion
 **kwargs_solver
Arbitrary keyword arguments for chosen
solver
Returns:  minv :
np.ndarray
Inverted reflectivity model of size \(\lbrack (n_y \times) n_x \times n_z \rbrack\)
 d :
 z :