pylops.waveeqprocessing.LSM

class pylops.waveeqprocessing.LSM(z, x, t, srcs, recs, vel, wav, wavcenter, y=None, mode='eikonal', dottest=False)

Least-squares 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 or float

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 3-dimensional problems)

mode : numpy.ndarray, optional

Computation mode (eikonal, analytic - only for constant velocity)

dottest : bool, optional

Apply dot-test

See also

pylops.waveeqprocessing.Demigration

Demigration operator

Notes

Inverting a demigration operator is generally referred in the literature as least-squares migration (LSM) as historically a least-squares 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 (band-limited) image of the subsurface is created. This process is referred to in the literature as migration.

Attributes:

Demop : pylops.LinearOperator

Demigration operator

Methods

__init__(self, z, x, t, srcs, recs, vel, …)	Initialize self.
solve(self, d[, solver])	Solve least-squares migration equations with chosen solver

solve(self, d, solver=<function lsqr at 0x7f7ad5588048>, **kwargs_solver)

Solve least-squares 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 \(\lbrack (n_y \times) n_x \times n_z \rbrack\)

Examples using pylops.waveeqprocessing.LSM

13. Least-squares migration