pylops_distributed.waveeqprocessing.Demigration¶

pylops_distributed.waveeqprocessing.Demigration(z, x, t, srcs, recs, vel, wav, wavcenter, y=None, mode='eikonal', trav=None, nprocesses=None, client=None)[source]¶

Demigration operator.

Seismic demigration/migration operator.

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 : `str`, optional Computation mode (`analytic`, `eikonal` or `byot`, see Notes for more details) trav : `numpy.ndarray` or `dask.array.core.Array`, optional Traveltime table of size \(\lbrack n_rn_s \times (n_y) n_xn_z \rbrack\) To be provided only when `mode='byot'` nprocesses* : `str`, optional Number of processes to split computations client : `dask.distributed.client.Client`, optional Dask client. If provided, the traveltime computation will be persisted.
Returns:	demop : `pylops.LinearOperator` Demigration/Migration operator
Raises:	NotImplementedError If `mode` is neither `analytic`, `eikonal`, or `byot`

Notes

The demigration operator synthetizes seismic data given from a propagation velocity model \(v\) and a reflectivity model \(m\). In forward mode:

\[d(\mathbf{x_r}, \mathbf{x_s}, t) = w(t) * \int_V G(\mathbf{x}, \mathbf{x_s}, t) G(\mathbf{x_r}, \mathbf{x}, t) m(\mathbf{x}) d\mathbf{x}\]

where \(m(\mathbf{x})\) is the model and it represents the reflectivity at every location in the subsurface, \(G(\mathbf{x}, \mathbf{x_s}, t)\) and \(G(\mathbf{x_r}, \mathbf{x}, t)\) are the Green’s functions from source-to-subsurface-to-receiver and finally \(w(t)\) is the wavelet. Depending on the choice of mode the Green’s function will be computed and applied differently:

mode=analytic or mode=eikonal: traveltime curves between source to receiver pairs are computed for every subsurface point and Green’s functions are implemented from traveltime look-up tables, placing the reflectivity values at corresponding source-to-receiver time in the data.
byot: bring your own table. Traveltime table provided directly by user using trav input parameter. Green’s functions are then implemented in the same way as previous options.

The adjoint of the demigration operator is a migration operator which projects data in the model domain creating an image of the subsurface reflectivity.