__all__ = ["PWSprayer2D", "PWSmoother2D"]
import numpy as np
from pylops import LinearOperator
from pylops.utils.decorators import reshaped
from pylops.utils.typing import DTypeLike, NDArray
from ._spraying2d_numba import _spray_adjoint_numba, _spray_forward_numba
[docs]
class PWSprayer2D(LinearOperator):
r"""2D Plane-Wave Sprayer.
Spray (or paint) each input value along local structural
slopes in :math:`\pm x` direction with exponential decay
in forward mode, and gather contributions back along the same
slope trajectories in adjoint mode. Together, this pair of
operators defines a linear operator that propagates information
preferentially along structural dips (implemented in
:class:`pylops.signalprocessing.PWSmoother2D`).
Parameters
----------
dims : :obj:`tuple` of :obj:`int`
Number of samples for each dimension - ``(nz, nx)``.
sigma : :obj:`numpy.ndarray`
Local slope field of shape ``(nz, nx)`` defined in samples per trace
(:math:`\Delta z / \Delta x`).
radius : :obj:`int`, optional
Maximum number of steps along each :math:`\pm x` direction to spray
or gather. Controls the spatial extent of spreading. Default is ``8``.
alpha : :obj:`float`, optional
Geometric decay factor per step (:math:`0 < \alpha \leq 1`).
Higher values propagate energy farther. Default is ``0.9``.
dtype : :obj:`str`, optional
Type of elements in input array.
name : :obj:`str`, optional
Name of operator (to be used by :func:`pylops.utils.describe.describe`)
Attributes
----------
dims : :obj:`tuple`
Shape of the array after the adjoint, but before flattening.
For example, ``x_reshaped = (Op.H * y.ravel()).reshape(Op.dims)``.
dimsd : :obj:`tuple`
Shape of the array after the forward, but before flattening. In
this case, same as ``dims``.
shape : :obj:`tuple`
Operator shape.
See Also
--------
PWSmoother2D : Structure-aligned smoother
pwd_slope_estimate : Local slope estimation using plane-wave destruction
Notes
-----
- The forward operator distributes each sample along rays following
local slope :math:`\sigma(z,x)`, using bilinear interpolation in depth.
- The adjoint operator gathers contributions back from the same rays,
making this a true linear operator pair.
- Effective smoothing along dip grows with larger ``radius`` and
higher ``alpha``.
"""
def __init__(
self,
dims: tuple[int, int],
sigma: NDArray,
radius: int = 8,
alpha: float = 0.9,
dtype: DTypeLike = "float64",
name: str = "P",
):
if len(dims) != 2:
msg = f"Wrong number of dimensions. Expected 2, but received {len(dims)}."
raise ValueError(msg)
self._radius = int(radius)
self._alpha = float(alpha)
self._sigma = np.ascontiguousarray(sigma)
super().__init__(dtype=np.dtype(dtype), dims=dims, dimsd=dims, name=name)
@reshaped
def _matvec(self, x: NDArray) -> NDArray:
y = np.zeros_like(x)
_spray_forward_numba(x, self._sigma, self._radius, self._alpha, y)
return y
@reshaped
def _rmatvec(self, x: NDArray) -> NDArray:
y = np.zeros_like(x)
_spray_adjoint_numba(x, self._sigma, self._radius, self._alpha, y)
return y
[docs]
class PWSmoother2D(LinearOperator):
r"""2D Structure-aligned smoother.
This operator builds a symmetric, positive semi-definite (PSD) smoother
aligned over local structural dips (``sigma``). It is defined as:
.. math::
S = P^H P
where :math:`P` is a :class:`pylops.signalprocessing.PWSprayer2D` operator that
propagates values along local slopes. The composition ``P.H @ P`` produces a
correlation-like operator that smooths preferentially along the defined
slopes.
The resulting operator can be used as a regularizer or preconditioner
in inverse problems to enforce structural smoothness.
Parameters
----------
dims : :obj:`tuple` of :obj:`int`
Number of samples for each dimension - ``(nz, nx)``.
sigma : :obj:`numpy.ndarray`
Local slope field of shape ``(nz, nx)`` defined in samples per trace
(:math:`\Delta z / \Delta x`).
radius : :obj:`int`, optional
Maximum number of steps along each :math:`\pm x` direction to spray
or gather. Controls the spatial extent of spreading. Default is ``8``.
alpha : :obj:`float`, optional
Geometric decay factor per step (:math:`0 < \alpha \leq 1`).
Higher values propagate energy farther. Default is ``0.9``.
dtype : :obj:`str`, optional
Type of elements in input array.
name : :obj:`str`, optional
Name of operator (to be used by :func:`pylops.utils.describe.describe`)
Attributes
----------
dims : :obj:`tuple`
Shape of the array after the adjoint, but before flattening.
For example, ``x_reshaped = (Op.H * y.ravel()).reshape(Op.dims)``.
dimsd : :obj:`tuple`
Shape of the array after the forward, but before flattening. In
this case, same as ``dims``.
shape : :obj:`tuple`
Operator shape.
Notes
-----
- The smoother is symmetric by construction.
- Effective correlation length along dip increases with larger
``radius`` and higher ``alpha``.
- Across-dip coupling is minimal (only through interpolation and dip
variability).
See Also
--------
PWSprayer2D : Forward sprayer/gather operator
pwd_slope_estimate : Local slope estimation using plane-wave destruction
"""
def __init__(
self,
dims: tuple[int, int],
sigma: NDArray,
radius: int = 8,
alpha: float = 0.9,
dtype: DTypeLike = "float64",
name: str = "P",
):
if len(dims) != 2:
msg = f"Wrong number of dimensions. Expected 2, but received {len(dims)}."
raise ValueError(msg)
self._sprayer = PWSprayer2D(
dims=dims, sigma=sigma, radius=radius, alpha=alpha, dtype=dtype
)
super().__init__(dtype=np.dtype(dtype), dims=dims, dimsd=dims, name=name)
@reshaped
def _matvec(self, x: NDArray) -> NDArray:
y = self._sprayer @ x
y = self._sprayer.H @ y
return y
@reshaped
def _rmatvec(self, x: NDArray) -> NDArray:
return self._matvec(x)
PyLops