pylops.avo.avo.AVOLinearModelling

class pylops.avo.avo.AVOLinearModelling(theta, vsvp=0.5, nt0=1, spatdims=None, linearization='akirich', dtype='float64')[source]

AVO Linearized modelling.

Create operator to be applied to a combination of elastic parameters for generation of seismic pre-stack reflectivity.

Parameters:
theta : np.ndarray

Incident angles in degrees

vsvp : np.ndarray or float

VS/VP ratio

nt0 : int, optional

number of samples (if vsvp is a scalar)

spatdims : int or tuple, optional

Number of samples along spatial axis (or axes) (None if only one dimension is available)

linearization : str, optional

choice of linearization, akirich: Aki-Richards, fatti: Fatti

dtype : str, optional

Type of elements in input array.
Raises:
NotImplementedError

If linearization is not an implemented linearization

Notes

The AVO linearized operator performs a linear combination of three (or two) elastic parameters arranged in input vector \(\mathbf{m}\) of size \(n_{t0} \times N\) to create the so-called seismic reflectivity:

\[r(t, \theta, x, y) = \sum_{i=1}^N G_i(t, \theta) m_i(t, x, y) \qquad \forall \quad t, \theta\]

where \(N=2/3\). Note that the reflectivity can be in 1d, 2d or 3d and spatdims contains the dimensions of the spatial axis (or axes) \(x\) and \(y\).

Attributes:
shape : tuple

Operator shape

explicit : bool

Operator contains a matrix that can be solved explicitly (True) or not (False)

Methods

__init__(self, theta[, vsvp, nt0, spatdims, …]) Initialize this LinearOperator.
adjoint(self) Hermitian adjoint.
apply_columns(self, cols) Apply subset of columns of operator
cond(self, \*\*kwargs_eig) Condition number of linear operator.
conj(self) Complex conjugate operator
div(self, y[, niter]) Solve the linear problem \(\mathbf{y}=\mathbf{A}\mathbf{x}\).
dot(self, x) Matrix-matrix or matrix-vector multiplication.
eigs(self[, neigs, symmetric, niter]) Most significant eigenvalues of linear operator.
matmat(self, X) Matrix-matrix multiplication.
matvec(self, x) Matrix-vector multiplication.
rmatmat(self, X) Adjoint matrix-matrix multiplication.
rmatvec(self, x) Adjoint matrix-vector multiplication.
todense(self) Return dense matrix.
transpose(self) Transpose this linear operator.

Examples using pylops.avo.avo.AVOLinearModelling