pylops.avo.avo.AVOLinearModelling

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

\(V_S/V_P\) 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 : {“akirich”, “fatti”, “PS”}, optional
dtype : str, optional

Type of elements in input array.

name : str, optional

New in version 2.0.0.

Name of operator (to be used by pylops.utils.describe.describe)

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 \(n_{t_0} \times N\) to create the so-called seismic reflectivity:

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

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__(theta[, vsvp, nt0, spatdims, …]) Initialize this LinearOperator.
adjoint() Hermitian adjoint.
apply_columns(cols) Apply subset of columns of operator
cond([uselobpcg]) Condition number of linear operator.
conj() Complex conjugate operator
div(y[, niter, densesolver]) Solve the linear problem \(\mathbf{y}=\mathbf{A}\mathbf{x}\).
dot(x) Matrix-matrix or matrix-vector multiplication.
eigs([neigs, symmetric, niter, uselobpcg]) Most significant eigenvalues of linear operator.
matmat(X) Matrix-matrix multiplication.
matvec(x) Matrix-vector multiplication.
reset_count() Reset counters
rmatmat(X) Matrix-matrix multiplication.
rmatvec(x) Adjoint matrix-vector multiplication.
todense([backend]) Return dense matrix.
toimag([forw, adj]) Imag operator
toreal([forw, adj]) Real operator
tosparse() Return sparse matrix.
trace([neval, method, backend]) Trace of linear operator.
transpose() Transpose this linear operator.