pylops.avo.avo.AVOLinearModelling

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

AVO Linearized modelling.

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

Parameters

thetanumpy.ndarray

Incident angles in degrees

vsvpnumpy.ndarray or float

\(V_S/V_P\) ratio

nt0int, optional

Number of samples (if vsvp is a scalar)

spatdimsint or tuple, optional

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

linearization{“akirich”, “fatti”, “PS”}, optional

• “akirich”: Aki-Richards. See pylops.avo.avo.akirichards.

• “fatti”: Fatti. See pylops.avo.avo.fatti.

• “PS”: PS. See pylops.avo.avo.ps.

dtypestr, optional

Type of elements in input array.

namestr, 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

nthetaint

Number of angles.

Gnumpy.ndarray

AVO coefficients of shape \([n_{\theta} \times N \times 1 \times \ldots \times 1]\) where \(N=2,\, 3\) is the number of elastic parameters and the remaining dimensions are singleton dimensions to account for spatial axes.

dimstuple

Shape of the array after the adjoint, but before flattening.

For example, x_reshaped = (Op.H * y.ravel()).reshape(Op.dims).

dimsdtuple

Shape of the array after the forward, but before flattening.

For example, y_reshaped = (Op * x.ravel()).reshape(Op.dimsd).

shapetuple

Operator shape.

Methods

__init__(theta[, vsvp, nt0, spatdims, ...])
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()