pylops.avo.prestack.PrestackWaveletModelling

pylops.avo.prestack.PrestackWaveletModelling(m, theta, nwav, wavc=None, vsvp=0.5, linearization='akirich', name=None)

Pre-stack linearized seismic modelling operator for wavelet.

Create operator to be applied to a wavelet for generation of band-limited seismic angle gathers using a linearized version of the Zoeppritz equation.

Parameters:

mnumpy.ndarray

elastic parameter profles of size \([n_{t_0} \times N]\) where \(N=3,\,2\). Note that the dtype of this variable will define that of the operator

thetaint

Incident angles in degrees. Must have same dtype of m (or it will be automatically cast to it)

nwavnumpy.ndarray

Number of samples of wavelet to be applied/estimated

wavcint, optional

Index of the center of the wavelet

vsvpnumpy.ndarray or float, optional

\(V_S/V_P\) ratio

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

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

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

• “PS”: PS. See pylops.avo.avo.ps.

• Function with the same signature as pylops.avo.avo.akirichards

namestr, optional

Added in version 2.0.0.

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

Returns:

MconvLinearOperator

pre-stack modelling operator for wavelet estimation.

Raises:

NotImplementedError

If linearization is not an implemented linearization

Notes

Pre-stack seismic modelling for wavelet estimate is the process of constructing seismic reflectivities using three (or two) profiles of elastic parameters in time (or depth) domain arranged in an input vector \(\mathbf{m}\) of size \(n_{t_0} \times N\):

\[d(t, \theta) = \sum_{i=1}^N G_i(t, \theta) m_i(t) * w(t)\]

where \(w(t)\) is the time domain seismic wavelet. In compact form:

\[\mathbf{d}= \mathbf{G} \mathbf{w}\]

On the other hand, pre-stack wavelet estimation aims at recovering the wavelet given knowledge of the band-limited seismic pre-stack data and the elastic parameter profiles.