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

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.

m : np.ndarray

elastic parameter profles of size \([n_{t0} \times N]\) where \(N=3/2\). Note that the dtype of this variable will define that of the operator

theta : int

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

nwav : np.ndarray

Number of samples of wavelet to be applied/estimated

wavc : int, optional

Index of the center of the wavelet

vsvp : np.ndarray or float, optional

VS/VP ratio

linearization : str, optional

choice of linearization, akirich: Aki-Richards, fatti: Fatti, ps: PS, or any function on the form of pylops.avo.avo.akirichards

Mconv : LinearOperator

pre-stack modelling operator for wavelet estimation.


If linearization is not an implemented linearization


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 \(nt0 \times N\):

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

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.

Examples using pylops.avo.prestack.PrestackWaveletModelling