Weighted stacking of seismic AVO data using hybrid AB semblance and local similarity |

where is a known function, and and are two coefficients from Shuey equation (Shuey, 1985). In the simplest form, can be chosen as the offset at trace . In order to estimate and , it can be turned to minimize the following objection function of misfit between the trend and trace amplitude:

Taking derivatives with respect to and in equation A-2, setting them to zero, and solving the two linear equations, the following two least-squares fitting coefficients are obtained:

Substituting into equation 2 leads to the AB semblance.

where and are vectors with the elements and . Let be a diagonal operator composed of the elements and be a diagonal operator composed of the elements . Localizing equations B-2 and B-3 is equivalent to adding regularization to inversion. Scalars and then turn into vectors and .

where is a shaping regularization (Fomel, 2007b) and is scaling factor that controls the relative scaling of and . The square root of a component-wise product of vectors and defines a local-similarity measure.

Weighted stacking of seismic AVO data using hybrid AB semblance and local similarity |

2017-01-17