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# Acknowledgments

We would like to thank Sergey Fomel and Guochang Liu for the introduction to the techniques of AB semblance and local-similarity-weighted stacking and for many useful discussions. Helpful comments and suggestions from three referees greatly improved the quality of the manuscript. Pan Deng appreciated August Lau for providing much advice in generalizing the application of the weighted stacking. This work is supported by the Research Assistantship at the University of Houston, the China Scholarship Council (grant No. 2011645012), and the SEG Foundation Scholarships.

# AB semblance: Least-squares fitting for the trend

Suppose that the weight in equation 2 has a trend of trace amplitude , (5)

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: (6)

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: (7) (8)

Substituting into equation 2 leads to the AB semblance.

# Review of local similarity measured by local correlation

Equations B-1 to B-5 review the derivation of the local correlation measure from Fomel (2007a). In linear algebra notation, the correlation of two signals can be expressed as a product of two least-squares scalar inverses and .   (9)   (10)   (11)

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 .   (12)   (13)

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  Next: Bibliography Up: Deng etc.: AVO stacking Previous: Conclusions

2017-01-17