Velocity analysis using $AB$ semblance

Sensitivity analysis of $AB$ semblance

Sarkar et al. (2002,2001) observed a decrease of resolution in $AB$ semblance in comparison with the conventional semblance when applying it on synthetic examples. The explicit equation (7) allows us to access the resolution limits of both methods by measuring their effect on random noise.

As shown in Appendix A, the semblance of a sequence of uncorrelated normally-distributed zero-mean noise samples has the expectation value of $1/N$ , where $N$ is the number of samples. The corresponding $AB$ semblance has the expectation $2/N$ or twice higher. Moreover, while the standard deviation of the conventional semblance decreases as $1/N$ , the deviation of the $AB$ semblance decreases as $2/N$ . This analysis shows that the $AB$ measurement is generally twice as sensitive to noise and has a twice lower resolution. This is the price one has to pay for the ability to handle amplitude trends.

Velocity analysis using $AB$ semblance