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![]() | Velocity analysis using ![]() | ![]() |
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Sarkar et al. (2002,2001) observed a decrease of resolution
in
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
, where
is the number of samples. The corresponding
semblance has the expectation
or twice
higher. Moreover, while the standard deviation of the conventional
semblance decreases as
, the deviation of the
semblance decreases as
. This analysis shows that the
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.
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![]() | Velocity analysis using ![]() | ![]() |
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