C.-S. CHEN ET AL.

170

111

tis

QQQ

Neep et al. [25] propose that this equation is valid if at

least one full wavelength propagates through the medium,

and the relationship appears to be valid in the spectral

ratio method despite the scattering Q having both posi-

tive and negative values. The scattering Q in the near-

surface is more significant due to thin bed scattering, and

therefore, it may contribute more errors to the total Q

because the geometrical spreading factor is insignificant

in the near-surface Q estimation [7].

The real data example in this paper demonstrates that

the standard error of the estimated Q is strongly related

to the numerical values of ks and ns of the power law

model; thus the accuracy of the estimated Q depends on

the frequency bandwidth of data. This is also a coinci-

dent result proposed by White [14].

The total error associated with the near-surface Q es-

timation can be obtained by summing up all the relative

errors if they are independent and that the change of Q is

linear. Because these conditions may not be true in

reality, the total error only describes the maximum or the

worst-case scenario.

7. Conclusions

The attributes of uncertainties in estimating Q depend on

the methods used. The approach discussed in this study

suggests that the accuracy of near surface Q is affected

by a variety of factors resulting from errors of small dis-

sipation assumption, over-parameterized model, noise

effect, slope of the optimum linear regression model, and

optimum power law model.

Except under exceptionally favorable conditions, the

value of Q is always unstable and far from a definite

value no matter what method is applied. Our statistical

analysis can help understand the stability of the Q esti-

mated. However, the noise effect is the most uncertain

factor that may affect the accuracy of near surface Q.

Since no any filtering technique may remove noises

completely, it is suggested that every endeavor should be

made to acquire accurate estimates of error in the field.

The errors in estimating Q can be handled well by the

proposed method if the data acquisition errors have zero

mean, are approximately Gaussian, and have been well

estimated.

8. Acknowledgements

The authors thank Jeffrey C. Green for his assistance in

manuscript preparation. Special thanks go to the editor

and one anonymous reviewer for their interest in this

work and constructive comments. This research was par-

tially funded by the National Science Council of Taiwan,

ROC, Grant NSC 98-2116-M-003-007.

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