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Table 1 Expectations and standard deviations of \(\xi _1\) obtained through Monte Carlo simulation and Equation (13) for various values of L

From: Estimation of phase velocity using array observation of microtremors with arbitrary shape

 

\(\textrm{E}[\xi _1]\)

\(\sqrt{\textrm{Var}[\xi _1]}\)

L

Monte Carlo

Eq. (13)

Monte Carlo

Eq. (13)

1

\(-0.0001\)

0

0.7014

0.8165

3

0.0037

0

0.4641

0.4714

5

\(-0.0129\)

0

0.3640

0.3651

10

\(-0.0002\)

0

0.2590

0.2582

100

\(-0.0010\)

0

0.0832

0.0816

1000

\(-0.0002\)

0

0.0257

0.0258

10000

0.00001

0

0.0081

0.0082