Table 2 Expectations and standard deviations of \(\xi _n(\phi _0; \Delta \phi )\) and \(\zeta _n(\phi _0; \Delta \phi )\) (\(n=1,2\); \(\phi _0=\pi /6\), \(\Delta \phi =\pi /4\), \(L=100\))
From: Estimation of phase velocity using array observation of microtremors with arbitrary shape
| Â | Eqs.(15) to (18) | Using Monte Carlo | |
|---|---|---|---|
| Â | \(\alpha _{\ell } \equiv \frac{\hat{\alpha _{\ell }}}{\sum \hat{\alpha _{\ell }}}\) | Eq.(10) | |
\(E[\xi _1]\) | − 0.2328 | − 0.2329 | − 0.2329 |
\(\sqrt{Var[\xi _1]}\) | 0.04947 | 0.04778 | 0.04958 |
\(E[\zeta _1]\) | 0.8697 | 0.8697 | 0.8697 |
\(\sqrt{Var[\zeta _1]}\) | 0.05277 | 0.01612 | 0.05278 |
\(E[\xi _2]\) | − 0.5513 | − 0.5515 | − 0.5515 |
\(\sqrt{Var[\xi _2]}\) | 0.06022 | 0.05126 | 0.06039 |
\(E[\zeta _2]\) | − 0.3183 | − 0.3182 | − 0.3181 |
\(\sqrt{Var[\zeta _2]}\) | 0.07519 | 0.07315 | 0.07534 |