N1 |
Null |
NA |
NA |
\(r_{t,i}\,=\alpha_{1}+\ \epsilon_{t,i}\) |
NA |
N2 |
Phase-locked |
NA |
NA |
\(r_{t,i}=\alpha_{1}+f\left(T_{t,i}\right)\ +\ \epsilon_{t,i}\) |
NA |
N3 |
Static spatial pattern |
NA |
NA |
\(r_{t,i}=\alpha_{1}+f_{p}\left(X_{t,i}Y_{t,i}\right)\ +\ \epsilon_{t,i}\) |
NA |
RE |
Single expanding radial wave |
\(D_{i}=-\sqrt{\left(\gamma-X_{i}\right)^{2}+\left(\psi-Y_{i}\right)^{2}}\) |
\(\rho_{t,i}=T_{t,i}+\left(\frac{1}{\zeta}\right)D_{i}\) |
\(r_{t,i}=\alpha_{1}+f\left(\rho_{t,i}\right)+\epsilon_{t,i}\) |
3 |
RC |
Single contracting radial wave |
\(D_{i}=\sqrt{\left(\gamma-X_{i}\right)^{2}+\left(\psi-Y_{i}\right)^{2}}\) |
\(\rho_{t,i}=T_{t,i}+\left(\frac{1}{\zeta}\right)D_{i}\) |
\(r_{t,i}=\alpha_{1}+f\left(\rho_{t,i}\right)+\epsilon_{t,i}\) |
3 |
P |
Single planar wave |
\(D_{i}=\sin\left(\theta\right)X_{i}+\cos\left(\theta\right)Y_{i}\) |
\(\rho_{t,i}=T_{t,i}+\left(\frac{1}{\zeta}\right)D_{i}\) |
\(r_{t,i}=\alpha_{1}+f\left(\rho_{t,i}\right)+\epsilon_{t,i}\) |
2 |
RFE |
Two expanding radial waves separated by river |
\(D_{N,i}=-\sqrt{\left(\gamma_{N}-X_{i}\right)^{2}+\left(\psi_{N}-Y_{i}\right)^{2}},\ \ \ \ \ \ if\text{\ Y}_{i}\geq 5,068m\) |
\(\rho_{N,t,i}=T_{t,i}+\left(\frac{1}{\zeta_{N}}\right)D_{N,i}\) |
\(r_{t,i}=\alpha_{1}+f_{\text{North}}\left(\rho_{N,t,i}\right)+f_{\text{South}}\left(\rho_{S,t,i}\right)+\epsilon_{t,i}\) |
6 |
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\(D_{S,i}=-\sqrt{\left(\gamma_{S}-X_{i}\right)^{2}+\left(\psi_{S}-Y_{i}\right)^{2}},\ \ \ \ \ \ if\ Y_{i}<5,068m\) |
\(\rho_{S,t,i}=T_{t,i}+\left(\frac{1}{\zeta_{S}}\right)D_{S,i}\) |
|
|
RDE |
Dual overlapping expanding radial waves |
\(D_{1,i}=-\sqrt{\left(\gamma_{1}-X_{i}\right)^{2}+\left(\psi_{1}-Y_{i}\right)^{2}}\) |
\(\rho_{A,t,i}=T_{t,i}+\left(\frac{1}{\zeta_{1}}\right)D_{1,i}\) |
\(r_{t,i}=\alpha_{1}+f_{1}\left(\rho_{1,t,i}\right)+f_{2}\left(\rho_{2,i,t}\right)+\epsilon_{i,t}\) |
6 |
|
|
\(D_{2,i}=-\sqrt{\left(\gamma_{2}-X_{i}\right)^{2}+\left(\psi_{2}-Y_{i}\right)^{2}}\) |
\(\rho_{I,t,i}=T_{t,i}+\left(\frac{1}{\zeta_{2}}\right)D_{2,i}\) |
|
|
RFC |
Two contracting radial waves separated by river |
\(D_{N,i}=\sqrt{\left(\gamma_{N}-X_{i}\right)^{2}+\left(\psi_{N}-Y_{i}\right)^{2}},\ \ \ \ \ \ if\text{\ Y}_{i}\geq 5,068m\) |
\(\rho_{N,t,i}=T_{t,i}+\left(\frac{1}{\zeta_{N}}\right)D_{N,i}\) |
\(r_{t,i}=\alpha_{1}+f_{\text{North}}\left(\rho_{N,t,i}\right)+f_{\text{South}}\left(\rho_{S,t,i}\right)+\epsilon_{t,i}\) |
6 |
|
|
\(D_{S,i}=\sqrt{\left(\gamma_{S}-X_{i}\right)^{2}+\left(\psi_{S}-Y_{i}\right)^{2}},\ \ \ \ \ \ if\ Y_{i}<5,068m\) |
\(\rho_{S,t,i}=T_{t,i}+\left(\frac{1}{\zeta_{S}}\right)D_{S,i}\) |
|
|
RDC |
Dual overlapping contracting radial waves |
\(D_{1,i}=\sqrt{\left(\gamma_{1}-X_{i}\right)^{2}+\left(\psi_{1}-Y_{i}\right)^{2}}\) |
\(\rho_{1,t,i}=T_{t,i}+\left(\frac{1}{\zeta_{1}}\right)D_{1,i}\) |
\(r_{t,i}=\alpha_{1}+f_{1}\left(\rho_{1,t,i}\right)+f_{2}\left(\rho_{2,i,t}\right)+\epsilon_{i,t}\) |
6 |
|
|
\(D_{2,i}=\sqrt{\left(\gamma_{2}-X_{i}\right)^{2}+\left(\psi_{2}-Y_{i}\right)^{2}}\) |
\(\rho_{2,t,i}=T_{t,i}+\left(\frac{1}{\zeta_{2}}\right)D_{2,i}\) |
|
|
PF |
Two planar waves separated by river |
\(D_{N,i}=\sin\left(\theta_{N}\right)X_{i}+\cos\left(\theta_{N}\right)Y_{i},\ \ \ \ \ \ if\text{\ Y}_{i}\geq 5,068m\) |
\(\rho_{N,t,i}=T_{t,i}+\left(\frac{1}{\zeta_{N}}\right)D_{N,i}\) |
\(r_{t,i}=\alpha_{1}+f_{\text{North}}\left(\rho_{N,t,i}\right)+f_{\text{South}}\left(\rho_{S,t,i}\right)+\epsilon_{t,i}\) |
4 |
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|
\(D_{S,i}=\sin\left(\theta_{S}\right)X_{i}+\cos\left(\theta_{S}\right)Y_{i},\ \ \ \ \ \ if\ Y_{i}<5,068m\) |
\(\rho_{S,t,i}=T_{t,i}+\left(\frac{1}{\zeta_{S}}\right)D_{S,i}\) |
|
|
PD |
Dual overlapping planar waves |
\(D_{1,i}=\sin\left(\theta_{1}\right)X_{i}+\cos\left(\theta_{1}\right)Y_{i}\) |
\(\rho_{A,t,i}=T_{t,i}+\left(\frac{1}{\zeta_{1}}\right)D_{1,i}\) |
\(r_{t,i}=\alpha_{1}+f_{1}\left(\rho_{1,t,i}\right)+f_{2}\left(\rho_{2,t,i}\right)+\epsilon_{i,t}\) |
4 |
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\(D_{2,i}=\sin\left(\theta_{2}\right)X_{i}+\cos\left(\theta_{2}\right)Y_{i}\) |
\(\rho_{I,t,i}=T_{t,i}+\left(\frac{1}{\zeta_{2}}\right)D_{2,i}\) |
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