Table 1 Classification of the components of an arbitrary MT tensor \(\hat{X}\) from the standpoint of the DR validity
From: Validity of the dispersion relations in magnetotellurics. Part II: synthetic and field data
\(X_{ij}\) component | Class 1 | Class 2 | Class 3 |
|---|---|---|---|
\(\hat{X}\) causality | Causal | Causal | Non-causal |
DR-II validity | Valid | Violated by the amount of a positive monotonic phase lag \(\theta_{n}\) (Eq. 8 in Part I) | Violated by the amount of a negative monotonic phase lag \(- \theta_{m}\), or a non-monotonic phase lag \(\theta_{n} - \theta_{m}\) (Eq. 8 in Part I) |
DR-I validity | Valid | Valid | Invalid (unless \(\theta_{n} \equiv \theta_{m}\)) |
Characteristic features of \(\arg X_{ij}\) on log-period scale | – | Rolls out of its regular range upwards and/or rolls in from below | Rolls out of its regular range downwards and/or rolls in from above at least at some angle of \(\hat{X}\) rotation |
Typical features of \(\ln \left| {X_{ij} } \right|\) | – | May reveal a negative cusp if \(\hat{X}\) is rotated | May reveal a cusp if \(\hat{X}\) is rotated |
How the DR-II can applied | Directly | Using (Eq. 7 in Part I) with \(n\) unknowns | Consider the DR application to the inverse tensor \(\hat{X}^{ - 1}\) or the corresponding inter-site tensors instead |
How the DR-I can applied | Directly | Directly |