BLQ phases explained


Concerning BLQ-files for gravity and tilt, the phase values specify lag in degrees with respect to the astronomical argument of the corresponding external tide generating potential. If you are to compute time series for a specific epoch, the astronomical arguments can be computed with program ARG2.F available from the IERS at
http://iers-conventions.obspm.fr/2010/2010_update/chapter7/software/ARG2.F

In oceanography a lag of a tide wave is reckoned positive while in earth tides (geodesy, astronomy) lags are reckoned negative.
BLQ follows the oceanographic convention. A partial tide j at time t after epoch T computes then as

g_j(t) = A_j cos[a_j(T) + f_j (t-T) - P_j pi/180] (1)

where Aj and Pj are the amplitude and phase values in the BLQ tables, respectively. The frequencies in cyc/d are

    Ssa 0.0054758
    Mm  0.0362916
    Mf  0.0732022
    Q1  0.8932441
    O1  0.9295357
    P1  0.9972621
    K1  1.0027379
    N2  1.8959820
    M2  1.9322736
    S2  2.0000000
    K2  2.0054758

aj(T) is a combination of the fundamental astronomical arguments at epoch T multiplied with small integers.

For use with the popular tide data utility TSOFT (van Camp, ROB, http://seismologie.oma.be/en/downloads/tsoft ) a perl script olgte.pl is available at
http://holt.oso.chalmers.se/loading/olgte.pl to adapt BLQ coefficients (with thanks to Hartmut Wziontek). This concerns gravity only.

Concerning tilt, applying (1) yields north and east components (positive values in north and east direction).

A frequent application  of ocean loading parameters is in reducing observations for loading effects. For instance in gravity, a load-free observation would show a phasor with an amplitude (delta-value) somewhere between 1.14 and 1.17 and a phase lag close to zero. The task requires that the astronomical (a.k.a. rigid-earth) gravity tide is evaluated. This exercise implicates a number of preconditions, ranging from the effective bandwidth assigned to wavegroups to site location parameters (height in the first case). This part of applications is beyond the scope of BLQ. See Boy et al. (2003).

However, it might be useful to present the phase relation between loading tide and rigid-earth tide in gravity and tilt for a range of latitudes

   latitude     60        10       -10       -60  
              -------   -------   -------   ------- 
       m      0  1  2   0  1  2   0  1  2   0  1  2 
   ------------------------------------------------
       G      2  2  2   2  2  2   2  2  2   2  2  2
      T_e     *  1  1   *  1  1   * -1  1   * -1  1
      T_n     2  2  2   2  0  2   0  0  0   0  2  0
In order to convert BLQ-phases to phase values relative to the local astronomical tide, observe the following relations
\[ a_j(T) = \phi_{c,\lambda} - m\lambda - v\times 90 \]
\[ \Phi_{load,0} = a_j(T) - \Phi_{BLQ} \]
\[ \Phi_{load,\lambda} - \phi_{c,\lambda} = -\Phi_{BLQ} + m\lambda + v\times 90 \]
where subscript c denotes an observed solid-earth effect (gravity, tilt),
subscript  j  1) enumerates the tide waves, m = 0, 1, 2 for long-period, diurnal, semi-diurnal, respectively,
λ is east longitude,
v is a table element,
phases and longitudes are in degrees, and
an asterisk appears when the astronomical component of the effect is zero.

 1) not written out with phase symbols

References

Agnew, D.C., Earth Tides, Chap. 3-06 in: G. Schubert (ed.) Treatise on Geophysics, 2nd ed., , 2015  (1st ed. PDF)

Boy, J.-P., M. Llubes, J. Hinderer, and N. Florsch, A comparison of tidal ocean loading models using superconducting gravimeter data, J. Geophys. Res., 108(B4), 2193, doi:10.1029/2002JB002050, 2003.

.bye