We follow Wagner et al., 1997 and Klokocnik et al., 1999 and represent the effect on the radius of the orbit from the geopotential (most compactly) for both SSCs and DSCs by the following geographical form [due fundamentally to Rosborough (1986) who transformed the time series elemental representation in Kaula, 1966]:
where
where i is either A or D for the first satellite and
j is either A or D for the second;
and 
,
if 
(i.e. for AD,DA)
if i=j (i.e. for AA,DD)
,
if i=A (i.e. for AD,AA)
,
if i=D (i.e. for DA,DD)
;
where A is for an ascending pass and D for a descending at crossover
location ( 
in geocentric latitude and 
in longitude),
and the 
, 
are the geopotential harmonic
coefficients to be resolved by the data.
(Note the 
here are for sea height
differences: pass i - pass j, the negative of orbit-radial differences).
When the upper index 1 = 2, we have one satellite only, and
(2) degenerates to the SSC case. Note also
the 
are the sensitivities
of these effects to the geopotential and depend on the height
and inclination of the orbits involved as well as the latitude.
[They are the sum of the products of the dynamic factors 
and the latitude functions
in Rosborough (1986, eq. 5.35) over all frequencies p from
0 to l in Kaula's (1966, eq. 3.70) time series
form for the geopotential on an orbit].
In the inverse application, since the data are residual observations with
respect to a Jgm3 orbit model, the geopotential coefficients in (2) are added
adjustments to the Jgm3 values. In transforming crossover data from one
orbit model field basis to another these coefficients are the differences
in the field values and the resulting
in (2) gives
the appropriate adjustment of the data. Thus:
where 
are computed according to Eq. (1), replacing the LLCs
by 
, 
which are computed from
, 
, using Eq. (2) accordingly.