How is coherence computed in StaMPS?

[Alberto Refice]

Dear all,

maybe the following issue has a simple explanation, so please forgive my
ignorance. Anyway, at first sight the PS results I am sharing seem
counterintuitive, I couldn't find any explanation in the group or in the
StaMPS manual, so maybe answers to this post could help generally in
clarifying the software's operation.

The attached figure shows time series for two close PS points belonging
to the same dataset. The plots were obtained through the ps_plot
function ("driven" by the viStaMPS software). The underlying plot is the
ps_plot('v-dos'), so orbital ramps, DEM error and slave atmospheric
effects should have been subtracted from the data.
I could add details on the dataset (and I will upon request), but the
main issue is not dependent on that. Let me just mention that stamps
processing went through without errors, all processing steps 1 to 8 were
performed, steps 6 to 8 were repeated as recommended in the manual, so
that SCLA error was subtracted before unwrapping, and the final overall
PS mean velocity map seems reliable and in line with expectations.

However, as you can notice, although the two points have both very high
"nominal" coherence, the two time series appear dramatically different:
in particular, the one with the highest (>0.94) coherence appears much
more "jagged" and noisy than the other one, which has a "nominal"
coherence of only about 0.90. Note also that y-axis scale limits are the
same in the two plots.

Now, the most common definition of PS phase coherence (at least, the one
most PSI scientists would agree on) can be described as "the phase noise
(intended as phase st.dev.) remaining in the PS time series after all
the "modeled" signal parts have been subtracted (i.e. DEM error,
velocity, APS and any other spatially correlated noise)". According to
this definition, one should not expect to see such a counterintuitive
result (noisier time series for higher coherence).

If nobody has ever noticed a similar effect, then the simplest
explanation is that I am doing something wrong, but what? Apparently,
phase coherence is calculated on some time series which is not the one
plotted through the 'v-dos' option. Then, which one should I use? Other
options, e.g. 'v-d','v-do',etc., remove less components from the data,
so they should give nosier time series with respect to the 'v-dos' case.
How can I plot in a sufficiently simple way (say, without delving in the
code) a time series which shows a noise level consistent with the
"nominal" coherence printed on top of the graph?

Thanks in advance for your help,

Alberto

[Karsten Spaans]

Hi Alberto,

StaMPS differs from most other timeseries techniques in that it doesn't
estimate the coherence based on the difference between the phase and an
assumed model. In stead, it estimates the phase noise as the residual
left after removing the spatially correlated phase (any deformation,
atmospheric signals, and part of the DEM error) and the spatially
uncorrelated DEM error. It then calculates the coherence based on the
phase residual. This has the advantage that you do not need to assume a
deformation model. For more details on the coherence estimation, see
Andy's 2007 JGR paper "Persistent scatterer interferometric synthetic
aperture radar for crustal deformation analysis, with application to
Volcan Alcedo, Galapagos".

The way that the coherence is estimated means that highest coherence
points do not necessarily have the smoothest timeseries. It is also
worth pointing out that 0.9 and 0.94 are very close in terms of
coherence, and looking at the timeseries, I would classify both as very
reliable PS points.

Hope this helps,
Karsten