[ivca-cz]

Hello,

For the first time, I am looking at velocity standard deviations.

With a coherence of 0.88, the velocity standard deviation is 1.4 mm/y, and with a coherence of 0.46, the estimated velocity standard deviation is 1.7 mm/y (velocity 18 mm/y). Is this right, having a set of 33 scenes? I am (hopefully) attaching the CSV.

[ivca-cz]

ok, as the csv could not be attached, i am putting some lines from the file:

VEL SIGMA VEL KTEMP CUM DISP COHER
0.8 1.4326105 0 0.73271138 0.89
0.8 1.4212119 0 0.77367592 0.89
-0.4 1.58295 0 -0.40666919 0.81
0.1 1.4669876 0 0.10243065 0.87
0.3 1.4730457 0 0.31198077 0.86
-0.2 1.4565904 0 -0.19430225 0.88
-0.9 1.4874729 0 -0.85717327 0.85
-0.1 1.4745953 0 -0.12713547 0.85
-0.3 1.4427017 0 -0.28537148 0.88
-1.1 1.4782571 0 -1.0736993 0.85
-0.4 1.4461435 0 -0.36197319 0.87
-28.8 1.7265991 0 -27.792348 0.55
-0.5 1.5086196 0 -0.46273584 0.88
-0.5 1.5024023 0 -0.43816302 0.86
-0.1 1.411291 0 -0.11820703 0.89
-0.1 1.4672098 0 -0.06068527 0.88
0.7 1.3975295 0 0.67269871 0.88
0.6 1.4076104 0 0.55844103 0.9
-0.5 1.4500579 0 -0.44458811 0.88
23.9 1.6666382 0 23.07521 0.51
-0.5 1.4514726 0 -0.49590007 0.88
-4 1.3778692 0 -3.8143167 0.9
-0.1 1.4490802 0 -0.092182995 0.88
-0.3 1.4196231 0 -0.32834043 0.87
-0.4 1.4610608 0 -0.34686251 0.88
-0.7 1.4488488 0 -0.64417241 0.88
-0.5 1.4600447 0 -0.43862747 0.86
-1.5 1.4617713 0 -1.4367451 0.87
-0.9 1.4623307 0 -0.84711712 0.87
18.3 1.7659887 0 17.602751 0.46
0.2 1.7143648 0 0.15044039 0.75
0.6 1.6729283 0 0.61420549 0.76
1.2 1.6403428 0 1.1847963 0.76
-1 1.5922634 0 -0.95713928 0.8
0.2 1.5562343 0 0.16926025 0.81
0.7 1.6016046 0 0.69661594 0.77
1.2 1.6008123 0 1.1701539 0.78
-9 1.5424199 0 -8.6601346 0.62
-0.2 1.5520004 0 -0.22512163 0.82
-2.9 1.4897697 0 -2.7940446 0.6
1 1.5518991 0 0.93410172 0.81
1 1.516355 0 0.92930333 0.81
-21.6 1.6085228 0 -20.824488 0.67
0.2 1.6306099 0 0.2259664 0.81
-3.3 1.6864063 0 -3.1341834 0.8
-2 1.4938928 0 -1.9192764 0.86
-2.4 1.6910603 0 -2.3280546 0.81
-3.2 1.698862 0 -3.0703365 0.8
-3.3 1.8240584 0 -3.1386467 0.76
-4.3 1.7028998 0 -4.1365987 0.81
-4 1.7788642 0 -3.8960754 0.79
-2.9 1.4461136 0 -2.8082917 0.86
-2.8 1.4255943 0 -2.6864613 0.89
-3.6 1.7063835 0 -3.4468794 0.79
-3 1.4767138 0 -2.8529891 0.87
-2.9 1.7189512 0 -2.8415534 0.79
-3 1.8164955 0 -2.9046802 0.76
-5.7 1.5511588 0 -5.4601729 0.83
-1.5 1.5648194 0 -1.4904225 0.84
-1.6 1.5854953 0 -1.5693828 0.83
-3.2 1.8038812 0 -3.0409635 0.73
-2.9 1.7284898 0 -2.7897243 0.77
-3.3 1.5597129 0 -3.1604185 0.84
-1 1.5851657 0 -0.98629264 0.82
-2.9 1.7011178 0 -2.7962666 0.79
-3.5 1.6464573 0 -3.3875623 0.8
-13.7 1.6479542 0 -13.17597 0.68
-3 1.64455 0 -2.9224919 0.81
-2.2 1.6022294 0 -2.0952836 0.83
-3.8 1.6790911 0 -3.6807342 0.78
-2.7 1.5244937 0 -2.5922527 0.86
-2.6 1.6008347 0 -2.5240572 0.81
-3.1 1.5751147 0 -3.012251 0.83
-2.3 1.684932 0 -2.2200347 0.8

[periz]

Hi Ivana,
some comments:
a. the standard deviation of the velocity is a measure of the peak width of the periodogram. It’s not a global parameter as the temporal coherence, it’s local (giving a view around the estimated parameter).
b. if it would simply be correlated to the coherence, it would not be useful. By already having the coherence, you would not need it. So, don’t be surprised that low coherence does not correspond to low velocity standard deviation.
c. the point is that you cannot unequivocally interpret a low value of temporal coherence. The temporal coherence can be low because of a noisy time series, or it can be low because the displacement model is wrong. The velocity standard deviation should complement this information.
d. since this is a new parameter, we need lots of samples to be able to give you a precise and definitive answer on its usefulness. In some ways, we are hoping that you (and the other users) can give us more hints on its usefulness.
e. you should not just look at the coherence and at the vel std dev. At least, you should consider also the standard deviation of the height. All together, these parameters should give a better view on the target at hand. But again, we are still collecting observations on this matter. Your contribution will surely be useful!!

[ivca-cz]

Hello Daniele,

I am getting slowly into it.

I understand there are two standard deviations – one evaluated from the coherence, using e.g. Colesanti 2003, and the other one evaluated here (can you recommend a paper where to read more?)

I understand it is a measure by which the variable (velocity, height) could change with no (significant) change of coherence. Is it right? As the periodogram is also built on coherence, am I right?

I also understand that a velocity is a number and if the velocity is nonlinear, that its stddev is high even if the point phase does not contain much noise. But I do not understand how to interpret lower velocity stddev due to the fact that the point is stable – and I also do not understand what effect it has on the width of the periodogram peak.

Is it a measure of the phase stability, independently on the model? Can it help interpreting the particular phase values in the time series?

Regarding only the height: an interesting fact is that while coherence-related stddev starts at 0.15 m (33x TSX, sqrt(var(Bn))=190 m, corresponding to h_a of 25 m) and mostly ends at 0.6 m (excluding overliers), sarproz-evaluated stddev starts at 0.6 m and ends somewhere around 0.9 m, so its range is even smaller (regarding the less quality points, coherence-related stddev ends at 1 m, sarproz-evaluated ends at 1.6 m).

However, when using two different sets of temperatures (air and surface, difference of up to 11 degrees for 2 dates), for about 1.8%/2.4% of the points the difference in the estimated height was higher than 1 m/0.5 m (velocity was not estimated in this case). For 60% of the points, the difference is lower than 0.1 m.

I am sorry for silly comments, I am trying to understand the fact that there are two standard deviations with different values. I know that the coherence-related is valid for the real PS (high coherence) and it includes model uncorrespondance to the reality (that is why I am very careful with coherence-thresholding).

Please specify what kind of feedback you expect.

Thank you, Ivana

[periz]

Hi Ivana
at this moment this calculation is not published.
The std dev in the paper mentioned by you is a statistical quantity.
The one listed in the sarproz output is a value calculated for that single time series.
The point is: the solution of the estimation is found as the peak of the periodogram.
How sharp is the peak? If the movement is perfectly linear, the sharpness will be constrained by the dataset configuration (baselines) and by the phase noise. If the movement is non-linear, the peak will be wider and less sharp.
So, do not stitch to the absolute values of this standard deviations (you may be right, we may need to calibrate them). What is mostly important here is to see the variation from one point to an other, in relation with the coherence variation.
What you say is also interesting: if you change the temperatures, you are changing the dataset configuration. The coherence may be the same, but the precision with which you estimate e.g. the height is different. And you can see the difference looking at the height std dev change. This is a nice feedback….

[ivca-cz]

Hi Daniele,

thank you very much for the explanation and also for the implementation.

Can you also please let me know how is the periodogram peak width defined? If e.g. the width of 90% of the peak coherence. Just to consider if really plus minus three sigma_vel are the “limits” of the velocity estimation as the values really look quite high.

Thank you very much,
Ivana

[periz]

Ivana,
+/- 3*sigma is an operation that has nothing to do with this quantity.
As previously stated, this quantity is not calibrated and it should be simply considered as a measure of the curvature (how wide) is the peak. But again, the value is not much meaningful by itself alone, it’s useful when compared with that of an other target.
Nobody ever said that the peak equals to a gaussian distribution (for which +/- 3*sigma defines reasonable limits to isolate outliers). This is simply wrong.
I analyzed some cases of non linear deformation and the values of sigma vel were helpful to highlight the areas affected by non-linearity. I think this should be the use of such quantity.

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