# Consult about results near to Ocean

Dear all,

I work on earthquake modeling using InSAR result. Today, I got the InSAR results of the area near to the ocean, where two earthquakes have happened with a magnitude of 6.9. As you can see in the following, I face the noise in the water part in Interferogram result.

Whenever I did unwrapping using SNAPHU and then convert the unwrapped output to displacement, I saw the following figure with two parts with blue and white colors. I know that the radar signal cannot penetrate into the water and touch the surface under the water but do you think these parts can have an especial meaning? like, change water level because of changes in height of the crust after the earthquakes.

You can see the points of earthquake centers, reported by USGS, in both figures. I am almost sure that it is not a true value but I need to be confident by others.

Best regards,
Sayyed

not at all. These patterns were generated during the unwrapping and (as you see in the interferogram) based on quite random phase information. During the unwrapping pahse is converted from cyclical values to absolute values but these patterns over water have no meaning (low coherence). You can crop water bodies in the terrain correction step.
Your interferogram over land looks great and nicely delineates the topography. If you intend to measure subsidence/uplift by differential interferometry, you should consider removing the topographic phase as well (checkbox in the interferogram generation) so that only the change between the two images remains.

@ABraun Thank you so much for your great description. I completely agree with the first part of what you said. They show the quite random phase information in Interferogram result.

I would like to see the fringes generated by an earthquake in Interferogram which I cannot see in the land part. About removing the topographic phase, I always apply the topographic phase removal after Interferogram generation and before multilooking. I think it is enough. Yes?

that is fine then

If you have some doubt, look at the coherence. You can mathematically relate the uncertainty of the phase/displacement to the coherence

@qglaude Thank you so much for your nice suggestion

1 Like

has this been investigated empirically somewhere? I use it as a qualitative indicator but if there is a relationship or something similar I would be interested in references .

@ABraun From [Rodriguez & Martin 1992] (Theory and design of interferometric synthetic aperture radars), you can demonstrate (not an empiric stuff) that the standard deviation of the interferometric phase has a lower bound given using the unbiased estimation of the coherence and is given by :

\sigma_{insar} \geq \dfrac{1}{\sqrt{2N}}\cdot \dfrac{\sqrt{1-\gamma^2}}{\gamma}

With N the number of samples to compute the interferogram (for full resolution interferogram as SNAP does, you have N equal to 1). Then, empirically, they showed that even with only 4 samples, the standard deviation can be approximated by the lower bound. From that, you clearly understand that multilooking is not just about â€śmaking pixels squareâ€ť as I often read but above all to get a better estimate of the expected interferometric phase value.

Note : re-reading my stuffs, I realized that this assertion is verified for coherence above 0.6. So maybe my previous comment on this topic is a bit off.

1 Like

but does this also apply for SNAPâ€™s multi-looking (space-domain averaging) or only for frequency-domain averaging?

Both are aiming at the same objective, using different methods.

Just careful in the terminology : multi looking in the frequency domain is not frequency-domain averaging. Well, in the end, when you go back in the time-domain (or space-domain), you have a space-averaged result but you donâ€™t average within the frequency domain.

1 Like