Phase Advance due to Atmosphere in InSAR

Effects from atmosphere, mainly due to troposphere and ionosphere, along with the temporal and geometrical decorrelation, are the major challenges of InSAR. Troposphere alone, could cause a differential phase signal equivalent to a real deformation of up to 20 cm, according to latest poster of H. Fattahi’s poster at AGU 2014 fall meeting. And ionosphere could a even larger phase than troposphere. Check interferometric phase below for example. To better retrieve real deformation signal from the earth surface, we have to estimate these “noise” more accurately.

The basic theory behind these phenomena is: electrons in the ionosphere and water vapor in the troposphere change the refractivity of the air. When the radar signal propagates through these layers of atmosphere, its speed changes (slow down compared to the vacuum) due to the changed refractivity, which results in a delay in travel time of the echo. In the interferogram, we call this Atmospheric Phase Screen (APS). Qualitatively, it will cause a Phase Advance (a larger unwrapped phase).

Refractivity in ionosphere n_iono < 1 and the refractivity in troposphere n_tropo > 1, these difference have influence of the phase velocity, and needs more digging.

Since InSAR measures the phase difference with reference both in time (reference or master date) and space (reference point), here I make a more simple scenario: assuming no geometric and temporal decorrelation, and only consider the contribution of interferometric phase from atmosphere compared to vacuum. When the radar signal enter the air from vacuum, the refractivity of medium increases, and the signal’s velocity decreases, so there would be a time delay for the signal reaches to the receiver, which is called Group Delay. And the question is:

  • How does a group delay of the radar signal cause a opposite phase advance (negative phase delay)?

This regular pattern is known in signal processing field, but to better understand this, we could consider a Biking Experiment, see drawing shown below.

biking_Yunjun

Think the microwave as a rotating tire of a bicycle, its radius is proportional to the wavelength and rotated angle equivalent to the unwrapped phase of interferogram. When it enters the atmosphere, its frequency remains the same (rotating speed w remains the same), but velocity and wavelength decrease, like sudden shrinking. With smaller tire and lower speed, it would take more time to reach to the terminal (receiver for radar), which is the Group Delay. Since the rotating speed won’t change, more time leads to more rotated angle, which is the Negative Phase Delay, or Phase Advance. Based on the analysis on the drawing, there will be no phase shift in the boundary.

A conventional drawing would be as follows:

 phase_delay_Yunjun

References

3. H. Fattahi, F. Amelung, Uncertainty of InSAR velocity fields for measuring long-wavelength displacement, poster, AGU Fall Meeting, 2014.

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